Download - Emily Barrentine
The Development of a Transition-Edge Hot-Electron
Microbolometer for Observation of the Cosmic
Microwave Background
by
Emily Margaret Barrentine
A dissertation submitted in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
(Physics)
at the
University of Wisconsin – Madison
2011
c© Copyright by Emily Margaret Barrentine 2011
All Rights Reserved
i
Abstract
In this thesis the development of a Transition-Edge Hot-Electron Microbolometer
(THM) is presented. This detector will have the capacity to make sensitive and
broadband astrophysical observations when deployed in large detector arrays in fu-
ture ground- or space-based instruments, over frequencies ranging from 30-300 GHz
(10-1 mm). This thesis focuses on the development of the THM for observations of the
Cosmic Microwave Background (CMB), and specifically for observations of the CMB
polarization signal.
The THM is a micron-sized bolometer that is fabricated photolithographically.
It consists of a superconducting Molybdenum/Gold Transition-Edge Sensor (TES)
and a thin-film semi-metal Bismuth microwave absorber, both of which are deposited
directly on the substrate. The THM employs the decoupling between electrons and
phonons at low temperatures (∼100-300 mK) to provide thermal isolation for the
bolometer. The devices are read out with Superconducting Quantum Interference
Devices (SQUIDs).
In this thesis a summary of the thermal and electrical models for the THM
detector is presented. The physical processes within the detector, with particular
attention to electron-phonon decoupling, and the lateral proximity effect between the
superconducting leads and the TES, are also discussed. This understanding of the
ii
detector and these models are used to interpret measurements of thermal conductance,
noise, responsivity and the transition behaviour of a variety of THM test devices. The
optimization of the THM design, based on these models and measurements, is also
discussed, and the thesis concludes with a presentation of the recommended THM
design for CMB applications. In addition, a planar-microwave circuit design and
a quasi-optical scheme for coupling microwave radiation to the THM detector are
presented.
iii
Acknowledgements
An adequate acknowledgement is very difficult to write at this point. I am im-
mensely grateful and lucky for the many people who have contributed both directly
to the work described in this thesis or who have provided expertise, advice and assis-
tance. None of the work presented here would be possible if it were not for their input
or contributions. It also goes without saying that any deficiencies in this thesis are due
to my own modest abilities and do not reflect upon the quality of their contributions.
This research project and my graduate education have been completed in very
close collaboration with colleagues and advisers at NASA-Goddard Space Flight Cen-
ter. I must thank the Wisconsin Space Grant Consortium, the NASA-Goddard Grad-
uate Student Researcher’s Program, the NASA Co-operative Education Program and
all those at the Detector Systems Branch and Detector Development Laboratory at
NASA-Goddard Space Flight Center.
Specifically, I would like to thank my NASA adviser, Thomas Stevenson, who
initially agreed to sponsor me in the GSRP program and who provided excellent
guidance as well as much direct input into the THM design. I must thank as well, Wen-
Ting Hsieh, who contributed to and oversaw much of the THM fabrication. I am very
indebted to Kongpop U-Yen who contributed to much of the THM microwave design,
provided helpful advice on microwave simulations and who assisted and oversaw the
preliminary CPW probe station measurements. I must also thank Nga Cao who
contributed to the THM microwave termination design and who also advised on early
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microwave simulations. I must especially thank Ari Brown and Kevin Denis who
dedicated an extraordinary amount of time and patience to training me in the Detector
Development Laboratory and who also completed fabrication of the THM test devices.
I also wish to thank Fred Finkbeiner who completed additional measurements of one
of the S-N-S test devices.
I would like to acknowledge the very specific contributions of those at NASA-
Goddard DDL in the fabrication of these THM test devices. Fabrication of the
‘THM2003’ devices was completed by Tim Miller and Christine Jhabvala. Fabrication
of the ‘THM4/THM5’ devices was completed with the assistance of Kevin Denis, Ari
Brown and Travis Travers. Fabrication of the ‘us25/us23’ devices was completed by
Kevin Denis, Peter Nagler and Dorothy Talley. Fabrication of the ‘THMA4/THMA24’
test devices was completed with assistance from Ari Brown.
Thanks also go to the originators of this project, mainly Shafinaz Ali, who with
assistance from Kari Kripps, and advice from Thomas Stevenson, Jay Chervenak, Ed
Wollack, Harvey Moseley and Dominic Benford at NASA-Goddard, guided the design
of the first THM detectors. I would like to thank Kent Irwin of NIST who provided
a two-stage SQUID readout. I am grateful for the experience and explanations of
Dan McCammon and Mark Lindeman who made the theoretical aspects of TESs and
bolometers understandable and applicable and who provided advice for interpreting
many of the THM measurements. I wish to thank Jack Sadleir for his advice con-
cerning the lateral proximity effect. I also wish to thank Don Brandl for enjoyable
and illuminating discussions of superconductivity theory and TESs and who created
some of the initial numerical programs to make predictions about the S-N-S effect.
v
I wish to thank my fellow graduate students during my time in the Observational
Cosmology lab here at University of Wisconsin, Amanda Gault, Peter Hyland, and
Siddharth Malu, who provided assistance and advice in the laboratory and discussions
about cosmology and who made the lab a very supportive and fun place to work. I
am extraordinarily grateful for the work done by Sara Stanchfield, who completed the
cryogenic testing of the black body source described in this thesis, and who also com-
pleted some of the E-M simulations and microwave measurements for the design of
the THM optical coupling scheme. I also thank Zubair Abdulla, Eric Katzlenick and
Amy Lowitz for their important contributions to the THM optical coupling design.
As this is a culmination of a very specific dream I have had since I was about
10 years old, I also wish to express my gratitude at this moment to my teachers
throughout all levels of my schooling. I thank my elementary school teacher, Mr.
Steve Kaio-Maddox, who handed me the first book I ever read about physics, and put
up with my persistent questions. I also need to acknowledge the late Carl Sagan, who
gave meaning and purpose to my life though he had already passed away by the time
I read his first book in high school. I thank the dedicated and caring teachers I had
in all disciplines at Deer Park High School. I also thank the gifted teachers on the
faculty of the Bryn Mawr College Physics Department during my years there from
1999-2003, and especially my advisers there, Matthew Rice and Juan Burciaga. It is
through their support and the exceptional environment which they nurtured within
that department that I gained both the ability and the confidence to pursue this degree
at the graduate level.
Most importantly however, I need to express my gratitude to my adviser, Peter
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Timbie. I feel extraordinarily lucky to have been his student. His unequaled patience,
guidance, as well as enthusiasm and understanding, made both this project, and my
happiness as a graduate student during these last five years, possible. One could not
ask for a better mentor.
vii
Dedication
I wish to dedicate this thesis to my family. To my mother and father, Marianne
and Wayne Barrentine. To my grandmother, Delores Barrentine, and in memory of
my grandfather, Harold Barrentine. To my grandmother and grandfather, Janet and
John Salomone. This is dedicated to them because of their care, encouragement and
love, and their support of my education and the development of my curiosity and
seriousness towards all areas of life. It is also dedicated to them because they have
accepted my absence from their daily lives for much of the last twelve and a half years
in the pursuit of this degree. I also wish to dedicate this thesis to my uncle, Carl
Barrentine, for his encouragement of all of his nieces to pursue higher education and
to ask questions about the deeper meanings of life and the workings of the universe.
Above all, however, this thesis is dedicated to my sister, Erin Barrentine, without
whom I would not be able to even contemplate existence.
viii
Contents
Abstract i
1 Introduction 1
1.1 The History and Science of the CMB . . . . . . . . . . . . . . . . . . . 1
1.1.1 CMB Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Inflation & Gravitational Waves . . . . . . . . . . . . . . . . . . 6
1.1.3 CMB Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1.4 Other Detector Science Applications . . . . . . . . . . . . . . . 15
1.2 CMB Detector Technology & THM Advantages . . . . . . . . . . . . . 16
1.2.1 History of CMB Detectors & Future Detector Needs . . . . . . . 18
1.2.2 THM Detector Advantages . . . . . . . . . . . . . . . . . . . . . 22
1.3 Thesis Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2 General Bolometer & TES Theory 24
2.1 Basic Bolometer Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2 The Superconducting Transition . . . . . . . . . . . . . . . . . . . . . . 27
2.3 The Transition Edge Sensor . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4 Basics of SQUIDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
ix
2.5 SQUID Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.6 The TES Bolometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.7 Electrothermal Feedback & Bias Conditions . . . . . . . . . . . . . . . 52
2.8 Bolometer Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3 Physical Effects in the THM Detector 56
3.1 The Hot-Electron Effect . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.1.1 Hot-Electron Effect Theory . . . . . . . . . . . . . . . . . . . . 58
3.1.2 Measurements of the Hot-Electron Effect . . . . . . . . . . . . . 61
3.1.3 HEB Detector History . . . . . . . . . . . . . . . . . . . . . . . 62
3.2 Other Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.2.1 Andreev Reflection . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.2.2 Boundary Conductance . . . . . . . . . . . . . . . . . . . . . . . 65
3.2.3 Wiedemann-Franz Conductance . . . . . . . . . . . . . . . . . . 69
3.2.4 Radiation Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.3 The Superconducting Proximity Effect . . . . . . . . . . . . . . . . . . 71
3.3.1 Superconductivity Theory & the Proximity Effect . . . . . . . . 72
3.3.2 Ginzburg-Landau Theory . . . . . . . . . . . . . . . . . . . . . 74
3.3.3 Usadel Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.3.4 The Characteristic Lengths of the Proximity Effect . . . . . . . 78
3.3.5 S-N Bilayer Theory . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.3.6 S-N Bilayer Measurements . . . . . . . . . . . . . . . . . . . . . 83
3.3.7 S-S’-S Theory & Predictions . . . . . . . . . . . . . . . . . . . . 84
3.3.8 S-S’-S Measurements in the Literature . . . . . . . . . . . . . . 85
x
3.3.9 S-N-S Theory & Predictions . . . . . . . . . . . . . . . . . . . . 87
3.3.9.1 Likharev-Usadel Model . . . . . . . . . . . . . . . . . . 87
3.3.9.2 deGennes-GL Model . . . . . . . . . . . . . . . . . . . 87
3.3.9.3 Dubos-Usadel Model . . . . . . . . . . . . . . . . . . . 89
3.3.9.4 van Dover-GL Model . . . . . . . . . . . . . . . . . . . 91
3.3.9.5 Kuprianov-Lukichev-Usadel Model . . . . . . . . . . . 93
3.3.10 S-N-S Measurements in the Literature . . . . . . . . . . . . . . 97
3.3.11 Conclusions of Modeling the Lateral Proximity Effect . . . . . . 99
4 The THM Thermal Model & Detector Optimization 100
4.1 THM Thermal Model & Noise Sources . . . . . . . . . . . . . . . . . . 100
4.1.1 Ideal Model Theory & Noise . . . . . . . . . . . . . . . . . . . . 102
4.1.2 Non-Ideal Model Theory & Noise . . . . . . . . . . . . . . . . . 108
4.2 Thermal & Microwave Optimization . . . . . . . . . . . . . . . . . . . . 116
4.2.1 Photon Background Noise & Detector Loading Conditions . . . 117
4.2.2 Microwave Circuit Constraints . . . . . . . . . . . . . . . . . . . 119
4.2.3 Fabrication & Material Constraints . . . . . . . . . . . . . . . . 121
4.2.4 Stability Constraints & Optimal Bias Conditions . . . . . . . . 122
4.2.5 Electron-Phonon Versus Electron-Electron . . . . . . . . . . . . 123
4.2.6 Phonon-Phonon Versus Electron-Phonon . . . . . . . . . . . . . 130
4.2.7 SQUID & Johnson Noise Constraints . . . . . . . . . . . . . . . 132
4.2.8 The Optimal Design for the THM Detector . . . . . . . . . . . . 134
4.2.9 General Optimization for CMB Bolometric Detectors . . . . . . 143
xi
5 THM Test Devices & “Dark” Measurements 150
5.1 Test Devices & Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . 150
5.2 “Dark” Cryogenic Test Setup . . . . . . . . . . . . . . . . . . . . . . . 157
5.2.1 Dewar & Cryogenic Setup . . . . . . . . . . . . . . . . . . . . . 157
5.2.2 SQUID Readout Setup . . . . . . . . . . . . . . . . . . . . . . . 160
5.3 Inquiry into a Non-Ideal THM Model . . . . . . . . . . . . . . . . . . . 162
5.3.1 I-V Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 165
5.3.2 Thermal Conductance Measurements . . . . . . . . . . . . . . . 168
5.3.3 Responsivity Measurements . . . . . . . . . . . . . . . . . . . . 172
5.3.4 Noise measurements . . . . . . . . . . . . . . . . . . . . . . . . 172
5.4 Inquiry into the Hot-Electron Effect . . . . . . . . . . . . . . . . . . . . 179
5.4.1 THM2003 Test Device . . . . . . . . . . . . . . . . . . . . . . . 179
5.4.2 us25 Test Devices . . . . . . . . . . . . . . . . . . . . . . . . . . 180
5.4.3 Conclusions of Inquiry into Electron-Phonon Effect . . . . . . . 188
5.5 Inquiry into the Lateral Proximity Effect . . . . . . . . . . . . . . . . . 189
5.5.1 S-S’-S Junction Measurements . . . . . . . . . . . . . . . . . . . 189
5.5.2 S-S’-S Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 196
5.5.3 S-N-S Junction Measurements . . . . . . . . . . . . . . . . . . . 196
5.5.4 S-N-S Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 204
5.6 Inquiry into Detector NEP . . . . . . . . . . . . . . . . . . . . . . . . . 205
6 THM Microwave Design & Simulations 207
6.1 THM Microwave Design . . . . . . . . . . . . . . . . . . . . . . . . . . 207
6.1.1 Microstrip Transmission Lines . . . . . . . . . . . . . . . . . . . 210
xii
6.1.2 Double Slot Antenna Design . . . . . . . . . . . . . . . . . . . . 215
6.1.3 Four-Fold Slot Antenna Design . . . . . . . . . . . . . . . . . . 217
6.1.4 Radial & Rectangular Stubs . . . . . . . . . . . . . . . . . . . . 223
6.1.5 Low-pass Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
6.1.6 Couplers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
6.1.7 Termination Structure . . . . . . . . . . . . . . . . . . . . . . . 228
6.1.8 DC Chokes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
6.1.9 Impedance Transformers . . . . . . . . . . . . . . . . . . . . . . 237
6.2 THM Microwave Testing Schemes & Preliminary Measurements . . . . 239
6.2.1 CPW Probe Station Microwave Design & Measurements . . . . 239
6.2.2 Optical Coupling Schemes . . . . . . . . . . . . . . . . . . . . . 249
6.2.2.1 The Horn Antenna . . . . . . . . . . . . . . . . . . . . 250
6.2.2.2 The Extended Hemispherical Lens . . . . . . . . . . . 253
6.2.2.3 The Rexolite Lens . . . . . . . . . . . . . . . . . . . . 256
6.2.3 Black Body Source . . . . . . . . . . . . . . . . . . . . . . . . . 257
6.2.3.1 Nichrome Black Body Source . . . . . . . . . . . . . . 259
6.2.3.2 Finline Black Body Source . . . . . . . . . . . . . . . . 263
6.2.4 External RF Source Coupling . . . . . . . . . . . . . . . . . . . 268
7 Conclusion 269
7.1 Summary of Understanding of the THM Design . . . . . . . . . . . . . 269
7.2 Future Work Involving The Lateral Proximity Effect . . . . . . . . . . 271
7.3 Future Microwave Work . . . . . . . . . . . . . . . . . . . . . . . . . . 273
7.4 Future Work for Scaling to Large Arrays . . . . . . . . . . . . . . . . . 274
xiii
7.5 A Last Word: The Recommended THM Design . . . . . . . . . . . . . 274
xiv
List of Figures
1.1 Timeline of the universe, courtesy WMAP-Science team [114]. . . . . . 2
1.2 The history of CMB experiments. . . . . . . . . . . . . . . . . . . . . . 5
1.3 The Thompson scattering process through which a quadrupole moment
in the photon anisotropy from the perspective of the target electron
gives rise to a polarization in the CMB. Blue field lines on the incoming
photons indicate colder and thus lower energy photons and the red field
lines indicate hotter and thus higher energy photons. The net effect is
an outgoing electric field magnitude which is stronger in one direction.
Figure adapted from Hu & White [47]. . . . . . . . . . . . . . . . . . . 12
1.4 The two types of polarization patterns in the CMB. An example of an
E-mode polarization pattern which exhibits a divergence and a B-mode
polarization pattern which exhibits a curl. . . . . . . . . . . . . . . . . 13
1.5 The measured temperature angular power spectrum of the CMB. (Cour-
tesy WMAP science team [114]). The amplitude here is plotted in terms
of the variance of the fluctuations multiplied by the average CMB tem-
perature T = 2.73 K squared, such that the plot has units temperature
squared. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
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1.6 The measured E-mode polarization (EE) and temperature-E-mode cross-
correlation (EB) power spectra, and measured upper limits on B-mode
polarization (BB) power spectrum of the CMB. (Courtesy BICEP Sci-
ence Team [15]). The predicted B-mode polarization angular power
spectrum in the CMB is also shown by the grey line, with the contri-
butions near l ∼ 100 coming from primordial gravitational waves. The
B-mode component from gravitational lensing of E-mode to B-mode
peaks at l ∼ 1000. The signal is plotted in terms of the variance of the
fluctuations multiplied by the average CMB temperature T = 2.73 K
squared, such that the plot has units of temperature squared. . . . . . . 14
1.7 The basic detection schemes for CMB observing using coherent receivers
or incoherent bolometric detectors. . . . . . . . . . . . . . . . . . . . . 17
1.8 The frequency range of CMB experiments by type as a function of time. 19
1.9 The number of detector/receivers for CMB experiments as a function
of time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.1 The components to a simple bolometer. . . . . . . . . . . . . . . . . . . 25
2.2 The energy gap interpretation of superconductivity. Quasiparticles oc-
cupy the free electron states in the superconductor and electrons bound
in Cooper pairs occupy the bound states. Note however, that unlike
bound electron states in the other cases, in a superconductor, electrons
bound in Cooper-pair states do carry an electrical current. . . . . . . . 30
xvi
2.3 The RTES vs. T curve of a superconducting TES from a THM test
device of variation THM5 (this and other THM test devices will be
described in Chapter 5). . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4 A superconducting ring allows only quantized values of magnetic flux
through the center due to quantization of the superconducting wave-
function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5 A Josephson junction is two superconductors separated by a thin insu-
lating link. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.6 A “two-fluid” circuit diagram for a Josephson junction. . . . . . . . . . 39
2.7 An example of the I-V characteristics of a Josephson junction with zero
capacitance. Figure courtesy Gallop [31]. . . . . . . . . . . . . . . . . . 40
2.8 A simple SQUID: a superconducting ring broken by two Josephson junc-
tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.9 An example of the I-V characteristics of a current-biased SQUID for
different magnetic flux values. . . . . . . . . . . . . . . . . . . . . . . . 42
2.10 The measured voltage as a function of magnetic flux for the current-
biased NIST-Series Array SQUID which was used to read out the THM
test devices. Further measurements and details of this SQUID readout
are presented in Chapter 5. . . . . . . . . . . . . . . . . . . . . . . . . 43
2.11 A SQUID as a magnetometer. . . . . . . . . . . . . . . . . . . . . . . . 45
2.12 Electronic feedback to linearise SQUID. . . . . . . . . . . . . . . . . . . 46
2.13 The linear output of the NIST series array SQUID used to read out
THM test devices with feedback. . . . . . . . . . . . . . . . . . . . . . 46
xvii
2.14 The electical circuit for a voltage-biased TES read out by a SQUID
amplifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.15 The thermal circuit for an ideal bolometer detector. . . . . . . . . . . . 49
3.1 (a) The bilayer superconducting proximity effect. (b) A lateral super-
conducting proximity effect. (c) The two different TES designs where
the lateral or bilayer proximity effect play a role: a S-S’-S junction (left)
and a S-N-S junction (right). . . . . . . . . . . . . . . . . . . . . . . . . 73
3.2 Superconductivity theories, their relationships, and applicability. . . . . 75
3.3 The normal metal coherence length for a dirty Nb-Au-Nb junction (fol-
lowing Equation 3.21) as a function of temperature for Au RRR = 1&2
is plotted for 30 nm and 300 nm Au thicknesses. Room temperature
Au resistivity is assumed to be 3 · 10−8 Ω · m and Nb Tc = 8.3 K is
assumed. For typical S-N-S THM devices one expects ξN = 0.1− 0.4 µm. 80
3.4 The normal metal coherence length for a Nb-Mo/Au-Nb junction as
a function of temperature for Au RRR = 1 is plotted for 300 nm Au
thickness. Room temperature Au resistivity of 3·10−8 Ω·m, Nb Tc = 8.3
K and Mo/Au Tc = 200 mK are assumed. For the Sadleir-G-L model
(which matches the low temperature Usadel Model), the normal metal
coherence length is also plotted assuming Mo resistivity of 5.3 · 10−8
Ω ·m, and also assuming Sadleir et al.’s measured fit to ξi = 738 nm.
For all these models for typical THM devices ξN ∼ 0.1 − 1.0 µm is
predicted, with the coherence lengths predicted by the fit values on the
higher side of this range. . . . . . . . . . . . . . . . . . . . . . . . . . . 82
xviii
3.5 Critical current behaviour of a Nb-Mo/Au-Nb S-S’-S TES as predicted
by the Sadleir et al. model using Equation 3.29. The legends on each
plot indicate lead-to-lead lengths in meters. a) Ic calculated assuming
Au resistivity of ρ = 3.3 · 10−8 Ω·m, and Au thickness of 300 nm. b)
Ic assuming Mo resistivity of ρ = 5.3 · 10−8 Ω·m with bilayer thickness
dominated by Au thickness of 300 nm. c) Ic calculated assuming the
measured fit value by Sadleir et al. for ξi = 738 nm. For all predictions
λr = 79 nm (the measured value from Sadleir et al.), Nb Tc = 8.4 K,
and Mo/Au TcN = 170 mK have been assumed. The predictions for Ic
using the measured fit ξi value are ∼ 0.5−4 orders of magnitude higher
than predictions using ξi values calculated from resistivity. . . . . . . . 86
3.6 Critical current behaviour of a Nb-Au-Nb S-N-S TES predicted by the
Likharev-Usadel model using Equation 3.31. The legend on each of the
graphs indicates different lead-to-lead lengths in meters. a) Assuming
a Au resistivity of ρ = 3.3 · 10−8 Ω ·m and a Au thickness of 30 nm. b)
Assuming a Au resistivity of ρ = 3.3 · 10−8 Ω ·m and a Au thickness of
300 nm. In both cases a Nb transition temperature Tc = 8.4 K and a 3
µm wide device is assumed. This model predicts Ic ∼ 0.1 − 100 µA at
∼ 200 mK for a 3 µm long THM device. . . . . . . . . . . . . . . . . . 88
xix
3.7 Critical current behaviour of a Nb-Au-Nb S-N-S TES predicted by the
deGennes-GL model using Equation 3.32. The legend on each of the
graphs indicates different lead-to-lead lengths in meters. a) Assuming
a Au resistivity of ρ = 3.3 · 10−8 Ω ·m and a Au thickness of 30 nm. b)
Assuming a Au resistivity of ρ = 3.3 · 10−8 Ω ·m and a Au thickness of
300 nm. In both cases a Nb transition temperature Tc = 8.4 K and a 3
µm wide device is assumed. This model predicts Ic ∼ 10 nA-10 µA at
∼ 200 mK for a 3 µm long THM device. . . . . . . . . . . . . . . . . . 90
3.8 Critical current behaviour of a Nb-Au-Nb S-N-S TES predicted by the
Dubos-Usadel model using Equations 3.33 and 3.34. The legend on each
of the graphs indicates lead-to-lead lengths in meters. a) Assuming Au
resistivity of ρ = 3.3·10−8 Ω·m and Au thickness of 30 nm. b) Assuming
Au resistivity of ρ = 3.3 · 10−8 Ω ·m and Au thickness of 300 nm. In
both cases Nb Tc = 8.4 K and a 3 µm wide device is assumed. This
model predicts Ic ∼ 1 nA-0.1 µA at ∼ 200 mK for a 3 µm long TES.
The discontinuity in the curve for the shortest devices indicates the
crossover from the high to the low temperature limit. . . . . . . . . . . 92
xx
3.9 Critical current behaviour of a Nb-Au-Nb S-N-S TES predicted by the
van Dover-GL model using Equation 3.35. The legend on each of the
graphs indicates different lead-to-lead lengths in meters. a) Assuming
a Au resistivity of ρ = 3.3 · 10−8 Ω ·m and a Au thickness of 30 nm. b)
Assuming a Au resistivity of ρ = 3.3 · 10−8 Ω ·m and a Au thickness
of 300 nm. In both cases a Nb transition temperature Tc = 8.4 K and
Aρnγρs
= 0.24 is assumed. This model predicts Ic ∼ 0.1− 10 µA at ∼ 200
mK for a 3 µm long THM device. . . . . . . . . . . . . . . . . . . . . . 94
3.10 Critical current predictions for a Nb-Au-Nb S-N-S TES for the Likharev-
Usadel, deGennes-GL, Dubos-Usadel and van Dover-GL models. Here
a Nb transition temperature Tc = 8.4 K, Au resistivity of ρ = 3.3 · 10−8
Ω ·m, and Au thickness of 180 nm is assumed for a 3 µm x 3 µm device.
Also plotted for comparison purposes is the critical current behaviour
for a 3 µ long Mo/Au S-S’-S TES, following the Sadleir et al. model
and using their measured fit values for ξi and λr, with TcN = 180 mK.
For the S-N-S case, with a bias current of ∼1 µA, an effective TES Tc
of 100-400 mK is expected across the junction. . . . . . . . . . . . . . . 95
xxi
3.11 Limiting Γc =Rc
Rjunctionpredicted from Kuprianov-Lukichev-Usadel the-
ory requiring there be less than 20% change in critical current due to
finite contact resistance between superconducting Nb leads and a nor-
mal Au TES. A Au resistivity of ρ = 3.3 ·10−8Ω·m, thickness of 30−300
nm, and a 3 µm wide device is assumed at 150 mK. For typical THM
test devices, for Γ . 10 − 15%, only a small shift in critical current is
expected. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.1 The basic geometry of the THM components. . . . . . . . . . . . . . . 101
4.2 The complete thermal model for the THM. . . . . . . . . . . . . . . . . 103
4.3 The ideal thermal model for the THM detector. . . . . . . . . . . . . . 104
4.4 A thermal model for a non-ideal THM. . . . . . . . . . . . . . . . . . . 109
4.5 The non-ideal THM thermal model, simplified by the symmetry of the
device. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.6 Microstrip line geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.7 Stability limits on the SQUID readout input inductance, L. The r.h.s.
and l.h.s of Equation 2.21 are plotted and the maximum L for stability
is given by the point where the lines cross. (a) 20 µm2 TES, assuming
‘CMB-ground’ conditions, for Tbath = 240 mK.(b) 20 µm2 TES, assum-
ing ‘CMB-space’ conditions, for Tbath = 50 mK. (c) 3 µm2 TES, as-
suming ‘CMB-ground’ conditions, for Tbath = 240 mK.(d) 3 µm2 TES,
assuming ‘CMB-space’ conditions, for Tbath = 50 mK. ‘CMB-ground’
results are similar for Tbath = 50 mK. For these THM designs, stability
requires L ≤ 10 nH−1 µH. . . . . . . . . . . . . . . . . . . . . . . . . 124
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4.8 The electron-phonon conductance of the combined TES and absorber
structure, Ge−p, the electron-electron conductance across the entire
TES and absorbing structure (absorber dominated in this case), Ge−e,
and the electron-phonon conductance of the absorber only, Ge−p,Abs
plotted as a function of absorber resistance, RAbs. Here we have as-
sumed a 10 µm x 10 µm x 300 nm Au TES and a 3 µm wide, 800 nm
thick, Bi absorber. For electron-phonon thermal conductance we have
assumed n = 5 and ‘literature values’ for Σs. (a) ‘CMB-ground’ condi-
tions and Tbath = 240 mK (b) ‘CMB-ground’ conditions and Tbath = 50
mK (c) ‘CMB-space’ conditions and Tbath = 50 mK. For these designs
RAbs . 80 − 100 Ω is required to avoid power bypassing the TES, and
RAbs . 3 − 80 Ω is required to avoid a temperature differential across
the absorber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.9 The estimated fraction of power which flows through the TES (PTES ∼Ge−e
Ge−e+Ge−p) as a function of absorber resistance, RAbs. Here we have
assumed a 10 µm x 10 µm x 300 nm Au TES and a 3 µm wide, 800 nm
thick, Bi absorber. For electron-phonon thermal conductance we have
assumed n = 5 and literature Σ values. (a) ‘CMB-ground’ conditions
and Tbath = 240 mK (b) ‘CMB-ground’ conditions and Tbath = 50 mK
(c) ‘CMB-space’ conditions and Tbath = 50 mK. For these designs Rabs .
40−100 Ω is necessary to obtain at least 80−100% power flow through
the TES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
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4.10 The TES electron-electron thermal conductance, Ge−e,TES plotted with
the total electron-phonon thermal conductance, Ge−p, as a function of
TES resistance, RTES. In this case we assume a Bi absorber geometry
of 3 µm x 6 µm x 800 nm. We also assume a Mo/Au TES of a fixed
width 10 µm and thickness of 300 nm (resulting in ρ ∼0.1 Ω). For
electron-phonon thermal conductance we have assumed n = 5 and lit-
erature Σ values. (a) ‘CMB-ground’ conditions and Tbath = 240 mK (b)
‘CMB-ground’ conditions and Tbath = 50 mK (c) ‘CMB-space’ condi-
tions and Tbath = 50 mK. Requiring Ge−p < Ge−e,TES, gives a constraint
of RTES < 0.5− 5 Ω depending on the application and bath temperature.129
4.11 The total electron-electron thermal conductance across the absorber
and TES, Ge−e, plotted with the total electron-phonon thermal conduc-
tance, Ge−p, and the absorber electron-phonon conductance, Ge−p,Abs,
as a function of TES width, wAu, for a square Mo/Au TES with Au
thickness 300 nm. Here we have assumed a 3 µm x 6 µm x 800 nm Bi
absorber for RAbs = 30 Ω. For electron-phonon thermal conductance we
have assumed n = 5 and literature Σ values. (a) ‘CMB-ground’ condi-
tions and Tbath = 240 mK (b) ‘CMB-ground’ conditions and Tbath = 50
mK (c) ‘CMB-space’ conditions and Tbath = 50 mK. For these designs
wAu . 1− 20 µm is required to avoid a temperature differential across
the absorber (requiring Ge−e > Ge−p). There is no requirement to avoid
power bypassing the TES (requiring Ge−e > Ge−p,Abs). . . . . . . . . . . 131
xxiv
4.12 The electron-phonon thermal conductance, Ge−p, boundary thermal
conductance, Gboundary, and total thermal conductance Gtot, of a THM
detector as a function of TES width, wAu. Here we have assumed a
Bi absorber of size 3 µm x 6 µm x 800 nm and a square Mo/Au TES
with a Au thickness of 300 nm. We have assumed n = 5 and coupling
‘literature values’ for Σs, and a average literature value for the bound-
ary thermal conductance coefficient, Cb = 15.5 · 10−4 Km2
W[111]. (a)
‘CMB-ground’ conditions and Tbath = 240 mK (b) ‘CMB-ground’ con-
ditions and Tbath = 50 mK (c) ‘CMB-space’ conditions and Tbath = 50
mK. Gboundary is predicted to have some impact or dominate the total
thermal conductance over the full range of TES size scales for ground
and space observing conditions. . . . . . . . . . . . . . . . . . . . . . . 133
4.13 SQUID and Johnson noise as a function of TES resistance, RTES. We
assume a Bi absorber of size 3 µm x 6 µm x 800 nm and a 3 µ wide
Mo/Au TES with Au thickness of 300 nm (RTES = 0.1 Ω) and an
adjustable length and total resistance. We assume a shunt resistor with
Rs = 0.025 Ω and SQUID current noise of NEI = 4√Tbath · 10−12 A√
Hz.
(a) ‘CMB-ground’ conditions and Tbath = 240 mK (b) ‘CMB-ground’
conditions and Tbath = 50 mK (c) ‘CMB-space’ conditions and Tbath =
50 mK. A bath temperature of Tbath = 240 mK requires RTES < 1
Ω for ground-based observing to ensure that the Johnson and SQUID
noise are insignificant. At bath temperature of Tbath = 50 mK, RTES <
20− 100 Ω is required for ground- or space-based observing. . . . . . . 135
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4.14 Thermal detector NEP as a function of TES width, wAu, for a square
Mo/Au TES with Au thickness 300 nm assuming a 3 µm x 6 µm
x 800 nm Bi absorber. Detector and background photon NEP for
‘CMB-ground’, ‘CMB-space’ and ‘FIR-spectral’ observing conditions
are shown. We have assumed n = 5 and ‘literature values’ for
Σs. (a) Tbath = 240 mK. (b) Tbath = 50 mK. At Tbath = 240 mK back-
ground limited NEP is obtainable for CMB ground observing only, for
wAu . 3 µm. At Tbath = 50 mK background limited NEP is obtainable
for both CMB ground and space observing for wAu = 3− 50 µm. . . . . 137
4.15 Thermal detector NEP as a function of TES width, wAu, for a square
Mo/Au TES with Au thickness 300 nm, assuming a 3 µm x 6 µm
x 800 nm Bi absorber. Detector and background photon NEP for
‘CMB-ground’, ‘CMB-space’ and ‘FIR-spectral’ observing conditions
are shown. We have assumed ‘measured n = 5’ values for Σs.
(a) Tbath = 240 mK. (b) Tbath = 50 mK. At Tbath = 240 mK background
limited NEP is obtainable for ground observing only, for wAu . 10 µm.
At Tbath = 50 mK background limited NEP is obtainable for both CMB
ground and space observing for wAu = 1− 100 µm. . . . . . . . . . . . 138
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4.16 Thermal detector NEP as a function of TES width, wAu, for a square
Mo/Au TES with Au thickness 300 nm, assuming a 3 µm x 6 µm
x 800 nm Bi absorber. Detector and background photon NEP for
‘CMB-ground’, ‘CMB-space’ and‘FIR-spectral’ conditions are shown.
We have assumed ‘measure n = 6’ values for Σ. (a) Tbath = 240
mK. (b) Tbath = 50 mK. At Tbath = 240 mK near background limited
NEP is obtainable for CMB ground and space observing, for wAu . 40
µm and wAu . 4 µm, respectively. At Tbath = 50 mK background
limited NEP is obtainable for CMB observing for wAu = 1− 1000 µm. . 139
4.17 The bolometer temperature, Tbolo, as a function of TES width, wAu, for
the THM design variations of Figure 4.14 for CMB observing conditions
(for FIR observing Tbolo = Tbath). (a) Tbath = 240 mK. (b) Tbath = 50 mK.140
4.18 The bolometer temperature, Tbolo, as a function of TES width, wAu, for
the THM design variations of Figure 4.15 for CMB observing conditions
(for FIR observing Tbolo = Tbath). (a) Tbath = 240 mK. (b) Tbath = 50 mK.141
4.19 The bolometer temperature, Tbolo, as a function of TES width, wAu, for
the THM design variations of Figure 4.16 for CMB observing conditions
(for FIR observing Tbolo = Tbath). (a) Tbath = 240 mK. (b) Tbath = 50 mK.142
xxvii
4.20 The thermal fluctuation NEP of a generic CMB observing bolometer
in comparison to background photon NEP. A temperature depen-
dence of the power flow, n = 2 is assumed. (a) ‘CMB-ground’
observing conditions with Tbath = 240 mK. (b) ‘CMB-space’ observing
conditions with Tbath = 240 mK.(c) ‘CMB-ground’ observing condi-
tions with Tbath = 50 mK. (d) ‘CMB-space’ observing conditions with
Tbath = 50 mK. For all of these cases, the thermal detector NEP in the
low power loading limit is also plotted. . . . . . . . . . . . . . . . . . . 145
4.21 The thermal fluctuation NEP of a generic CMB observing bolometer
in comparison to background photon NEP. A temperature depen-
dence of the power flow, n = 3 is assumed. (a) ‘CMB-ground’
observing conditions with Tbath = 240 mK. (b) ‘CMB-space’ observing
conditions with Tbath = 240 mK.(c) ‘CMB-ground’ observing condi-
tions with Tbath = 50 mK. (d) ‘CMB-space’ observing conditions with
Tbath = 50 mK. For all of these cases, the thermal detector NEP in the
low power loading limit is also plotted. . . . . . . . . . . . . . . . . . . 146
xxviii
4.22 The thermal fluctuation NEP of a generic CMB observing bolometer
in comparison to background photon NEP. A temperature depen-
dence of the power flow, n = 4 is assumed. (a) ‘CMB-ground’
observing conditions with Tbath = 240 mK. (b) ‘CMB-space’ observing
conditions with Tbath = 240 mK.(c) ‘CMB-ground’ observing condi-
tions with Tbath = 50 mK. (d) ‘CMB-space’ observing conditions with
Tbath = 50 mK. For all of these cases, the thermal detector NEP in the
low power loading limit is also plotted. . . . . . . . . . . . . . . . . . . 147
4.23 The thermal fluctuation NEP of a generic CMB observing bolometer
in comparison to background photon NEP. A temperature depen-
dence of the power flow, n = 5 is assumed. (a) ‘CMB-ground’
observing conditions with Tbath = 240 mK. (b) ‘CMB-space’ observing
conditions with Tbath = 240 mK.(c) ‘CMB-ground’ observing condi-
tions with Tbath = 50 mK. (d) ‘CMB-space’ observing conditions with
Tbath = 50 mK. For all of these cases, the thermal detector NEP in the
low power loading limit is also plotted. . . . . . . . . . . . . . . . . . . 148
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4.24 The thermal fluctuation NEP of a generic CMB observing bolometer
in comparison to background photon NEP. A temperature depen-
dence of the power flow, n = 6 is assumed. (a) ‘CMB-ground’
observing conditions with Tbath = 240 mK. (b) ‘CMB-space’ observing
conditions with Tbath = 240 mK.(c) ‘CMB-ground’ observing condi-
tions with Tbath = 50 mK. (d) ‘CMB-space’ observing conditions with
Tbath = 50 mK. For all of these cases, the thermal detector NEP in the
low power loading limit is also plotted. . . . . . . . . . . . . . . . . . . 149
5.1 In-process images of some of the key fabrication steps for the THM
test devices. (a) Optical image of bilayer TES on wafer THM5 after
completion of the Au ionmill and Mo RIE patterning. The Mo extends
out to make contact with the Nb leads which will be deposited next.
The Mo on the non-lead sides of the TES will be etched away during the
Nb patterning step. (b) Optical image of wafer THM4 after completion
of Nb (SF6 + 02) RI sloped sidewall etch. The sidewall can been seen
even in this optical image as Nb (blue) extends past the dark top edge. 153
xxx
5.2 In-process images of some of the key fabrication steps for the THM test
devices. (a) SEM image of THM4 showing good step coverage over a
Nb sloped sidewall. This view shows the Nb microstripline crossing the
gap in the Nb ground plane(see Chapter 6). The ground plane is seen
through the AlO dielectric layer. (b) SEM image of a 3 µm x 9 µm Bi
absorber test device (not incorporated into a THM) after liftoff. The
grainy structure of the evaporated Bi is observable. Thin Au contact
pads under the Bi help make contact to the Nb leads. . . . . . . . . . . 154
5.3 The resistivity of evaporated Bi resistivity measured for several test
wafers (with Bi thickness listed) as a function of temperature. An
increase in resistivity is seen as the temperature decreases. . . . . . . . 156
5.4 The dewar shielding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
5.5 The coldstage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
5.6 The THM chip and 1st stage SQUID mount which fits inside a Nb
shielded cylindrical can. . . . . . . . . . . . . . . . . . . . . . . . . . . 160
5.7 Diagram of the 2-stage SQUID electrical connections for the read out
of the THM TES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
5.8 The 2nd stage SQUID bias line voltage as a function of the input cali-
bration signal to the 1st stage SQUID input coil. With feedback off the
second stage signal follows the input signal. With feedback on the bias
signal is zero no matter the input signal, as a nulling feedback signal,
which tracks the input signal, is being fed back to the 1st stage SQUID. 163
xxxi
5.9 The SQUID calibration curve. Plotted is the feedback signal to the
first stage SQUID as a function of the signal to the input coil. The 1st
stage feedback signal is what is read out. The gain factor is given by
the slope of this linear curve. . . . . . . . . . . . . . . . . . . . . . . . . 164
5.10 (a) Fabrication steps and cross-sectional view showing the layers for
each of the THM2003 test devices. Thicknesses are not drawn to scale,
but are listed on the labels for each layer. (b) Optical image of a test
device of variation THM2003. . . . . . . . . . . . . . . . . . . . . . . . 166
5.11 I-V curves for a device from wafer THM2003 at different bath tempera-
tures (labelled in the figure). The solid black line indicates RTES =0.32
Ω. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
5.12 P vs. Tbath measurement for devices from wafer THM2003. . . . . . . . 169
5.13 Noise measurements of the THM2003 test devices at 1 µV bias, 311 mK
bath temperature. The best fit is given by the non-ideal model. . . . . 174
5.14 Noise measurements of the THM2003 test devices at 0.5 µV bias, 311
mK bath temperature. The best fit is given by the non-ideal model. . . 175
5.15 Noise measurements of the THM2003 test devices at 0.2 µV bias, 311
mK bath temperature. The best fit is given by the non-ideal model. . . 176
5.16 Predictions of detector NEP for the ideal electron-phonon model and
the non-ideal model at 1 µV bias, showing contributions from thermal,
Johnson, and SQUID noise sources. The non-ideal model matches the
measured noise (Figure 5.13) best. . . . . . . . . . . . . . . . . . . . . . 178
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5.17 (a) Fabrication steps and cross-sectional view showing the layers for
each of the us23/us25 test devices. Thicknesses are not drawn to scale,
but are listed on the labels for each layer. (b) SEM image of a test
device of variation us23/us25. . . . . . . . . . . . . . . . . . . . . . . . 181
5.18 The layer overlap and active thermal area of the TES and absorber for
the two micron-sized test devices of variation us25. . . . . . . . . . . . 183
5.19 Joule power applied to the absorber versus hot-electron temperature,
Tbolo, while the bath was held constant at 190 mK for the THM test
device of variation us25 with Au TES volume of 0.27 µm3. Fits to the
predicted forms of the power law dependence are shown. . . . . . . . . 185
5.20 Joule power applied to the absorber versus hot-electron temperature,
Tbolo, while the bath was held constant at 190 mK for the THM test
device of variation us25 with Au TES volume of 0.58 µm3. Fits to the
predicted forms of the power law dependence are shown. . . . . . . . . 186
5.21 (a) Fabrication steps and cross-sectional view showing the layers for
each of the THM4/THM5 test devices. Thicknesses are not drawn to
scale, but are listed on the labels for each layer. (b) Optical image of a
test device of variation THM4/THM5. . . . . . . . . . . . . . . . . . . 190
xxxiii
5.22 (a) Schematic of contact between the Mo/Au TES and the Nb leads for
devices THM4/THM5. (b) SEM image of contact between the Nb leads
and TES for a 3 µm x 3 µm THM4/THM5 device with no absorber or
microwave circuit. The Mo layer which extends from the TES is visible
as a slight change in Nb thickness. The over-etching of the Nb leads
during the Nb etch on top of the Mo/Au TES is also clearly visible. . . 192
5.23 (a) Tc vs. lead-to-lead distance, L, for the 65 nm Mo/350 nm Au bilayer
devices of variation THM5. A curve fit is shown for the parameters TcN
= 240 mK, LN = 12 µm and m = 5. (b) Tc vs. lead-to-lead distance,
L, for the 55 nm Mo/350 nm Au bilayer devices of variation THM4.
A curve fit is shown for the parameters TcN = 170 mK, LN = 12 µm
and m = 5. Data points indicate nominal L values while the error bars
indicate uncertainties due to over-etching. Error bars for Tc indicate
uncertainty distinguishing the TES from the Nb lead transition. . . . . 193
5.24 Resistance vs. temperature curves for two of the THM test devices.
(a) Nominal 12 µm x 12 µm, 55 nm/350 nm thick, Mo/Au TES with
absorber of variation THM4. (b) Nominal 3 µm x 3 µm, 55 nm/350 nm
thick Mo/Au TES with absorber of variation THM4 with a transition
near the Nb lead transition. . . . . . . . . . . . . . . . . . . . . . . . . 195
5.25 (a) Fabrication steps and cross-sectional view showing the layers for
each of the THMA4/THMA24 test devices. Thicknesses are not drawn
to scale, but are listed on the labels for each layer. (b) SEM image of
a test device of variation THMA4/THMA24. . . . . . . . . . . . . . . . 198
xxxiv
5.26 SEM and AFM images after ion-milling, cleaning of the Au surface, and
Nb deposition. A rough surface of the Au metal is seen, but no organic
contamination which would be indicated by dark or stringy residue can
be seen in these images. . . . . . . . . . . . . . . . . . . . . . . . . . . 200
5.27 Measured contact resistance, Rc (with error), for all devices tested.
These measurements are normalized to assume a 3 µm2 contact area
for each device. Error bars indicate error due to the measurement noise. 201
5.28 Chart summary of Table 5.8. The Kuprianov and Lukichev Rc limits
are also shown in the plot. . . . . . . . . . . . . . . . . . . . . . . . . . 202
6.1 Microwave design at 92 GHz to couple radiation to the THM detector
for the THM4 and THM5 test devices. Devices at 43 GHz were also
designed and fabricated. The signal from the double slot antenna is
transmitted via a low-pass filter to the RF-terminated THM detector.
Choked bias leads provide DC connections to both the TES (for bias
and SQUID read out) and the absorber (for DC Joule heating of the
absorber). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
6.2 Microwave design at 92 GHz to couple radiation to an array of 128
individual THM detectors for the us23/us25 test devices. The coupling
to such a large number of detectors was done in an attempt to find
the optimal lateral proximity effect S-N-S TES, with each of the 128
detectors of varying TES lead-to-lead length. In actual operation, with
an optimized THM device, one imagines only a single detector coupling
to the slot antenna without the branching network. . . . . . . . . . . . 212
xxxv
6.3 Optical image of one of the us23/us25 test device detector chips. Chip
size is 15 mm x 15 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
6.4 Two-detector coupled alternative slot antenna design for test devices
THM4/THM5. This device was designed specifically to test the perfor-
mance of the low-pass filter. A directional coupled line coupler trans-
mits the signal to two separate detectors, one line via a low-pass filter
and another line without the filter. By coupling a swept microwave sig-
nal into the slot antenna the filter response as a function of frequency
can be determined. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
6.5 The geometry of the THM4/THM5 double slot antenna design. . . . . 216
6.6 The simulated reflection (S11) from an input signal sent into a port
which feeds the single-line microstrip to the double slot antenna for
devices of variation THM4/THM5. The low level of reflection near 92
GHz indicates power radiated by the antenna. . . . . . . . . . . . . . . 218
6.7 An optical image of the 92 GHz double slot antenna on a test device of
variation THM5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
6.8 The geometry of the us23/us25 four-fold slot antenna design. . . . . . . 221
6.9 The simulated reflection (S11) at the port which feeds the microstrip to
the four-fold slot antenna for the test devices of variation us23/us25.
The low level of reflection indicates power radiated by the antenna. . . 222
6.10 The predicted beam pattern at 92 GHz for the four-fold slot antenna
design for the test devices of variation us23/us25. As expected, the gain
into the Si substrate is greater than into vacuum. . . . . . . . . . . . . 223
xxxvi
6.11 The geometry of the radial stub design for devices of variation THM4/THM5.224
6.12 The geometry of the rectangular stub design for devices of variation
us23/us25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
6.13 Input impedance for the THM4/THM5 radial stub design. A very broad
bandwidth at 92 GHz indicating a short to ground (with impedance
Z ≪ 20 Ω) is predicted. . . . . . . . . . . . . . . . . . . . . . . . . . . 226
6.14 The geometry of the low-pass filter, consisting of three sub-filters, indi-
cated as “Part 1”, “Part 2”, and “Part 3”. “Part 1” and “Part 3” are
“stub” type filters and “Part 2” is a “stepped impedance” type filter. . 227
6.15 Optical image of the low-pass filter from test device of variation THM5. 228
6.16 Simulated transmission (S12) through the low-pass filter parts. Part “2”
defines the low frequency cut-off. Part “1” blocks the higher frequency
leaks from part “2”. Part “3” blocks the higher frequency leaks from
part “1”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
6.17 The simulated transmission (S12) through the low-pass filter for the
us23/us25 design. Note that “in-band” (∼ 75 − 110 GHz) the loss is
< −3 dB while the out of band rejection at frequencies > 180 GHz is
excellent (< −20 dB transmission). . . . . . . . . . . . . . . . . . . . . 230
6.18 The Wilkinson coupler design [91]. The design requirements are shown
in terms of the charateristic impedances of the input and output mi-
crostripline, Z0, and the microwave wavelength in the dielectric, λ. . . . 231
6.19 An optical image of the Wilkinson couplers in part of the 128-channel
splitter network on a test device of variation us23. . . . . . . . . . . . . 232
xxxvii
6.20 S-parameters showing transmission from port 1 (output of coupler) to
ports 2 and 3 (inputs to coupler) for the us23/us25 Wilkinson coupler
design. A 3 dB (equal) coupling/splitting is expected near 92 GHz. . . 233
6.21 The THMmicrostrip termination structure geometry. The large rectan-
gular microstrip structures provide capacitive coupling to ground. For
the us23/us25 design optimal dimensions at 92 GHz were W1 = 41 µm,
W2 = 21 µm, L1 = 72 µm, and L2 = 29 µm. For the THM4/THM5
design the optimal dimensions at 92 GHz were W1 = 54 µm, W2 = 10
µm, L1 = 90 µm and L2 = 30 µm. . . . . . . . . . . . . . . . . . . . . 235
6.22 Simulated reflection (S11) for an input signal into the microstrip termi-
nation structure with matched THM absorber (Z0 = RAbs = 31 Ω) for
the us23/us25 design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
6.23 The geometry and placement of the DC chokes on the us23/us25 devices
in order to provide TES bias and absorber access. A close up of the RF
termination on the THM absorber is shown in Figure 6.21. . . . . . . . 237
6.24 Simulated microwave transmission (S12) and reflection (S11) through a
microstripline (above) which is intersected by the DC choke design used
in test devices us23/us25. In the desired RF band of the detector the
presence of the DC connection has little effect on the RF performance. 238
6.25 The geometry of one of the stepped impedance transformers from the
us23/us25 test devices which transitions from a 19 Ω (6 µm wide) to a
30 Ω (3 µm wide) microstrip line. Lengths/widths are not drawn to scale.239
xxxviii
6.26 The simulated transmission (S12) and reflection (S11) through the mi-
crostrip impedance transformer shown in Figure 6.25. . . . . . . . . . . 240
6.27 One of the THM 43 GHz CPW test chip designs. Used mainly for cal-
ibration purposes, it includes microstrip throughlines of various length
as well as two microstrip line “opens”. Contact to each lines is made
by 3 CPW probe tip pads at the edges of the chip. . . . . . . . . . . . 242
6.28 Another of the THM CPW designs, with test lines to test the low-pass
filter, termination structure, and impedance transformer performances. 243
6.29 The predicted transmission (S11) and reflection (S12) through the coplaner
waveguide to microstrip transformer for the 43 GHz THM4/THM5
CPW test chip design. . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
6.30 The CPW cryogenic probe station measurement setup. . . . . . . . . . 245
6.31 Measured loss per millimeter of 3 µm wide microstrip throughline on
a test device of variation THM5. This measured loss is within the
measurement noise (∼ ±0.01 dB). . . . . . . . . . . . . . . . . . . . . . 246
6.32 Measured relative dielectric constant of Al2O3 dielectric found via cali-
bration measurement of the microstrip throughlines and opens on a test
device of variation THM5. Expected ǫr ≈ 10. . . . . . . . . . . . . . . . 247
6.33 Measured characteristic impedance of a 3 µm wide microstrip line,
found via calibration measurements of microstrip throughlines and open
lines on a test device of variation THM5. The measured impedance is
close to the 20 Ω design impedance. . . . . . . . . . . . . . . . . . . . . 248
xxxix
6.34 The two optical coupling schemes for testing the microwave compo-
nents and microwave response of the THM in the laboratory cryostat.
Components are not drawn to scale. . . . . . . . . . . . . . . . . . . . . 251
6.35 Dimensions of the optical components, separation distances and beam
waists. Figures are not drawn to scale. . . . . . . . . . . . . . . . . . . 252
6.36 The horn antenna geometry and dimensions. Here SE and SH are the
pyramidal horn dimensions projected into the E-field and H-field planes. 254
6.37 The simulated (above) and measured (below) beam pattern from the
pyramidal horn antenna at 92 GHz. Courtesy Sara Stanchfield. . . . . . 255
6.38 The extended hemispherical lens geometry. R is the spherical radius,
L is the cylindrical extension length. . . . . . . . . . . . . . . . . . . . 256
6.39 The simulated and measured beam pattern at 92 GHz from the horn
antenna after focusing by the Rexolite lens. Courtesy Sara Stanchfield.
Measurements are consistent with the simulated beam pattern. . . . . . 258
6.40 The nichrome blackbody source. . . . . . . . . . . . . . . . . . . . . . . 260
6.41 The measured emissivity of the nichrome black body source. . . . . . . 262
6.42 The geometry and layout of the finline black body source. . . . . . . . 263
6.43 The finline black body source. . . . . . . . . . . . . . . . . . . . . . . . 264
6.44 The measured emissivity of the finline black body source. Courtesy
Sara Stanchfield. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
6.45 The simulated emissivity of the finline black body source with a 0.22
inch long extended resistor with resistivity of 250 Ωand total terminat-
ing resistance of 28.5 Ω. Courtesy Sara Stanchfield. . . . . . . . . . . . 267
xl
7.1 The basic microwave circuit for the recommended THM design. A
close-up of the THM detector is shown in Figure 7.2. . . . . . . . . . . 278
7.2 The geometry of the recommended THM design for CMB applications. 279
1
Chapter 1
Introduction
1.1 The History and Science of the CMB
1.1.1 CMB Cosmology
The early universe was a very dense and hot place. When it was only a few
minutes old it contained baryonic matter (protons, neutrons and electrons), neutri-
nos, ‘cold’ dark matter, radiation (photons), and presumably dark energy. Since the
beginning of the universe around 13.7 billion years ago, after an event called the Big
Bang, the universe has been expanding, becoming less dense and cooling. As the uni-
verse has expanded and cooled, the constituents of the universe have been interacting
and evolving. In the very early universe most of the energy of the universe was in
the form of radiation, but not very long after (70,000 years after the Big Bang) the
universe became matter dominated. Just recently we appear to be entering an era of
dark energy domination.
As the universe has cooled both dark matter and baryonic matter have condensed
through gravity from small inhomogeneities at early times, eventually forming the
2
Figure 1.1: Timeline of the universe, courtesy WMAP-Science team [114].
clusters, galaxies, stars and planets that we observe today. This standard cosmological
account (depicted in Figure 1.1) is based on observational evidence of the recession
of distant galaxies (and the supernovae embedded in them), observation of large scale
structure traced by galaxy surveys, observation of element abundances leftover from
primordial nucleosynthesis, and perhaps most importantly, from observations of the
Cosmic Microwave Background (CMB). It is these precision measurements of the CMB
which will be the focus and motivation of the detector technology developed in this
thesis, a Transition-Edge Hot-Electron Microboloter (or THM).
In the early universe, the temperature and density were high enough that photons
were continuously colliding via Thomson scattering with electrons, ionizing atoms that
3
tried to form. However, about 380,000 years after the Big Bang the universe had
cooled enough that the photons no longer had enough energy to ionize these atoms,
and the electrons and protons recombined, leaving the photons free to travel, for the
most part undeflected. These photons are observed today as the Cosmic Microwave
Background (CMB), a surprisingly uniform background radiation which arrives at our
telescopes from all directions in the sky. The CMB provides us with a snapshot of
the universe at the time of this recombination. Indeed, it is the earliest radiation, and
thus information, that we receive from the early universe.
The CMB is near perfect blackbody radiation with a temperature of 2.725 K
today (at the time of recombination it would have had a temperature of 3000 K).
Today the peak of the CMB blackbody spectrum is near 100 GHz, which corresponds
to a peak wavelength near 3 mm. The CMB was first observed by Penzias and Wilson
in 1964, a discovery for which they later earned the Nobel Prize in physics. An
incomplete history of past CMB experiments and their science goals (and detector
type which will be discussed in the following section) is listed in Figure 1.2. Early
observations of the CMB traced out this near perfect blackbody frequency spectrum
of the CMB. This was most accurately done by the FIRAS instrument on the COBE
satellite in 1994 for which another Nobel Prize was earned in 2006 [82]. Work in the
last two decades has gone into detailed mapping of the low-level temperature and ‘E-
mode’ polarization fluctuations in the CMB. These measurements are expressed as an
angular power spectrum where the amplitude of fluctuations in the CMB is plotted
as a function of the angular size scale of these fluctuations on the sky. This power
spectrum is a spatial frequency Fourier transform of the CMB as function of position
4
on the sky.
Before recombination the proton-electron-photon fluid in the early universe was
undergoing acoustic oscillations on all scales. These initial perturbations were seeded
by inflation. Over-dense regions in the fluid attracted more mass to them through grav-
ity. As these regions grew, radiation pressure built up, eventually forcing the fluid to
expand again. This interaction of gravity and radiation pressure led to over-dense and
under-dense oscillations in the proton-electron-photon plasma. Like a 3-dimensional
version of waves on a bound string, and like sound waves travelling through the air
in a closed pipe, these acoustic oscillations in the early universe plasma at the time
of last scattering were occurring at harmonic mode frequencies. Each harmonic mode
corresponded to a spatial scale of the universe and today corresponds to an angular
scale on the CMB sky. The temperature power-spectrum of the CMB is a measure
of the amplitude of these fluctuations at the time of last scattering, as a function of
angular size scale, or spherical harmonic mode number, l. Here large l corresponds to
a small angular distance on the sky.
The location and precise shape of acoustic peaks in the angular power spectrum
is determined by the density of dark matter and dark energy in the universe, the
expansion rate history of the universe and is also related to the timeline for structure
and star formation in the universe. The CMB has provided us with the most precise
method to pinpoint such cosmological parameters. The most recent constraints on
such cosmological parameters have been put in place by the WMAP satellite 7-year
results [75, 69].
Hope for extracting further cosmological information from the CMB focuses on
5
Figure 1.2: The history of CMB experiments.
6
observing the ‘B-Mode’ polarization in the CMB sky. A measurement of this signal will
allow us to challenge theories about events in the early universe at times significantly
earlier than recombination. The CMB polarization signal provides a unique probe
of inflation theory, an era in the universe’s history which occurred during the first
10−32 − 10−34 seconds.
1.1.2 Inflation & Gravitational Waves
Fundamentally there are three cosmological observations of the universe which
lead to puzzling questions about the origins of the universe. Together, the first two,
called the Cosmological Principal, are: 1) On large scales the universe is homogeneous;
2) On large scales the universe is isotropic. This principle states that on large scales
the universe has a uniform matter and photon density and that from any place in
the universe on average an observer sees the same thing. For instance, the Cosmic
Microwave Background is extremely smooth, so much so that regions on the sky that
are too far apart to ever have been in causal contact given our present expansion rate
have the same temperature. The last observation is: 3) The total density of the uni-
verse (including baryonic matter, neutrinos, radiation, dark matter and dark energy)
is very nearly identical to the critical density (ρ = 1.88h210−29 g·cm−3 at the present
time). According to Einstein’s general relativity, which relates the gravitational effect
of energy density to the curvature of space-time, a critical density means that the
universe is flat (curvature parameter, k = 0). In a general relativistic account of the
universe, the acceleration and curvature of the universe are defined by Friedmann’s
acceleration equation:
da2
dt2= −8πG
3a2ρ− kc2. (1.1)
7
Applying energy conservation this equation takes the form of:
da2
dt2= −4
3πGa(ρ+
3P
c2). (1.2)
Here a is the scale factor of the universe, and is defined to have current value of 1; at
earlier times it had a value < 1. The physical distance between any two points scales
with this factor. Thus da2
dt2is the acceleration of the expansion of the universe, which
is often written in terms of the Hubble constant, H = dadt
1a. P and ρ are the pressure
and density of the universe which can be also be written as a function of a and the
current density. Terms must be included in these equations to describe each type of
energy in the universe (matter, radiation, nuetrinos, dark energy etc.). For any given
type of energy, the density scales as a particular function of a where ρ ∼ 1an. n = 3 for
baryonic matter and dark matter, and n = 4 for radiation and relativistic neutrinos.
For dark energy in the form of a cosmological constant n = 0. In addition, for a given
type of energy, the density and pressure are related by an ‘equation of state’ (which
determines the value of n).
Inflation was initially proposed in 1981 by Guth [45] (with subsequent versions
in 1982 by Linde [77] and Albrecht & Steinhardt [2]) as a solution to the questions
posed by the three fundamental cosmological observations and which are assumed by
this standard model of cosmology. Inflation says that there was an era of very rapid
expansion for a very short time, very early on in the universe (the first 10−32 − 10−34
seconds). Due to this rapid expansion what were previously very small regions of space
expanded to a size much greater than the horizon-size of the early universe. This
meant that a universe that may have had curvature or inhomogeneities in the past
would now be approximately flat and smooth. In addition to providing an explanation
8
for the three cosmological observations, inflation also provides a way to set the initial
conditions of the universe and to seed the small scale perturbations that we observe in
the Cosmic Microwave Background. Inflation explains that these initial perturbations
began as quantum fluctuations that were blown up by this rapid early expansion.
Inflation also explains why there is no substantial number of magnetic monopoles
in our universe and provides the initial ‘setting into motion’ of cosmic or Hubble
expansion which we now observe at a much slower rate.
In inflation, the mechanism for this rapid expansion is a scalar ‘inflaton’ field. As
the scalar field value of the universe slowly ‘rolled’ down the slope of this inflationary
potential an exponential expansion occurred. During this short inflation era this scalar
field dominated the energy density of the universe. The inflationary field energy
density is described by an equation of state which produces a negative pressure. Thus
the r.h.s of equation 1.2 was dominated by a negative pressure term and a rapid
acceleration occurred, rather than a deceleration as occurs for the positive pressure
characteristic of matter and radiation. Interestingly, this negative pressure term is of
the same form that is needed to explain the dark energy contribution to the universe
which dominates our present day universe and is causing the current acceleration.
However, there is as of yet no clear connection between dark energy and inflation.
Inflation, although providing an explanation for the cosmological observations
and the origin of inhomogeneities which we already observe, has not yet provided a
unique prediction that has been adequately tested. Because of the large energy scales
involved in the inflation process, the theory predicts the production of gravitational
waves in the early universe [22]. The effect of these gravitational waves would be
9
observable in the CMB ‘B-mode’ polarization. The amplitude of the gravitational
waves produced during this time and their imprint left in the CMB would be directly
proportional to the height of the inflaton field potential and the energy scale of in-
flation (thought to be near 1015 GeV). The observation of B-mode polarization from
gravitational waves would be the first instance where a direct and unique prediction
of inflation could be confirmed. Gaussianity of the primordial acoustic oscillations
and a small spectral tilt in these oscillations are other predictions of inflation theory
which have been observed in the CMB, but these predictions do not provide such a
direct connection to the details of the inflation theory and process like the B-mode
polarization signal.
Although inflation is the most popular theory of the early universe due to its
great explanatory power, there are other theories about the earliest moments of the
universe. For example, a ‘cyclical’ model of the early universe may be able to explain
these cosmological observations as well [116]. This lower-energy model would not
create gravitational waves and thus would leave no imprint in the CMB in the form
of B-modes. Recently, it has been suggested that due to issues arising from the un-
predictive, eternal nature of inflation and fine-tuning that is required, that a cyclical
universe theory is a sounder and a more likely theory than inflation [116, 110]. Thus
a measurement of the B-mode polarization is a very important test. If B-modes are
not observed it may push theorists towards a new direction in our understanding of
the earliest times of our universe.
10
1.1.3 CMB Polarization
Polarization is defined as the direction of the E-field of an electromagnetic wave.
Unpolarized light is the superposition of waves with random E-field orientations. Po-
larized light has an E-field with a greater amplitude in one particular direction. The
polarization in the CMB is a result of Thomson scattering at the time of recombina-
tion [22, 47]. In an isotropic medium the net result from this scattering is unpolarized
light. However from observations of the CMB we observe that the medium was not
completely isotropic at the time of last scattering. These anisotropies can be modelled
as spherical harmonics made up of hot and cold spots from the perspective of the scat-
tering target electron at the center of the incoming CMB photons as shown in Figure
1.3. In the case of a quadrupole moment of the spherical harmonic, the incoming
hot/cold/hot/cold photons will sum to give a net polarization. In all other moments
the scattering photons sum to give a net zero polarization. Thus a quadrupole moment
is the sole cause of polarization in the CMB.
There are three possible types of inflation-seeded perturbations which give rise to
a quadrupole moment in the electron-proton-photon fluid at the time of last scattering
and thus to polarization in the CMB. These are: 1) scalar perturbations, which lead
to over- and under-densities in the fluid; 2) vector perturbations, which lead to vortex
flows in the fluid; 3) tensor perturbations, which lead to gravitational waves which
stretch space as they travel through the fluid [22, 47]. Scalar perturbations give rise
to an ‘E-mode’ type of polarization. They are also the source of the CMB temperature
fluctuations. Thus there is an expected correlation between the E-mode polarization
and the temperature signal in the CMB. The vector perturbations are expected to be so
11
small that no effects are observable in the CMB. The tensor fluctuations are expected
to give rise to both E-mode and B-mode polarization. The terms E-mode and B-
mode polarization indicate different types of patterns which the CMB polarization
can form on the sky. In Figure 1.4 these two patterns are shown. Although it can be
difficult to distinguish by eye, mathematically an E-mode polarization pattern exhibits
a divergence, while a B-mode pattern exhibits a curl.
In Figures 1.5 and 1.6 recent measurements and predictions of the CMB power
spectra are shown courtesy of the WMAP Science team [114] and the BICEP Science
team [15]. The well-measured temperature spectrum is shown in Figure 1.5, which has
now been mapped on an extensive range of angular scales. The first measurements
of the E-mode spectrum are also shown, and a confirmed correlation between this
type of polarization and the temperature power spectrum are shown in Figure 1.6.
The measured upper limit and predicted B-mode signal from an optimistic inflation
theory prediction is also shown in Figure 1.6. This predicted primordial B-mode signal
occurs at low l value and is an order of magnitude below the E-mode polarization
signal. At high l values a B-mode signal from the transferring of the primordial E-
mode polarization to a B-mode polarization due to gravitational lensing is expected. A
foreground B-mode polarization signal due to diffuse galactic sources from synchrotron,
thermal dust and spinning dust emission is also expected. In addition to improving
our ability to distinguish and remove these foreground signals, further improvements
in detector sensitivity are required to reach this predicted B-mode signal which occurs
at the 0.1 µK level.
In addition to a measurement of the primordial ‘B-mode’ polarization signal in
12
Get polarized light!
Figure 1.3: The Thompson scattering process through which a quadrupole
moment in the photon anisotropy from the perspective of the target elec-
tron gives rise to a polarization in the CMB. Blue field lines on the incom-
ing photons indicate colder and thus lower energy photons and the red
field lines indicate hotter and thus higher energy photons. The net effect
is an outgoing electric field magnitude which is stronger in one direction.
Figure adapted from Hu & White [47].
13
Figure 1.4: The two types of polarization patterns in the CMB. An exam-
ple of an E-mode polarization pattern which exhibits a divergence and a
B-mode polarization pattern which exhibits a curl.
Figure 1.5: The measured temperature angular power spectrum of the
CMB. (Courtesy WMAP science team [114]). The amplitude here is plot-
ted in terms of the variance of the fluctuations multiplied by the average
CMB temperature T = 2.73 K squared, such that the plot has units tem-
perature squared.
14
Figure 1.6: The measured E-mode polarization (EE) and temperature-E-
mode cross-correlation (EB) power spectra, and measured upper limits
on B-mode polarization (BB) power spectrum of the CMB. (Courtesy
BICEP Science Team [15]). The predicted B-mode polarization angular
power spectrum in the CMB is also shown by the grey line, with the
contributions near l ∼ 100 coming from primordial gravitational waves.
The B-mode component from gravitational lensing of E-mode to B-mode
peaks at l ∼ 1000. The signal is plotted in terms of the variance of
the fluctuations multiplied by the average CMB temperature T = 2.73 K
squared, such that the plot has units of temperature squared.
15
the CMB, there are other scientific rewards which can come from further and more
sensitive observations of the CMB polarization. These include measurements of gravi-
tational lensing in the ‘B-mode’ spectrum and observations of the post-recombination
re-scattering of CMB photons in the ‘E-mode’ spectrum to gain knowledge about the
re-ionization history of the universe. Measurements of the CMB temperature at small
angular scales to observe the Sunyaev-Zeldovich effect give cosmological information
about the history of the matter distribution in the universe.
1.1.4 Other Detector Science Applications
Although the THM detector as it is developed in this thesis is designed to op-
timally match a CMB observing scheme the THM detector also has applications to
far-infrared and sub-millimeter astronomy where bolometric detectors are also used. In
particular, the very low background noise requirements for these types of applications
make the use of a hot-electron rather than a membrane-isolated detector advanta-
geous, due to the ability of this detector to reach low noise levels without requiring
difficult fabrication of fragile membrane structures or legs [59].
Astrophysical sources in the sub-millimeter and far-infrared (300 GHz-400 THz,
wavelengths of 1 mm-700 nm) include faint optical and ultra-violet continuum emission
from galactic, AGN and star-forming region sources from the early universe which
have now red-shifted down to lower energies. Observations of such sources also probe
cosmology and the growth of structure in the universe. Other astrophysical sources
in the sub-millimeter and far-infrared are line emission sources in the local universe
from interstellar gas clouds, and the hot gas in the atmosphere of planets. In the sub-
millimeter and infrared applications high resolution spectroscopic capability is often
16
desired. Future science missions where a THM detector may have application include
SPICA, SAFARI and Millimetron [112, 10, 125]. Due to the cross-over applications
of the THM detector to this regime, in Chapters 4 & 5 the THM performance under
these conditions will also be discussed.
1.2 CMB Detector Technology & THM Advantages
For CMB applications there are two main schemes which have been developed:
1) coherent receivers and 2) incoherent bolometers. A basic ‘black box’ diagram of
the coherent receiver scheme and the incoherent bolometer scheme is shown in Figure
1.7. In both schemes one imagines microwave radiation from the sky coupling to an
antenna (which in the past has usually been a feedhorn antenna as is shown in the
diagram) with some filtering done to define the band and bandwidth of the signal. In
the coherent receiver the signal is first amplified by a low-noise amplifier, usually a
HEMT amplifier, and then detected by a square-law detector. In addition, mixers are
sometimes used to down-convert the signal to a lower frequency before amplification,
mainly due to increased amplifier noise and cost at higher frequencies. In this coherent
receiver scheme both the amplitude and phase of the incoming electromagnetic wave
are retained in the detection process. In the bolometer scheme the signal is absorbed
in the bolometer and the electromagnetic wave is converted to thermal power (this
process and the readout of this power signal is described in greater detail in Chapter
2). In this detection process the phase of the signal is not retained and the output is
only proportional to the power of the incoming signal.
There is a huge variety of detectors available for detecting the full spectrum of
radiation from astrophysical and non-astrophysical sources, from gamma-rays to radio
17
Basic Coherent Detector:Basic Coherent Detector:
Filter Amp Detector
OutputFeedhorn
Filter
Feedhorn/Antenna
Bolometer
Basic Bolometer (Incoherent) Detector:Basic Bolometer (Incoherent) Detector:
Output
Figure 1.7: The basic detection schemes for CMB observing using coherent
receivers or incoherent bolometric detectors.
waves. What is meant by a “detector” here is the device which actually detects the
electromagnetic radiation and converts it into a electronic signal one can measure,
such as a voltage or current. This output voltage or current is proportional to the
incoming radiation’s power/energy density/electric field. In addition to a detector
other components such as antennas, optics, transmission lines, filters, mixers, phase-
shifters, and polarization sensitive components are often used to help pick out and
channel the radiation signal as it travels from the source to the detector.
When choosing a specific type of detector one must appropriately match the
detector to the desired application. Considerations when choosing a detector for a
specific application include, but are not limited to: 1) the compatibility of the detector
to coupling to the sky with a particular type of antenna, optics, or transmission line
design; 2) the intrinsic detector noise, the noise of the detector readout, and noise from
18
optical components; 3) the incoming radiation frequency and bandwidth; 4) the time
response and speed of the detector; 5) the readout power dissipation and the readout
scheme required; 6) whether and/or what type of cryogenic system is necessary; 7) the
detector efficiency (which may include optical efficiency, quantum efficiency or thermal
efficiency); 8) the power or energy saturation level of the detector.
In general there are two types of radiation detectors: those which produce charge
and light in response to radiation, and those which convert the incoming radiation
into thermal power. The THM is a thermal-type detector: a bolometer. In these next
sections, the detector schemes for previous and future CMB-observing instruments will
be reviewed. The advantages that the THM detector has for fulfilling the requirements
of future CMB-observing instruments will also be highlighted.
1.2.1 History of CMB Detectors & Future Detector Needs
In general, even the low-noise amplifier of choice, the HEMT amplifier, has large
noise at high frequencies. In fact, the sensitivity of coherent receivers is limited by
quantum mechanics, with noise temperature TN ∼ hνkB. Thus for frequencies >100
GHz receiver schemes are usually not used and bolometers are preferred. In the past,
bolometer size has also scaled with the radiation wavelength, as a structure with size
on order of the radiation wavelength is needed to absorb this radiation. Due to this
constraint, at frequencies <100 GHz bolometers were typically not used and receivers
were preferable. This has now changed somewhat, due to the introduction of planar
microwave technology, where bolometer absorbers can be made that are significantly
smaller then the wavelength of the transmitted wave. An example of such a planar
microwave circuit adapted to the THM detector is discussed in Chapter 6. In Figure
19
Figure 1.8: The frequency range of CMB experiments by type as a function
of time.
1.8 the frequency range of the current and past CMB experiments which are listed in
Figure 1.2 is shown as a function of year and detector type.
To reach the predicted B-mode level, an order of magnitude improvement in
sensitivity from current instruments is required. The current single pixel noise of CMB
instruments is now near the background photon noise level for CMB observations from
space and the ground, for both receiver and bolometer technologies. (As a side note,
this is not the case for sub-millimeter and far-infrared detectors where single pixel
noise improvements are still possible.) For CMB observations, however, there are two
ways that sensitivity can be improved. One is to take a longer measurement and in
doing so take a longer time average of the noise signal. The other option is to take more
20
Figure 1.9: The number of detector/receivers for CMB experiments as a
function of time.
measurements at the same time by using an array of detectors. As we have already
reached the limit of reasonable observing times, lasting 3-7 years, the motivation for
current CMB detector development is not to reduce the noise of a single detector or
single pixel, but to develop detectors which can be easily scaled to 1,000-10,0000 pixel
size arrays. To show the trend towards large arrays in CMB instruments, in Figure 1.9
CMB observing instruments are plotted, for both coherent receiver- and bolometer-
based instruments, to show the total number of bolometers or receivers as a function
of time.
There is a variety of difficulties to scaling to large detector arrays. These dif-
21
ficulties are usually compounded when considering the constraints for a space-based
satellite mission, presumably a requirement for detecting primordial ‘B-mode’ polar-
ization. These main difficulties include: 1) the added power dissipation to read out a
larger number of detectors since both receiver and bolometer schemes require cryogen-
ics with limited cooling power; 2) the added space in the focal plane and instrument
itself to fit all these pixels and their readout wiring and optics; 3) the need to keep all
the devices in the array within certain uniformity bounds and with a high fabrication
yield across an array. The first of these issues can be addressed by adding a multi-
plexing scheme to the detector read out. The second challenge can be addressed by
moving from larger microwave components like feedhorns and waveguides to planar
microwave technology. The third challenge is a fabrication challenge and may provide
the ultimate fundamental limit to the ability to use larger and larger detector arrays.
Due to advantages in addressing all of the issues listed above, bolometers will
likely be preferable to HEMT-based receivers for larger CMB arrays. TES thermome-
ters when used in a bolometeric detector can be read out by multiplexed low-noise and
low-power dissipating Superconducting Quantum Interference Device (SQUID) ampli-
fiers. This multiplexing capability is unique for TES thermometers and is not the case
for semiconducting thermistors (a popular thermometer type for CMB bolometers pre-
viously). Bolometers and planar microwave components can also be fabricated pho-
tolithographically with great uniformity. Typical TES bolometers use micro-machined
structures or membranes to thermally isolate the detector. TES bolometers are con-
sidered one of the most promising candidates for large CMB arrays [11] and are already
in use in arrays of sizes 100-1000 [1, 12].
22
A relatively new technology, the Microwave Kinetic Inductance Detector (MKID)
has presented another option for CMB detector arrays [11]. Like TES bolometers,
MKIDs can easily couple to planar microwave transmission lines. Unlike most TES
bolometers, however, they do not require micro-machined structures, simplifying fab-
rication. They can also be frequency multiplexed in a simpler manner than that of
a TES bolometer SQUID multiplexing scheme. This multiplexing advantage is due
to the intrinsic resonance property of these detectors. Currently, MKID detectors
have not reached single-pixel background noise levels and the technology is much less
well understood than that for TES bolometers and the SQUID multiplexing associated
with these detectors. However, MKID detectors have the potential to be a competitive
alternative to TES bolometers in the future.
1.2.2 THM Detector Advantages
The THM is a type of TES bolometer which has several advantages for future
applications to large array CMB instruments. It shares some of these advantages
with the competitor detectors mentioned above, but some advantages are unique to
the THM detector design. As with other TES bolometers, it can be read out by a
multiplexed SQUID system, a technology which has now reached advanced stages.
Additionally the fabrication of these detectors is much simpler and more robust than
that for a typical TES bolometer as no fragile thermal isolation membranes are neces-
sary. This simplification could lead to higher fabrication yields for large arrays. The
lack of membranes is also advantageous as the size of the detector is very small, thus a
denser packing of the focal plane is possible. The absorbing part of the detector itself
is also much smaller than a typical TES bolometer, providing a smaller cross-section
23
to cosmic rays. The small size also leads to a very short thermal time constant in the
device (.1-100 µs) which will allow for rapid scanning of the sky. Like other TES
bolometers, background-limited noise performance is obtainable. Although the THM
is in the development stages, as we will present in this thesis, it is very near to becom-
ing an integrated and functioning CMB-type detector, and a competitive alternative
to membrane-based TES bolometers designs.
1.3 Thesis Summary
The structure of this thesis, which presents work done to develop a Transition-
Edge Hot-Electron Microbolometer (THM), is broken into three parts. The first part
(Chapters 2 & 3) gives a summary of the background knowledge necessary to under-
stand this type of detector, including general theory of how this type of TES bolometric
detector works and the physical processes involved within the detector. This section
is mainly a summary of previous work done by others. The second part is an overview
of the THM detector thermal model and design and the optimization of this THM
design (Chapter 4). The third and final part (Chapters 5, 6) presents “dark” DC,
and RF measurements of THM test devices, analysis of these measurements, as well
an introduction to the microwave design for radiation coupling to the THM detector.
The thesis concludes (Chapter 7) with a discussion of future work and prospects for
the THM detector and a presentation of the recommended THM design for CMB
applications.
24
Chapter 2
General Bolometer & TES Theory
2.1 Basic Bolometer Model
A bolometer consists of three basic parts: an absorber, thermometer, and a
thermal link to a cold reservoir. Sometimes these parts exist as separate physical
structures within the detector and sometimes these parts exist within the same physical
structure. An illustration of this simple bolometer model is shown in Figure 2.1. A
bolometer detects electromagnetic radiation via the thermalization of the incoming
electromagnetic waves by an appropriate absorbing structure. Thermalization occurs
when the power carried in the electric and magnetic fields of the observed radiation
is transferred to thermal energy in the absorbing material. Usually this energy is
transferred first to the kinetic energy of the electrons in the absorbing structure.
After the initial capture of electromagnetic power and thermalization within the
detector, energy flows out of the bolometer to the cold reservoir via the thermal link.
This cold reservoir may be a different part of the detector, or a detector substrate
which is heat-sunk to a cold stage. For most astrophysical bolometer applications this
cold stage is cooled to sub-kelvin temperatures to reduce noise. The mechanism for
25
Figure 2.1: The components to a simple bolometer.
heat flow along this thermal link involves scattering between energy carriers (usually
phonons or electrons). One of the unique properties of the Transition-Edge Hot-
Electron Bolometer (THM) is the “hot-electron” property of this thermal link which
will be discussed in more detail in Chapters 3 and 4. The properties of the thermal
link of a bolometer have important repercussions for the sensitivity and response of
the bolometer.
Unlike coherent detectors, no phase information of the incoming electromagnetic
wave is retained in the bolometer detection process. Rather, the thermal response in
the time domain of the detector is determined by the intrinsic thermal time constants of
the bolometer system. These internal thermal time constants, as well as the electrical
time constants of the thermometer readout, occur on time scales much longer than
the detected radiation frequency. For bolometers observing the Cosmic Microwave
Background this means that the internal time constants occur on scales much longer
than 10s of picoseconds.
In a bolometer, the incoming power that one wishes to measure is directly pro-
26
portional to the temperature of the absorbing detector. This temperature is measured
by a thermometer in good thermal contact with the absorber and is eventually read
out electrically as a voltage or current. There are many types of thermometers which
can be used in a bolometer, and indeed, in principle all that is necessary is a structure
which exhibits a property change with temperature. Some examples of these tem-
perature dependent properties are paramagnetization, which is utilized by magnetic
calorimeter detectors, kinetic inductance, utilized by Microwave Kinetic Inductance
Detectors (MKIDS), current flow, seen in Superconducting Tunneling Junction (STJ)
detectors, or resistance, as in semiconductor thermistors.
The THM uses one of the most sensitive resistive thermometers for astrophysical
bolometer detector applications called a Transition-Edge Sensor (TES). A TES is a
thermometer which makes use of the steep change in the resistance versus temperature
curve of a superconductor at its transition. TESs are currently being introduced into
astrophysical bolometer applications (see Figure 1.2), replacing the semiconductor
thermistors of the previous generation of bolometer detector arrays.
A bolometer detector is quite similar to a calorimeter detector, one of the pre-
ferred detectors in high energy astrophysics and x-ray astronomy. The thermal model
of the bolometer and the calorimeter are the same, however a bolometer measures
the continuous influx of power, while a calorimeter measures the energy of individual
photons. Thus, although there are no differences in the physical models nor the theory
that describes these two types of detectors, different figures of merit and detector qual-
ities are important. For example, for a calorimeter the important sensitivity parameter
is energy resolution, whereas for a bolometer the important sensitivity requirement is
27
the noise equivalent power (NEP). These differences, however, are not fundamental.
The theory which is reviewed in this and following chapters is applicable to both types
of detectors, and in fact one may imagine some applications where the THM could be
used in the photon-counting, calorimetric regime.
In the following sections a brief review of the basics of superconductivity theory
and the superconducting transition which are necessary to fully understand a TES
and the TES readout for the THM detector are given. This is followed by a review of
some of the details of bolometer theory and bolometer behaviour when it incorporates
the TES.
2.2 The Superconducting Transition
In a normal metal, a portion of the electrons, called free or conduction electrons,
are loosely bound to the atomic lattice. Thus a current is easily induced by applying
a potential difference across the metal. As these electrons travel through the metal
they scatter from the crystal structure due to deviations in the perfect periodicity
of the lattice caused by impurities in the metal, deviations in the lattice symmetry,
and thermal vibrations of the lattice structure. Quantized vibrations of the lattice
structure are called “phonons” in an analogy to the photon, the quantization of elec-
tromagnetic waves. Scattering of free electrons from impurities and with phonons
create a resistance to electron flow.
As the temperature of a metal decreases the thermal vibrations of the lattice
also decrease and the electrical “resistivity” of the material decreases. This is why a
measurement of the residual resistance ratio (RRR) of a material, the ratio of resistance
at room temperature to resistance at temperatures near absolute zero, is an important
28
indication of the purity of the material. Even at absolute zero one expects an electrical
resistance due to residual impurities in the metal. Surprisingly, in certain materials
this is not observed to be the case. Instead, as the temperature is lowered, the material
suddenly undergoes a phase transition to a new “condensed” state characterized by
zero resistivity. This is the phenomenon of superconductivity.
Below a critical temperature, Tc, critical current, Ic, and a critical applied mag-
netic field, Hc, a superconducting material will exhibit zero resistance. It is important
to note that each of these critical values is a function of the temperature, current
and applied field. The values of this critical temperature (for zero applied magnetic
field, and zero applied current) for elemental superconductors ranges from 10 mK to
10 K [115]. Critical temperatures as high as 130 K have more recently been observed
for “high-temperature” types of superconducting materials [115]. In addition to the
property of zero resistivity, below these critical values a superconductor also exhibits
the Meissner effect [86]. The Meissner effect occurs when superconducting currents,
induced on the surface of the metal, null any penetrating magnetic flux through the
superconducting surface.
Superconductors have been classified into two different types, Type I and Type
II, according to their magnetic transition behaviour. A Type I superconductor under-
goes a homogeneous magnetic transition. The transition of a Type II superconductor
is not so uniform. For a Type II superconductor there are two critical points to the
applied magnetic field as the superconductor transitions to a normal state. When
the applied field surpasses the first critical value, small normal regions which allow
magnetic field penetration, called vortices or fluxons, occur in the superconductor. As
29
the temperature and/or magnetic field increases these regions grow and spread across
the entire superconductor until a second critical magnetic field point when the entire
superconductor becomes normal. Though magnetic flux is allowed in these fluxon re-
gions, superconducting currents still persist across the superconductor until the second
critical point is reached, and thus there are not two separate transitions in the resis-
tance versus temperature transition curve of the superconductor. We expect the thin
film TES (a Mo/Au bilayer) for our THM bolometer to be a Type I superconductor.
A microscopic theory, called Bardeen-Cooper-Schrieffer (BCS) theory, explains
superconductivity (although it is still unclear whether this theory adequately explains
the microscopic behaviour of high-temperature superconductors) by introducing an
attractive force between electrons in the metal. This attractive force occurs via an
interaction called a Frohlich interaction with a phonon. Below a critical temperature
and current in certain materials this attractive force is stronger than the Coulomb
repulsion between the two negatively charged free electrons and the two electrons
become bound together into a condensed state called a “Cooper pair”. A property
of the coupling in this Cooper pair state is zero total momentum, with each of the
paired electrons contributing equal and opposite momenta to the Cooper pair total
momentum. In the Cooper pair state scattering which leads to resistance to current
flow is not allowed as such a collision would require a change in the total momentum
of the Cooper pair and a breaking of the Cooper pair. Thus electron pairs in the
superconducting state travel through the material with zero resistance.
One way to interpret the superconducting phase transition is in terms of an
energy gap, just as one might see in an insulator or semiconductor. This analogy is
30
Normal Metal Insulator Semiconductor Superconductor Normal Metal Insulator Semiconductor Superconductor
Free Electrons Energy Gap Bound Free Electrons Energy Gap Bound
E
Figure 2.2: The energy gap interpretation of superconductivity. Quasipar-
ticles occupy the free electron states in the superconductor and electrons
bound in Cooper pairs occupy the bound states. Note however, that unlike
bound electron states in the other cases, in a superconductor, electrons
bound in Cooper-pair states do carry an electrical current.
illustrated in Figure 2.2. In a superconductor an energy gap exists between the energy
of an electron bound together in a Cooper pair and the energy of a free electron in
the normal metal state. In a superconductor at absolute zero this energy gap is at a
maximum (ǫgap = 3.528kBTc) and all the electrons are in the superconducting state.
As the temperature rises the energy gap shrinks, and a small portion of the electrons
enter an unpaired, free electron state in the superconductor, called a “quasi-particle
state”. At the critical transition point, the energy gap rapidly shrinks to zero and all
the electrons in the metal enter the normal metal state.
One of the other striking properties of a superconductor is the extremely long
31
range coherence of the Cooper pairs in the material. This is also the result of the
inability of the Cooper pairs to scatter in the metal. Unlike a normal metal where
the electrons constantly scatter and change phase, the coupling of electrons in Cooper
pairs means that the Cooper pairs retain their phase over long distances. In addition
to the phase coherence of individual Cooper pairs, all of the Cooper pairs in the same
superconductor are described by the same quantum wave function and phase.
This coherence property is directly responsible for many other technological ap-
plications of superconductivity beyond the TES. One of the most notable examples of
this is the development and use of Josephson junctions. A Josephson junction is a weak
insulating link between two separate superconductors. These Josephson junctions are
useful devices which exploit the quantum coherence property of the superconductor
and the interference effects that result. Josephson junctions have had an important
impact on the development of the TES bolometer since they were integral to the de-
velopment of Superconducting Quantum Interference Devices (SQUIDS). SQUIDs are
sensitive meters of magnetic field and current which are uniquely qualified to read out
the TES, and which will be described in more detail in the following sections of this
chapter.
In addition to providing a method to read out the TES thermometer, the the-
ory of Josephson junction behaviour and theory of weak link (and specifically the
superconducting proximity effect) has an unexpected overlap with the theory of TES
behaviour. This overlap is especially applicable in small TES devices on the micron
size scale. Understanding these small size TES devices is particularly important to the
design of the THM due to the important role size plays in the sensitivity and thermal
32
properties of these detectors.
The review of superconductivity given above will be sufficient for understanding
some of the basics of the TES detector operation. In Chapter 3 some of the semi-
microscopic superconductivity theories will be reviewed in more detail, in particular
the theories that lead to understanding of the superconducting proximity effect, in
order to more fully understand the physics and optimal design properties of the THM
and to put measurements in context.
2.3 The Transition Edge Sensor
A Transition-Edge Sensor is a superconductor used as a resistive thermometer.
The superconducting transition makes a very sensitive thermometer since the slope
of the resistance versus temperature curve can be very steep (the transition width in
a superconductor with no applied current is only limited by thermal and magnetic
field fluctuations). Thus a very small change in the TES temperature can result in
a very large change in resistance. An example of a sharp transition resistance versus
temperature (RTES vs. T ) curve of a superconducting TES from one of the THM
test devices is shown in Figure 2.3. There are three main challenges to using the TES
as a thermometer, all of which have been addressed by the low temperature detector
community within the last two decades. Although these challenges have been solved in
both practice and theory there are still application-specific solutions to be considered,
and the issues are important when considering the optimal THM design.
One of these challenges is to design a TES that has the precise Tc necessary to
fulfil application-specific noise requirements. One way to do this is to simply select an
appropriate bulk superconducting material which exhibits a transition temperature
33
Figure 2.3: The RTES vs. T curve of a superconducting TES from a THM
test device of variation THM5 (this and other THM test devices will be
described in Chapter 5).
34
at the required Tc for the detector. However, when bulk superconductors are not
adequate, and more precision in Tc is required, a modification of the bulk Tc is possible
by modifying the bulk superconducting material. One of these methods is by magnetic
doping of the superconductor. The most widely used process, however, is to employ
the superconducting bilayer proximity effect. Here a normal metal layer is sandwiched
together with a superconducting layer such that the proximity of the normal metal
layer shifts the superconducting Tc [80].
Another challenge is to find a way to keep the TES in the sensitive resistive
transition region during operation. This problem of stability is partially solved by
the concept of electrothermal feedback. A feedback loop exists between the electrical
power dissipated in the detector when it is electrically biased and the thermal power
dissipated in the detector by incoming radiation. This feedback will be negative when
the TES is voltage-biased to read out the TES resistance [49]. The electrical power
dissipation from the bias circuit follows the usual Joule power dependence (P0 =
V 20
RTES) where V0 is the voltage applied across the TES and RTES is the TES resistance.
To illustrate this feedback concept, one imagines a resistive TES detector where
the voltage across the TES resistor is kept constant. When incoming power dissipates
in the detector the temperature of the TES rises by a small amount. This increase
in temperature results in an increase in TES resistance due to the positive slope of
the superconducting resistance versus temperature curve. The increase in resistance
reduces the Joule power since the voltage is constant. The drop in Joule power leads
to a decrease in temperature, stabilizing the detector back in the transition region.
One of the final obstacles to developing TES bolometric detectors for astrophysi-
35
cal applications was to develop a low-noise method to read out the TES resistance. As
TES detectors are typically low impedance devices (RTES . 1 Ω), the read out for the
device must also have a low input impedance in order to read out the detector signal
with low noise. One method of doing so is to use the most sensitive low-impedance
ammeters, a SQUID. Since SQUID performance is integral to TES operation and ap-
plications, in the next two sections a brief overview of SQUID theory and operation
is given.
2.4 Basics of SQUIDs
A simple design for a SQUID is a superconducting ring intersected by two Joseph-
son junctions (two weak insulating layers). It is helpful to first examine what happens
in a superconducting ring, and then what happens in a single Josephson junction to
gain a more intuitive understanding of SQUID behaviour.
A superconducting current travelling through a single superconducting ring sur-
rounding a normal region, like the one shown in Figure 2.4, can be describe by a
single BCS wavefunction. The geometry of the ring requires the important boundary
condition that the phase and amplitude of the wavefunction match as the wavefunc-
tion completes each integral number of loops around the ring. Specifically, the phase
difference must be equal to 2πn, where n is an integer. Thus the wavelength of the su-
perconducting wavefunction is quantized, just like a Bohr electron orbiting the nucleus
of a hydrogen atom. The wavelength of the superconducting wavefunction is related
to the magnetic flux, Φ, through the center of the ring produced by the circulating
superconducting current due to Ampere’s law. Thus the allowed magnetic flux is also
36
i s
Φ
Figure 2.4: A superconducting ring allows only quantized values of mag-
netic flux through the center due to quantization of the superconducting
wavefunction.
quantized by the relation [95]:
Φ = nh
2e= nΦ0 (2.1)
Here h is Planck’s constant, e is the electron charge and Φ0 is the flux quantum called
a fluxon which has a value of 2.07 · 10−15 T ·m2.
A single Josephson junction consists of a single superconductor broken by a weak
insulating link as is shown in Figure 2.5. As the insulating region is so thin a supercur-
rent may tunnel across this weak link. Because the two superconducting sections are
separate, the superconducting current in each can no longer be described by the same
wavefunction with the same phase, but rather each is described by separate wave-
functions. In the weak link region the two separate supercurrents interfere and this
interference manifests itself in the amplitude of the superconducting current, which
has a sinusoidal dependence on the phase difference across the link. The maximum
37
Insulator
Superconductor 1 Superconductor 2
is
Insulator
Superconductor 1 Superconductor 2
is
Insulator
Superconductor 1 Superconductor 2
is
Superconductor 1 Superconductor 2Superconductor 1 Superconductor 2Superconductor 1 Superconductor 2Superconductor 1 Superconductor 2
is
Figure 2.5: A Josephson junction is two superconductors separated by a
thin insulating link.
superconducting current, is, is set by the critical current of the weak link, ic [95]:
is = ic sin∆φ. (2.2)
Here ∆φ is the phase difference across the junction. This dependence is called the
DC Josephson effect. In the absence of any applied voltage a superconducting current
will tunnel across the junction with a sinusoidal dependence on the phase difference
across the link.
When a voltage is applied across the link another effect also occurs, called the
AC Josephson effect. This effect is due to the fact that an AC current cannot travel
through a superconductor without some impedance, creating a voltage across the
superconductor. To understand this one must think of a superconductor with changing
current in terms of a ‘two-fluid’ model, where for a changing current, some of the
current is carried by a small number of quasi-particles (this is not the case for a DC
supercurrent). A changing current creates an electric field in the superconductor which
will accelerate the quasi-particles and create resistance. Thus if there is a changing
current (or phase difference across the Josephson junction, following the DC Josephson
38
effect) then a voltage, V , will develop as well. This dependence is given by [54]:
V =ℏ
2e
d∆φ
dt. (2.3)
With these two relations one can examine the current-voltage (I-V) properties of a
Josephson junction. The Josephson junction can be represented electronically as the
circuit shown in Figure 2.6 and an equation describing the total current flow through
a Josephson junction, I, as:
I = CdV
dt+V
R+ ic sin∆φ. (2.4)
Relating the voltage to the phase difference,
I =Cℏ
2e
d2φ
dt2+
ℏ
2eR
d∆φ
dt+ ic sin∆φ. (2.5)
Now one can imagine that a DC current is sent through the Josephson junction.
If the current is less than the critical current of the junction no voltage appears and the
current is entirely superconducting. If the current is greater than the critical current
of the junction then a voltage will appear across the junction, and in addition, an AC
superconducting current will tunnel back and forth across the junction. From these
equations one can plot the I-V curve of the Josephson junction. An analytical solution
is possible to the equations for the case where there is no capacitance. In the more
realistic case of a capacitive junction the solution can only be solved numerically [31].
A plot of the shape for the low-capacitive case is shown in Figure 2.7.
In addition to an insulating weak link between the separate superconductors, a
similar weak link can occur when two superconductors are intersected by a thin normal
layer, or a thin superconductor with a lower transition temperature than the super-
conducting leads [76]. In these cases instead of a tunnelling current a superconducting
39
C
R
isI I
in,C
in,R
Figure 2.6: A “two-fluid” circuit diagram for a Josephson junction.
40
Figure 2.7: An example of the I-V characteristics of a Josephson junction
with zero capacitance. Figure courtesy Gallop [31].
41
proximity effect can effectively allow a superconducting current to travel across the
normal junction. The criterion for such a weak link is that the critical current of the
junction be less than the critical current of the superconducting leads. These types
of weak links will produce behaviour similar to that of a Josephson junction. This
theory will be returned to in Chapter 3 when the lateral proximity effect in the TES
is discussed.
One can now begin to understand what might occur in a simple SQUID device
where a superconducting ring is intersected by two weak links as shown in Figure 2.8.
First, unlike the superconducting ring without junctions, the magnetic flux through
the ring is neither quantized nor frozen in. Instead magnetic flux is allowed to pene-
trate via the weak link portions of the ring while the remaining ring remains super-
conducting. Although the flux is no longer quantized, the amplitude of the current
able to flow through the link and the magnetic flux through the center of the ring
is dependent on the phase difference across the weak link regions. In the case of a
current-biased SQUID where a constant current is sent through the device, the I-V
characteristics of the SQUID obtained by numerical solution of the Josephson junction
equations, Kirchoff’s laws and energy analysis [31] are reproduced in Figure 2.9. Here
one sees that at a particular current bias the voltage across the SQUID has a periodic
dependence on the magnetic flux through the SQUID. In Figure 2.10 a measurement
of this dependence is shown for a current-biased NIST series array SQUID. One can
see that the SQUID is sensitive to magnetic flux at a scale far below the fluxon level.
Although the details of SQUID theory are complex, the basic physical process
is at heart the interference pattern seen in the voltage and current characteristics of
42
Josephson junctionscurrent bias
direction
Figure 2.8: A simple SQUID: a superconducting ring broken by two
Josephson junctions.
Figure 2.9: An example of the I-V characteristics of a current-biased
SQUID for different magnetic flux values.
43
0
0.50
1..00
1.50 0Φ
SQ
UID
Vo
ltag
e
(m
V)
Magnetic Flux
-0.50
1..00
1.50-
-
Figure 2.10: The measured voltage as a function of magnetic flux for the
current-biased NIST-Series Array SQUID which was used to read out the
THM test devices. Further measurements and details of this SQUID read-
out are presented in Chapter 5.
44
a SQUID as a result of the coherence properties of a superconductor and a phase
difference across the Josephson junction weak links.
2.5 SQUID Operation
How can the SQUID work in actual operation as an ammeter or magnetometer?
Perhaps the most obvious answer to this is as a magnetometer. The set-up of the
SQUID as a magnetometer is shown in Figure 2.11. Here the SQUID is current-biased
and the signal which is read out is the voltage across the SQUID. The SQUID voltage
is directly proportional to the magnetic flux through the SQUID. In a more flexible
magnetometer design an input coil is used and magnetic flux through the input coil
is coupled to the SQUID loop. The SQUID voltage is directly proportional to the
magnetic flux through the input coil and the mutual-inductance of the input coil and
SQUID loop. In most cases an additional pick-up coil is also added to the input coil
of the SQUID to provide further amplification and flexibility.
From this set up it is fairly straightforward to see how the SQUID functions
as a ammeter. The current one wishes to measure can be sent through the input
coil that couples to the SQUID loop. Again, the voltage across the SQUID is directly
proportional to the mutual inductance of the input coil and SQUID loop and the input
coil current. In the case of the TES bolometer readout, the TES is voltage-biased
and the TES current is passed through the SQUID input coil. This TES current is
proportional to the TES resistance and thus the bolometer temperature and incoming
bolometer power.
In actual operation the SQUID is usually operated with electronic feedback as
shown in Figure 2.12. A feedback coil is placed near the SQUID loop and electronic
45
Pick-up Coil
SQUID
Iin
X X
Ibias
Iin
X X
Ibias
Iin
X X
Ibias
Iin
X X
Ibias
Iin
X X
Ibias
Iinput
X X
Ibias
X X
Ibias
X X
Ibias
X X
Ibias
X X
Ibias
X X
Ibias
X XX X
Ibias
V
Input Coil
SQUID
Figure 2.11: A SQUID as a magnetometer.
feedback is set up by monitoring the voltage output of the SQUID and sending a nulling
current through the feedback coil to keep the magnetic flux through the SQUID loop
constant. This linearises the output of the SQUID as is shown in Figure 2.13. SQUIDs
can also be operated with multiple SQUIDs in series in order to increase amplification.
One of the main advantages to using SQUIDs to read out TES detector arrays
is the ability to easily multiplex the SQUID readout. Many different multiplexing
schemes are possible and are being developed for the readout of TES arrays using
both frequency-division, time-division and code-division methods [52, 50, 66]. This
multiplexing provides a low-power dissipation method to read out the large TES de-
tector arrays, which are necessary for the next generation of precision astrophysical
instruments.
46
Feedback
box
Feedback
coil
Input
coil
Feedback
box
Feedback
box
Feedback
box
Feedback
box
Feedback
coil
Input
coil
SQUID
Figure 2.12: Electronic feedback to linearise SQUID.
Fee dback Lock October 23, 2005
-0.0003
-0.00025
-0.0002
-0.00015
-0.0001
-0.00005
0
0.00005
0.0001
-0.00003 -0.00002 -0.00001 0 0.00001 0.00002 0.00003
Input Coil (A)
Fe
ed
ba
ck
Cu
rre
nt
(A)
Figure 2.13: The linear output of the NIST series array SQUID used to
read out THM test devices with feedback.
47
2.6 The TES Bolometer
Some of the details of the thermal and electrical behaviour of the TES in op-
eration will now be reviewed. To do so the basic equations governing the behaviour
of a voltage-biased TES bolometer will be presented, following the derivations and
procedure found in Chapter 1 and 3 of Cryogenic Particle Detection [26] and in the
PhD Thesis of M. Lindeman [78]. In Chapter 4 explicit expressions for the noise and
response of the THM detector will be derived from these equations. In Figure 2.14
and Figure 2.15 two schematics of the TES electrical and thermal circuits are shown.
The voltage-bias of the TES is accomplished by current-biasing a shunt resistor, Rs,
in parallel with the TES, where Rs ≪ RTES. The TES resistor is in series with the
SQUID input coil, with inductance L. Here any parasitic resistances or inductances in
the circuit are neglected. The thermal circuit shown for the TES is an ideal thermal
model for a bolometer where the detector, an absorber/TES at temperature Tbolo and
with heat capacity C, is in thermal contact with a cold bath at temperature Tbath via
a thermal link with thermal conductance, G.
One can write down a differential equation describing both the thermal and
electrical behaviour. The two equations are coupled by the introduction of Joule
power into the device with the voltage-bias of the TES:
CdTbolodt
= Psignal + P0 − Pbath (2.6)
LdITESdt
= V0 − ITESRs − ITESRTES(ITES, Tbolo). (2.7)
Here P0 =V 2
0
RTES= I2TESRTES is the Joule power dissipated in the TES. RTES is the
resistance of the TES, which is a function of both the TES temperature, Tbolo, and
TES current, ITES. V0 is the voltage bias. Psignal is the incident radiation on the TES
48
VSQUID
X X
ISQUID Bias
Rt
RTES
t
IBias
SQUID
VSQUID
ISQUID Bias
R
RTES
IBias
SQUID
VSQUID
X X
ISQUID Bias
Rs
R
IBias
SQUID
Input
Coil
L
EST
V0
ITES
Figure 2.14: The electical circuit for a voltage-biased TES read out by a
SQUID amplifier.
49
G
Tbolo
TES/
Absorber
T bath
P + P signal 0
C
Pbath
Figure 2.15: The thermal circuit for an ideal bolometer detector.
50
absorber and Pbath is the power that flows from the detector to the cold bath. This
power flow from the detector to the cold bath (as will be detailed further in Chapters
3 and 4) usually follows a power law dependence on temperature as below [26]:
Pbath = κ(T nbolo − T nbath). (2.8)
Here κ and n depend on the method of energy flow across the thermal link and are
directly related to the thermal conductance of the link G(T ) by
G(T ) =dPbathdT
= nκT n−1. (2.9)
To learn about the detector response during operation, these equations are usu-
ally examined in the small signal/linear limit where the change in current and temper-
ature of the device are small compared to the current and temperature with only the
TES bias [26]. In this regime, the current, and temperature variables are expanded in
terms of ∆T and ∆I:
∆I = ITES − I0 (2.10)
∆T = Tbolo − T0 (2.11)
Here T0 and I0 are the equilibrium values of the TES when voltage-biased with no in-
coming signal power. Inserting a Taylor expansion of these definitions in the electrical
and thermal equations results in the following:
CdTbolodt
≈ ∂
∂Tbolo[I2TESRTES(ITES, Tbolo)− κ(T nbolo − T nbath)]0∆T
+∂
∂ITES[I2TESRTES(ITES, Tbolo)]0∆I + Psignal (2.12)
LdITESdt
≈ ∂
∂Tbolo[−ITESRTES(ITES, Tbolo)]0∆I
+∂
∂ITES[−ITESRs − ITESRTES(ITES, Tbolo)]0∆I (2.13)
51
which becomes, after applying the partial derivative,
Cd∆T
dt= I20
∂RTES(ITES, Tbolo)
∂Tbolo|0 ∆T − nκT n−1
0 ∆T + 2I0R0∆I
+I20∂RTES(ITES, Tbolo)
∂ITES|0 ∆I + Psignal (2.14)
Ld∆I
dt= −I0
∂RTES(I0, Tbolo)
∂Tbolo|0 ∆T + [−Rs −RTES(I0, T0)
−I0∂RTES(ITES, Tbolo)
∂ITES|0]∆I (2.15)
Using the definitions for thermal conductance, G, given by Equation 2.9 and the
current and temperature dependence of the TES resistance given by the definitions:
α ≡ T0R0
∂RTES(Tbolo, ITES)
∂Tbolo|I0 (2.16)
β ≡ I0R0
∂RTES(Tbolo, ITES)
∂ITES|T0 (2.17)
the two equations can be rewritten as:
Cd∆T
dt= [
P0α
T0−G(T0)]∆T + (2 + β)V0∆I + Psignal (2.18)
Ld∆I
dt= −V0α
T0∆T + (−Rs − (1 + β)R0)∆I. (2.19)
Here R0 ≡ RTES(I0, T0).
Several methods have been used to solve these two coupled differential equations
in both the time and frequency domain for both simple and more complex thermal
models and assuming different functions for the signal power with time [78], [83], [81],
[30]. Perhaps the most straightforward method to solve these equations and to learn
about the detector response is to arrange them into matrix form following the method
developed by Lindeman [78]. When this is done the two coupled differential equations
52
are solvable in either the time or frequency domain. From these solutions fall out the
response of the detector, the time response and the noise performance. In Chapter 4
this will be done step-by-step for two specific THM thermal models in order to predict
the responsivity and noise performance of the THM detector. However, at the moment
only a few of the consequences of the general TES bolometer model in the effects of
electrothermal feedback, stability and noise in the TES detector will be discussed. For
the derivation and details of these effects and the bolometer/calorimeter electrical-
thermal model from the above equations the reader is again referred to Chapters 1
and 3 of Cryogenic Particle Detection [26], and the PhD thesis of M. Lindeman [78].
2.7 Electrothermal Feedback & Bias Conditions
The application of a voltage bias to the TES creates a negative feedback between
the electrical and thermal systems. This greatly improves the range of operating
conditions under which the TES is stable. Under negative feedback the detector can
still become unstable however due to phase shifts of electrothermal oscillations in the
detector caused by the inductance in the TES electrical circuit. The stability of the
detector under a constant voltage-bias depends on both the electrical bias circuit and
the TES thermal response and is guaranteed when the conditions for strong negative
feedback are met [26]:
Rs ≪ RTES (2.20)
C
G> (
P0α
G(T0)T0− 1)
L
Rs +R0(1 + β)(2.21)
The constraints this puts on the bias conditions of the THM detector will be examined
in Chapter 4.
53
The natural thermal response time of the detector under un-biased conditions is
determined by the ratio of the heat capacity and thermal conductance, τ = CG. The
influence of negative feedback in the detector due to voltage-biasing decreases this
thermal time constant. In the case of the strong negative feedback the thermal time
constant can be significantly faster than the natural thermal time constant.
2.8 Bolometer Noise
Noise in the detection process comes from three sources: photon background
noise (which is ‘external’ to the detector), ‘internal’ detector noise, and detector read-
out noise. These noise sources are important to the THM design optimization, which
will be discussed later in Chapter 4. All these sources of noise contribute to the total
NEP (Noise Equivalent Power) of a detector.
Photon background noise is an external, unavoidable noise source, due to statis-
tical fluctuations in the arrival rate of photons at the detector. This fluctuation noise
is given by:
NEPphoton = hν
√
2∆ν
ννηn0(1 + ηn0) (2.22)
for single mode observing [128]. Here ν is the observing frequency, ∆νν
is the fractional
bandwidth, and η is the optical efficiency. n0 is the photon occupation number, and is
a function of the observing frequency and in the case of the CMB, the CMB blackbody
temperature and emissivity. To achieve the best possible detector performance for a
specific observing condition requires that NEPdetector < NEPphoton where NEPdetector
is the noise due to internal detector noise and readout noise. Thus in this thesis the
photon noise, specifically photon noise for CMB observing conditions, will be used as
54
a sensitivity benchmark for the THM design.
The internal detector noise and read out noise comes from thermal fluctuations
between the hot detector and the cold reservoir, from Johnson noise fluctuations in
the resistive TES, as well as Johnson voltage/current noise from the bias circuit, and
current noise from the SQUID amplifier read out. Each of these “detector” noise
sources will be described briefly below.
The Johnson noise sources in the detector are the resistive TES itself, the shunt
resistor and any other parasitic resistance in the TES electronic circuit. The Johnson
noise from the TES resistance in terms of a voltage fluctuation across the TES is given
by:
NEVJ,TES =√
4kBTboloRTES. (2.23)
Similarly, the Johnson noise in terms of an equivalent voltage fluctuation noise across
the TES due to the shunt resistor is given by:
NEVJ,s =√
4kBTbathRs. (2.24)
The SQUID amplifier noise in the form of current noise in the readout circuit is given
by [51]:
NEISQUID =
√
2ξh
L. (2.25)
Here h is Planck’s constant, L is the input inductance of the SQUID, which is de-
termined by the number of turns in the input coil, and ξ is a multiplicative constant
which typically ranges from 10-1000. In the next chapter the manner in which these
voltage and current noise sources contribute to the total noise in terms of an equivalent
power fluctuation noise at the input of the detector will be derived.
55
Thermal power fluctuation noise across the bolometer link is given by [26]:
NEPthermal =√
4kBT 2bathG(Tbath) (2.26)
in the case that Tbolo ∼ Tbath. When the TES temperature is considerably higher than
the bath temperature (Tbolo ≫ Tbath) an additional factor is added to this expression.
This factor describes the thermal conductance along the temperature differential of
the weak link. In the case of radiative energy transfer, which holds for cases where the
mean free path of the energy carriers is large compared to the length of the thermal
link the expression is given by [26]:
NEPthermal =
√
4kBT 2bathG(Tbath)
( TboloTbath
)n+1 + 1
2. (2.27)
In the case of the THM where the thermal link occurs between the electrons and
phonons of the detector directly on the substrate this radiative limit holds. In the case
of diffusive energy transfer, where the mean free path of the energy carriers is small
compared to the length of the link, which may apply to typical bolometers where the
thermal link is controlled by phonon scattering along membranes or suspended legs,
the expression is given by [26]:
NEPthermal =
√
√
√
√4kBT 2bathG(Tbath)
n
2n+ 1
( TboloTbath
)2n+1 − 1
( TboloTbath
)n − 1. (2.28)
Numerically, the increase to the NEP by these added factors is similar for both the
radiative and diffusive cases. This additional factor becomes important to the THM
detector performance. It imposes a fundamental limit to the NEP possible for the
THM detector under CMB-observing conditions, and indeed CMB bolometric detec-
tors in general, as will be shown in Chapter 4.
56
Chapter 3
Physical Effects in the THM Detector
Although the THM detector appears to be a relatively simple device, consisting of a
thin metal film absorber, and a thin bilayer or monolayer superconducting TES, the
physical processes occurring within the THM detector are many and complex. Due
to the low operating temperature of these detectors, as well as their small size, the
physical processes which dominate the the THM behaviour are also ones not usually
observed in larger or warmer detectors and devices. In the first part of this chapter
some of the dominant thermal processes within the THM detector, and the present
theoretical understanding of these processes in the literature are reviewed. In Chapter
4 these thermal processes will be used to construct a thermal model for the THM
bolometer. In the second part of this chapter the theory of the superconducting
proximity effect will be reviewed. In these sections some of the applicable S-N-S and
S-S’-S proximity effect theoretical models will be used to make predictions for the
THM detector. In Chapter 5 these predictions will be compared to measurements of
THM test devices.
57
3.1 The Hot-Electron Effect
As was described in Section 2.2 when the phenomenon of superconductivity was
discussed, vibrational states called phonons exist in the crystal lattice. These vi-
brational states can be modelled as quantum harmonic oscillators with a quantized
phonon energy and frequency in a manner analogous to the quantization of electro-
magnetic waves as photons [65]. These quantized waves can occupy three dimensions
in a bulk solid, and can exist as either transverse or longitudinal modes. The energy
distribution of phonons in a solid is dependent on temperature. In Debye theory the
maximum phonon frequency is given by the Debye frequency, ωD = (6π2)1
3v, or the
Debye Temperature, TD = ℏ(6π2n)1
3 v, where v is the sound velocity of the solid and
n is the ion density. The phonon population peaks at phonon energies of kT , and at
phonon wavenumber q = kT~v
[65].
These vibrational states shift the positions of the atoms from their static states
and change the periodic potential that the conduction electrons in a metal see. This
effect is noticed in both the electron effective mass, the property of electrical resistivity
and in the appearance of superconductivity, where electron pairs couple together via
a phonon interaction. However, even in a non-superconducting metal, conduction
electrons scatter via the emission or absorption of a phonon. The rate at which
this scattering occurs is dependent on the energy spectrum and the density of states
of phonons and electrons in the metal. This scattering rate also depends on the
dimensionality of the metal, the dominant phonon modes (transverse or longitudinal),
and the level of disorder. During this scattering process a net thermal energy can be
exchanged between the electron and phonon systems. At low temperatures and within
58
small volumes electron-phonon scattering becomes infrequent and the electron-phonon
thermal conductance becomes very small. It is this small electron-phonon conductance
which will provide the dominant thermal isolation mechanism for the THM detector.
In this section the theories that describe this electron-phonon scattering in metals
under various regimes are reviewed. Measurements from the literature which confirm
or do not confirm parts of these theories for various materials are also presented, with a
focus on gold and bismuth, the materials chosen for the THM detector. A brief history
is then given of the application of this effect as a basis of electromagnetic radiation
detectors, and specifically, the development of Hot-Electron Bolometers (HEBs) and
Hot Electron Direct Detectors (HEDDs).
3.1.1 Hot-Electron Effect Theory
Theoretical models of the electron-phonon scattering time in a metal, τe−p, at
least over a limited temperature range, follow the form of [25],[123]:
1
τe−p= α∗T n−2
e . (3.1)
The power-law parameter, n, and the constant α∗ depend on the temperature regime
and properties of the material with predicted values ranging from n = 3.5 − 6. This
scattering rate can be converted to a net heat flow between the two systems which
follows the form of:
Pe−p = ΣV (T ne − T np ) (3.2)
Ge−p = nΣV T n−1e . (3.3)
Here Pe−p is the power flowing from the electron system to the phonon system, and
Ge−p is the thermal conductance that describes that link. These thermal models
59
assume a ‘2-Temperature’ model in which other methods of thermal exchange are
ignored and both the electron and phonon system are assumed to be in equilibrium
with themselves [55]. This assumption will be examined in the context of the THM
design in Chapter 4.
Σ is a temperature independent, material dependent constant, and V is the
volume. The temperature independent constant, Σ, is related to the scattering rate
constant, α∗ and in various models can be derived theoretically. In one of the most
general electron-phonon model it is given by [123]:
Σ = 0.524α∗γ (3.4)
Here γ is the electronic heat capacity constant of the metal. However, agreement
between measured and theoretical values of Σ vary. Instead of using theoretical pre-
dictions for Σ values in the design of the THM previously measured values are used,
reviewed in the following section.
The most general models of electron-phonon scattering take place in a pure 3-
dimensional metal. Most of these theories argue that the electrons scatter only with
longitudinal phonon modes [127, 32, 4, 123], however, some work has considered a
model where scattering with transverse phonon modes is also possible [93]. In this
pure 3-dimensional model the electrons interact via emission or absorption of a single
phonon but do not scatter with impurities in the metal. For temperatures below the
Debye temperature, these models all predict n = 5 with differing Σ prefactors.
Electron-phonon scattering has also been examined for the case where the metal
exhibits a large amount of disorder. In a disordered film the electron-phonon interac-
tion is complicated by interference effects due to electrons scattering with impurities.
60
A film’s disorder is characterized by the quantity ql where q is the dominant phonon
mode wave-vector and l is the electron mean free path. It should be noted that this
quantity is temperature and mode dependent. In the case that ql > 1 then the pure
metal model holds. However, when ql < 1 the metal is considered disordered and scat-
tering theories predict n = 6, assuming three-dimensionality and that the scattering
is dominated by longitudinal phonon modes [100]. A disordered theory, allowing for
the possibility of coupling to transverse phonon modes to dominate the scattering pre-
dicts n = 4 [104]. In disordered metals, a transition region between longitudinal and
transverse mode domination (qT l ∼ 1 where qT is the transverse phonon wavevector)
is also predicted. In this transition region n = 5 may be expected [104]. It should be
noted that in addition to n, Σ may depend on the level of disorder as well.
There have also been attempts to model 2-dimensional thin metal films where
the phonons are confined to a thin layer. These models predict an amplification of the
electron-phonon coupling with n = 3−3.5 in the pure limit [40] and n = 4.5−5 in the
disordered limit [25], [9]. It is important to note that measured values of n = 4, while
conforming to a possible 2D model of electron-phonon scattering (and a disordered 3D
model with transverse dominated scattering) also conform to heat flow determined by
a boundary thermal conductance between the phonons in the film and phonons in the
detector substrate. This boundary thermal conductance and how it may complicate
the simple hot-electron model of the detector will be discussed in Sections 3.2.2 and
4.2.6.
One can justify the extension of the theory of the electron-phonon effect in
a metal to a superconductor like a TES by considering the two-fluid model of the
61
superconductor as was described in Section 2.2. In this model there are normal-
acting electrons, called quasiparticles, excited out of the bound Cooper pair state,
and also superconducting electrons bound in Cooper pairs. In the transition region,
as is the case for a TES, the energy gap is rapidly approaching zero. In this operating
region, the superconductor is so close to the normal state that the vast majority of
the electrons are in the normal quasi-particle state, with very few Cooper pairs. Thus
a superconducting hot-electron bolometer in the transition can be treated as a normal
metal from the perspective of the hot-electron effect [103], [37].
3.1.2 Measurements of the Hot-Electron Effect
There have been many measurements of the hot-electron effect in a variety of
metals including both noble metals and alloys (such as AuCu, Cu, Au, NiCu, Nb)
which support a pure 3D model for electron phonon scattering, and demonstrate n = 5
temperature dependence [123], [32], [35], [102]. Disordered n = 6 behaviour has been
observed in some semi-metals (Ti, Hf, Bi) [38], [70] and alloys. There have also been
measurements of disordered n = 4 behaviour in Au films [105]. Presently there have
been no measurements of disordered noble-metal films which demonstrate n = 6 be-
haviour, and even in such metals which would be considered disordered, n = 5 has been
measured [25],[34], [96]. These measurements of n = 5 behaviour in disordered metals
could possibly be explained as occurring in the transition region between longitudinal
and transverse phonon domination [104]. There are a few measurements indicating the
possibility of 2D effects with measured values of n = 4− 4.5 in both thin membrane-
suspended films and thin films on a bulk substrate indicating a strengthening of the
electron-phonon effect [21], [73], [60].
62
The THM detector is a two-component bolometer with a Au or Mo/Au TES
and a Bi absorber. Previous hot-electron measurements of Au films have indicated
n = 5 [25], [60] and there have also been indications of n = 4 in disordered Au films
[105]. Bismuth, a semi-metal, has shown instances of n = 6 behaviour [70] as well as
n = 5 behaviour [23]. These previous measurements of the hot-electron effect in both
Bi and Au were instrumental in the design and optimization of the THM detector.
For this purpose we chose to use an average literature value of ΣAu = 4.2 · 109 Wm3K5
for Au and ΣBi = 2.4 · 108 Wm3K5 for Bi (assuming n = 5) [89], [23] as a guide to design
and for measurement comparison. These values will be referred to in later sections as
‘literature values’. In Chapter 5 measurements of the thermal conductance of THM
test devices are presented, and κ, Σ and n values for these Au-Bi composite THM test
devices are extracted.
3.1.3 HEB Detector History
The idea of employing the hot electron effect in a bolometer detector scheme was
first realized in semi-conductors [94], [64]. The possibility of using a superconduct-
ing thin film to detect the hot-electron effect when heated by a bias or optical signal
was then explored [106], [88] [103]. The details and possible optimization of a super-
conducting hot-electron bolometer was first formally proposed by Gershenzon et al.
[36] and the first measurements of a millimeter-size superconducting Nb hot-electron
bolometer by the same group [33], [36].
In parallel to the development of a hot-electron bolometer for direct detection,
hot-electron bolometers were also developed for use in coherent receivers as RF mixers
[130]. In fact, HEB technology in this application is more mature than that for
63
HEDDs. Superconducting Nb HEBs currently perform at the lowest sensitivity levels
in coherent mixer technology, and are in use in astrophysical applications [61]. The
THM and other HEDDs are employed in a different operating scheme, however, and
thus have very different requirements than the HEB mixers.
Since the first HEDD by Gershenzon et al., the development of a direct super-
conducting bolometer detector for astrophysical applications has made major leaps
forward in sensitivity. At the forefront of this push towards greater sensitivity has
been the development of a bulk Ti bolometer on nanometer size-scales by a contin-
uation of the Gershenzon et al. group. In their most recent work, reported by Wei
et al. they report minimum thermal conductance measurements of G ∼ 1 · 10−16 WK
[122], [58]. This HEDD design is optimized for terahertz frequencies and currently
holds the record for the lowest thermal conductance of a bolometer, with predicted
NEP below the background limit for spectroscopy from space. This group reports a
measured optical NEP of 3·10−19 W√Hz
[59].
Solar “boundary” microcalorimeters for use in high-count rate solar x-ray obser-
vations have also employed micron-sized Mo/Au bilayer TESs with larger and thicker
Au absorbers [5]. The size and temperature range of their operation, makes it likely
that an electron-phonon effect may play some role in the calorimeter thermal bot-
tleneck. Another group is also developing a Mo/Au bilayer TES with a separate Bi
absorber for far-infrared spectral observing and report G = 1 · 10−10 WK, with further
improvement still necessary to reach background limited levels [53].
The THM described in this thesis is a Mo/Au bilayer or Au TES with a Bi
absorber. The separate absorber allows for separate matching to a microwave trans-
64
mission line and antenna and the SQUID readout, a flexibility not possible for single-
element TES bolometers. The bilayer TES also allows for greater flexibility and tuning
of the TES Tc, an important detector requirement, especially when trying to obtain
great uniformity in large detector arrays (this is cited as one of the main limits to
present array application for the infrared single-element Ti hot-electron nanobolome-
ters [59]).
In addition, the THM is optimized for CMB observing conditions in the millime-
ter wavelength regime. As will be discussed in Section 4.2.8 and 4.2.9 a low thermal
conductance, although optimal for far-infrared applications, is not necessarily opti-
mal for CMB observing. With modifications to the coupling scheme, however, the
THM might also have applications to this sub-millimeter regime. We present our
measurements of the performance of test THM devices in detail in Chapter 5. Based
on thermal conductance measurements in our hot-electron devices NEP near or below
the photon background noise for CMB and far-infrared spectral observing is predicted,
making the THM a competitive detector choice for future astrophysical applications,
in particular in large detector arrays.
3.2 Other Effects
3.2.1 Andreev Reflection
Another effect in the THM device concerns the thermal isolation of the detector
from heat flow into the superconducting leads. Superconducting leads are necessary
to couple the incoming microwave power to the absorber as well as to provide the
DC voltage bias across the TES and to make a connection to the SQUID readout
65
circuit. When electrons attempts to flow from the detector across the boundary to the
leads, there are no quasi-particle states available to the majority of the electrons due
to the energy gap in the superconducting leads and most of the electrons are reflected
back into the detector. A Cooper pair can flow across the interface and current flow
is possible, however to conserve the number of particles, a ‘hole’ is reflected back at
the interface, and no thermal energy is carried across. This process is called Andreev
reflection [3]. The thermal conductance from the lower Tc/normal TES into the higher
Tc leads is described by [3]:
GAndreev =π
4f0(
mevfπ
)2ǫgap
√
ǫgap2kBT
e−ǫgap2kBT . (3.5)
Here me is the electron mass and vf is the Fermi velocity of the electrons in the TES.
ǫgap is the energy gap between the Cooper pair state of the superconductor and the
normal metal or the superconductor with a lower Tc. f0 ∼ 1 is a constant. In the case
of a THM TES with Tc = 200 mK and with Nb leads of Tc = 8 K, this results in a
predicted GAndreev ∼ 10−100 WK, significantly lower then the expected electron-phonon
thermal conductance to the bolometer cold bath. It is possible for multiple Andreev
reflections to occur, which may increase this thermal conductance [67].
3.2.2 Boundary Conductance
As the THM detector is a thin film deposited directly on the substrate the ther-
mal conductance between the film and substrate at the interface must also be consid-
ered. A thermal boundary ‘Kapitza’ resistance at the interface between two materials
was first discovered at the solid/liquid He II boundary by Kapitza in 1961 [56]. Fol-
lowing this discovery further theoretical and experimental work was undertaken to
66
try to understand this thermal boundary resistance, not only between a solid/liquid
barrier, but also between a liquid/liquid interface and a solid/solid interface such as
occurs between the detector and substrate in the THM [79].
The theoretical work broadly falls into two models which describe the phonon
transmission across a mismatched impedance boundary: the acoustic mismatch model
(AMM) and the diffuse mismatch model (DMM). In both of these models the thermal
conductance calculation depends on the number of incident (and counter-incident)
phonons, and the probability of their transmission across the boundary. The acoustic
mismatch model uses the acoustic analog of optical laws to describe the transmission
of photons at an interface between two boundaries [84], [63], [79]. In this model the
transmission of phonons across a boundary is determined by the angle of incidence of
the phonons, the phonon modes (transverse or longitudinal) and the respective sound
velocities on either side of the interface.
For solid/solid interfaces where the surface is not clean, and at higher temper-
atures where the majority of phonons have frequencies greater than 100 GHz, many
of the phonons scatter from the rough surface. In this case the thermal boundary
conductance is better described by the diffuse mismatch model first introduced by
Swartz [111]. The diffuse mismatch model assumes that all of the phonons scatter
back into the material from the rough surface and lose all correlation or “memory”.
In this model the phonon transmission is determined only by the density of states on
either side of the boundary. Thus if two solids have the same acoustic properties then
half of the incident phonons will be transmitted, and half reflected. The effect of the
diffuse model is to decrease the thermal conductance slightly from what is predicted
67
by the acoustic model for dissimilar solids.
The two mismatch models have been shown to be in relatively close agreement
with solid/solid boundary thermal conductances measured for temperatures below 50
K [111]. More recent models of thermal boundary resistance to describe experimental
results which differ from the simple analytical AMM and DMM models have focused
on atomic level computational simulations of the crystal interfaces [14].
Mathematically, the power flow across the boundary for both the acoustic and
diffuse model is given by the expression:
Pboundary =A
4Cb(T 4
1 − T 42 ) (3.6)
and the thermal conductance is given by:
Gboundary =A
CbT 3 (3.7)
Here A is the surface contact area at the boundary and Cb is a material dependent
constant which depends on the material properties of both sides of the interface and
whether the transmission follows an acoustic or diffuse model. T1 is the temperature
of the hotter material, and T2 is the temperature of the colder material. For Au on
Si or AlO, which will be applicable to our THM detectors, theoretical predictions for
Cb range from 12− 19 · 10−4 Km2
Wfor both the acoustic or diffuse models [111]. In the
upcoming chapters of this thesis, an average value of Cb = 15.5 ·10−4 Km2
Wwill be used
for design considerations and measurement comparison purposes.
What is the effect on the boundary resistance when a very thin film is deposited
on the substrate? The AMM and DMM models discussed so far occur in a bulk regime
where the typical phonon wavelength is much smaller than the film thickness. In thin
68
films at room temperature, the dominant phonon wavelength is often on the same
order as the the film thickness and interference wave-effects between phonons become
important, altering the boundary conductance theory [14]. There has been some
work examining thin films at Kelvin and sub-Kelvin temperatures where the phonon
wavelength can be much longer than the film thickness. The problem of adequately
defining a phonon temperature at this local scale also complicates the interpretation
of the boundary conductance of a thin film [14], [48].
Wellstood et al. [123], while discussing the hot-electron effect in low temperature
thin films, make the argument that when the phonon wavelength is much larger than
the film thickness, it is impossible to talk about phonons within the film itself, but
rather the phonons in the substrate and the thin film may be considered the same
system. Huberman et al. [48] apply this same argument to interpret anomalous room
temperature thermal conductance measurements in Pb on diamond, by assuming that
the phonons within a mean free path of the interface are strongly coupled together
with the substrate phonons and may be considered the same system.
As far as the author is aware there is still disagreement about this interpreta-
tion, and others argue that a boundary conductance due to the impedance mismatch
between thin film and substrate will still exist, even when long wavelength phonons
dominate, although this mismatch model might need to be refined [21], [87] [111] [29].
Some early work into the boundary conductance in thin low temperature films ar-
gues that the transmitted phonon rate and spectrum is modified from bulk behaviour
[29]. According to this model, and confirmed by measurements, one expects to see an
increase in the phonon transmission rate across the boundary up to an order of mag-
69
nitude depending on power dissipation level for regimes where the dominant phonon
wavelength is larger than 2x the film thickness [29]. In semiconductor multilayers
there are also theoretical models taking into account wave-interference effect which
predict that an increase in thermal boundary conductance will occur when the film
layer is much smaller than the phonon mean free path [107].
In Chapter 4 the question of hot-electron versus boundary conductance domi-
nation in the THM detector design will be explored using the predictions from the
bulk AMM and DMM models, while acknowledging that a boundary conductance
significantly higher then these values might be expected due to the thin film effect.
Ultimately, however, since theoretical models are still in disagreement, measurements
of the thermal conductance of THM test devices, which will be presented in Chap-
ter 5, will be allowed to make the argument that the hot-electron effect provides the
dominant thermal isolation mechanism for the THM detector.
3.2.3 Wiedemann-Franz Conductance
Another important thermal exchange mechanism in the THM detector involves
electron-electron scattering within the absorber and TES and between the absorber
and TES. This thermal exchange provides for thermal equilibrium within the ‘hot’
electron system of the detector. The electron-electron thermal conductance in a metal
is linearly related to the temperature and is given by the free electron Fermi gas model
as [65]:
Ge−e =πn2
ek2BTτe
3me. (3.8)
Here ne is the electron density and τe is the electron scattering time. Because the
electrical resistivity in a metal is also related to the electron density and scattering
70
rate ρ = mnee2τe
[65], the electron-electron thermal conductance can be related to the
resistance. In this way the electron thermal conductance can be predicted from a
measurement of the electrical resistivity of a metal without knowing the electron-
scattering rate or the electron concentration. This expression for the electron-electron
thermal conductance is given by the Wiedemann-Franz law:
Ge−e =L0T
R(3.9)
Here R is the resistance across the length of the device and L0 is the Lorenz number
which is given by L0 =π2k2
B
2e. The Wiedemann-Franz law is usually applicable at
low temperatures where the temperature is much less than the Debye temperature
(T < TD10) [90].
3.2.4 Radiation Loss
The hot-electron gas in the THM detector is also able to transfer heat to the
external environment via blackbody radiation into the impedance-matched transmis-
sion line. This radiation loss is determined by a thermal conductance modelled by
one-dimensional blackbody radiation given by [101]:
Gγ =rπ2k2bTe
3h(3.10)
Here r is the transmission factor, where r = 1 for a matched load and r < 1 for
an unmatched load, and where Te is the electron temperature. For a hot-electron
bolometer at 50 mK and r = 1, Gγ = 4.7 · 10−14 WK. Here the thermal conductance is
evaluated for the full photon frequency range of the 1-D blackbody radiation, which
is dominated by photons with frequencies between 0 − 5kBTeh
. This radiation thermal
conductance is usually much lower than the electron-phonon conductance, and we
71
expect that even for our smallest THM sizes (volumes on order 1 µm3, Ge−p ∼ 10−13
WK) it can be ignored. However, in smaller, nanometer hot-electron bolometers it may
become necessary to account for this heat loss [101].
3.3 The Superconducting Proximity Effect
The superconducting proximity effect occurs a short distance from the interface
between a normal metal and a superconductor. The presence of a normal metal mod-
ifies the superconductor’s properties and the presence of the superconductor modifies
the normal metal’s properties a short distance from the interface. In the superconduc-
tor, the BCS energy gap, ǫgap, is minimized near the interface. In the normal metal,
superconducting Cooper pairs from the superconductor are able to travel a distance
into the metal while retaining their coherence and the normal metal may exhibit su-
perconducting characteristics. The proximity effect can also occur at the interface of
superconductors of differing energy gaps.
The design of the TES in the THM detector includes two mechanisms by which a
superconducting proximity effect can occur. The first mechanism is a proximity effect
in the bilayer Mo/Au TES between the superconducting Mo film and the normal Au
film. This first effect is exploited intentionally in the THM design to modify the TES
transition temperature to the precise temperature necessary for the application-specific
noise requirements. The second mechanism is a lateral proximity effect between the
Nb superconducting leads of the TES and the superconducting bilayer Mo/Au TES.
Because of this lateral proximity effect the TES can effectively become an S-S’-S
junction in certain designs. This second effect was discovered as the TES lead-to-lead
length was decreased to the micron scale, and the TES transition temperature shifted
72
closer to the superconducting lead transition temperature (these results are detailed
in Section 5.5).
Strong shifts in Tc make it difficult to fabricate micron-sized Mo/Au TESs with
the low Tcs (50-300 mK) necessary for the THM application-specific noise require-
ments. With this motivation in mind, we have also explored the possibility of using
a micron-sized Nb-Au-Nb, S-N-S junction as a TES. The advantages in this concept
is a simplification of the system, freedom from thickness constraints due to bilayer
thickness ratios, and a lowering of the unmodified junction transition temperature,
TcN , since the normal Au metal has an unmodified transition temperature of TcN = 0
K, compared to TcN = 50− 300 mK for a bilayer S-S’-S junction.
In Figure 3.1 two different THM designs with these two different geometries are
shown. In the following sections the superconductivity theories which describes the
superconducting proximity effect in each of these designs will be reviewed in more
detail. Some predictions of the effect of the lateral proximitization on TES transition
temperatures for various S-N-S and S-S’-S THM test devices will also be presented. In
Section 5.5 these predictions will be compared to measurements of S-N-S and S-S’-S
THM test devices.
3.3.1 Superconductivity Theory & the Proximity Effect
The first experimental investigations into superconductivity took place at a
macroscopic level. London theory and theories which describe the electrodynamics of
a superconductor were developed and applied at this level to describe properties such
as penetration depth and the Meissner effect without a fundamental understanding
of the microscopic origin of superconductivity. Later on, a fundamental microscopic
73
normal metal
superconductor
superconductor normal metal
normal metal
SS’
NS
Lead LeadTES
S N S
Lead LeadTES
(a)
(b)
(c)
Figure 3.1: (a) The bilayer superconducting proximity effect. (b) A lateral
superconducting proximity effect. (c) The two different TES designs where
the lateral or bilayer proximity effect play a role: a S-S’-S junction (left)
and a S-N-S junction (right).
74
theory, BCS theory, was able to describe the macroscopic properties of superconduc-
tors by proposing that the electrons paired together into Cooper pairs via a phonon
interaction.
Although BCS theory works well to describe some properties of bulk super-
conductors such as the energy gap in a superconductor as a function of temperature,
infinite electrical conductivity and phase coherence, it is too unwieldy to describe more
detailed systems where there is a great deal of variation as a function of position or if
there are high magnetic fields. In these situations, as is the case when describing the
lateral proximity effect, more general phenomenological or ‘semi-macroscopic’ theo-
ries are usually applied instead. There are two branches of superconductivity theories
which will be focused on in this thesis in order to understand and make predictions
for the proximity effect in the THM detector: Ginzburg-Landau Theory and Usadel
Theory. A flow chart summarizing these theories, their range of applicability, and a
list of the specific applied theories which will be discussed in this thesis, is shown in
Figure 3.2.
3.3.2 Ginzburg-Landau Theory
Ginzburg-Landau theory introduces a quantity, called an order-parameter, ψ, to
describe the superconducting state, where ψ can be a function of both position and
temperature. This quantity is analogous to the superconducting wavefunction given
by BCS Theory. Ginzburg-Landau theory in fact pre-dates BCS theory and does not
rely on fundamental assumptions about the microscopic properties of a superconductor
[39]. However, the Ginzburg-Landau psuedowavefunction can be related physically to
75
BCS Theory:
No variation with position
No high fields
Ginzburg-Landau Theory:
T~Tc, or ~small,
vary slowly with position
No energy dependence
Usadel Theory:
Full T range
& A vary slowly with position
Energy dependence
Microscopic
Semi-microscopic
S-N-S Theories:deGennes
van Dover et al.
S-N-S Theories:Likharev
Dubos et al.
Kuprianov & Lukichev
S-S’-S Theory:Sadleir et al.
S-S’-S Theory:Kozorezov et al.
S-N Bilayer Theory:Martinis et al.
Θ
or Phenomemological
Figure 3.2: Superconductivity theories, their relationships, and applicabil-
ity.
the density of superconducting electrons, ns, by [115]:
|ψ|2 = ns. (3.11)
Near the superconducting transition Ginzburg-Landau theory can be derived from
BCS theory and the psuedo-wavefunction can also be related to the BCS energy gap
by [42]:
ψ = √
7ζ(3)ne4πTc
. (3.12)
where ζ is Riemann’s function, ne is the number density of electrons in the normal
metal and = ǫgap2.
Ginzburg-Landau theory as it is applied to superconductors is an application of a
more general theory, Landau’s homogeneous theory of second order phase transitions.
This theory applies to any physical process which undergoes a second order phase
transition which can be defined by a complex order parameter [74]. Landau’s theory
76
defines the free energy of a system which undergoes a phase transition in terms of this
complex energy parameter and applies a minimization principle which requires the
thermodynamic system find the state which minimizes this free energy with respect
to the order parameter and the magnetic field distribution. For a superconductor
this free energy minimization requirement is described by the two Ginzburg-Landau
differential equations [98, 17, 115], the first describing the order parameter:
αψ + β|ψ|2ψ +1
2me(~
i∇− 2e
c~A)2ψ = 0; (3.13)
and the second defining the superconducting current density, ~j, due to the diamag-
netism of the superconductor:
~j =e~
ime
(ψ∗∇ψ − ψ∇ψ∗)− 4e2
mecψ∗ψ~A. (3.14)
Here ~A is the vector potential responsible for the magnetic field in the superconductor.
The coefficients α and β determine the solution for ψ and ~j.
The solution to these two differential equations in terms of both the order param-
eter ψ, or the current density ~j, can be found by applying the appropriate boundary
conditions. In certain applications analytical solutions are possible, usually when sim-
plifying assumptions are made. If analytical solutions are not possible then numerical
solutions can be found. Ginzburg-Landau theory has been shown to work well to
describe situations where the superconductor is near the transition, and the order pa-
rameter and current vary slowly with position. For situations beyond this description
a more general semi-microscopic theory, Usadel theory, can be applied.
77
3.3.3 Usadel Theory
Usadel theory is a phenomenological microscopic approach based on a “non-
equilibrium” theory of superconductivity in which the correlations corresponding to
normal or superconducting electrons in a metal are both described by a Green’s func-
tion that depends on position, x, and electron energy, E [43, 118]. Usadel theory
describes superconductivity by a complex order parameter, θ(x, E), which relates to
the density of superconducting or normal electrons. In a normal reservoir θ(x, E) = 0.
In an infinite superconductor, the order parameter θ(x, E) is related to the BCS energy
gap by [44]:
tan θ(x, E) = iE
(3.15)
and the order parameter is related to the density of states, n, by:
n(x, E) = n0Re[cos θ(x, E)] (3.16)
There are 2, 1-D Usadel equations [44],[118]:
~D
2
∂2θ(x, E)
∂x2+ [iE − (
~
τsf+
~D
2(∂ϕ(x, E)
∂x+
2e
~Ax)
2) cos θ(x, E)] sin θ(x, E)
+∆(x) cos θ(x, E) = 0 (3.17)
∂
∂x[(∂ϕ(x, E)
∂x+
2e
~Ax)
2)(sin θ(x, E))2] = 0. (3.18)
Here ϕ is the real superconducting phase, τsf is the spin-flip scattering rate, Ax is the
component of the potential along the x direction andD is the diffusivity in the normal-
state metal where D = vF l and l is the electron mean free path. The Usadel differential
equations are solved by applying the appropriate boundary conditions. With further
simplifications analytical solutions are often possible, in other cases numerical solutions
are necessary.
78
The author will not proceed to discuss or derive any more of the details of
the Usadel or Ginzburg-Landau theories in this thesis, but in the following sections
solutions will be reproduced which have already been derived for THM-applicable
situations. These solutions will be used in order to make specific predictions for the
THM test devices. For the details of the derivations the reader is referred the references
given.
3.3.4 The Characteristic Lengths of the Proximity Effect
Before presenting specific solutions, the characteristic length scale of the su-
perconducting proximity effect will first be introduced. The normal metal coherence
length, ξN , is the distance into which electron-pairs retain their coherence, and thus
superconducting behaviour, as they travel from a superconductor into a normal metal.
Specifically, the critical current through a S-N-S junction, as will be shown explicitly
in the following sections, scales as Ic ∼ e−L/ξN , where L is the lead-to-lead distance
(the length of the normal metal). In a S-S’-S junction, this critical current dependence
does not necessarily follow this form, however, the normal metal coherence length of
the junction region still plays an important role.
The mean free path of an electron in a normal metal is given by [4]:
l =r2n9.2 · 10−17m
ρ. (3.19)
Here rn is the dimensionless radius parameter for the metal and ρ is the electrical
resistivity. The effective mean free path of a thin film, taking into account thickness
dependence, is [68]:
leff = (1
l+
1
d)−1 (3.20)
79
where d is the metal film thickness. This expression requires that the electron mean
free path does not significantly exceed the film thickness.
For an S-N-S junction (where TcN = 0) following both microscopic theory [16]
and semi-macroscopic Usadel theory [76],[68] the temperature dependent normal metal
coherence length in the dirty limit is given by:
ξN,d =
√
~vF leff6πkbT
. (3.21)
This dirty limit is characterized by electron mean free path, l < ξ0 where ξ0 is the
Cooper pair coherence length (the size of an individual Cooper pair) given by ξ0 =
~vF2πkBT
[68],[76]. In the clean limit, l > ξ0, the normal metal coherence length is given
by [68]:
ξN,c = (2πT
~vF+
1
leff)−1. (3.22)
THM devices (with normal Au film of thicknesses, d ∼ 30 − 300 nm) have
effective mean free paths of l ∼ 10− 40 nm, which is much less than the Cooper pair
coherence length (ξ0 ∼ 200 nm). Thus, although the clean limit expressions will be
included in this section, the dirty limit will be assumed for the S-N-S and S-S’-S THM
predictions in the following sections. In Figure 3.3 the normal metal coherence length
in the dirty limit for a Nb-Au-Nb junction as a function of temperature is plotted for
a typical THM devices.
In the case of an S-S’-S junction (TcN > 0) there are two temperature regimes
that are considered when deriving the normal metal coherence length. In the regime
where T ∼ TcN , in the clean limit, Usadel theory and G-L theory give [68]:
ξN,c =~vF
2πkbTcN
√
0.701TTcN
− 1. (3.23)
80
0 1 2 3 4 5 6 7 8
4.0x10-8
8.0x10-8
1.2x10-7
1.6x10-7
2.0x10-7
2.4x10-7
2.8x10-7
3.2x10-7
3.6x10-7
N
(m
)
Temperature (K)
30 nm, RRR=1
30 nm, RRR=2
300 nn, RRR=1
300 nm, RRR=2
ξ
Figure 3.3: The normal metal coherence length for a dirty Nb-Au-Nb
junction (following Equation 3.21) as a function of temperature for Au
RRR = 1&2 is plotted for 30 nm and 300 nm Au thicknesses. Room
temperature Au resistivity is assumed to be 3 ·10−8 Ω ·m and Nb Tc = 8.3
K is assumed. For typical S-N-S THM devices one expects ξN = 0.1− 0.4
µm.
81
And in the regime where T ≫ TcN , in the clean limit, Usadel theory gives [68]:
ξN,c =~vF
2πkbT(1− 0.28TcN
T)−1. (3.24)
In the dirty limit where T & TcN , Usadel and G-L theory give [68]:
ξN,d =
√
π~vF leff24(T − TcN)
. (3.25)
In the dirty limit where T ≫ TcN , Usadel theory gives [68]:
ξN,d =
√
~vF leff6πkBT
(1− 2
ln 4TTcN
)−1. (3.26)
Sadleir et al. have also developed a theory for S-S’-S bilayer devices following
Ginzburg-Landau theory where the temperature dependent normal metal coherence
length is given by [97]:
ξN =ξi
√
TTcN
− 1(3.27)
where ξi is the normal metal coherence length at absolute zero, and a parameter which
they fit to their measurements. Here T > TcN is assumed. They assume for prediction
purposes that ξi =√
π~vF leff24kBTcN
such that Equation 3.27 matches Equation 3.25. Sadleir
et al. found that theoretical predictions using this expression (calculated based on
the superconducting layer of the bilayer only) matched their results to an order of
magnitude. However, they stress that no theoretical expression exists to calculate this
parameter for the bilayer system. In Figure 3.4 the normal metal coherence length
in the dirty limit for a Nb-Mo/Au-Nb junction as a function of temperature for Au
or Mo resisitivity is plotted for a typical bilayer thickness following the expressions
from Equations 3.25, 3.26 and 3.27. The normal metal coherence length is also plotted
assuming Sadleir et al.’s measured fit values for ξi. For both S-N-S and S-S’-S models
for a typical THM detector, ξN ∼ 0.1− 1.0 µm.
82
2 4 6 8
0.0
2.0x10-7
4.0x10-7
6.0x10-7
8.0x10-7
1.0x10-6
1.2x10-6
1.4x10-6
1.6x10-6
1.8x10-6
2.0x10-6
N (
m)
Temperature (K)
Usadel 300 nm Au RRR=1
Sadleir-G-L, 300 nm Au RRR=1
Sadleir-G-L, 300 nm Mo RRR=1
Sadleir-G-L, Sadleir et al. !t
ξ
Figure 3.4: The normal metal coherence length for a Nb-Mo/Au-Nb junc-
tion as a function of temperature for Au RRR = 1 is plotted for 300
nm Au thickness. Room temperature Au resistivity of 3 · 10−8 Ω ·m, Nb
Tc = 8.3 K and Mo/Au Tc = 200 mK are assumed. For the Sadleir-G-L
model (which matches the low temperature Usadel Model), the normal
metal coherence length is also plotted assuming Mo resistivity of 5.3 ·10−8
Ω ·m, and also assuming Sadleir et al.’s measured fit to ξi = 738 nm. For
all these models for typical THM devices ξN ∼ 0.1− 1.0 µm is predicted,
with the coherence lengths predicted by the fit values on the higher side
of this range.
83
3.3.5 S-N Bilayer Theory
Applying Usadel theory Martinis et al. derive an expression for the transition
temperature of a normal-superconducting bilayer film as [80]:
Tc = TcN [2ds
πkBTc0λ2Fns
1
1.13(1 + dsns
dnnn)
1
t]dsnsdnnn . (3.28)
Here TcN is the unmodified superconducting film transition temperature, ds is the
superconducting film thickness, dn is the normal metal thickness, and ns and nn are
the electron density of states in the superconducting and normal metal films respec-
tively. λF is the Fermi wavelength for the normal metal, and t is the transmission
coefficient, which characterizes the transparency of the interface between the normal
and superconducting sandwich and is directly related to the electrical resistivity of
this interface. t = 1 indicates a perfectly transparent interface.
3.3.6 S-N Bilayer Measurements
In practice the Martinis et al. equation must be fit to experimental results to
develop a consistent recipe for bilayer Tc in a specific deposition system. In bilayer
deposition, the deposition is best done in a dedicated and conditioned system, without
breaking vacuum in order to increase the transparency between the layers and the
reproducibility of the transition temperature.
Many of the TESs developed and in use as astrophysical detectors are bilayer
TESs due to the flexibility the bilayers allows in the choice of the transition temper-
ature of the TES. The fabrication techniques for Mo/Au and Mo/Cu bilayer TESs
have been widely perfected [28, 108] and such devices are now in use in astrophysical
applications [109]. We haven chosen to use the Mo/Au bilayer system in the THM due
84
to this maturity of the Mo/Au TES design as it is in use in membrane-isolated TES
detectors for microcalorimeter and bolometer detector arrays and due to the fact that
transition temperatures of bilayer films can be produced to conform to the desired Tc
for CMB applications (50-300 mK). In the next sections of this chapter we discuss
the details of the ‘lateral’ proximity effect, an addition to this bilayer proximity effect,
which can complicate the obtainable Tcs for the THM detector.
3.3.7 S-S’-S Theory & Predictions
Sadleir et al. [97] have developed a model of the lateral proximity effect for
Nb-Mo/Au-Nb S-S’-S junctions based on Ginzburg-Landau theory. Here the solution
for the critical current at the center of the junction is given by:
Ic(T, L) =hf 2
rLd
6πeµ0λ2rξN(T )exp
−LξN(T )
. (3.29)
Here fr ∼ 1, λr is the local penetration depth in the leads and ξN is the temperature-
dependent normal metal coherence length given by Equation 3.27 and d is the Mo/Au
film thickness. The transition temperature, Tc, is defined as the temperature at which
voltage appears across the junction, and thus marks the beginning of the TES transi-
tion. It is shifted from the bulk bilayer transition temperture, TcN , due to this effect.
The Tc is given by the relation [97]:
Tc − TcNTcN
= (ξiLln
hf 2r λrLd
6πeµ0λ2rξN(Tc))2. (3.30)
This solution applies when T > TcN and L ≫ ξN . Here the normal metal coherence
length is given by equation 3.27. In Figure 3.5 predictions for Ic are plotted as a func-
tion of temperature following Equation 3.29 assuming a typical THM bilayer device.
This model predicts a transition temperature which is shifted from TcN = 170 mK
85
to Tc = 600 mK−1 K for a 3 µm long device with bias current of ∼ 1 µA. For the
lead-to-lead lengths we have considered here, the predictions for Ic using measured
fit ξi values from Sadleir et al. are ∼ 1 − 4 orders of magnitude higher than those
predicted using electrical resistivity.
Kozorezov et al. [71] have also developed a model based on the more general Us-
adel equations to describe the behaviour of a bilayer TES as a S-S’-S weak link. They
derive an analytical solution for the case of a large contact resistance at the interface
and more general numerical solutions in the case of a transparent interface. They find
that unlike the Sadleir et al. S-S’-S model and the models for S-N-S junctions (which
will be examined in the next section) the critical current does not fall exponentially as
Ic ∼ exp−L/ξN (here they assume ξN follows the form given in Equation 3.21 rather
than the S-S’-S forms) and that even for T ≫ TcN there is a finite energy gap in the
junction region.
3.3.8 S-S’-S Measurements in the Literature
Recent measurements of micron-sized Mo/Au bilayer TESs, similar to THM
devices with Nb leads, have indicated strong shifts in the TES Tc due to this lateral
effect [97]. For example, for devices with lead-to-lead lengths of 8 µm (the shortest they
tested), Sadleir et al. saw Ic = 1 mA at 200 mK (for TcN = 180 mK) and measured
an effective Tc = 400 mK with a bias current of 1 µA. Although these measurements
fit to the model developed by Sadleir et al. using ξi as a fitting parameter, they do
not fit as well to predictions of this model when ξi is calculated from resistivity, as
is shown in Figure 3.5. Measurements of our own similar THM devices are presented
in Chapter 5 where an even stronger proximity effect is observed in the smallest 3
86
c)
b)a)
Figure 3.5: Critical current behaviour of a Nb-Mo/Au-Nb S-S’-S TES as
predicted by the Sadleir et al. model using Equation 3.29. The legends on
each plot indicate lead-to-lead lengths in meters. a) Ic calculated assuming
Au resistivity of ρ = 3.3 · 10−8 Ω·m, and Au thickness of 300 nm. b)
Ic assuming Mo resistivity of ρ = 5.3 · 10−8 Ω·m with bilayer thickness
dominated by Au thickness of 300 nm. c) Ic calculated assuming the
measured fit value by Sadleir et al. for ξi = 738 nm. For all predictions
λr = 79 nm (the measured value from Sadleir et al.), Nb Tc = 8.4 K, and
Mo/Au TcN = 170 mK have been assumed. The predictions for Ic using
the measured fit ξi value are ∼ 0.5 − 4 orders of magnitude higher than
predictions using ξi values calculated from resistivity.
87
µm long devices. Interestingly, a strong lateral proximity effect has not been seen in
hot-electron Ti nano-bolometers [122], likely because of the high resistivity of these
devices.
3.3.9 S-N-S Theory & Predictions
We now summarize models which predict the critical current behaviour of a S-
N-S junction where the normal metal has a critical temperature of TcN = 0. For all
of these models the form of the normal metal coherence length given in Equation 3.21
has been assumed.
3.3.9.1 Likharev-Usadel Model
The first model comes from the application of Usadel theory in the dirty limit.
The solution to this ‘Likharev-Usadel’ model, in terms of the critical current through
the junction region as a function of the lead to lead length, L, is given by [76]:
Ic(T, L) =π∆2
4ekBTΣ∞i=1
8√2i+ 1L
π2(2i+ 1)2ξN(T ) sinh(√2i+1LξN (T )
). (3.31)
In Figure 3.6 the critical current given by this expression is plotted as a function of
temperature for a variety of L values for a typical THM device. This model predicts
Ic ∼ 0.1− 100 µA at ∼ 200 mK for a 3 µm long device.
3.3.9.2 deGennes-GL Model
The second model was originally derived by deGennes [16] applying Ginzburg-
Landau theory in the dirty limit. In this ‘deGennes-GL’ model the critical current as
a function of lead-to-lead length and temperature is given by [46]:
Ic(T, L) =π∆2
2ekBTcRn
L
ξN(T )exp
−LξN(T )
. (3.32)
88
a)
b)
Figure 3.6: Critical current behaviour of a Nb-Au-Nb S-N-S TES predicted
by the Likharev-Usadel model using Equation 3.31. The legend on each of
the graphs indicates different lead-to-lead lengths in meters. a) Assuming
a Au resistivity of ρ = 3.3 · 10−8 Ω ·m and a Au thickness of 30 nm. b)
Assuming a Au resistivity of ρ = 3.3 ·10−8 Ω ·m and a Au thickness of 300
nm. In both cases a Nb transition temperature Tc = 8.4 K and a 3 µm
wide device is assumed. This model predicts Ic ∼ 0.1 − 100 µA at ∼ 200
mK for a 3 µm long THM device.
89
Here Rn is the total normal resistance of the junction and Tc is the transition temper-
ature of the superconducting leads, not the junction region. In Figure 3.7 the critical
current given by this expression is plotted as a function of temperature for a variety
of L values for a typical THM device. This model predicts Ic ∼ 10 nA-10 µA at ∼ 200
mK for a 3 µm long device.
3.3.9.3 Dubos-Usadel Model
The third model is a Usadel-based model which extends the Usadel model to
a broader temperature range in the long junction device limit regime. This model,
derived by Dubos et al. [24] examines two different temperature regimes, characterized
by the quantity defined as the Thouless energy of the junction, ǫc, when ǫc(T, L) =
2kBTξN (T )2
L2 . The Dubos high temperature regime is defined when ǫc ≪ kBT and the low
temperature regime where ǫc ≫ kBT . In addition to these two temperature regimes,
the junction may be considered a long junction if ǫc ≪ ∆, where ∆ is the energy
gap in the superconducting leads. In most of the device size and temperature range
for the THM the long device limit holds, with a maximum ǫc ∼ 10−24J, compared
to ∆ ∼ 10−22 J in the Nb leads. In this high temperature, long device regime, the
solution is given by [24]:
Ic(T, L) =32
eRn(3 + 2√2)ǫc(T, L)
L3
ξN(T )3exp
−LξN(T )
. (3.33)
In the low temperature, long junction regime, the solution is given by [24]:
Ic(T, L) =10.82ǫc(T, L)
eRn
(1− 1.30 exp−10.82ǫc(T, L)
3.2kBT). (3.34)
In Figure 3.8 the predictions following both Equation 3.33 and Equation 3.34 are
shown for a variety of possible THM devices. This model predicts Ic ∼ 1 nA-0.1 µA
90
a)
b)
Figure 3.7: Critical current behaviour of a Nb-Au-Nb S-N-S TES predicted
by the deGennes-GL model using Equation 3.32. The legend on each of
the graphs indicates different lead-to-lead lengths in meters. a) Assuming
a Au resistivity of ρ = 3.3 · 10−8 Ω ·m and a Au thickness of 30 nm. b)
Assuming a Au resistivity of ρ = 3.3 ·10−8 Ω ·m and a Au thickness of 300
nm. In both cases a Nb transition temperature Tc = 8.4 K and a 3 µm
wide device is assumed. This model predicts Ic ∼ 10 nA-10 µA at ∼ 200
mK for a 3 µm long THM device.
91
at ∼ 200 mK for a 3 µm long device.
3.3.9.4 van Dover-GL Model
Another correction to the Likarev-Usadel theory is given by van Dover et al.
[119]. Here they apply Ginzburg-Landau theory and allow for the suppression of the
superconducting energy gap at the boundary due to the inverse proximity effect from
the normal metal, mimicking a SN-N-NS junction model. In this ‘van Dover-GL’
model the critical current of the junction is given by [119]:
Ic(T, L) =π∆2
2ekBTf 2(T )
Aρnγρs
L
ξN(T )exp
−LξN(T )
(3.35)
Here A = ψN (0)ψS(0)
is the ratio of Ginzburg-Landau order parameter on either side of the
boundary, ρn and ρs are the respective normal state electrical resistivities, γ = mn
msis
the ratio of the effective electron mass in the normal state for the superconducting
leads and the normal metal and f(T ) ∼ 1 for T ≪ Tc, where Tc is the transition
temperature of the Nb leads.
van Dover et al. note that the parameter A, in addition to modelling the sup-
pression of the order parameter at the boundary due to the inverse proximity effect,
can also model the effect of a finite contact resistance between the superconducting
and normal contacts. Experimentally, they found the relation Aρnγρs
= 0.24 in their
Nb-Au-Nb devices, though they argue that this parameter cannot be known a priori
and should be fit to measurements. However, this value will be used as a guide for
predictions for THM devices. In Figure 3.9 the predictions for the critical current fol-
lowing Equation 3.35 are shown, assuming this experimental relation holds, for typical
THM devices. This model predicts Ic ∼ 0.1− 10 µA for a 3 µm long device at ∼ 200
92
a)
b)
Figure 3.8: Critical current behaviour of a Nb-Au-Nb S-N-S TES predicted
by the Dubos-Usadel model using Equations 3.33 and 3.34. The legend on
each of the graphs indicates lead-to-lead lengths in meters. a) Assuming
Au resistivity of ρ = 3.3 · 10−8 Ω · m and Au thickness of 30 nm. b)
Assuming Au resistivity of ρ = 3.3 · 10−8 Ω ·m and Au thickness of 300
nm. In both cases Nb Tc = 8.4 K and a 3 µm wide device is assumed. This
model predicts Ic ∼ 1 nA-0.1 µA at ∼ 200 mK for a 3 µm long TES. The
discontinuity in the curve for the shortest devices indicates the crossover
from the high to the low temperature limit.
93
mK.
Figure 3.10 shows a comparison of all the S-N-S theories (the Likharev-Usadel,
deGennes-GL, Dubos-Usadel and van Dover-GL models) that have been introduced
thus far for a 3 µm x 3 µm TES device. This plot also includes the Sadleir et al. fit
model for a similar S-S’-S device. This plot provides a relevant theoretical comparison
for the results of transition measurements for some of the shortest 3 µm long S-N-S
and S-S’-S THM test devices, which will be presented in Chapter 5. For the S-N-S
case, with a bias current of 1 µA, an effective Tc of 100− 400 mK is expected across
the junction.
3.3.9.5 Kuprianov-Lukichev-Usadel Model
The final S-N-S model is one which explicitly takes into account a finite contact
resistance or non-unity transmission factor between the boundaries by Kuprianov and
Lukichev [72] applying Usadel theory. They define a contact resistance Rc at the
interface between the superconducting leads and normal junction, which modifies the
critical current behaviour of the junction. This contact resistance is parametrized in
terms of the ratio Γc =Rc
Rjunction, where the normal resistance across the junction region
is Rjunction and where the total resistance across the junction is Rn = (1+2Γc)Rjunction.
The general solutions to the theory are numerical. However, in the case of a S-N-S
junction where Γc . ξNL
their numerical solutions predict a decrease in the critical
current of less than 20%. In Figure 3.11 we plot this requirement for Γc as a function
of device length, for a typical THM device. As long as the contact resistance is less
than 10− 15% of the normal metal resistances of the junction then one expects only
small shifts in the critical current.
94
a)
b)
Figure 3.9: Critical current behaviour of a Nb-Au-Nb S-N-S TES predicted
by the van Dover-GL model using Equation 3.35. The legend on each of
the graphs indicates different lead-to-lead lengths in meters. a) Assuming
a Au resistivity of ρ = 3.3 · 10−8 Ω ·m and a Au thickness of 30 nm. b)
Assuming a Au resistivity of ρ = 3.3 ·10−8 Ω ·m and a Au thickness of 300
nm. In both cases a Nb transition temperature Tc = 8.4 K and Aρnγρs
= 0.24
is assumed. This model predicts Ic ∼ 0.1 − 10 µA at ∼ 200 mK for a 3
µm long THM device.
95
Figure 3.10: Critical current predictions for a Nb-Au-Nb S-N-S TES for the
Likharev-Usadel, deGennes-GL, Dubos-Usadel and van Dover-GL models.
Here a Nb transition temperature Tc = 8.4 K, Au resistivity of ρ = 3.3 ·
10−8 Ω·m, and Au thickness of 180 nm is assumed for a 3 µm x 3 µm device.
Also plotted for comparison purposes is the critical current behaviour for
a 3 µ long Mo/Au S-S’-S TES, following the Sadleir et al. model and
using their measured fit values for ξi and λr, with TcN = 180 mK. For the
S-N-S case, with a bias current of ∼1 µA, an effective TES Tc of 100-400
mK is expected across the junction.
96
2.0x10-6
4.0x10-6
6.0x10-6
8.0x10-6
1.0x10-5
0.0
0.1
0.2
0.3
0.4
L (m)
30 nm
300 nm
Γ
Figure 3.11: Limiting Γc =Rc
Rjunctionpredicted from Kuprianov-Lukichev-
Usadel theory requiring there be less than 20% change in critical current
due to finite contact resistance between superconducting Nb leads and a
normal Au TES. A Au resistivity of ρ = 3.3·10−8Ω·m, thickness of 30−300
nm, and a 3 µm wide device is assumed at 150 mK. For typical THM test
devices, for Γ . 10−15%, only a small shift in critical current is expected.
97
3.3.10 S-N-S Measurements in the Literature
Sub-micron size S-N-S junctions at Kelvin temperatures, called “microbridges”,
made with Nb superconducting leads and normal metal film junctions have been de-
veloped previously for Josephson junction applications. We now examine this previous
work and the agreement and disagreement to the theories considered here in order to
provide context for measurements of THM S-N-S devices which will be presented in
Chapter 5. This previous work is summarized in Table 3.1.
Warlaumont and Buhrman [121] developed Nb-Cu-Nb microbridges where the
normal metal junctions ranged from 0.2−2 µm in length and the Cu bridge region was
60 nm thick. They claim consistency in magnitude and shape to the Likharev-Usadel
model for these Nb-Cu-Nb devices, although they only explicitly present results for
similarly sized Pb-Cu-Pb devices, where they measure critical currents of 100 µA for
a 0.2 µm device at sub-Kelvin temperatures.
van Dover et al. [120],[119] and de Lozanne et al [18] (both from the same
group) present measurements of Nb-Au-Nb and Nb-Cu-Nb microbridges where the
normal metal junction lengths range from 0.2−1.6 µm and thicknesses from 120−240
nm. They measured a critical current of 0.2 mA at 3.7 K for their longest 1.6 µm
Cu device and a critical current of 1 − 10 mA at sub-Kelvin temperatures for their
0.2 − 0.5 µm long Au devices. To explain measurements where they observed lower
critical currents then expected from the Likharev-Usadel model, they developed the
van Dover-GL model described in the previous section.
van Dover et al. also fit Ic(T ) measurements to the normal metal coherence
98
length parameter, ξN . In this case the normal metal coherence length measured agreed
within a factor of 2 with the predicted normal metal coherence length assuming the
dirty model definition and the measured normal metal resistivity. In all their devices
they measure Aρnγρs
= 0.1 − 0.5, except in one of their devices where they measure
Aρnγρs
= 0.00016, they believe due to poor interface conditions between the Nb and
normal metal. Thus, they find that a poor interface can have striking effects on the
predicted Ic, lowering it by several orders of magnitude in an unpredictable manner.
Sauvageau et al. [99] also fabricated Nb-Cu-Nb junctions, with lengths ranging
from 0.25− 0.8 µm and thicknesses of 50− 100 nm. They also followed a fabrication
procedure where the Cu and Nb depositions where completed in quick succession
without breaking vacuum to avoid contamination at the interface. They measured
critical currents of 70 µA for their longest 0.8 µm device at 1.6 K. They saw Ic
behaviour as a function of temperature which fit the form predicted by all of the S-
N-S models which feature the Ic ∼ exp −Lξn
dependence. Fitting these measurements
to the normal metal coherence length given in the dirty limit, their measurement of
the electron mean free path matched that predicted from the normal metal resistivity
and thickness within a factor of 2. In some devices they measure what appears to be
a residual contact resistance which may be due to contamination at the interface.
Dubos et al. [24] made Nb-Cu-Nb devices with length ranging from 0.7− 1 µm
and thicknesses from 370-670 nm. They measured a critical current of 55 µA near 1 K
for their longest 1 µm device, and critical current of 1 mA near 400 mK for their 0.8
µm long device. The behaviour of the Ic vs. T curve matches the Dubos-GL model
very closely where they fit their measurements to the Thouless energy parameter.
99
Table 3.1: A summary of S-N-S ‘microbridge’ devices which have been
developed previously and which are similar to the Nb-Au-Nb THM design.Group Type Length Typical Ic Theory match
Warlaumont & Buhrman Pb-Au-PB
Nb-Cu-Nb
0.2-2.0 µm 100 µA Likharev-Usadel
van Dover et al. & de
Lozanne et al.
Nb-Cu-Nb
Nb-Au-Nb
0.2-1.6 µm 1-10 mA van Dover-GL
Sauvageau et al. Nb-Cu-Nb 0.25-0.8 µm 70 µA all, ∼ exp −LξN
Dubos et al. Nb-Cu-Nb 0.7-1.0 µm 50 µA-1 mA Dubos-GL
The measured Thouless energy for their model matches that predicted from resistivity
measurements and the thickness by a factor of 1− 3.
3.3.11 Conclusions of Modeling the Lateral Proximity Effect
Measurements of S-N-S and S-S’-S devices have been shown to match behaviour
predicted from semi-microscopic theory. However, there is usually some disagreement
(if small in some cases) between critical current behaviour and measured fit values
for the normal metal coherence length and similar parameters when calculated from
resistivity alone. There also exists uncertainty concerning the role of contact resistance
in measurements of test devices when compared to models which assume a transparent
interface. This concern will be returned to in Chapter 5 when measurements of similar
THM devices are presented. Nevertheless, there is reason to believe that these S-
N-S and S-S’-S models and predictions should give a good indication of the lateral
proximity effect in THM test devices.
100
Chapter 4
The THM Thermal Model & Detector
Optimization
4.1 THM Thermal Model & Noise Sources
The basic design of the THM detector consists of a thin-film semi-metal Bi
microwave absorber/RF termination in contact with a micron-sized superconducting
bilayer Mo/Au TES deposited directly on the detector chip substrate. Nb supercon-
ducting leads provide electrical contact to the TES in order to voltage bias the TES
and also provide for microwave termination. A Nb microstrip transmission line trans-
mits microwave radiation to the detector and terminates in the absorber. This basic
structure is shown in Figure 4.1. Unlike typical bolometers where the thermal link
is controlled by carefully designed and fabricated membrane structures, the thermal
isolation between “hot” electrons in the detector and cooler phonons in the detector
(and detector substrate) is controlled by the weak electron-phonon coupling at low
temperatures within the small THM volume.
There are many different physical processes involved in the THM detector that
101
Nb µstrip
Nb lead
Bi
Absorber
Mo/Au TES
Nb lead
RF power
Dielectric substrate
DC bias leads and
µstrip termination structure
Figure 4.1: The basic geometry of the THM components.
102
affect the heat flow within the detector and the heat flow from the detector to the
colder reservoir. The physical processes for these heat flow mechanisms were described
in Chapter 3. In the complete THM thermal model shown in Figure 4.2 all of these
physical processes are denoted as thermal conductances connecting thermal and/or
physical regions of the detector together. Incoming microwave power is deposited first
in the electrons in the absorber. These electrons are in contact with electrons in the
TES and absorber via Weidemann-Franz scattering, characterized by thermal conduc-
tance, Ge−e. The electrons in both the absorber and TES are in thermal contact with
phonons via electron-phonon scattering, characterized by thermal conductance, Ge−p.
Phonon-phonon scattering occurs at the interface of the absorber and TES with the
detector substrate, and is characterized by thermal conductance, Gboundary. Andreev
reflection due to the energy gap between the superconducting TES with a lower Tc and
the higher Tc leads, and between the normal absorber and superconducting microstrip
line, inhibits heat loss through the leads and transmission line connections, and is
characterized by thermal conductance GAndreev,.
4.1.1 Ideal Model Theory & Noise
In this section, expressions for the noise and responsivity of the THM detector
will now be derived for an ideal thermal model. For this ideal model of the THM
detector the hot-electron thermal conductance, Ge−p, controls the heat-flow from the
bolometer to the substrate and the other paths of thermal heat flow are neglected.
This assumption holds for Ge−p < Ge−e, Gboundary and GAndreev < Ge−p. A schematic
for this ideal thermal model is shown in Figure 4.3. The derivation below follows the
matrix method developed by M. Lindeman [78].
103
Absorber
Electrons
TES
Electrons
RF Power
µstrip
Ge-p
GAndreev Ge-e
Ge-p
TES
Phonons
Absorber
Phonons
Substrate Phonons
Gboundary
GAndreev
Leads
Figure 4.2: The complete thermal model for the THM.
104
G e-p
Tbolo
TES/
Absorber
T bath
P + P signal 0
Pbath
Figure 4.3: The ideal thermal model for the THM detector.
105
The derivation begins with the two electrical and thermal differential equations
in the small signal limit given by Equations 2.18 and 2.19. This time, however, noise
source terms (described in Chapter 2) are also taken into account. Power fluctuations
in the detector due to thermal fluctuations, NEPthermal, and the power fluctuations
inside the detector due to Johnson noise voltage fluctuations of the resistive TES
(NEPJ,TES = I0NEVJ,TES where I0 is the bias current) are added as source terms
in the thermal equation. This TES voltage fluctuation noise, as well as the voltage
fluctuations across the shunt resistor, NEVJ,s, are also added to the source terms in
the electrical equation. It is important to note that only voltage fluctuations inside
the detector and not those which occur outside the detector in the readout circuit
contribute to the power fluctuation source terms. Equations 2.18 and 2.19 become
respectively:
Cd∆T
dt= [
P0α
T0−Ge−p(T0]∆T+(2+β)V0∆I+Psignal+NEPthermal+NEPJ,TES (4.1)
Ld∆I
dt= −V0α
T0∆T + (−Rs − (1 + β)R0)∆I +NEVJ,s −NEVJ,TES. (4.2)
It happens that for bolometer performance one is usually interested in solving
these equations in the frequency domain. This is useful since a bolometric instrument
is usually operated in a chopping mode between a signal and calibrated source at a
particular frequency. Thus at this point a Fourier transform of the equations from
time to frequency space is completed as below:
∆T (t) −→ ∆T (ω) (4.3)
d∆T (t)
dt−→ ıω∆T (ω) (4.4)
∆I(t) −→ ∆I(ω) (4.5)
106
d∆I(t)
dt−→ ıω∆I(ω). (4.6)
The thermal and electrical equations can be written in frequency space as:
ıωC∆T = [P0α
T0−Ge−p(T0)]∆T+(2+β)V0∆I+Psignal+NEPthermal+NEPJ,TES. (4.7)
ıωL∆I = −V0αT0
∆T + (−Rs − (1 + β)R0)∆I +NEVJ,s −NEVJ,TES (4.8)
Dividing both sides of each of the equations above by C and L respectively it becomes
apparent that the two equations can be written in matrix form:
ıω
(
∆T
∆I
)
=
(
P0αT0C
− Ge−p(T0)C
(2+β)V0C
−V0αLT0
−Rs−(1+β)V0L
)
(
∆T
∆I
)
+
(
Psignal+NEPthermal+NEPJ,TES
CNEVJ,s−NEVJ,TES
L
)
(4.9)
Combining the like terms, the expression simplifies to:
M
(
∆T
∆I
)
=
(
Psignal+NEPthermal+NEPJ,TES
CNEVJ,s−NEVJ,TES
L
)
(4.10)
where the matrix M is given by:
M =
(
m1 m2
m3 m4
)
≡(
ıω +Ge−p(T0)
C− P0α
T0C−1(2+β)V0
CV0αLT0
ıω + Rs+(1+β)R0
L
)
. (4.11)
To solve for the response of the THM, the inverse of the matrix M is taken:
(
∆T
∆I
)
=M−1
(
Psignal+NEPthermal+NEPJ,TES
CNEVJ,s−NEVJ,TES
L
)
(4.12)
where M−1 is given by
M−1 =
(
m−11 m−1
2
m−13 m−1
4
)
≡(
m4
m1m4−m2m3
−m2
m1m4−m2m3
−m3
m1m4−m2m3
m1
m1m4−m2m3
)
. (4.13)
The response of the detector to the incoming signal power can now be read off by
completing the matrix multiplication in Equation 4.12 and ignoring the noise terms.
107
The responsivity of the device, S(ω), is defined as the ratio of change in TES current
to a change in input power:
S(ω) ≡ ∆I
Psignal=m−1
3
C(4.14)
where the value ofm−13 in terms of the bolometer properties can be read off from theM
and M−1 definitions in Equations 4.11 & 4.13. The current noise (NEI ≡ 〈∆I ·∆I〉)
also falls out from the matrix equations by completing the matric multiplication and
ignoring the input signal term:
∆I =m−1
3
C(NEPthermal + I0NEVJ,TES) +
m−14
L(NEVJ,s −NEVJ,TES) (4.15)
NEI(ω) = [(m−1
3
C)2(NEP 2
thermal + I20NEV2J,TES)
+(m−1
4
L)2(NEV 2
J,s +NEV 2J,TES)
−m−13 m−1
4 I0CL
NEV 2J,TES +NEI2SQUID]
1
2 . (4.16)
Here only the correlated terms have survived and the uncorrelated current noise from
the SQUID readout has been added directly into the current noise expression at this
point. To convert to an equivalent power fluctuation in the detector one divides by
the responsivity:
NEP (ω) =NEI(ω)
S(ω)(4.17)
The results for responsivity, NEI and NEP will be left in this form, however
the matrix elements can be read off from Equations 4.11 and 4.13. The expressions
for the noise terms, NEVJ,TES, NEVJ,s, NEPthermal are given by Equation 2.23, 2.24
and 2.27. For the case of a THM with a Au or Mo/Au TES with Au volume VTES
108
and a Bi absorbing structure with volume VAbs, Ge−p(T ) = ne−pκe−pTne−p−1 where
κe−p = ΣAuVTES + ΣBiVAbs.
4.1.2 Non-Ideal Model Theory & Noise
In this section, the noise and response of the THM detector will now be derived
for a thermal model of a device which is not “ideal”. Specifically, we will examine the
situation where the thermal conductance due to electron-electron scattering within
the detector is on the same order as the electron-phonon thermal conductance within
the detector (Ge−p & Ge−e). The other thermal conductances will continue to be
neglected. In this situation the THM detector is no longer in thermal equilibrium and
the absorber and TES must be divided into multiple thermal sections, each with its
own temperature.
An example of such a thermal model for a non-ideal, thermally disconnected
THM is shown in Figure 4.4 where a large absorber is divided into three parts. The
specific manner of thermal disconnection in this model matches that of THM test de-
vices of variation ‘THM2003’ which are described and presented in Chapter 5. How-
ever, other types of thermal disconnection or other geometries will lead to similar
effects on the THM response and noise, and the method of calculating these proper-
ties would follow the method described here. Two effects result from this thermally
disconnected model: additional noise terms arise from internal thermal fluctuations,
and the detector responsivity is reduced because some of the incident power to the
device bypasses the TES.
In this particular non-ideal THM the incoming signal power is dissipated evenly
along the absorber structure except in the central thermal region which overlaps the
109
Absorber End
T abs
½ Psignal ½ Psignal P 0
G e - p G e - p
T c
TES/ Central
Absorber
G e - e
G e - p
T bath
T abs Absorber
End
G e - e
Figure 4.4: A thermal model for a non-ideal THM.
TES. Due to the symmetry of the power dissipation in this device the thermal model
can be simplified to that shown in Figure 4.5. Here G1(T ) = ne−pκe−p,1Tne−p−1,
G2(T ) = ne−pκe−p,2Tn−1 and G3(T ) = ne−eκe−eT
ne−e−1. κe−p,1 = ΣBi23VAbs, κe−p,2 =
ΣBi13VAbs + ΣAuVTES and κe−e = 8L0
3RAbsfor this particular ‘THM2003’ device, where
RAbs is the total resistance across the absorber (see Chapter 5 for a description of this
device geometry) and ne−e = 2. Each section has a composite heat capacity of C1 and
C2.
To derive the noise and responsivity for this non-ideal THM one must take a
step back from the electrical and thermal equations simplified and applied in the low
signal limit that are given by Equations 2.18 and 2.19, as now there is more than one
temperature variable and more than one region of the detector to account for. For
section ‘1’ of the detector the thermal differential equation is:
C1dT1dt
= Psignal − Pbath,1 − P12. (4.18)
Here Pbath,1 is the net power flow out of part ‘1’ to the cold bath, and P12 is the net
110
P0 Psignal
G 1
T1
TES/ Central
Absorber
G2
T bath
Absorber Ends
G3
C1 T2 C2
Pbath,1 Pbath,2
P12
Figure 4.5: The non-ideal THM thermal model, simplified by the symme-
try of the device.
power flow out of part ‘1’ to part ‘2’. All the signal power is dissipated in the absorber
ends. This equation can be written more explicitly as:
C1dT1dt
= Psignal − κe−p,1(Tne−p
1 − Tne−p
bath )− κe−e(Tne−e
1 − Tne−e
2 ) (4.19)
A similar thermal differential equation for section ‘2’ of the detector can be written
as:
C2dT2dt
= P0 − Pbath,2 + P12 (4.20)
C2dT2dt
= I2TESRTES(ITES, T2)− κe−p,2(Tne−p
2 − Tne−p
bath ) + κe−e(Tne−e
2 − Tne−e
1 ). (4.21)
Here it is assumed that the signal power dissipation, Psignal, bypasses the central part
of the absorber because for this THM variation the absorber is short-circuited by
the low-resistance TES; there is no signal power source term and only Joule power
111
dissipation, P0. The electrical equation describing the TES behaviour remains the
same as in the ideal case:
LdITESdt
= V − ITESRs − ITESRTES(ITES, T2). (4.22)
A Taylor expansion of these three equations is completed as before in order to examine
the low-signal/linear limit, in terms of ∆T1 , ∆T2 and ∆I:
∆I = ITES − I0 (4.23)
∆T1 = T1 − T0,1 (4.24)
∆T2 = T2 − T0,2. (4.25)
Here I0, T0,1 and T0,2 are the equilibrium values with only bias power dissipation in
the device due to a voltage bias, V0. Completing a Taylor expansion of Equations
4.19, 4.21 and 4.22 results in:
C1dT1dt
≈ ∂
∂T1[−κe−p,1(T ne−p
1 − Tne−p
bath )− κe−e(Tne−e
1 − Tne−e
2 )]0∆T1
+∂
∂T2[−κe−p,1(T ne−p
1 − Tne−p
bath )− κe−e(Tne−e
1 − Tne−e
2 )]0∆T2
+Psignal (4.26)
C2dT2dt
≈ ∂
∂T1[−κe−p,2(T ne−p
2 − Tne−p
bath )− κe−e(Tne−e
2 − Tne−e
1 )]0∆T1
+∂
∂T2[−κe−p,2(T ne−p
2 − Tne−p
bath )− κe−e(Tne−e
2 − Tne−e
1 )]0∆T2
+∂
∂ITES[I2TESRTES(ITES, T2)]0∆I
+∂
∂T2[I2TESRTES(ITES, T2)]0∆T2 (4.27)
LdITESdt
≈ ∂
∂T2[−ITESRTES(ITES, T2)]0∆T2
+∂
∂ITES[−ITESRs − ITESRTES(ITES, T2)]0∆I. (4.28)
112
After partial differentiation, these equations become:
C1d∆T1dt
= −ne−pκe−p,1T ne−p−11,0 ∆T1 − ne−eκe−eT
ne−e−11,0 ∆T1 + ne−eκe−eT
ne−e−12,0 ∆T2
+Psignal (4.29)
C2d∆T2dt
= −ne−pκe−p,2T ne−p−12,0 ∆T1 − ne−eκe−eT
ne,e−12,0 ∆T2
+ne−eκe−eTne−e−11,0 ∆T1 + I20
∂RTES(ITES, T2)
∂T2|0 ∆T2
+2I0RTES(I0, T2,0)∆I + I20∂RTES(ITES, T2)
∂ITES|0 ∆I (4.30)
Ld∆I
dt= −I0
∂RTES(ITES, T2)
∂T2|0 ∆T2
+[−Rs −RTES(I0, T2,0)− I0∂RTES(ITES, T2,0)
∂ITES|0]∆I. (4.31)
When these equations are written in terms of the thermal conductances G1, G2 and
G3, and α and β, they become:
C1d∆T1dt
= [−G1(T1,0)−G3(T1,0)]∆T1 +G3(T2,0)∆T2 + Psignal (4.32)
C2d∆T2dt
= G3(T1,0)∆T1 + [−G2(T2,0)−G3(T2,0) +P0α
T2,0]∆T2 + (2 + β)V0∆I (4.33)
Ld∆I
dt= −V0α
T2,0∆T2 + (−Rs − (1 + β)R0)∆I. (4.34)
Here, R0 ≡ RTES(I0, T2,0).
The noise sources for this thermally disconnected model will now be considered.
There are now thermal power fluctuations across three thermal paths: NEPthermal,1,
NEPthermal,2, NEPthermal,3. Here NEPthermal,1 is the thermal fluctuation noise be-
tween region ‘1’ at temperature T1 and the bath at temperature Tbath. NEPthermal,2
is the thermal fluctuation noise between region ‘2’ at temperature T2 and the bath at
113
temperature Tbath. NEPthermal,3 is the thermal fluctuation noise between region ‘1’ at
temperature T1 and region ‘2’ at temperature T2. Adding these source noise terms,
along with the Johnson noise terms, to the three differential equations they become:
C1d∆T1dt
= [−G1(T1,0)−G3(T1,0)]∆T1 +G3(T2,0)∆T2 + Psignal
+NEPthermal,1 +NEPthermal,3 (4.35)
C2d∆T2dt
= G3(T1,0)∆T1 + [−G2(T2,0)−G3(T2,0) +P0α
T2,0]∆T2
+(2 + β)V0∆I +NEPthermal,2 −NEPthermal,3
+I0NEVJ,TES (4.36)
Ld∆I
dt= −V0α
T2,0∆T2 + (−Rs − (1 + β)R0)∆I +NEVJ,s −NEVJ,TES (4.37)
A Fourier transform to frequency space is again completed:
∆T1(t) −→ ∆T1(ω) (4.38)
d∆T1(t)
dt−→ ıω∆T1(ω) (4.39)
∆T2(t) −→ ∆T2(ω) (4.40)
d∆T2(t)
dt−→ ıω∆T2(ω) (4.41)
∆I(t) −→ ∆I(ω) (4.42)
d∆I(t)
dt−→ ıω∆I(ω) (4.43)
In frequency space, the three differential equations become:
ıωC1∆T1 = [−G1(T1,0)−G3(T1,0)]∆T1 +G3(T2,0)∆T2 + Psignal
+NEPthermal,1 +NEPthermal,3 (4.44)
114
ıωC2∆T2 = [−G2(T2,0)−G3(T2,0) +P0α
T2,0]∆T2 +G3(T1,0)∆T1
+(2 + β)V0∆I +NEPthermal,2 −NEPthermal,3
+I0NEVJ,TES (4.45)
ıωL∆I = −V0αT2,0
∆T2 + (−Rs − (1 + β)R0)∆I +NEVJ,s −NEVJ,TES. (4.46)
After some rearrangement this becomes:
ıω∆T1 =−G1(T1,0)−G3(T1,0)
C1∆T1 +
G3(T2,0)
C1∆T2
+Psignal +NEPthermal,1 +NEPthermal,3
C1(4.47)
ıω∆T2 =G3(T1,0)
C2∆T1 +
−G2(T2,0)−G3(T2,0) +P0αT2,0
C2∆T2 +
(2 + β)V0C2
∆I
+NEPthermal,2 −NEPthermal,3 + I0NEVJ,TES
C2(4.48)
ıωL∆I = − V0α
LT2,0∆T2 +
−Rs − (1 + β)R0
L∆I +
NEVJ,s −NEVJ,TESL
. (4.49)
Writing these equations into matrix equation form:
ıω
∆T1∆T2∆I
=
G1(T1,0)−G3(T1,0)
C1
G3(T2,0)
C10
G3(T1,0)
C2
−G2(T2,0)−G3(T2,0)+PαT2,0
C2
(2+β)V0C2
0 −V0αLT2,0
−Rs−(1+β)R0
L
∆T1∆T2∆I
+
Psignal+NEPthermal,1+NEPthermal,3
C1
NEPthermal,2−NEPthermal,3+I0NEVJ,TES
C2
NEVJ,s−NEVJ,TES
L
(4.50)
After rearranging, this matrix equation becomes:
M
∆T1∆T2∆I
=
Psignal+NEPthermal,1+NEPthermal,3
C1
NEPthermal,2−NEPthermal,3+I0NEVJ,TES
C2
NEVJ,s−NEVJ,TES
L
(4.51)
115
where the matrix M is defined as:
M =
m1 m2 m3
m4 m5 m6
m7 m8 m9
≡
ıω +G1(T1,0)+G3(T1,0)
C1G3(T2,0) 0
−G3(T1,0)
C2ıω +
G2(T2,0)+G3(T2,0)
C2− P0α
T2,0C2− (2+β)V0
C2
0 V0αLT2,0
ıω + Rs+(1+β)R0
L
. (4.52)
After inverting the matrix, this equation can be solved for the bolometer response in
the non-ideal case:
∆T1∆T2∆I
=M−1
Psignal+NEPthermal,1+NEPthermal,3
C1
NEPthermal,2−NEPthermal,3+I0NEVJ,TES
C2
NEVJ,s−NEVJ,TES
L
(4.53)
where the inverse matrix, M−1 is defined as
M−1 =
m−11 m−1
2 m−13
m−14 m−1
5 m−16
m−17 m−1
8 m−19
. (4.54)
Following the same procedure as before in the ideal case, completing the matrix mul-
tiplication, ignoring the noise terms, the relation for responsivity can be read off:
S(ω) ≡ ∆I
Psignal=m−1
7
C1. (4.55)
The detector current noise, NEI, can also be read off from the equation, ignoring the
signal power and inserting the uncorrelated SQUID current noise directly into the
solution at this point:
NEI(ω) = [(m−1
7
C1
)2(NEP 2thermal,1 +NEP 2
thermal,3)
+(m−1
8
C2
)2(NEP 2thermal,2 +NEP 2
thermal,3 + I20NEV2J,TES)
+(m−1
9
L2)2(NEV 2
J,s +NEV 2J,TES)−
m−17 m−1
8
C1C2
NEP 2thermal,3
−m−18 m−1
9
C2LNEV 2
J,TES +NEISQUID]1
2 . (4.56)
116
Finally, the detector NEP in given by:
NEP (ω) =NEI(ω)
S(ω). (4.57)
A conclusion of this derivation is that the noise performance of the THM suffers
in the thermally disconnected detector model. Additional noise terms arise due to
thermal power fluctuations between the thermally disconnected regions in the detector.
In addition, the responsivity of the device decreases due to some of the power bypassing
the TES. These effects will be confirmed in measurements of a THM test device in
Chapter 5. An important part of optimizing the THM design will be to require
that the electron-phonon thermal conductance of the THM be less than the internal
electron-electron thermal conductance across the detector. As the electron-electron
Wiedemann-Franz conductance scales inversely with the resistance, this translates
into keeping the resistance of the TES and absorber low. This constraint will be
parametrized in more detail in Section 4.2.5.
4.2 Thermal & Microwave Optimization
In the second part of this chapter the specific optimization concerns for the
THM detector will now be detailed. One of these concerns is detector optimization to
obtain a thermally ‘ideal’ device, however, there are also additional concerns related
to obtaining background limited noise performance. Other concerns which must be
considered in the THM design include more practical constraints on the detector
design in order to simplify fabrication and the microwave coupling design. Before this
detailed optimization of the THM design is presented, however, the specific observing
and operating conditions which will be assumed, and which are specific to optimizing
117
the THM detector for CMB observing, are presented.
4.2.1 Photon Background Noise & Detector Loading Conditions
To calculate the loading power on a THM detector observing the CMB from
space one starts by calculating the photon occupation number for the CMB blackbody
source which follows Bose-Einstein statistics [92]:
n0 =ε
ehν
kTbb − 1. (4.58)
Here ε is the emissivity of the blackbody, ν is the observation frequency, and Tbb is
the blackbody temperature. The sky power that is absorbed by the detector when
observing this blackbody source is given by:
Psky = hνηn0∆ν
νν (4.59)
for the single-mode case, where ∆νν
is the fractional bandwidth and η is the optical effi-
ciency. The photon noise under these blackbody loading conditions can be calculated
using the expression given by Equation 2.22.
We now consider two different background conditions for observing the CMB:
from ground and space. Observing the CMB blackbody with Tbb = 2.7 K, at ν =92
GHz from space, assuming a 50% optical efficiency and a broad bandwidth of 20%,
the background photon noise is NEPphoton = 4.3 · 10−18 W√Hz
and the power loading
from the sky is Psky = 1.4 · 10−13 W. Observing the CMB blackbody at 92 GHz from
the ground (with additional sky background which mimics an effective blackbody of
temperature Tbb = 25 K) and assuming a 50% optical efficiency and a broad bandwidth
of 20%, the background photon noise is NEPphoton = 3.6 · 10−17 W√Hz
and the power
loading from the ground is Psky = 2.9 · 10−12 W. These two observing conditions will
118
be designated ‘CMB-ground’ and ‘CMB-Space’ in this chapter and in later chapters
of this thesis.
In addition to these two CMB observing conditions, for comparison purposes
in Sections 4.2.8 and 4.2.9 of this chapter, and later when measurements of actual
test devices are presented in Chapter 5, the THM’s performance under the CMB
observing conditions described above will be compared to its performance when ob-
serving the far-infrared sky from space. As was discussed in Section 1.1.4, observing in
the far-infrared is another application of great scientific interest for hot-electron type
bolometers. For observations of spectral lines in the far-infrared, the background power
loading is much lower than the CMB power loading, and the detector performance and
optimization criteria are very different. For the ‘FIR-spectral’ observing case, we as-
sume an observed Psky = 6.6 · 10−20 W from space at 1 THz, assuming 25% optical
efficiency and a narrow bandwidth of 0.1% corresponding to a resolving power of ν∆ν
.
The background photon noise for these observing conditions is NEPphoton = 1 · 10−20
W√Hz
.
For optimization purposes and later for measurement comparison, throughout
this thesis an electrical bias power of twice the sky background power, P0 = 2Psky, will
be assumed for ‘CMB-ground’, ‘CMB-space’ and ‘FIR-spectral’ observing. Through-
out this thesis we will also consider two bath temperatures: Tbath = 240 mK, cor-
responding to a bath temperature easily obtainable using a 3He sorption fridge, and
Tbath = 50 mK corresponding to a lower bath temperature obtainable using an Adi-
abatic Demagnetization Refrigerator (ADR), for example. For optimization purposes
we will also assume specific values for the electron-phonon material coefficient Σ, cor-
119
responding to average ‘literature values’ (ΣAu = 4.2 · 109 Wm3K5 and ΣBi = 2.4 · 108
Wm3K5 , see Section 3.1.2) and measured values corresponding to THM test device re-
sults for ‘measured n = 5’ (ΣAu = 1.0 · 109 Wm3K5 and ΣBi = 3.0 · 108 W
m3K5 , see test
device ‘THM2003’ in Section 5.3) and ‘measured n = 6’ (ΣAu = 1.5 · 108 Wm3K6 and
ΣBi = 8.8 · 106 Wm3K6 , see test device ‘us25’ in Section 5.4).
4.2.2 Microwave Circuit Constraints
To couple incoming radiation from free space to the small volume of the THM
detector an optical coupling scheme is necessary as coupling from free space directly
into the small bismuth absorber is inefficient. This optical coupling method needs to
provide a directed beam pattern on the sky. One would also like to create filters to
define the the detection bandwidth and polarizers to provide polarization sensitivity.
One way to accomplish this is to optically couple the incoming radiation to a planar
antenna which is much larger than the absorber and to transmit the signal to the
THM detector via planar transmission lines. Optical coupling via a horn antenna and
waveguide transmission line is another possible method. For present purposes we will
consider a microwave coupling scheme which only incorporates a planar antenna which
couples to a planar microstrip transmission line. In Chapter 6, however, an optical
scheme which incorporates additional optical components in order to provide efficient
optical coupling to a microwave source will be presented.
A planar transmission line is a compact way to transmit microwaves. Unlike
transmission in a waveguide, the electromagnetic fields are transmitted on a scale
much smaller than the radiation wavelength. A superconducting transmission line
also provides a low loss method to transmit the signal from one location to another.
120
In addition, it is possible to design microwave structures such as filters, couplers, and
terminations on a chip, allowing for the possibility to build a polarimeter (with a
polarization sensitive antenna and filter) on a single chip.
In the microwave design for the THM we have chosen to transmit the signal via a
superconducting microstrip transmission line which terminates on the THM absorber
as shown in Figure 4.1. More details of this microwave design and the coupling from a
planar antenna to the THM detector are given in Chapter 6. A microstrip termination
structure, which will also be described in Chapter 6, allows for the abrupt termination
of microwave power in the THM absorber.
A microstrip transmission line consists of a narrow conducting microstrip line
over a dielectrically insulated conducting ground plane as shown in Figure 4.6. The
characteristic impedance of a microstripline follows the form of [91]:
Zmicrostrip =120π
√ǫe[
Wd+ 1.393 + 0.667 ln W
d+ 1.444]
. (4.60)
Here ǫe is the effective dielectric constant of the dielectric between the ground plane
and microstrip line and is given by:
ǫe =ǫr + 1
2+ǫr − 1
2
1√
1 + 12dW
(4.61)
where ǫr is the relative dielectric constant, W is the microstrip width, and d is the
dielectric thickness.
The microstrip termination structure and the constraints this places on the ab-
sorber geometry and resistivity of the THM must be considered. Impedance matching
between the terminating microstrip characteristic impedance and the absorber resis-
tance is required. The width of the absorber must also match the microstrip width.
121
µstrip line
dielectricd
ground plane
W
Figure 4.6: Microstrip line geometry.
Thus there is a double constraint on the dimensions and resistivity of the absorber.
As will be detailed in the following sections, we would generally like to make the ab-
sorber as small as possible in order to minimize the electron-phonon conductance of
the bolometer for minimal thermal noise. A small microstrip/absorber width (higher
impedance) is compatible with this small absorber. An optimal size is a square,
micron-sized absorber coupling to micron-sized Nb microstrip line. A square absorber
of evaporated bismuth with resistance ∼ 20− 30 Ω (with thickness 0.8-1 µm) couples
well to a 3 µm wide Nb microstripline with characteristic impedance ∼ 20− 30 Ω on
a silicon or alumina dielectric of thickness ∼ 0.75− 1.5 µm.
4.2.3 Fabrication & Material Constraints
In the exploration of the THM design in this thesis we have only considered
device geometries obtainable by standard photolithography and fabrication techniques.
These fabrication processes are discussed in more detail in Chapter 5 when all of the
THM test devices are described. The main constraint these fabrication processes
122
impose is on the minimum square-area of the THM detector. Structures less than
2− 3 µm in size are not easily obtained with standard photolithography, and smaller
sizes are only possible by making use of e-beam lithography. As will be demonstrated
in this chapter, although a small size is usually desirable to minimize electron-phonon
coupling, other effects such as heating, and a strong lateral proximity effect from the
Nb leads will conspire to make the optimal absorber and TES size occur at, or above,
this photolithography size limit for CMB observing.
The material choice for the THM is a Mo/Au or Au superconducting TES and a
semi-metal Bi absorber. Bismuth was chosen both for its high resistivity at cryogenic
temperatures for impedance matching to the microstrip transmission line, and its low
electron-phonon coupling coefficient, Σ. A Mo/Au bilayer was chosen for the TES
due to the reliability of the Mo/Au bilayer system for obtaining precise transition
temperatures for the TES, as discussed in Sections 3.3.6 and 5.1.
4.2.4 Stability Constraints & Optimal Bias Conditions
Even with negative feedback a TES can become unstable if electrothermal fluc-
tuations are phase shifted in the feedback process. The requirements for stability are
given by Equations 2.20 and 2.21 and are determined by the time response of the
thermal and electrical circuits of the THM detector. We now investigate what con-
straints if any this places on the design of the THM bias circuit. In particular, we are
concerned with the inductance, L, the TES resistance, RTES, and the bias power, P0.
The second of these stability equations (Equation 2.21) indicates that for any
design or application, as the inductance in the readout circuit increases, the device
becomes less stable. As the load resistance and TES resistance increase (as long as
123
Rs ≪ RTES) the device becomes more stable (for a constant voltage bias, or constant
Joule power dissipation). For a THM device with a minimum volume absorber (3
µm x 6 µm x 800 nm), and a square TES (assuming RTES = 0.1 Ω) for both ground
and space-based observing conditions, stability requirements are met when L ≤ 10
nH−1 µH. This can be seen in Figure 4.7, where the left and right sides of Equation
2.21 are plotted for a 20 µm2 and 3 µm2 TES for ‘CMB-ground’ and ‘CMB-space’
loading conditions, respectively. As long as the inductance of the circuit is kept below
these limits the geometry and the operating conditions (such as the bath temperature
and bias power) of the THM detector are unconstrained. Typical single dc SQUID
amplifier readouts regularly obtain input inductances of L ∼ 1 nH-100 pH. However,
it should also be noted that SQUID current noise (see equation 2.25) also increases
with a low input inductance, and a balance between stability and current noise may
be necessary to consider when designing the SQUID readout.
The stability does not place any constraints on the bias power in principle.
However, the TES voltage bias should be chosen so that the TES is in the small
signal/linear regime. The responsivity is dependent on the bias conditions, but the
detector NEP, if thermally dominated, is independent of responsivity and bias power.
If the bias power is too high, however, heating occurs in the detector and the thermal
noise rises due to its temperature dependence. The degrading effect of this heating on
the thermal noise of the detector will be shown in more detail in Section 4.2.8.
4.2.5 Electron-Phonon Versus Electron-Electron
As argued in Section 4.1.2 an important component of the THM device opti-
mization is to require an ideal thermal design, where Gee > Gep, to avoid thermal
124
(a)
r.h.s
l.h.s
(b)
r.h.s
l.h.s
r.h.s
l.h.s
(c)
r.h.s
l.h.s
(d)
(H) (H)
(H)(H)
tim
e (
s)
tim
e (
s)
tim
e (
s)
tim
e (
s)
Figure 4.7: Stability limits on the SQUID readout input inductance, L.
The r.h.s. and l.h.s of Equation 2.21 are plotted and the maximum L for
stability is given by the point where the lines cross. (a) 20 µm2 TES,
assuming ‘CMB-ground’ conditions, for Tbath = 240 mK.(b) 20 µm2 TES,
assuming ‘CMB-space’ conditions, for Tbath = 50 mK. (c) 3 µm2 TES,
assuming ‘CMB-ground’ conditions, for Tbath = 240 mK.(d) 3 µm2 TES,
assuming ‘CMB-space’ conditions, for Tbath = 50 mK. ‘CMB-ground’ re-
sults are similar for Tbath = 50 mK. For these THM designs, stability
requires L ≤ 10 nH−1 µH.
125
disconnection within the detector and reductions to responsivity and sensitivity. To
illustrate this optimization we now consider a generic THM with a Mo/Au TES and
Bi absorber and examine what happens to the thermal conductances when the size
and/or resistance of the TES and absorber are varied. There are of course many
design variations possible which will meet this optimization requirement. The exer-
cises in this section are only to demonstrate the procedure and thought process for
THM optimization. As was noted in Section 4.2.2 both the absorber resistance and
the geometry of the absorber must be optimized to match the microstrip impedance.
However for the time being we will separate these two issues and only examine the
thermal properties due to the absorber resistance.
First we examine what happens when the absorber resistance is varied by ad-
justing the absorber length. In this case we assume a fixed Mo/Au TES geometry
with 300 nm thick Au layer, and a Au area of 10 µm x 10 µm. We also assume a Bi
absorber of a fixed width of 3 µm and thickness of 800 nm (resulting in ρ ∼ 30 Ω)
with a variable length which changes the absorber resistance, RAbs. The requirement
for an ideal model, such that there be no thermal disconnection across the absorber,
is that the total electron-phonon conductance of the detector, Ge−p ≪ Ge−e, where
Ge−e is the electron-electron conductance across the absorber. The requirement for
no power bypassing the TES is less stringent: Ge−p,Abs ≪ Ge−e, where Ge−p,Abs is the
electron-phonon thermal conductance of the absorber only. In Figure 4.8 these three
thermal conductances are plotted for a few typical THM designs. For these designs
RAbs . 80− 100 Ω is required to avoid power bypassing the TES, and RAbs . 3− 80
Ω is required to avoid a temperature differential across the absorber.
126
s
Ge-p
Ge-p, Abs
Ge-e
G (
W/
K)
(Ω)
(c)
G (
W/
K)
Ge-p
Ge-e
Ge-p, Abs
(a) (b)
G (
W/
K)
Ge-p, Abs
Ge-e
Ge-p
ss (Ω) (Ω)
Figure 4.8: The electron-phonon conductance of the combined TES and
absorber structure, Ge−p, the electron-electron conductance across the en-
tire TES and absorbing structure (absorber dominated in this case), Ge−e,
and the electron-phonon conductance of the absorber only, Ge−p,Abs plot-
ted as a function of absorber resistance, RAbs. Here we have assumed a 10
µm x 10 µm x 300 nm Au TES and a 3 µm wide, 800 nm thick, Bi absorber.
For electron-phonon thermal conductance we have assumed n = 5 and ‘lit-
erature values’ for Σs. (a) ‘CMB-ground’ conditions and Tbath = 240 mK
(b) ‘CMB-ground’ conditions and Tbath = 50 mK (c) ‘CMB-space’ condi-
tions and Tbath = 50 mK. For these designs RAbs . 80− 100 Ω is required
to avoid power bypassing the TES, and RAbs . 3 − 80 Ω is required to
avoid a temperature differential across the absorber.
127
This power separation in the detector as a function of this absorber resistance
can also be estimated. Assuming a similar and/or small temperature difference be-
tween the bath and absorber and absorber and TES, the fraction of incoming power
dissipated in the absorber which then flows through the TES, PTES, can be approx-
imated by PTES ∼ Ge−e
Ge−e+Ge−p,Abs. Plots of this power fraction are shown in Figure
4.9 for the same device assumptions used in Figure 4.8. For 80 − 100% power flow
through the TES, RAbs . 40− 100 Ω is required. Note that although this calculation
gives a useful indication of the power-loss effect, the true power ratio must be more
accurately calculated by doing a full responsivity calculation, assuming an appropriate
disconnected thermal model.
The dependence of these thermal conductances on the TES resistance can also
be examined. In Figure 4.10 the value of the electron-phonon conductance of the
entire detector, Ge−p is plotted against the electron-electron conductance across the
TES, Ge−e,TES, as a function of TES resistance, RTES. In this case we assume a fixed
Bi absorber geometry of 3 µm x 6 µm x 800 nm. We also assume a Mo/Au TES of a
fixed width of 10 µm and thickness of 300 nm (resulting in ρ ∼ 0.1 Ω) with a variable
length which changes with RTES. Requiring Ge−p < Ge−e,TES gives a constraint of
RTES < 0.5− 5 Ω for a typical THM device.
In addition to exploring this effect in terms of a constraint on the absorber or
TES resistance, it can also be explored in terms of its constraint on the geometry of the
THM. In Figure 4.11 the thermal conductances are plotted for a square TES device
(RTES = 0.1 Ω) as a function of TES width, wAu, assuming a fixed absorber geometry
with an absorber resistance that dominates the total device resistance (RAbs = 30 Ω).
128
(c)
(Ω)s
PT
ES
PT
ES
(Ω)s
(b)(Ω)s
(a)
PT
ES
Figure 4.9: The estimated fraction of power which flows through the TES
(PTES ∼ Ge−e
Ge−e+Ge−p) as a function of absorber resistance, RAbs. Here we
have assumed a 10 µm x 10 µm x 300 nm Au TES and a 3 µm wide, 800
nm thick, Bi absorber. For electron-phonon thermal conductance we have
assumed n = 5 and literature Σ values. (a) ‘CMB-ground’ conditions
and Tbath = 240 mK (b) ‘CMB-ground’ conditions and Tbath = 50 mK
(c) ‘CMB-space’ conditions and Tbath = 50 mK. For these designs Rabs .
40 − 100 Ω is necessary to obtain at least 80 − 100% power flow through
the TES.
129
(c)(Ω)
(Ω)
(b)(Ω)
(a)
G (
W/
K)
Ge-p
Ge-e,TES
Ge-e,TES
Ge-p
Ge-p
Ge-e,TES
G (
W/
K)
G (
W/
K)
Figure 4.10: The TES electron-electron thermal conductance, Ge−e,TES
plotted with the total electron-phonon thermal conductance, Ge−p, as a
function of TES resistance, RTES. In this case we assume a Bi absorber
geometry of 3 µm x 6 µm x 800 nm. We also assume a Mo/Au TES of
a fixed width 10 µm and thickness of 300 nm (resulting in ρ ∼0.1 Ω).
For electron-phonon thermal conductance we have assumed n = 5 and
literature Σ values. (a) ‘CMB-ground’ conditions and Tbath = 240 mK (b)
‘CMB-ground’ conditions and Tbath = 50 mK (c) ‘CMB-space’ conditions
and Tbath = 50 mK. Requiring Ge−p < Ge−e,TES, gives a constraint of
RTES < 0.5− 5 Ω depending on the application and bath temperature.
130
For these THM designs wAu . 1−20 µm is required to avoid a temperature differential
across the absorber (requiring Ge−e > Ge−p), but there is no requirement for wAu to
avoid power bypassing the TES (requiring Ge−e > Ge−p,Abs).
It should be noted that the usually cited requirement against self-heating and
a phase differential between superconducting and normal regions in a TES detector
due to this same effect of electron-electron scattering vs. electron-phonon scattering
(RTES ≤ π2L0TcG
nα) [51] gives a similar resistance requirement as is calculated here
for the more naive Ge−e > Ge−p requirement. Following the same THM design as-
sumptions as in Figure 4.10 this self-heating stability requirement gives optimal TES
resistance: RTES ≤ 0.4 Ω for Tbath = 240 mK and RTES ≤ 3 Ω for Tbath = 50 mK,
assuming n = 5 and α = 100.
4.2.6 Phonon-Phonon Versus Electron-Phonon
Thus far the phonon-phonon boundary thermal resistance between phonons in
the detector and the detector substrate/cold-stage has been neglected in our opti-
mization concerns. To do so we have assumed that the electron-phonon conductance
between the electrons to the phonons in the detector, Ge−p, is much smaller than the
phonon-phonon conductance between the detector phonons and substrate phonons,
Gboundary. This assumption will now be examined by comparing predictions for Ge−p
and Gboundary for the THM detector. Here we assume that the boundary thermal con-
ductance is given by Equation 3.7. Again, we assume a minimal Bi absorber of size 3
µm x 6 µm x 800 nm and a square Mo/Au TES with a Au thickness of 300 nm and
examine the thermal conductances dependence on TES width, wAu. In Figure 4.12
the relevant thermal conductances are compared for various bath temperatures and
131
(c)
Ge-p
Ge-e
Ge-p, Abs
G (
W/
K)
(m)
(a)
G (
W/
K)
Ge-p
Ge-e
Ge-p, Abs
G (
W/
K)
(b)
Ge-p
Ge-e
Ge-p, Abs
(m) (m)
Figure 4.11: The total electron-electron thermal conductance across the
absorber and TES, Ge−e, plotted with the total electron-phonon ther-
mal conductance, Ge−p, and the absorber electron-phonon conductance,
Ge−p,Abs, as a function of TES width, wAu, for a square Mo/Au TES with
Au thickness 300 nm. Here we have assumed a 3 µm x 6 µm x 800 nm
Bi absorber for RAbs = 30 Ω. For electron-phonon thermal conductance
we have assumed n = 5 and literature Σ values. (a) ‘CMB-ground’ con-
ditions and Tbath = 240 mK (b) ‘CMB-ground’ conditions and Tbath = 50
mK (c) ‘CMB-space’ conditions and Tbath = 50 mK. For these designs
wAu . 1 − 20 µm is required to avoid a temperature differential across
the absorber (requiring Ge−e > Ge−p). There is no requirement to avoid
power bypassing the TES (requiring Ge−e > Ge−p,Abs).
132
loading conditions. The total thermal conductance of the THM, Gtot (summing Ge−p
and Gboundary in series), is also plotted.
From Figure 4.12 one can see that the boundary conductance is predicted to have
some impact or even dominate the total thermal conductance (Ge−p ≥ Gboundary) over
the full range of TES size scales for ground and space observing conditions. As was
discussed in Chapter 3, however, there is some dispute to whether this prediction for
Gboundary is correct for thin films like the THM detector and there are arguments that
the actual boundary thermal conductance may be higher for thin films or that there
will be no effective boundary resistance at all since the phonons in the detector may
be considered as the same system as the substrate phonons. Thus we will allow for the
possibility that phonon-phonon boundary scattering plays some role in the thermal
bottleneck of the THM bolometer and look for confirmation in the temperature power-
law dependence of the thermal conductance measurements of actual THM devices
(n = 4 for boundary conductance, n = 4 − 6 for electron-phonon conductance) in
order to disprove or prove a hot-electron dominated assumption for the THM.
4.2.7 SQUID & Johnson Noise Constraints
Although for the remainder of the chapter we will consider device performance
where the detector noise is dominated by thermal fluctuation noise we now briefly
discuss the situations when this is not the case and the limits this places on the TES
resistance. In Figure 4.13 the NEP contributions to detector noise from the SQUID
readout and Johnson noise from the TES resistor and a shunt resistor in the bias
circuit are plotted as a function of TES resistance assuming a THM with a minimal Bi
absorber of size 3 µm x 6 µm x 800 nm and a 3 µm wide Mo/Au TES with Au thickness
133
(a)(m)
G (
W/
K)
Ge-p
Gboundary
Gtot
(m)
(b)
Gboundary
Ge-p
Gtot
G (
W/
K)
(c)(m)
G (
W/
K)
Gboundary
Ge-p
Gtot
Figure 4.12: The electron-phonon thermal conductance, Ge−p, boundary
thermal conductance, Gboundary, and total thermal conductance Gtot, of a
THM detector as a function of TES width, wAu. Here we have assumed
a Bi absorber of size 3 µm x 6 µm x 800 nm and a square Mo/Au TES
with a Au thickness of 300 nm. We have assumed n = 5 and coupling
‘literature values’ for Σs, and a average literature value for the boundary
thermal conductance coefficient, Cb = 15.5 · 10−4 Km2
W[111]. (a) ‘CMB-
ground’ conditions and Tbath = 240 mK (b) ‘CMB-ground’ conditions and
Tbath = 50 mK (c) ‘CMB-space’ conditions and Tbath = 50 mK. Gboundary is
predicted to have some impact or dominate the total thermal conductance
over the full range of TES size scales for ground and space observing
conditions.
134
of 300 nm (ρ = 0.1 Ω) and an adjustable length and total resistance. We assume a
shunt resistor with Rs = 0.025 Ω. The background photon NEP for CMB observing
is also plotted. For this estimate the measured current noise of the NIST Series Array
currently installed in our THM testing setup is assumed (NEI = 4√Tbath · 10−12
A√Hz
). A bath temperature of Tbath = 240 mK requires RTES < 1 Ω for ground-
based observing to ensure that the Johnson and SQUID noise are insignificant. At
bath temperature of Tbath = 50 mK, RTES < 20 − 100 Ω is required for ground- or
space-based observing.
4.2.8 The Optimal Design for the THM Detector
Now we examine the optimal geometry of the THM detector in terms of noise
performance given the constraints discussed in the preceding sections. If the detector
occupies the ideal thermal regime (the internal electron-electron conductance is high
compared to the electron-phonon conductance between the electrons and the cold
bath) further optimization is necessary to obtain a detector NEP at or below the
background photon NEP for the desired application.
In this section the detector NEP for a THM device is presented as a function of
TES area, for different observing conditions and bath temperatures. In this case we
have minimized the Bi absorber size as much as possible and also impedance matched
it to a 30 Ohm microstrip line. The absorber termination area is kept square to
maximize electron-electron thermal conductance and to keep the THM in the ideal
detector regime. The only variable is the TES volume, which is parametrized as the
square Mo/Au TES width, wAu, assuming a typical bilayer Au thickness of 300 nm.
‘Literature values’ for n = 5, ‘measured n = 5’, and ‘measured n = 6’ values are
135
(c)
(Ω)
NE
P (
W/wH
z)
Johnson
SQUID
Photon
(b)(Ω)
Photon
SQUID
Johnson
(a)(Ω)
NE
P (
W/wH
z)
NE
P (
W/wH
z)
Photon
SQUID
Johnson
Figure 4.13: SQUID and Johnson noise as a function of TES resistance,
RTES. We assume a Bi absorber of size 3 µm x 6 µm x 800 nm and a 3
µ wide Mo/Au TES with Au thickness of 300 nm (RTES = 0.1 Ω) and
an adjustable length and total resistance. We assume a shunt resistor
with Rs = 0.025 Ω and SQUID current noise of NEI = 4√Tbath · 10−12
A√Hz
. (a) ‘CMB-ground’ conditions and Tbath = 240 mK (b) ‘CMB-ground’
conditions and Tbath = 50 mK (c) ‘CMB-space’ conditions and Tbath = 50
mK. A bath temperature of Tbath = 240 mK requires RTES < 1 Ω for
ground-based observing to ensure that the Johnson and SQUID noise are
insignificant. At bath temperature of Tbath = 50 mK, RTES < 20− 100 Ω
is required for ground- or space-based observing.
136
investigated for the electron-phonon Σ. For CMB loading conditions (‘CMB-ground’
and ‘CMB-space’) the radiative expression for the thermal NEP (Equation 2.27) is
used. In addition, the THM noise performance for CMB observing is compared to
the THM noise performance under ‘FIR-spectral’ observing conditions and to the
far-infrared photon background noise. In all cases the thermal noise of the detector
is assumed to dominate the detector noise. These variations are shown in Figures
4.14-4.16.
There is a large difference in most cases between the thermal fluctuation noise
in the CMB loading case and the thermal fluctuation noise of the same device in the
low-loading limit for the FIR-spectral observing case. This is due to the detector
temperature rising significantly above the bath temperature under the relatively high
CMB loading power, especially as the device volume and thus electron-phonon thermal
conductance becomes small. The magnitude of this heating is shown in Figures 4.17,
4.18 and 4.19 where the bolometer temperature, Tbolo (the electron temperature) is
plotted versus TES width, wAu, for each of the respective variations which are shown
in terms of NEP in Figures 4.14, 4.15 and 4.16.
The naive assumption that the lowest thermal conductance and smallest volume
THM is optimal to obtain the lowest detector noise is not the case for CMB appli-
cations. Instead the optimal device geometry is dependent on the specific loading
application and most sensitively on the bath operation temperature. For n = 5, CMB
ground observing optimal values occur at square TES sizes of 3−10 µm for Tbath = 240
mK. Lowering the bath temperature to Tbath = 50 mK allows the detector NEP to
drop below photon background NEP for both ground and space observing over a wide
137
(b)
NE
P (
W/wH
z)
Photon CMB-ground
Photon CMB-space
Photon FIR-spectral
Detector CMB-ground
Detector CMB-space
Detector FIR-spectral
(m)
(a)(m)
NE
P (
W/wH
z)
Photon CMB-ground
Photon CMB-space
Photon FIR-spectral
Detector CMB-ground
Detector CMB-spaceDetector FIR-spectral
Figure 4.14: Thermal detector NEP as a function of TES width, wAu, for
a square Mo/Au TES with Au thickness 300 nm assuming a 3 µm x 6
µm x 800 nm Bi absorber. Detector and background photon NEP for
‘CMB-ground’, ‘CMB-space’ and ‘FIR-spectral’ observing conditions are
shown. We have assumed n = 5 and ‘literature values’ for Σs.
(a) Tbath = 240 mK. (b) Tbath = 50 mK. At Tbath = 240 mK background
limited NEP is obtainable for CMB ground observing only, for wAu . 3
µm. At Tbath = 50 mK background limited NEP is obtainable for both
CMB ground and space observing for wAu = 3− 50 µm.
138
(b)
NE
P (
W/wH
z)
Photon CMB-ground
Photon CMB-space
Photon FIR-spectral
Detector CMB-ground
Detector CMB-space
Detector FIR-spectral
(m)
(a)(m)
NE
P (
W/wH
z)
Photon CMB-ground
Photon CMB-space
Photon FIR-spectral
Detector CMB-ground
Detector CMB-spaceDetector FIR-spectral
Figure 4.15: Thermal detector NEP as a function of TES width, wAu, for
a square Mo/Au TES with Au thickness 300 nm, assuming a 3 µm x 6 µm
x 800 nm Bi absorber. Detector and background photon NEP for ‘CMB-
ground’, ‘CMB-space’ and ‘FIR-spectral’ observing conditions are shown.
We have assumed ‘measured n = 5’ values for Σs. (a) Tbath = 240
mK. (b) Tbath = 50 mK. At Tbath = 240 mK background limited NEP is
obtainable for ground observing only, for wAu . 10 µm. At Tbath = 50 mK
background limited NEP is obtainable for both CMB ground and space
observing for wAu = 1− 100 µm.
139
(b)
NE
P (
W/wH
z)
Photon CMB-ground
Photon CMB-space
Photon FIR-spectral
Detector CMB-ground
Detector CMB-space
Detector FIR-spectral
(m)
(a)(m)
NE
P (
W/wH
z)
Photon CMB-ground
Photon CMB-space
Photon FIR-spectral
Detector CMB-ground
Detector CMB-space
Detector FIR-spectral
Figure 4.16: Thermal detector NEP as a function of TES width, wAu, for
a square Mo/Au TES with Au thickness 300 nm, assuming a 3 µm x
6 µm x 800 nm Bi absorber. Detector and background photon NEP for
‘CMB-ground’, ‘CMB-space’ and‘FIR-spectral’ conditions are shown. We
have assumed ‘measure n = 6’ values for Σ. (a) Tbath = 240 mK.
(b) Tbath = 50 mK. At Tbath = 240 mK near background limited NEP is
obtainable for CMB ground and space observing, for wAu . 40 µm and
wAu . 4 µm, respectively. At Tbath = 50 mK background limited NEP is
obtainable for CMB observing for wAu = 1− 1000 µm.
140
(b)(m)
CMB-space
CMB-ground
FIR-spectral
Tb
olo
(K
)
(a)
Tb
olo
(K
)
CMB-ground
CMB-space
FIR-spectral
(m)
Figure 4.17: The bolometer temperature, Tbolo, as a function of TES width,
wAu, for the THM design variations of Figure 4.14 for CMB observing
conditions (for FIR observing Tbolo = Tbath). (a) Tbath = 240 mK. (b)
Tbath = 50 mK.
141
(b)(m)
CMB-space
CMB-ground
FIR-spectral
Tb
olo
(K
)
(a)
Tb
olo
(K
)CMB-ground
CMB-space
FIR-spectral
(m)
Figure 4.18: The bolometer temperature, Tbolo, as a function of TES width,
wAu, for the THM design variations of Figure 4.15 for CMB observing
conditions (for FIR observing Tbolo = Tbath). (a) Tbath = 240 mK. (b)
Tbath = 50 mK.
142
(b)(m)
CMB-space
CMB-ground
FIR-spectral
Tb
olo
(K
)
(a)
Tb
olo
(K
)
CMB-ground
CMB-space
FIR-spectral
(m)
Figure 4.19: The bolometer temperature, Tbolo, as a function of TES width,
wAu, for the THM design variations of Figure 4.16 for CMB observing
conditions (for FIR observing Tbolo = Tbath). (a) Tbath = 240 mK. (b)
Tbath = 50 mK.
143
spread of TES sizes, ranging from 1− 100 µm. For n = 6 and Tbath = 50 mK, optimal
TES sizes span an even wider range from 1− 1000 µm. In all cases, Tbath = 50 mK is
required for photon noise limited space-based CMB observing.
4.2.9 General Optimization for CMB Bolometric Detectors
One of the perhaps surprising results of the optimization of the THM detector
is that as the bath temperature is lowered the NEP dependence on size weakens. This
is the result of the competition between two effects in the detector. As the thermal
conductance is lowered (and the bath temperature and κ are lowered) the thermal
NEP tends to decrease (NEP ∼√
G(Tbath)). However, as the thermal conductance
decreases, the temperature of the detector, Tbolo, increases for a fixed power loading
to the device (Tbolo − Tbath ∼ P0
G) and this forces the thermal NEP to increase.
There is a fundamental limit to the improvement of detector thermal noise by
simply lowering the thermal conductance. Although we demonstrated that this was
the case for the THM detector design in the previous section, we can also demonstrate
that this is indeed the case for any bolometeric detector in a relatively high power
loading limit (like that for CMB observing) where T ≫ Tbath. This will be done in
this section for the case of a generic CMB detector with thermal conductance in the
form of Equation 2.9, and thermal NEP given in the radiative and the diffusive limits
by Equations 2.27 and 2.28. These radiative and diffusive limits hold for either a
detector directly on the cold substrate, as is the case for a boundary or hot-electron
type bolometer (radiative), or for the more common CMB-type bolometer where the
heat flow is controlled by phonon-phonon scattering along suspended thermal legs
(diffusive). Again it is assumed that the detector noise is dominated by the thermal
144
noise. And again the CMB observing performance is compared to that of a detector
in a low power loading limit (like the ‘FIR-spectral’ case) where the expression for
thermal NEP is given by Equation 2.26.
In Figures 4.20-4.24 the behaviour of a generic CMB-observing bolometer is
shown for n = 2− 6 (electron-electron, boundary or electron-phonon) controlled heat
flow as a function of the power flow coefficient, κ (P = κ(T nbolo−T nbath)). The difference
between the thermal noise in the radiative and diffusive regime is minimal. Again,
a large discrepancy exists in some regimes between the thermal noise in the CMB-
observing detector and the thermal noise in the low power loading limit. Although the
optimal κ and minimal thermal NEP do vary with the power law, n, and the chosen
bath temperature, Tbath, the behaviour across all devices is similar. Under the CMB
loading conditions the thermal noise minimum is limited to NEP ∼ 7 · 10−18 W√Hz
for ‘CMB-ground’ observing and NEP ∼ 2 · 10−18 W√Hz
for ‘CMB-space’ observing.
Significant improvements below this level, which might be naively assumed from the
low-power loading limit expression for thermal noise, are not possible. Although pho-
ton noise limited performance is certainly possible for certain optimal detector designs,
a CMB observing detector’s performance is fundamentally limited due to heating in
the bolometer.
145
NE
P (
W/wH
z)
(c)
Photon CMB-ground
Detector CMB-ground
Detector low power loading limit
(a)
Photon CMB-ground
Detector CMB-ground
Detector low power loading limit
NE
P (
W/wH
z)
(d)
Detector CMB-space
Detector low power loading limit
Photon CMB-space
(b)
NE
P (
W/wH
z)
Photon CMB-space
Detector CMB-space
Detector low power loading limit
NE
P (
W/wH
z)
Figure 4.20: The thermal fluctuation NEP of a generic CMB observing
bolometer in comparison to background photon NEP. A temperature
dependence of the power flow, n = 2 is assumed. (a) ‘CMB-ground’
observing conditions with Tbath = 240 mK. (b) ‘CMB-space’ observing
conditions with Tbath = 240 mK.(c) ‘CMB-ground’ observing conditions
with Tbath = 50 mK. (d) ‘CMB-space’ observing conditions with Tbath = 50
mK. For all of these cases, the thermal detector NEP in the low power
loading limit is also plotted.
146
NE
P (
W/wH
z)
(c)
Photon CMB-ground
Detector CMB-ground
Detector low power loading limit
(a)
Photon CMB-ground
Detector CMB-ground
Detector low power loading limit
NE
P (
W/wH
z)
(d)
Detector CMB-space
Detector low power loading limit
Photon CMB-space
(b)
NE
P (
W/wH
z) Photon CMB-space
Detector CMB-space
Detector low power loading limit
NE
P (
W/wH
z)
Figure 4.21: The thermal fluctuation NEP of a generic CMB observing
bolometer in comparison to background photon NEP. A temperature
dependence of the power flow, n = 3 is assumed. (a) ‘CMB-ground’
observing conditions with Tbath = 240 mK. (b) ‘CMB-space’ observing
conditions with Tbath = 240 mK.(c) ‘CMB-ground’ observing conditions
with Tbath = 50 mK. (d) ‘CMB-space’ observing conditions with Tbath = 50
mK. For all of these cases, the thermal detector NEP in the low power
loading limit is also plotted.
147
NE
P (
W/wH
z)
(c)
Photon CMB-ground
Detector CMB-ground
Detector low power loading limit
(a)
Photon CMB-ground
Detector CMB-ground
Detector low power loading limit
NE
P (
W/wH
z)
(d)
Detector CMB-space
Detector low power loading limit
Photon CMB-space
(b)
NE
P (
W/wH
z)
Photon CMB-space
Detector CMB-space
Detector low power loading limit
NE
P (
W/wH
z)
Figure 4.22: The thermal fluctuation NEP of a generic CMB observing
bolometer in comparison to background photon NEP. A temperature
dependence of the power flow, n = 4 is assumed. (a) ‘CMB-ground’
observing conditions with Tbath = 240 mK. (b) ‘CMB-space’ observing
conditions with Tbath = 240 mK.(c) ‘CMB-ground’ observing conditions
with Tbath = 50 mK. (d) ‘CMB-space’ observing conditions with Tbath = 50
mK. For all of these cases, the thermal detector NEP in the low power
loading limit is also plotted.
148
NE
P (
W/wH
z)
(c)
Photon CMB-ground
Detector CMB-ground
Detector low power loading limit
(a)
Photon CMB-ground
Detector CMB-ground
Detector low power loading limit
NE
P (
W/wH
z)
(d)
Detector CMB-space
Detector low power loading limit
Photon CMB-space
(b)
NE
P (
W/wH
z)
Photon CMB-space
Detector CMB-space
Detector low power loading limit
NE
P (
W/wH
z)
Figure 4.23: The thermal fluctuation NEP of a generic CMB observing
bolometer in comparison to background photon NEP. A temperature
dependence of the power flow, n = 5 is assumed. (a) ‘CMB-ground’
observing conditions with Tbath = 240 mK. (b) ‘CMB-space’ observing
conditions with Tbath = 240 mK.(c) ‘CMB-ground’ observing conditions
with Tbath = 50 mK. (d) ‘CMB-space’ observing conditions with Tbath = 50
mK. For all of these cases, the thermal detector NEP in the low power
loading limit is also plotted.
149
NE
P (
W/wH
z)
(c)
Photon CMB-ground
Detector CMB-ground
Detector low power loading limit
(a)
Photon CMB-ground
Detector CMB-ground
Detector low power loading limit
NE
P (
W/wH
z)
(d)
Detector CMB-space
Detector low power loading limit
Photon CMB-space
(b)
NE
P (
W/wH
z)
Photon CMB-space
Detector CMB-space
Detector low power loading limit
NE
P (
W/wH
z)
Figure 4.24: The thermal fluctuation NEP of a generic CMB observing
bolometer in comparison to background photon NEP. A temperature
dependence of the power flow, n = 6 is assumed. (a) ‘CMB-ground’
observing conditions with Tbath = 240 mK. (b) ‘CMB-space’ observing
conditions with Tbath = 240 mK.(c) ‘CMB-ground’ observing conditions
with Tbath = 50 mK. (d) ‘CMB-space’ observing conditions with Tbath = 50
mK. For all of these cases, the thermal detector NEP in the low power
loading limit is also plotted.
150
Chapter 5
THM Test Devices & “Dark”
Measurements
5.1 Test Devices & Fabrication
The general plan for developing this novel type of TES bolometer was to start by
fabricating large (10−100 µm) THM devices and then to push towards smaller (3−10
µm size) THM devices with a more optimal design. Additionally, the first test devices
had only simple DC lead connections in order to focus the investigation on the TES
and DC characteristics of the absorber. Later, RF microwave circuits were coupled to
the THM devices to investigate the detector coupling to an RF source (these designs
and measurements are presented in Chapter 6). Along the way in these development
tests a physical process was encountered which had not previously been considered: a
strong lateral superconducting proximity effect in micron-size TES devices. Thus, a
side project was undertaken to investigate this effect and additional test devices were
fabricated for this purpose.
In Table 5.1 all of the THM test devices presented in this thesis are listed by wafer
151
Table 5.1: A summary of the THM test devices which are presented in
this thesis.Device Label Fabrication
Date
General Description TES size Absorber size Microwave
circuit?
Main Result
THM2003 2003 Mo/Au TES with Bi
absorber & Mo DC
leads
10-20 µm ∼100 µm No NEP, S & G measure-
ments confirm non-ideal e-p
model.
THM4 & THM5 2007-2008 Mo/Au TES with Bi
absorber & Nb µstrip
with AlO dielectric
3-24 µm 3-24 µm Yes (3 µm size
only)
Strong lateral proximity ef-
fect, µstrip transmission
and microwave absorption
observed.
us23 & us25 2009-2010 Au TES with Bi ab-
sorber & Nb µstrip
with Si dielectric
3-30 µm 3 µm Yes G measurements confirm
ideal e-p model, but no
transitions observed.
THMA4 2010 Au TES with Nb DC
leads
3-30 µm - No Change in fabrication
method, no transitions
observed
THMA24 2011 Au TES with Nb DC
leads
3-30 µm - No Additional cleaning, no
transitions observed
name and a summary of the design and the findings for each device type. A depiction
of the device geometry and layer order, as well as descriptions of the fabrication steps
for each of these devices, and optical or SEM images of test devices, can be found
later in this chapter when measurements from each of these test devices are presented
(Figures 5.10, 5.21, 5.17 & 5.25).
Fabrication of all of these test devices was carried out at the NASA-Goddard
Detector Development Laboratory (DDL) making use of their excellent facilities and
detector fabrication expertise. Much of the processing involved standard photolithog-
raphy with resolutions of ∼ 1 µm. However, fabrication of these devices included
many novel fabrication techniques which have been perfected at the DDL, and some
of these steps can be seen in the in-process images shown in Figures 5.1 and 5.2. Some
152
of these techniques which will be briefly described here have also been described in
Denis et al. [20].
The Mo/Au bilayer TESs were deposited in a load-locked vacuum chamber using
a dedicated bilayer sputtering deposition system. Transition temperatures for the
device wafers were targeted after conditioning of the system and characterization of
Mo and Mo/Au films on test wafers. A common process was an ion-milling of the
Au or Mo/Au TES structure to create the well defined TES area. This ion-milling
process also provided a moderately sloped sidewall to the Au for better step coverage
of the Bi and Nb over the Au TES.
Another of the common process steps for the THM test devices was a sloped
sidewall Reactive Ion Etch (RIE) Nb etch (SF2 & O2) for good step coverage over
the microstrip groundplane features and over the Nb leads. During this etch a thick
layer of photoresist is deposited over the Nb lead and microstrip pattern and the
photoresist is simultaneously etched with the Nb. Because of this, care must be taken
not to over-etch into the Nb features. In the THM design this was especially true on
the small area of Nb overlap at the contacts to the TES leeds where the photoresist
was thinner. This was a problem in the fabrication of test devices THM4/THM5 as
will be discussed later in this chapter.
Another concern that arose during the fabrication of these THM test devices
was proper stripping of the protective photoresist layer from the Au TES surface after
the ion-milling process, due to burning of the resist during the ion-milling step. This
cleaning was complicated by the fact that ultrasonic solvent baths could not be used
after the bilayer deposition process because they would cause a shift of the bilayer Tc.
153
MoAu
Nb
9 µm
Mo/Au TES
9 µm
(a)
(b)
Figure 5.1: In-process images of some of the key fabrication steps for the
THM test devices. (a) Optical image of bilayer TES on wafer THM5 after
completion of the Au ionmill and Mo RIE patterning. The Mo extends
out to make contact with the Nb leads which will be deposited next. The
Mo on the non-lead sides of the TES will be etched away during the Nb
patterning step. (b) Optical image of wafer THM4 after completion of Nb
(SF6 + 02) RI sloped sidewall etch. The sidewall can been seen even in
this optical image as Nb (blue) extends past the dark top edge.
154
(a)
(b)
Nb (ground plane)
Nb (µstrip)
2 µm
Nb
Bi
Au
5 µm
Figure 5.2: In-process images of some of the key fabrication steps for the
THM test devices. (a) SEM image of THM4 showing good step coverage
over a Nb sloped sidewall. This view shows the Nb microstripline crossing
the gap in the Nb ground plane(see Chapter 6). The ground plane is
seen through the AlO dielectric layer. (b) SEM image of a 3 µm x 9 µm
Bi absorber test device (not incorporated into a THM) after liftoff. The
grainy structure of the evaporated Bi is observable. Thin Au contact pads
under the Bi help make contact to the Nb leads.
155
Improvement in the wafer heatsinking to the chilled mount during ion-milling, as well
as the use of an UV exposure and ethanol rinse de-scumming procedure, following the
usual O2 ash and solvent clean, were able to solve this problem. This cleaning step
of the Au surface was of particular concern in the fabrication of some of the lateral
proximity test devices (THMA4,THMA24) and will be discussed in more detail in
Section 5.5.
Another concern was obtaining a high quality dielectric layer for the microwave
circuit of the THM test devices. For wafers us25 and us23 a BenzoCycloButene (BCB)
bonding method was used to bond a 1.45 µm thick Si single crystal wafer to a Si
backing wafer for two-sided patterning, such that the Si wafer could be used as the
microwave dielectric layer. This Si dielectric was adopted after pinhole problems were
found in some devices (THM4 & THM5) which were fabricated using an Al2O3 film as
the dielectric. For adhesion purposes to this Si dielectric, a thin non-superconducting
Mo or Ti layer was deposited immediately before the Au TES deposition.
By using evaporated bismuth, a high resistivity for the RF absorbing structure
was obtained to match to the high impedance transmission lines. The electrical resis-
tivity of evaporated bismuth exhibits an unusual temperature dependence. In Figure
5.3 the resistivity of evaporated Bi is shown as a function of temperature for sev-
eral test wafers. By depositing bismuth of thickness ∼1 µm resistances of 20-30 Ω/
at sub-Kelvin to Kelvin temperatures were obtained in order to properly impedance
match to the Nb microstripline. The bismuth lift-off required the use of non-aggressive
resist remover solvents (Resist Remover 5 or Acetone) as the bismuth material is very
sensitive to chemical etchants. After bismuth deposition the wafer could not be heated
156
0.00E+00
5.00E-04
1.00E-03
1.50E-03
2.00E-03
2.50E-03
3.00E-03
3.50E-03
4.00E-03
4.50E-03
5.00E-03
3 53 103 153 203 253
Temperature (K)
Res
isti
vit
y (
Oh
ms
*cm
)
AB test wafer, 850 n m
THM D6 test wafer, 1200 n m
THM D7 test wafer, 830 n m
THM D8 test wafer, 1200 n m
Figure 5.3: The resistivity of evaporated Bi resistivity measured for several
test wafers (with Bi thickness listed) as a function of temperature. An
increase in resistivity is seen as the temperature decreases.
above 70 C in order to prevent Au/Bi diffusion from occurring at the absorber/TES
interface.
More fabrication details and devices dimensions will be included in the following
sections as they become applicable to understanding and analysing these measure-
ments. Rather than presenting the measurements of these test devices in a strict
chronological order, the measurements and analysis presented in the following sec-
tions is organized by topic, although each device is discussed separately within each
157
of these sections. This is done in order to call attention to how the characteriza-
tion of each of these test devices has furthered our understanding of the THM de-
sign. These sections are: 1) Inquiry into a non-ideal THM model (THM2003) 2)
Inquiry into the hot-electron effect (THM2003,us25) 3) Inquiry into the lateral prox-
imity effect (THM4,THM5,us23,us25,THMA4,THMA24) 4) Inquiry into detector NEP
(THM2003,us25).
5.2 “Dark” Cryogenic Test Setup
5.2.1 Dewar & Cryogenic Setup
All devices were cooled to temperatures between 4 K and 100 mK during testing
using an RF shielded dewar with a magnetically shielded Adiabatic Demagnetization
Refrigerator (ADR). The outside of the dewar and thermal shields are shown in Figure
5.4. The dewar has three insulating compartments, starting with the outer room
temperature shield at 300 K, which is vacuum tight, and transitioning to a 77 K
shield heatsunk to a liquid N2 tank. A further inner shield at 4 K and a support
platform for the ADR are heatsunk to a 4 K liquid 4He tank. The 100-300 mK
coldstage where the test devices are mounted is thermally isolated from this 4 K stage
via suspension on Kevlar strings (shown in Figure 5.5). A ferric ammoniom alum
(FAA) salt pill is also thermally isolated from this 4 K stage via Kevlar suspension
and a mechanical heatswitch. The magnetic coil surrounding the salt pill provides
a 3 T field and is magnetically shielded from the surrounding dewar by a vanadium
permendur cylinder. The base temperature of the ADR is near 240 mK from a 4.2
K bath. A base temperature of 140 mK is possible when pumping on the 4He bath
158
77K ShieldVacuum Shield
4K Shield
Vacuum feedthroughs
Liquid N2 tank fillLiquid He tank fill
Figure 5.4: The dewar shielding.
to pressures . 10 Torr. The ADR and cryostat was previously used on the MSAM
II balloon flight and details of the cryogenic system have been described previously
[126].
Test devices were mounted on the coldstage by one of two methods: 1) Inside a
superconducting Nb magnetically shielded cylindrical can with heatsinking via metal
clamping of this can to the coldstage 2) Direct mounting to the coldstage via a sand-
wich of metal-metal contacts. In both of these cases, the THM chips were mounted via
Stycast-2850 epoxy or Apiezon-N thermal grease to thin copper or Invar plates which
were clamped to a copper mount. Short superconducting Al wirebonds were used to
159
Unshielded mount
Nb shielded mount
Heatsinking wires
Superconducting cable
Kevlar suspension
GRT
RuthOx Thermometer
Detector chip
Figure 5.5: The coldstage.
make electrical contact from the Au or Nb pads on the detector chip to Cu or Au
wirebonding pads on the mount. Twisted pairs of copper wires soldered to these pads
on the chip mount were heatsunk to the coldstage and plug into multi-pin connectors
on the coldstage. Superconducting cables carry these signals out of the dewar via RF
filtered vacuum feedthroughs. The superconducting cables are heatsunk to the 4 K
stage (via GE varnish and Au-plated Cu metal clamps) and also at the 77 K stage
(via the feedthrough connectors). Pictures of this coldstage setup are shown in Figure
5.5, and images of the two types of chip mounts in Figures 5.5 & 5.6.
160
SQUID ChipTHM Detector ChipShunt Resistor
Figure 5.6: The THM chip and 1st stage SQUID mount which fits inside
a Nb shielded cylindrical can.
In addition to the test devices themselves, several diagnostic thermometers are
mounted at various locations in the dewar. Two Ge resistive thermometers are located
on the 77 K and the 4 K stages. Two other thermometers are mounted directly to the
coldstage, one a Ge resistive thermometer covering a temperature range from 50 mK-5
K, and the other a Ruthenium Oxide resistive thermometer covering the temperature
range from 1 − 40 K. These two coldstage thermometers provided a temperature
measurement of the bath temperature for the bolometer detectors.
5.2.2 SQUID Readout Setup
For some of the measurements of these THM test devices the TES was read
out with a 2-stage SQUID system from NIST. The chip containing the 1st stage
SQUID was mounted on a superconducting Al plate (acting as a magnetic shield)
161
X X
X X
2nd stage feedback
1st stage feedback
2nd stage bias
1st stage bias
1st stage
input coil
2nd Stage
SQUID
1st Stage
SQUID
TES
V0Rs
Figure 5.7: Diagram of the 2-stage SQUID electrical connections for the
read out of the THM TES.
near the detector chip inside the Nb shielded can. Al superconducting wirebonds, a
few millimeters in length, make electrical connections from the TES to the input coil
of the SQUID in parallel with a 25 mΩ shunt resistor. Superconducting wires from
the output pads of this 1st stage SQUID were brought out of the canister and wired to
the 2nd stage SQUID array mounted on the 4 K stage inside a magnetically shielded
box made of Cryoperm. The electrical connections for this SQUID setup are shown
in Figure 5.7.
In this SQUID setup, the TES is voltage-biased to provide electrothermal feed-
162
back. The 1st and 2nd stage SQUIDs are both DC current biased. SQUID feedback
electronics monitor the 2nd stage voltage signal (via the 2nd stage bias line) and re-
spond to current through the 1st stage input coil by sending an output nulling current
to the feedback coil near the 1st stage SQUID. The 2nd stage feedback line is usually
not used except for diagnostic purposes. The 1st stage feedback nulling signal is what
is read out and gives a voltage that is linearly proportional to the TES current.
The SQUID response was calibrated and the appropriate bias and feedback set-
tings found by removing the connections to the TES and sending a known AC current
through the input coil from a function generator. The DC current biases for the 1st
and 2nd stage SQUIDs were adjusted while monitoring the 2nd stage bias signal to
find the DC bias settings which gave the maximum amplitude response to this input
signal. The feedback gain and offset settings were also adjusted to make sure the
feedback electronics adequately nulled the input signal. This calibration procedure is
shown in Figures 5.8 and 5.9.
5.3 Inquiry into a Non-Ideal THM Model
In this section measurements of one of the THM test devices of variation THM2003
are presented. These results have previously been reported in Barrentine et al. 2008
[8]. This device was the first device we tested and we determined it conformed to the
non-ideal thermal model which is described in detail in Chapter 4. This THM test
device consisted of a thin Bi/Au absorber and bilayer Mo/Au TES. An optical image
and dimensions for this test device as well as the layer order and fabrication details are
shown in Figure 5.10. The Bi absorber layer is 500 nm thick under a 190 nm thick Au
layer. The bilayer TES is 40 nm thick Mo under a 180 nm thick Au layer. Mo leads
163
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
-0.0 -0.03 -0.01 0.01 0.03 0.05
Signal to input coil (
IN M
ON
(V
)
feedback off
feedback on
Input Coil
-6.0 -3.6 -1.2 1.2 3.6 6.0
(µA)
2n
d s
tag
e S
QU
ID B
ias
Figure 5.8: The 2nd stage SQUID bias line voltage as a function of the
input calibration signal to the 1st stage SQUID input coil. With feedback
off the second stage signal follows the input signal. With feedback on the
bias signal is zero no matter the input signal, as a nulling feedback signal,
which tracks the input signal, is being fed back to the 1st stage SQUID.
164
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
-0.05 -0.03 -0.01 0.01 0.03 0.05
Signal tInpu t Coil (V)
1st
Sta
ge F
B (
V)
Input Coil (µA)
-6.0 -3.6 -1.2 1.2 3.6 6.0
Figure 5.9: The SQUID calibration curve. Plotted is the feedback signal
to the first stage SQUID as a function of the signal to the input coil. The
1st stage feedback signal is what is read out. The gain factor is given by
the slope of this linear curve.
165
attached to the absorber allow for direct Joule heating of the absorber by applying a
DC current. The TES transitions at 310-317 mK and has a normal resistance of 0.32
Ω. The absorber has a resistance of 17 Ω across the absorber bias leads.
As described in the previous section, the TES was wired in parallel with a shunt
resistor of resistance, Rs = 25 mΩ, and was read out by the NIST 2-stage SQUID. The
test device and 1st stage SQUID chip were placed within the Nb cylindrical shield,
and cooled to 180− 300 mK.
5.3.1 I-V Measurements
The current-voltage (I-V) characteristics of the TES for this device were mea-
sured by applying a slow AC bias current to the TES bias circuit and observing the
SQUID response. In Figure 5.11 the I-V curves for the TES are shown at several
bath temperatures. With Tbath < Tc, at low TES bias-voltage, the TES remains in
the superconducting regime. As the TES voltage and current increase the TES transi-
tions to the normal linear regime. In the transition region the Joule power dissipation
(P0 = IV ) is constant since the TES temperature is approximately constant in the
transition and constant bias power is required to maintain the TES at this fixed tem-
perature above the cold stage. This accounts for the negative slope and non-ohmic
behaviour of the I-V curve in the transition. As the bath temperature approaches
Tc, the transition current decreases, and the I-V curve approaches the normal linear
regime with normal resistance, RTES =0.32 Ω. The I-V curves map out the TES bias
points in the transition. Possible bias points for this test device range from ∼ 0.2− 3
µV.
166
20um
Bi, 500 nm, evaporated deposition, liftoff
Au, 150nm, sputtering bilayer deposition, ionmill
superconducting Mo, 40nm, sputtering bilayer deposition, RIE
Au, 200 nm, evaporated deposition, liftoff
(a)
(b)
Figure 5.10: (a) Fabrication steps and cross-sectional view showing the
layers for each of the THM2003 test devices. Thicknesses are not drawn
to scale, but are listed on the labels for each layer. (b) Optical image of a
test device of variation THM2003.
167
Figure 5.11: I-V curves for a device from wafer THM2003 at different
bath temperatures (labelled in the figure). The solid black line indicates
RTES =0.32 Ω.
168
5.3.2 Thermal Conductance Measurements
To measure the thermal conductance which characterizes the bolometer thermal
link to the coldstage for this test device, measurements were made of the amount of
Joule power dissipation in the absorber, P , required to maintain the TES at Tc as
a function of the cold stage temperature. This was done by allowing the coldstage
temperature to gradually rise from 180 mK to 320 mK while applying a DC current
to the absorber via the separate DC leads. The I-V curve was monitored to see what
Joule power dissipation in the absorber was required to fully “normalize” the I-V
curve at each bath temperature (thus using the high temperature end of the RTES
vs. T superconducting transition curve for these measurements). A plot of these
measurements of P vs. Tbath is shown in Figure 5.12.
These P vs. Tbath measurements are fitted to the two thermal models introduced
in Section 4.1.1 and Section 4.1.2. The first is an ‘ideal model’, where electron-phonon
coupling is assumed to dominate and a n = 5 temperature dependence to the power
flow is assumed. Here the equation of fit is P = κe−p(T5c − T 5
bath). The other thermal
model is a ‘non-ideal model’, where the detector is broken into three geometrically and
thermally separate regions due to the high electrical resistance, and hence, low rate
of electron-electron scattering along the length of the absorber. In this model, both
electron-electron scattering and electron-phonon scattering are assumed to dominate
and n = 2 and n = 5 are assumed respectively. Here the equation of fit is:
P = (κe−p,TES +1
3κe−p,Abs)(T
5c − T 5
bath) +2
3κe−p,Abs(T
5Abs − T 5
bath) (5.1)
169
0.24 0.26 0.28 0.30 0.32
0.00E+000
1.00E-009
2.00E-009
3.00E-009
4.00E-009
5.00E-009 Non-Ideal Model Electron-Phonon
& Electron-Electron (n=5,2) Ideal Model Electron-Phonon (n=5) Ideal Model Phonon-Phonon (n=4)
Abs
orbe
r P
ower
(W
)
T bath
(K)
Figure 5.12: P vs. Tbath measurement for devices from wafer THM2003.
170
using the relation:
Tabs =
√
1
κe−e[(κe−p,TES + κe−p,Abs)(T 5
c − T 5bath) + κe−eT 2
c ]. (5.2)
Here TAbs is the temperature of the absorber ends and κe−e =8L0
3Rabsis assumed based
on the geometrical separation in this non-ideal thermal model and the measured re-
sistance of the absorber, RAbs = 17 Ω. In addition, an ideal model assuming bound-
ary (phonon-phonon) coupling is also fit to the data. Here the equation of fit is
P = κboundary(T4c − T 4
bath). It should kept in mind, that because of uncertainty in the
n value for electron-phonon coupling (see Chapter 3), n = 4 behaviour is not neces-
sarily exclusively indicative of phonon-phonon coupling, and n = 4 behaviour may be
indicative of electron-phonon coupling as well.
The fitted κ values for all three models are listed in Table 5.2. In the case of the
non-ideal model, Σ values are listed, since the sectioning inherent in the model allows
a fit to the Bi and Au portions of κe−p separately. These fit κ and Σ values are also
compared to κ values calculated from the device dimensions and ‘literature values’ for
electron-phonon scattering for Au and Bi or phonon-phonon boundary scattering (see
Section 4.2.1). Thermal conductances at 310 mK are calculated from each of these fit
values as well.
Due to the short temperature range of these measurements, all three of these fits
conform well to the measured P vs. Tbath curve. The non-ideal model fits to electron-
phonon Σ values only slightly lower than those predicted from the literature. The
ideal electron-phonon model also fits very closely to the predicted electron-phonon
κe−p values from literature. Although the ideal boundary model does give the best fit
to the measured curve, the fit κ value for this model is a factor of four below what
171
Table 5.2: Summary of P vs. Tbath fits for various models and thermal
conductances at 310 mK.Thermal Models Ideal e-p Ideal Boundary Non-Ideal Literature
κe−p,Abs+κe−p,TES
( WK5 )
1.73 · 10−6 - 4.38 · 10−7 1.23 · 10−6
κbounday =4ACb
( WK4 ) - 6.45 · 10−4 - 1.95 · 10−7
κe−e =L0
2RAbs( WK2 ) - - 2.87 · 10−9 -
ΣAu ( WK5m3 ) - - 1.0 · 109 4.5 · 109
ΣBi (W
K5m3 ) - - 3.0 · 108 2.4 · 108Ge−p,Abs (
WK) - - 5.84 · 10−9 1.58 · 10−8
Gep,tot (WK) 2.48 · 10−8 - 6.27 · 10−9 1.76 · 10−8
Gboundary (WK) - 7.69 · 10−8 - 2.32 · 10−8
Ge−e (WK) - - 4.5 · 10−10 -
might be expected from the literature. In all three cases the measured and calculated
electron-phonon or boundary conductance is significantly greater than the predicted
electron-electron conductance along the absorber, lending further support to a non-
ideal model for this test device. For the non-ideal model we measure electron-phonon
thermal conductance of Ge−p = 6.2 · 10−9 WK
at 310 mK, compared to an electron-
electron thermal conductance of Ge−e = 4.5 · 10−10 WK
along the absorber.
The P vs. Tbath measurements for this test device are consistent with any of these
three models, with preference going to a non-ideal based on the predicted electron-
electron thermal conductance from the absorber resistance measurement. In the fol-
lowing sections further measurements of these devices will provide more evidence for
this non-ideal model. These P vs. Tbath measurements also provide κ and Σ values
which will be used in the following sections to make predictions which can be compared
to measurements of responsivity and the noise performance for these devices.
172
5.3.3 Responsivity Measurements
The THM responsivity, S ( AW), was measured by passing a small AC current
through the absorber to provide direct Joule heating to the detector. The bolometer
response became non-linear for Joule power to the absorber, P > 0.35 nW. A lock-in
amplifier was used to read out the AC SQUID response, while the TES was DC voltage-
biased and the cold stage temperature was regulated. Table 5.3 lists the measured
responsivities of the THM test device at three TES voltage biases, (VBias = 0.2, 0.5, 1
µV), and two different cold stage temperatures, (Tbath = 309, 311 mK). These bias
points were chosen based on the I-V curves in Figure 5.11.
The measured responsivities are compared in Table 5.3 to the predicted respon-
sivities based on the ideal and non-ideal models using the fit values determined by the
P vs. Tbath measurements. The measured responsivities agree within a factor 1-2 to
the fit non-ideal thermal model predictions and to the fit electron-phonon ideal model.
However, the fit boundary ideal model overpredicts the responsivity by a factor of 1-4.
The extent to which the non-ideal model diverts power from the TES and reduces the
detector responsivity can be seen by comparing the predictions of the ideal models to
those for the non-ideal case.
5.3.4 Noise measurements
The measured NEP of this THM device at three TES bias points is shown in
Figures 5.13, 5.14 and 5.15. These noise measurements were done by measuring the
173
Table 5.3: Summary of responsivity measurements for the THM2003 test
device at three different voltage biases and two different temperatures.
Predictions for the expected responsivity are also shown using equations
for ideal and non-ideal models based on fit κ and Σ values from the P
vs. Tbath measurements (Table 5.2). The bias points corresponding to the
measured I-V curves in Figure 5.11 were also used for these predictions.Tbath (mK) V0 (µV) Measured S ( A
W) Non-ideal S ( A
W) Ideal e-p S ( A
W) Ideal boundary S
( AW)
309 0.2 2.7 · 104 8.1 · 103 1.1 · 104 3.1 · 104309 0.5 3.0 · 104 2.6 · 104 2.8 · 104 8.3 · 104309 1 3.3 · 104 5.2 · 104 5.6 · 104 1.7 · 105311 0.2 2.2 · 104 7.3 · 103 1.1 · 104 3.1 · 104311 0.5 2.6 · 104 2.0 · 104 2.8 · 104 7.98 · 104311 1 3.1 · 104 3.6 · 104 5.6 · 104 1.5 · 105
current fluctuation noise at the SQUID output (NEI), with zero power dissipation in
the absorber, and using the measured responsivity (Table 5.3) to convert to the equiv-
alent power fluctuation noise (NEP) of the detector. For these sensitive measurements,
the dewar (with only the SQUID feedback electronics powered by a battery source) was
placed inside a electromagnetically shielded room with the bias lines passing through
shielded connectors to the measurement electronics (a spectrum analyser and com-
puter readout). For the three bias points we measure detector NEP of 2 − 3 · 10−15
W√Hz
at 311 mK. For comparison, the predicted NEPs for this test device for both
thermal models (a non-ideal model or assuming a boundary or electron-phonon ideal
model) are also plotted.
For these predictions we use Equation 2.27 for the thermal NEP contributions.
The predicted NEPs also include contributions from SQUID noise. This SQUID
current noise was measured independently during the calibration setup, and was
174
101
102
103
104
1E-15
1E-14
NE
P (
W/H
z1
/2)
Frequency (Hz)
Non-ideal !t
Ideal e-p !t
Ideal boundary !t
Figure 5.13: Noise measurements of the THM2003 test devices at 1 µV
bias, 311 mK bath temperature. The best fit is given by the non-ideal
model.
175
101
102
103
104
1E-15
1E-14
1E-13
NE
P (
W/H
z1
/2)
Frequency (Hz)
Non-ideal !t
Ideal e-p !t
Ideal p-p !t
Figure 5.14: Noise measurements of the THM2003 test devices at 0.5 µV
bias, 311 mK bath temperature. The best fit is given by the non-ideal
model.
176
101
102
103
104
1E-15
1E-14
1E-13
NE
P (
W/H
z1
/2)
Frequency (Hz)
Non-ideal !t
Ideal e-p !t
Ideal p-p !t
Figure 5.15: Noise measurements of the THM2003 test devices at 0.2 µV
bias, 311 mK bath temperature. The best fit is given by the non-ideal
model.
177
2.3 · 10−11 A√Hz
at 4 K, with a predicted value at 300 mK of 5.57 · 10−12 A√Hz
, as
the SQUID noise for this device scales as NEI ∼ 1√T. The Johnson noise due to the
resistive TES and the shunt resistor in the TES bias circuit also contribute to the
detector NEP predictions.
In Figure 5.16 these individual contributions to the predicted noise are shown
for one of the bias points. In the case of the non-ideal model there is additional power
fluctuation noise due to thermal power fluctuations between the thermally separated
absorber ends and central absorber region and the TES, as well as a slightly increased
NEP from current noise sources due to the lower responsivity in this model. Thermal
noise dominates the detector noise for this device in both thermal models.
The peaks in the measured noise spectrum at low frequencies are believed to be
due to external electrical noise sources which can be minimized with further shielding
of the dewar. A high frequency roll off in the current noise (occurring at frequencies
> 30−70 kHz, and which is not shown in these plots) was observed due to the limited
bandwidth of the SQUID feedback loop. This roll off frequency shifted when the gain
settings of the feedback electronics were adjusted. This roll off in the noise spectrum
however is not related to the thermal time constants of the bolometer itself or the
TES electrical bias circuit. Based on the limits of the feedback electronics used in
our measurements this sets an upper limit for the measured thermal time constant of
the device with electrothermal feedback of τ < 10 µs. We expect, based on τ = CG, a
thermal time constant of τ < 0.1 µs at 300 mK for this test device.
The non-ideal model provides the best match to these noise measurements. The
ideal models do not adequately account for the noise. This result provides the final
178
101
102
103
104
1E-17
1E-16
1E-15
1E-14
NE
P (
W/H
z1
/2)
Frequency (Hz)
Non-ideal !t
Non-ideal !t Thermal
Non-ideal !t Johnson
Non-ideal !t SQUID
Ideal e-p !t
Ideal e-p !t Thermal
Ideal e-p !t Johnson
Ideal e-p !t SQUID
Figure 5.16: Predictions of detector NEP for the ideal electron-phonon
model and the non-ideal model at 1 µV bias, showing contributions
from thermal, Johnson, and SQUID noise sources. The non-ideal model
matches the measured noise (Figure 5.13) best.
179
evidence in support of a non-ideal model for this test device. As a side note, unlike
what is often observed in membrane-isolated bolometers and microcalorimeters we do
not observe any excess noise in this hot-electron device, once the non-ideal thermal na-
ture of the detector is accounted for. This may provide an indication that excess noise
may be less of a obstacle in substrate-type detectors and another possible advantage
of the THM design.
In the following sections we examine THM detector test devices with more
promising noise performances. These test devices are smaller devices, with a re-
designed absorber/TES coupling scheme for improved electron-electron vs. electron-
phonon optimization in order to fit to an ideal thermal THM model.
5.4 Inquiry into the Hot-Electron Effect
5.4.1 THM2003 Test Device
As was detailed in the preceding section thermal conductance measurements of
the THM2003 device alone were inconclusive in determining the hot-electron effect and
the power law dependence of power flow in the detector. However, the combination
of the DC measurements of this device (noise, responsivity and thermal conductance)
conform to a non-ideal model in which a hot-electron effect occurs with n = 5 be-
haviour. The best fits for the electron-phonon coupling coefficients in this model are
Σ = 1.0 · 109 WK5 for Au and Σ = 3.0 · 108 W
K5 for Bi, only slightly less than what
has been measured previously in the literature. No indications of a boundary thermal
resistance were seen, except for the slightly better fit of n = 4 to the P vs. T curve,
but some contribution to the thermal conductance from boundary resistance cannot
180
be ruled out by these measurements of this larger, non-optimal, THM test device.
5.4.2 us25 Test Devices
In this section thermal conductance measurements which provide more insight
into the hot-electron effect in a more optimally-sized THM detector are presented.
These results have previously been reported in Barrentine et al. 2011 [7]. These
are measurements of two micron-sized THM devices of variation us25 consisting of a
Ti/Au TES with niobium superconducting leads, and with an overlapping normal Bi
absorber. As will be discussed in section 5.5 these devices were fabricated to observe
the lateral proximity effect in a normal metal film. The Ti layer is for adhesion to
the Si substrate only and is non-superconducting. In Figure 5.17 the layers for test
devices of variation us23 and us25 are shown, as well as an optical image of one of the
larger us23/us25 test devices.
In this section measurements of two of the smallest THM test devices on wafer
us25 are presented. Device dimensions and resistances for these two test devices are
listed in Table 5.4. Here the TES active thermal volume (shown in Figure 5.18) is
considered to include only that volume between the Nb lead contacts and not the
volume which overlaps the contacts (due to the strong bilayer proximity effect with
the Nb lead). The absorber active thermal volume does include, however, the Bi
overlap onto the Nb microstrip transmission line.
Unfortunately, no superconducting transitions were observed in these us25 de-
vices. There was, however, a small linear drop in resistance from 4 K to 150 mK
181
(a)
(b)
3um Bi, 1.2 um, evaporated deposition, liftoff
Nb, 150nm, sputtering deposition, sloped-sidewall RIEnon-superconducting Ti, 5nm, sputtering deposition
Au (us25: 30nm, sputtering deposition, liftoff, presputter before Nb deposition) &
(us23: 60nm, sputtering deposition, wet-etch, presputter before Nb deposition)
Bi Absorber
Nb LeadsTES
Figure 5.17: (a) Fabrication steps and cross-sectional view showing the
layers for each of the us23/us25 test devices. Thicknesses are not drawn
to scale, but are listed on the labels for each layer. (b) SEM image of a
test device of variation us23/us25.
182
Table 5.4: Device dimensions and resistance measurements for the two
micron-sized test devices of variation us25.Au TES Volume (µm3) Bi Absorber Volume (µm3) TES Resistance at 190 mK R vs. T slope
3.2x6.0x.03= 0.58 3.0x12.0x0.8= 29 1.26 Ω .0127 ΩK
3.0x3.0x.03= 0.27 3.0x12.0x0.8= 29 2.52 Ω .0209 ΩK
(see Table 5.4). This shallow resistance versus temperature curve was sufficient to
provide thermometry for the measurement of the thermal conductance of these THM
devices. It also provided an advantage in that thermal conductance measurements
were possible over a wider temperature range than would normally be allowed for a
TES detector with a very sharp RTES vs. T curve. This wider temperature range al-
lowed for a more discriminatory measurement of the temperature dependence of power
flow in the detector and the corresponding n value.
These two test devices were cooled to 150 mK. 4-wire resistance versus tempera-
ture measurements were taken for each of the devices by passing a small AC excitation
current (1.22 µArms) through the TES and measuring the voltage with a lock-in am-
plifier while sweeping the bath temperature. To measure the thermal conductance,
the 4-wire resistance of each TES was measured at a fixed bath temperature while DC
power was applied directly to the absorber via separate bias leads to the absorber.
The TES temperature rise due to Joule heating in the absorber was inferred from the
zero power TES resistance vs. temperature curves.
In Figures 5.19 and 5.20 the applied power, P , is plotted as a function of hot-
electron temperature, Tbolo, up to temperatures of 6 K. Measurements below 300 mK
were not possible due to the shallow slope of the resistance vs. temperature curve.
The data was fit to the predicted ideal power law function for n values between 4 and
183
Figure 5.18: The layer overlap and active thermal area of the TES and
absorber for the two micron-sized test devices of variation us25.
184
Table 5.5: us25 thermal conductance measurements. Fits to κe−p values
for n = 5 and n = 6 are shown and compared to κe−p ‘literature values’.
Thermal conductances are predicted from these fits projecting down to
Tbath = 50 mK, assuming either ‘CMB-space’ or ‘FIR-spectral’ observing
conditions.TES volume 0.58 (µm3) 0.27 (µm3)
κe−p fit n = 5 ( WK5 ) 2.1 · 10−9 1.0 · 10−9
κe−p fit n = 6 ( WK6 ) 4.6 · 10−10 1.9 · 10−10
κe−p Literature ( WK5 ) 9.3 · 10−9 8.1 · 10−9
‘CMB-space’ Ge−p (WK) n = 5 1.1 · 10−11 9.7 · 10−12
‘CMB-space’ Ge−p (WK) n = 6 7.9 · 10−12 6.8 · 10−12
‘FIR-spectral’ Ge−p (WK) n = 5 6.6 · 10−14 3.1 · 10−14
‘FIR-spectral’ Ge−p (WK) n = 6 8.6 · 10−16 3.6 · 10−16
6. The best fit parameters and the resulting thermal conductances at 50 mK bath
temperature are listed in Table 5.5. Predicted thermal NEPs for the devices based on
these thermal conductances and also assuming a 50 mK bath temperature are listed
in Table 5.6. The values are calculated from the fit κe−p values. Here we assume that
thermal noise dominates and do not consider Johnson or SQUID noise contributions.
For the low loading far-infrared limit, NEP values are calculated using Equation 2.26.
For CMB observing the NEP values are calculated using Equation 2.27. For CMB
observing the detector temperature is determined assuming the ‘CMB-space’ loading
conditions described in Chapter 4. A TES bias power of twice the sky power is
assumed. For ‘CMB-space’ loading and n = 5, Tbolo ∼ 200 mK, for ‘CMB-space’
loading and n = 6, Tbolo ∼ 300 mK at a 50 mK bath temperature for the measured
thermal conductances.
185
Figure 5.19: Joule power applied to the absorber versus hot-electron tem-
perature, Tbolo, while the bath was held constant at 190 mK for the THM
test device of variation us25 with Au TES volume of 0.27 µm3. Fits to
the predicted forms of the power law dependence are shown.
186
Figure 5.20: Joule power applied to the absorber versus hot-electron tem-
perature, Tbolo, while the bath was held constant at 190 mK for the THM
test device of variation us25 with Au TES volume of 0.58 µm3. Fits to
the predicted forms of the power law dependence are shown.
187
Table 5.6: Predicted thermal NEP from thermal conductance measure-
ments of the two, micron-sized us25 test devices projecting down to
Tbath = 50 mK. These devices would make good CMB (or FIR) detec-
tors, with NEPdetector ≤ NEPphoton.
TES volume 0.58 (µm3) 0.27 (µm3)
‘CMB-space’ NEPthermal (W√Hz
) n = 5 3.2 · 10−18 3.4 · 10−18
‘CMB-space’ NEPthermal (W√Hz
) n = 6 4.6 · 10−18 4.9 · 10−18
‘FIR-spectral’ NEPthermal (W√Hz
) n = 5 9.5 · 10−20 6.6 · 10−20
‘FIR-spectral’ NEPthermal (W√Hz
) n = 6 1.1 · 10−20 7.0 · 10−21
‘CMB-space’ Photon NEP ( W√Hz
) 4 · 10−18 4 · 10−18
‘FIR-spectral’ Photon NEP ( W√Hz
) 1 · 10−20 1 · 10−20
In Table 5.5 κe−p ‘literature values’ are also calculated for these device dimen-
sions. Literature values for Au and Bi are characterized by an n = 5 dependence and
units for κe−p are thus in WK5 . As the detector is a hybrid TES/absorber structure,
Σ and n could not be determined for the Au and Bi structures independently. Based
on literature values we expect the Bi absorber structure to contribute more than 70%
of the total electron-phonon thermal conductance of these test devices. Interestingly,
however, the doubling in the measured best fit κe−p values, which corresponds to a
doubling of the gold TES volume in these two test devices, seems to indicate that the
gold structure may actually be dominating the thermal conductance.
The best fits for Tbolo =6 K-300 mK are consistent with n = 5 − 6, with a
better fit given by n = 6. A n = 4 fit, which might be expected from phonon-phonon
188
scattering at the boundary between the detector and substrate is not consistent with
our measurements. The best fit κe−p values however are a factor of 5-8 times lower
than what is predicted by literature κe−p values. The thermal conductance we measure
for these devices projecting down to a 50 mK bath temperature for CMB loading
conditions is Ge−p = 7− 8 · 10−12 W/K for n = 6. For the low power loading limit for
FIR observing conditions (Tbolo ∼ Tbath) this corresponds to Ge−p = 4 − 9 · 10−16 WK
for n = 6.
5.4.3 Conclusions of Inquiry into Electron-Phonon Effect
In conclusion, for both THM2003 and us25 test devices a power dissipation is
measured which is consistent with a hot-electron effect dominating the power flow in
the detector from the absorber and TES into the substrate cold bath. The measure-
ment of n ≥ 5 for the us25 test devices in particular confirmed this hot-electron effect.
The measured κe−p values are slightly or significantly lower than those measured for
Au and Bi in the literature, with a temperature dependence of the power flow following
a power law of n = 5 − 6. The observed n = 6 dependence in the us25 devices hints
that the previously unobserved disordered n = 6 behaviour in Au might be being ob-
served, but due to the composite nature of the detector in the ideal model, this n = 6
behaviour could also be due to the influence of the Bi layer. It is also interesting that
no indications of any electron-phonon 2-D effects which would suppress the n value
were seen in the thinner (30nm) Au TES devices. In the THM2003 non-ideal device
and in the us25 micron-size devices no conclusive evidence of a finite boundary resis-
tance, which would be characterized by n = 4 behaviour, is found. Electron-phonon
scattering appears to dominate the thermal resistance from the bolometer to the cold
189
bath for the THM detector.
5.5 Inquiry into the Lateral Proximity Effect
5.5.1 S-S’-S Junction Measurements
Measurements of the superconducting transition behaviour of THM test devices
on the micron-size scales are now presented. These measurements provided surprising
evidence for a dramatic lateral proximity effect on these size scales in the THM TES
devices. These results have previously been reported in Barrentine et al. 2009 [6].
These measurements corroborate measurements of similar TES devices of similar size
[97].
These antenna-coupled THM test devices from wafers THM4 & THM5 consist
of a 1.2 µm thick, 3 µm x 6 µm, 20 Ω evaporated Bi absorber which terminates
a 3 µm-wide Nb microstrip line as is shown in Figure 5.21. The absorber overlaps
a Mo/Au TES with superconducting Nb leads. The Mo pad extends out from the
Mo/Au TES bilayer, providing one of two avenues for contact to the Nb leads, as
depicted in Figure 5.21. The Nb leads and Nb microstrip were deposited over the
TES and then RI-etched to obtain a sloped Nb sidewall for good step coverage by the
absorber. The Bi absorber was deposited using the liftoff procedure and overlaps both
the Nb microstrip line and TES.
These test devices were fabricated with two different TES bilayer thicknesses, 55
nm Mo/350 nm Au (THM4) and 65 nm Mo/350 nm Au (THM5). The smallest TES
area is 3 µm x 3 µm square. TES devices were also fabricated with areas of 6 µm x
6 µm, 12 µm x 12 µm and 24 µm x 24 µm. As is visible in Figure 5.22, the actual
190
(a)
(b)
Au, 350nm, sputtering bilayer deposition, ionmill, reverse bias etch before Nb deposition
superconducting Mo (THM4: 55nm, sputtering bilayer deposition, ion mill)
(THM5: 65nm , sputtering bilayer deposition, ion mill)
3um Bi, 800nm, evaporated deposition, liftoff
Nb, 350nm, sputtering deposition, sloped-sidewall RIE
Figure 5.21: (a) Fabrication steps and cross-sectional view showing the
layers for each of the THM4/THM5 test devices. Thicknesses are not
drawn to scale, but are listed on the labels for each layer. (b) Optical
image of a test device of variation THM4/THM5.
191
lead-to-lead dimensions for the TES devices varied from device to device on the same
wafer due to a fabrication issue in which the Nb leads were over-etched at the point
of contact with the Au TES layer.
The test devices were cooled to 150 mK in the unshielded mount setup. 4-wire
resistance vs. temperature measurements were taken using a lock-in amplifier to send
a low amplitude (1.2 µArms) excitation current to the TES and to read out the TES
voltage via an isolation-amplifer. The TES transition temperature was discovered
to vary dramatically from device to device, depending on the distance between the
Nb lead contacts. In Figure 5.23 the measured TES Tc as a function of lead-to-lead
distance, L, for the two different bilayers is plotted. The large uncertainties in lead-
to-lead distance are due to the variation in the Nb over-etching at the leads for each
device. A dramatic shift towards higher Tc is seen with lead-to-lead distances L ≤ 12
µm. In fact, with some of the nominal 3 µm x 3 µm devices the transition temperature
is found to have shifted to the base of the Nb transition.
A curve fit is done for these measurements based on a relationship found for
resistance vs. temperature measurements of similar Mo/Au TES devices with Nb
leads [97] that follows the form:
Tc = TcN(1 + (LNL
)m). (5.3)
Here L is the lead-to-lead distance and LN is the characteristic distance scale at which
a shift in the Tc occurs. Our measurements follow this trend but with large scatter at
short distances, possibly due to the variation in actual lead-to-lead distance and/or
variation in the quality of the Nb contact with the TES. A best fit, however, is provided
by LN = 11-13 µm and m = 4− 6.
192
Figure 5.22: (a) Schematic of contact between the Mo/Au TES and the
Nb leads for devices THM4/THM5. (b) SEM image of contact between
the Nb leads and TES for a 3 µm x 3 µm THM4/THM5 device with no
absorber or microwave circuit. The Mo layer which extends from the TES
is visible as a slight change in Nb thickness. The over-etching of the Nb
leads during the Nb etch on top of the Mo/Au TES is also clearly visible.
193
Figure 5.23: (a) Tc vs. lead-to-lead distance, L, for the 65 nm Mo/350
nm Au bilayer devices of variation THM5. A curve fit is shown for the
parameters TcN = 240 mK, LN = 12 µm and m = 5. (b) Tc vs. lead-to-
lead distance, L, for the 55 nm Mo/350 nm Au bilayer devices of variation
THM4. A curve fit is shown for the parameters TcN = 170 mK, LN = 12
µm and m = 5. Data points indicate nominal L values while the error
bars indicate uncertainties due to over-etching. Error bars for Tc indicate
uncertainty distinguishing the TES from the Nb lead transition.
194
Table 5.7: Transition measurements for individual test devices from wafer
THM4/THM5.Lead to lead length, L (µm) Mo/Au Thickness Tc (K) ∆Tc (K) Normal Resistance (Ω) Absorber?
1977 65/350 0.243 0.007 13.82 no
24-30 65/350 0.263 0.010 0.033 yes
12-18 65/350 0.264 0.012 0.067 no
12-18 65/350 0.253 0.008 0.038 yes
6-12 65/350 ≥ 5.4 ≤ 3 - yes
3-9 65/350 ≥ 2.0 ≤ 6 - yes
3-9 65/350 7.3-8.5 ≤ 1.2 - yes
24-30 55/350 ≤ .240 ≤ 0.2 - yes
12-18 55/350 0.193 0.012 0.078 no
6-12 55/350 3.58 0.760 0.214 yes
3-9 55/350 7.6-8.1 ≤ 0.5 - yes
3-9 55/350 7.0-8.2 ≤ 1.2 - yes
The width of the transition was also found to increase with decreasing L. In
some of the smallest devices the transition is shifted so close to the Nb transition that
the true transition and transition width for the TES becomes difficult to determine.
The R vs. T curves at 1.2 µArms excitation current are shown in Figure 5.24 for a
nominal 12 µm long TES device (where the transition is hardly shifted at all from
the bulk transition temperature) and for a smaller nominally 3 µm long TES device
where the lateral proximity effect has shifted the TES transition up to the base of the
Nb lead transition at 8.1 K.
The transition temperature, normal resistance and the transition width for all of
the individual devices are listed in Table 5.7. The transition width, ∆Tc, was measured
as the width between 10% and 90% of the normal resistance. Tc was measured as the
midpoint between 10% and 90% normal resistance. For smaller devices the transition
temperature and breadth could not be determined in this manner and limits are given
instead. Most devices have an overlapping 3 µm wide Bi absorber.
195
Nb transition
Figure 5.24: Resistance vs. temperature curves for two of the THM test
devices. (a) Nominal 12 µm x 12 µm, 55 nm/350 nm thick, Mo/Au TES
with absorber of variation THM4. (b) Nominal 3 µm x 3 µm, 55 nm/350
nm thick Mo/Au TES with absorber of variation THM4 with a transition
near the Nb lead transition.
196
5.5.2 S-S’-S Conclusions
Based on the transition measurements of these micron-sized Mo/Au bilayer
TESs, the lateral proximity effect limits similar TES devices to lengths ≥12 µm in
order to retain a transition temperature within ∼200 mK of the Tc for long devices.
In addition to the shifting of the Tc and the increase in thermal noise due to this
higher bolometer temperature, the proximity effect will also increase the SQUID am-
plifier and Johnson noise contributions by broadening the transition, lowering α, and
decreasing the responsivity of the device.
There are still many unknowns about this bilayer S-S’-S system, such as the
role of contact resistance at the lead to TES interface and the nature of how the
bilayer aspect of the TES complicates the behaviour of the S-S’-S system. In Chapter
7 several possible steps are discussed which could be taken to minimize the lateral
proximity effect on micron-sized TES devices. The possibility of fabricating slightly
longer devices in order to work around this effect to create an optimal THM design is
also discussed. In addition, the possibility of using a single layer of Au for the TES,
and to make use of the Nb lateral proximity effect to obtain a reasonable transition
temperature as an S-N-S type junction has been suggested. The nascent exploration
of this idea, to create a novel type of TES device, is presented in the following section.
5.5.3 S-N-S Junction Measurements
We have explored the possibility of using a micron-sized Nb-Au-Nb, S-N-S junc-
tion as a TES. The advantages in this concept are a simplification of the system,
freedom from the thickness constraints due to bilayer thickness ratios, and a lowering
of the unmodified transition temperature, TcN , since the normal metal Au junction
197
has an unmodified transition temperature of TcN = 0 K. To explore this possibility
test devices were fabricated following procedures similar to those for Mo/Au bilayer
TES devices THM4 & THM5 where large shifts in Tc were observed as was presented
in the previous section. Figures 5.25 & 5.17 summarize the layer order and fabrication
method for the S-N-S devices that are presented here, and comparisons can be made
between these devices and the layer order and fabrication methods for the previous
bilayer devices THM4/THM5.
Four S-N-S variations were tested, which are designated: THMA4, THMA24,
us23 & us25. For devices designated us23 and us25, the Nb layer was deposited first
by sputtering, after which the vacuum was broken and the Nb layer patterned. Au was
then deposited via sputtering, preceded by a pre-sputter cleaning of the Nb surface.
The Au was patterned by liftoff in the case of us25, and wet-etch in the case of us23.
For the devices designated THMA4 and THMA24, the Au was deposited first via e-
beam deposition, then patterned via ion-milling, followed by a separate Nb deposition.
In the case of wafer THMA24, after the Au patterning an intensive cleaning of the
Au surface was performed, including a standard solvent clean, UV exposure clean and
in-situ reverse-bias etch immediately preceding the Nb deposition. This reverse bias
etch cleaning step etched ∼10 nm into the Au surface.
The Au surface of a test wafer which underwent the same processing as THMA24
was inspected with AFM and SEM imaging before and after the Nb deposition and
no organic residue was seen. Some of the images from this test wafer are shown in
Figure 5.26. For all of these S-N-S devices, an insulating, non-superconducting thin
layer of Mo (for THMA2 & THMA24) or Ti (for us23 & us25) was deposited beneath
198
(a)
(b)
Au (THMA4: 30nm, e-beam deposition & ionmill) &
(THMA24: 180nm, e-beam deposition & ion mill, reverse bias etch before Nb dep)
Non-superconducting Mo, 5nm, e-beam deposition, RIENb (THMA4: 150nm, sputtering deposition, sloped-sidewall RIE) &
(THMA24: 500nm, sputtering deposition, straight-sidewall RIE)
3um
Figure 5.25: (a) Fabrication steps and cross-sectional view showing the
layers for each of the THMA4/THMA24 test devices. Thicknesses are not
drawn to scale, but are listed on the labels for each layer. (b) SEM image
of a test device of variation THMA4/THMA24.
199
the Au for adhesion purposes to the Si substrate.
These S-N-S junctions, with lead-to-lead lengths ranging from 3-23 µm (and
widths ranging from 3-12 µm) were cooled in the unshielded mount setup. The tem-
perature was swept while monitoring the 4-wire resistance of each device with a lock-in
amplifier and a small AC excitation current. No transitions below the Nb transition
at 8.4 K were seen down to temperatures of 140 mK (and down to 50 mK for one
device of variation THMA24), using currents as low as 13-130 nArms. A magnetic coil
which provided a field up to 5-10 G in the vicinity of the TES device was also mounted
under the chip in order to test the device response to magnetic field. This was done
since a diffraction pattern due to a Josephson junction-like interference effect has been
observed in the critical current in response to magnetic flux in micron-sized bilayer
TES devices [97]. No effect was seen in the resistance measurements of THM test
devices when this field was ramped up and down in both directions perpendicular to
the TES plane.
In Table 5.8 a summary of these S-N-S measurements, indicating the limits
placed on the critical current for each of these variations, is shown. Limits on a
possible contact resistance, Rc, between the Nb and Au, which might impede the
lateral proximity effect are also listed. We measured non-zero Rc on a few devices on
us23, us25, and THMA4, however measurements of Rc are consistent with zero within
measurement error for devices of variation THMA24, which underwent more extensive
cleaning of the interface. These contact resistance measurements are shown in Figure
5.27.
The measured limit on contact resistance for THMA24 also falls near the min-
200
SEM image (left) and AFM image (right) of TES Au pad after ion-miling step and solvent, descum clean.
AFM image of TES Au after ion-milling, solvent, descum clean and reverse bias etch step..
SEM images of the TES Au pad (left) and the Au/Nb lead contacts (right) after Nb deposition.
5µm
µm
µm
2 µm 2 µm
Figure 5.26: SEM and AFM images after ion-milling, cleaning of the Au
surface, and Nb deposition. A rough surface of the Au metal is seen, but
no organic contamination which would be indicated by dark or stringy
residue can be seen in these images.
201
Figure 5.27: Measured contact resistance, Rc (with error), for all devices
tested. These measurements are normalized to assume a 3 µm2 contact
area for each device. Error bars indicate error due to the measurement
noise.
202
Ω
Figure 5.28: Chart summary of Table 5.8. The Kuprianov and Lukichev
Rc limits are also shown in the plot.
imum contact resistance limit given by Kuprianov and Lukichev [72] (discussed in
Chapter 3) for seeing noticeable shifts in Ic. In Table 5.8 the range for critical cur-
rents predicted by the S-N-S models discussed in Chapter 3 are also listed. For all
variations we rule out all or most of the critical current parameter space predicted by
these S-N-S models. The measurements and predictions in Table 5.8 are also summa-
rized in chart format in Figure 5.28.
203
Table 5.8: Summary of 4-wire resistance measurements of S-N-S test de-
vices. Ic limits with predictions for four variations of Nb-Au-Nb devices
are listed. Predictions were calculated using the Au thickness, d, measured
Au resistivity, ρ, measured Nb Tc = 8.4 K and the four S-N-S models de-
scribed in Chapter 3. Predictions for us23, us25, THMA2 & THMA24-1
were calculated for a 3µm × 3µm device at 140 mK, and measurements
were taken from 8 K-140 mK. The prediction for device THMA24-2 was
calculated for a 3µm × 12µm device at 50 mK and measurements were
taken from 4 K-50 mK. The resistivity, ρ, was measured using a larger
resistance, 960µm × 10µm Au test device on the same chip. Limits on
Rc were calculated by comparing the measured resistivity of each device
(with error due to measurement noise and dimension uncertainty) to ρ.
The contact resistance listed is for an assumed 3 µm2 contact area between
the Nb and Au. For the low contact resistances and low currents used in
the measurements we expected to see some evidence for superconducting
behaviour in these devices.Device L (µm) d (nm) ρ (Ω ·m) Ic predicted Ic Rc
us23 3− 23 60 2.4 · 10−8 190µA− 150nA ≤ 18nA ≤ 0.4Ω
us25 3− 23 30 4.0 · 10−8 3µA− 2nA ≤ 18nA ≤ 1Ω
THMA4 3− 15 30 3.1 · 10−8 8µA− 6nA ≤ 18nA ≤ 0.4Ω
THMA24-1 3− 12 180 3.2 · 10−8 490µA− 380nA ≤ 180nA ≤ 0.08Ω
THMA24-2 3.6 180 3.2 · 10−8 144µA− 5µA ≤ 425nA ≤ 0.05Ω
204
5.5.4 S-N-S Conclusions
Following typical TES fabrication procedures, in which the superconducting Nb
lead deposition and Au deposition are done separately, with robust cleaning of the
Au or Nb surface before deposition, we do not see any transitions in micron-sized
Nb-Au-Nb junctions at sub-Kelvin temperatures indicating that they could be used
as sensitive TESs in micro-bolometers. This result is in disagreement with theoretical
predictions for S-N-S type junctions, including those which allow for a small contact
resistance between the normal and superconducting layers.
It is possible that in contrast with the theoretical S-N-S models considered here,
and in contrast to what is observed in similar S-S’-S bilayer devices, even a small
contact resistance has a large weakening effect on S-N-S critical current behaviour. It
is also possible that magnetic impurities in the Au film which are also not considered in
these models are having a strong suppressive effect on the superconducting behaviour
of the films.
Previous results (Section 5.5.1) would appear to argue that the lateral proximity
effect in Nb-Mo/Au-Nb S-S’-S junctions is less sensitive to contact resistance between
the Nb and Au layer or impurity contaminations than for the Nb/Au/Nb S-N-S devices
described here. However, these null results for S-N-S junction test devices do indicate
that one possible method to weaken the lateral proximity effect and Tc shift in S-
S’-S devices would be to purposely create a dirty interface between the TES and
superconducting lead layers or to introduce sources of magnetic impurities into the
THM design. These options with regards to the lateral proximity effect in both S-S’-S
and S-N-S devices will be discussed in more length in Chapter 7.
205
5.6 Inquiry into Detector NEP
Under ‘CMB-space’ observing conditions the background photon noise level is
4 · 10−18 W√Hz
and for ‘FIR-spectral’ applications the background photon noise level
is 1 · 10−20 W√Hz
(see Section 4.2.1). The measured noise of the larger THM2003 test
device presented Section 5.3, which conformed to a non-ideal model, is thus still well
above CMB photon-noise levels at the device transition temperature near 300 mK.
Even projecting this device design down to temperatures of 50 mK and calculating
the NEP for this non-ideal model the noise is still slightly above background levels
(see Table 5.9).
In Table 5.6, and listed again in Table 5.9, the expected thermal fluctuation
noise is also calculated for each of the measured thermal conductances for the us25
test devices projected down to 50 mK. For these micron-sized us25 devices NEPs
near or below the background noise limit for CMB observing in space, and below the
background noise limit in the far-infrared are predicted. Unfortunately, at this device
size scale, the lateral proximity effect makes the low transition temperature necessary
to reach these low NEPs difficult to achieve. At this moment this is true for either a
3 µm long S-S’-S or a 3 µm long S-N-S device.
In the concluding Chapter 7 a new recommended mid-size design for the THM
will be presented. This design is necessary to make a functioning THM detector
which is not affected by a strong lateral proximity effect, and with the desired photon
noise limited noise performance for CMB observing, when it is operated at low (50
mK) bath temperatures. This design will not be optimal, however, for far-infrared
applications, where a smaller volume is still ultimately required to reach photon noise
206
Table 5.9: NEPthermal & Gep for the THM test device designs THM2003
and us25 predicted at 50 mK bath temperature assuming ‘CMB-space’
conditions. For THM2003 predictions the measured fit Σ values for this
device, n = 5 and a non-ideal model are assumed. For us25 predictions
the measured fit values κ value for the smallest device (with 3 µm long
TES), n = 6 and an ideal model are assumed. Predictions for the new
recommended design assume an ideal model and are based on these mea-
sured fit Σ and κ results where the exact Σ values assumed for ‘measured
n = 5’ and ‘measured n = 6’ are given in Section 4.2.1. For the THM
test devices thermal NEP is slightly above photon background noise. For
the new recommended design thermal noise below the photon background
noise is predicted.Device Label THM2003 us25 recommended THM-
‘measured n = 5’
recommended THM-
‘measured n = 6’
Au TES Volume 190nmx10µmx20µm 30nmx3µmx3µm 300nmx20µmx20µm 300nmx20µmx20µm
Bi Absorber Volume 500nmx20µmx100µm 800nmx3µmx12µm 800nmx3µmx12µm 800nmx3µmx12µm
κe−p (WKn ) 4.4 · 10−7 1.9·10−10 (n = 6) 1.3·10−7 (n = 5) 1.8·10−8 (n = 6)
Gep (WK) 3.8 · 10−11 6.8 · 10−12 (n = 6) 2.8 · 10−11 (n = 5) 3.0 · 10−12 (n = 6)
NEPthermal (W√Hz
) 9.0 · 10−18 5.0 ·10−18 2.3 ·10−18 3.3 ·10−18
NEPphoton ( W√Hz
) 4 · 10−18 4 · 10−18 4 · 10−18 4 · 10−18
limited levels. Further work and development following the suggestions which will be
discussed in Chapter 7 will be necessary to either make use of the lateral proximity
effect in a S-N-S type device, or avoid this lateral proximity effect in a S-S’-S type
device for a far-infrared THM detector. As a preview, the dimensions and performance
characteristics of the new recommended CMB THM design are also listed in Table 5.9.
207
Chapter 6
THM Microwave Design & Simulations
6.1 THM Microwave Design
In this chapter a microwave coupling scheme to the THM detector is presented.
This scheme makes use of planar microwave technology. The microwave designs pre-
sented here have been optimized for the 92 and 43 GHz frequency bands, however
via relatively simple scaling these designs are applicable over a wider range of CMB
frequencies (∼ 30 − 300 GHz). This planar microwave technology has a distinct ad-
vantage, and is probably necessary, for scaling to large detector arrays. In addition
to providing the THM with array-scalability, the planar microwave components of the
THM design also provide polarization sensitivity via the coupling of the detector to a
planar slot-antenna design. Other planar antenna designs are also possible (bow-tie,
spiral etc.) however the slot antenna approach is one which has been well-studied and
is most commonly used. This slot antenna is only sensitive to E-M radiation of a single
polarization direction. An array of detectors coupling to two slot antennas of orthog-
onal polarization directions would be capable of taking a polarization measurement of
the CMB.
208
In Figure 6.1 and Figure 6.2 the two microwave designs developed for the THM
detector test devices us23/25 and THM4/THM5 are shown and the main components
for each of these designs labelled. A chip-size optical image of a test device of variation
us23 is also shown in Figure 6.3. In addition to the two slot antenna chip designs de-
scribed in Figures 6.1 & 6.2, alternative variations to this slot antenna chip design were
also fabricated for test devices THM4/THM5. These alternative designs included a
two-detector arrangement for testing of the filter response shown in Figure 6.4. Addi-
tionally, 43 GHz coplaner waveguide (CPW) test chip designs were fabricated in order
to make cryogenic probe station measurements of individual microwave components.
These tests and the design of these CPW test devices are briefly described in Section
6.2.1.
The components to the THM microwave coupling design include: a slot antenna,
microstrip transmission line, a low-pass filter, various couplers, DC bias lead chokes,
and a microstrip termination structure. In the first part of this chapter, each of
the individual components to this design will be described and some of the E-M
simulations (using Sonnet, Ansoft Designer, Ansoft HFSS or CST Microwave Studio
E-M simulation software) which predict the performance of these components are also
presented.
These E-M simulation software programs all work by 2-D or 3-D modelling of the
microwave component under design. Common input parameters for these models are
the component geometry, and the microwave material properties, such as the relative
dielectric constant, the kinetic inductance and the resistivity. The simulations are
completed by dividing the model of the microwave component into small regions via
209
a meshing algorithm. An input microwave signal (usually at a particular frequency)
is modelled as an excitation via a microwave port on the design and the response of
the microwave component under design is simulated by solving Maxwell’s equations
within each of the mesh boundaries, solving for the E-field, H-field, current, voltage
and impedance properties at all locations in the microwave model geometry as a
function of the input microwave signal frequency.
A useful feature of many of these simulation software programs is the ability to
optimize the geometry of a design. For example, if a minimum transmission loss is de-
sired at a particular center band frequency an optimization routine can be run which
explores the geometry parameter space within a certain range and finds the optimal ge-
ometry which gives a maximum throughput at a certain frequency. This optimization
ability was used in the design of many of the THM microwave components.
These E-M simulation results are reported in terms of S-parameters. These S-
parameters assume that a microwave input signal is sent in via an input port in the
microwave design and the output signal at another port in the microwave design is
measured. The S-parameter, Sij , is a measure of the power transmission from one
port “j” to another port “i”. Likewise the S-parameter, Sii, is a measure of the power
reflection back into the input port “i”. S-parameters are reported in this chapter in
terms of decibels (dB). Here the relation between decibels to the magnitude of the
power ratio in and out of each of these ports is given by:
Sij = 10 logPi,outputPj,input
(6.1)
In the final part of this chapter, in Section 6.2, two off-chip optical coupling
schemes are introduced. These schemes have been developed to test the microwave
210
performance of these THM test devices in a laboratory cryostat. However, one could
imagine adapting a similar off-chip coupling scheme to couple the THM detector or
detector array to the CMB sky as part of a ground- or space-based telescope.
6.1.1 Microstrip Transmission Lines
The microwave circuit for the THM test devices consists of portions of supercon-
ducting Nb microstrip transmission line (previously discussed in Section 4.2.2). At its
narrowest, this microstrip transmission line is 3 µm wide. In the case of test devices
THM4/THM5 the transmission line consists of a 350 nm thick Nb microstrip line
over a 150 nm thick Nb ground plane separated by a 750 nm thick Al2O3 dielectric
(with expected relative dielectric constant of ǫR = 10). In the case of test devices
us23/us25 the microstrip is a 150 nm thick Nb microstrip line over a 250 nm thick
Nb ground plane separated by a 1.45 µm thick Si dielectric (with expected relative
dielectric constant of ǫR = 11.7).
The characteristic impedance of the narrowest 3 µm wide line is ∼20 Ω for
variations THM4/THM5 and ∼30 Ω for variations us23/us25. The small line width
of the 3 µm wide microstrip line makes geometrical and impedance matching possible
between the microstrip line and the optimal THM Bi absorber. This superconducting
Nb microstrip had a measured transition temperature between 8 and 8.5 K, with
measured critical currents > 10 mA. A surface kinetic inductance of Ls = 0.13 pH
was
assumed for the Nb microstrip lines during the E-M simulations of the microstripline
and other microstrip-type components based on surface impedance calculations [62].
The thin-film Nb, with a large energy gap of ǫgap ∼ 3.5kBTc at 200 mK, remains
superconducting at microwave frequencies below ∼ 600 GHz (fmax ∼ ǫgaph), allowing
211
Double Slot Antenna
Figure 6.1: Microwave design at 92 GHz to couple radiation to the THM
detector for the THM4 and THM5 test devices. Devices at 43 GHz were
also designed and fabricated. The signal from the double slot antenna
is transmitted via a low-pass filter to the RF-terminated THM detector.
Choked bias leads provide DC connections to both the TES (for bias and
SQUID read out) and the absorber (for DC Joule heating of the absorber).
212
Slot Antenna
Low-pass Filter
Coupler
THM and Microstrip Termination Structure
DC Chokes
Figure 6.2: Microwave design at 92 GHz to couple radiation to an array
of 128 individual THM detectors for the us23/us25 test devices. The
coupling to such a large number of detectors was done in an attempt to
find the optimal lateral proximity effect S-N-S TES, with each of the 128
detectors of varying TES lead-to-lead length. In actual operation, with
an optimized THM device, one imagines only a single detector coupling
to the slot antenna without the branching network.
213
Figure 6.3: Optical image of one of the us23/us25 test device detector
chips. Chip size is 15 mm x 15 mm.
214
THM Termination
Low Pass Filter
Coupled Line Coupler
Figure 6.4: Two-detector coupled alternative slot antenna design for test
devices THM4/THM5. This device was designed specifically to test the
performance of the low-pass filter. A directional coupled line coupler trans-
mits the signal to two separate detectors, one line via a low-pass filter and
another line without the filter. By coupling a swept microwave signal
into the slot antenna the filter response as a function of frequency can be
determined.
215
for near lossless transmission through the straight microstrip line portions of the THM
microwave circuit.
6.1.2 Double Slot Antenna Design
The slot antenna design for the test devices THM4 & THM5 (Figure 6.1) is a
double-slot design based on a similar design by Zmuidzinas & LeDuc [129]. In this de-
sign two slots are made in the ground plane of the superconducting microstrip circuit.
An incident E-M wave excites current in the superconductor surface surrounding these
slots. The slot antenna is sensitive to electric field modes which are perpendicular to
the direction of the slot length. A single slot gives an asymmetric beam pattern; the
double slot beam pattern is more symmetric. In this slot antenna design coupling
to the microstrip transmission lines is done by crossing the microstrip line over the
center of the ground plane slots and shorting the microstrip line to ground via a radial
stub described in Section 6.1.4. The two microstrip lines are combined into a single
microstrip line which then transmits the signal to the THM detector. The geometry
of the double slot antenna design is shown in Figure 6.5.
To find the correct design parameters, the impedance equations given in Zmuidz-
inas & LeDuc were solved, requiring an impedance matching of the antenna to the
microstrip line. Near 90 GHz, a match to the ∼20 Ω microstrip line was satisfied by a
23 Ω+0.156i Ω input impedance to the slot antenna, resulting in the following design
equations:
f0 = 100GHz · 1mmL
(6.2)
W
L= 0.04. (6.3)
216
L
S
W
narrowing radial stub
microstrip
Figure 6.5: The geometry of the THM4/THM5 double slot antenna design.
217
For a symmetric beam:
S
L= 0.5662. (6.4)
For a slightly antisymmetric beam, but lower sidelobes:
S
L= 0.5. (6.5)
Here the length of the slot antennas, L, is equal to the microwave wavelength in the
dielectric. In the Al2O3 dielectric the 92 GHz wavelength is ∼1 mm. The slot width
is W and the separation between the two slot antennas is S. To reduce the stray
input inductance for the microstrip to slot antenna coupling, the ground plane slot
is narrowed in the region where the microstrip overlaps. For this design the slot is
narrowed to a minimum width of 3 µm.
The two microstrip lines are coupled together via a Wilkinson power divider [91].
This design is discussed in Section 6.1.6. The signal from an E-M wave excitation
should excite the two antennas in phase. The Wilkinson coupler requires all out of
phase signals be absorbed in a resistive (Bi) film. An Ansoft HFSS simulation showing
the expected performance (S11) of this slot antenna design is shown in Figure 6.6. For
this design a ∼ 10 % bandwidth near 92 GHz is expected. Harmonic resonances > 150
GHz (not shown in Figure 6.6) are also predicted. These high frequency “leaks” are
eliminated by the introduction of the low-pass filter described in Section 6.1.5. Optical
images of the 92 GHz slot antenna from test device THM5 are shown in Figure 6.7.
6.1.3 Four-Fold Slot Antenna Design
The second slot antenna design, which was introduced for test devices us23 and
us25, is a four-fold slot antenna design by K. U-Yen (unpublished). This design, which
218
S11
Figure 6.6: The simulated reflection (S11) from an input signal sent into
a port which feeds the single-line microstrip to the double slot antenna
for devices of variation THM4/THM5. The low level of reflection near 92
GHz indicates power radiated by the antenna.
219
1 mm
Figure 6.7: An optical image of the 92 GHz double slot antenna on a test
device of variation THM5.
220
was optimized for a center frequency at 92 GHz for the THM test devices, consists of
four aperture slots in the ground plane. Slot line transmission lines couple to the end
of the slots and transmit the signal to a horizontal slot transmission line. This manner
of coupling transmission lines to the slot antenna provides a broad bandwidth for the
antenna. A microstrip transmission line (with a rectangular stub which provides a
short to ground) couples to the horizontal slot line in a similar manner as in the
double slot antenna design. The geometry of this four-fold antenna design is shown in
Figure 6.8. As was the case with the double slot antenna design, this antenna is also
only sensitive to incident E-M radiation which has electric field lines perpendicular to
the length of the slots.
Here the slot antenna length, L = 0.575 mm, is a half-wavelength of the 92 GHz
wavelength in the Si dielectric. The other slot antenna dimensions are optimized for
maximum absorption around the center frequency using Ansoft Designer, with optimal
dimensions for the 92 GHz design of W = 42 µm, S = 1 mm, WV = 10 µm, WH = 3
µm. Microwave simulations of this design included the effect of a 2 µm thick BCB
bonding material (ǫR = 2.6) directly under the ground plane layer on the opposite side
to the 1.45 µm thick Si dielectric. The simulated optimized four-fold 92 GHz antenna
performance is shown in Figure 6.9.
This four-fold antenna design has a broader bandwidth than the double slot
antenna design, with -10 dB bandwidth of ∼50% at 90 GHz. Harmonics (not shown
in Figure 6.9) are expected at frequencies > 150 GHz. A low-pass filter is again used
to limit transmission above these frequencies. The beam pattern for the slot antenna
(with no further optical coupling schemes, such as those which will be described in
221
wh
wv
L
W
S
Rectangular StubSlot lines in ground plane
Slot aperature in ground plane
Microstripline
Figure 6.8: The geometry of the us23/us25 four-fold slot antenna design.
222
1 0 3 0 5 0 7 0 9 0 1 1 0 1 3 0 1 5 0-4 0
-3 5
-3 0
-2 5
-2 0
-1 5
-1 0
-5
0
Frequency (GHz)
S1
1 (
dB
)
Figure 6.9: The simulated reflection (S11) at the port which feeds the mi-
crostrip to the four-fold slot antenna for the test devices of variation
us23/us25. The low level of reflection indicates power radiated by the
antenna.
223
Si wafer
Vacuum
Nb Groundplane
Vacuum
Figure 6.10: The predicted beam pattern at 92 GHz for the four-fold slot
antenna design for the test devices of variation us23/us25. As expected,
the gain into the Si substrate is greater than into vacuum.
Section 6.2.2) is also shown in Figure 6.10.
6.1.4 Radial & Rectangular Stubs
The radial stub design [113] and rectangular stub design, shown in Figures 6.11
& 6.12 respectively, provide for an effective microwave short circuit at the base of the
stub on the top microstrip layer to the ground plane. This provides coupling of the
slot antenna excitation currents in the ground plane to the microstrip transmission
line. The dimensions for the radial stub design at 92 GHz for devices THM4/THM5
are: α = 60 and R = 104 µm. The dimensions of the rectangular stub design at
92 GHz for devices us23/us25 are: L1 = 106 µm, L2 = 105 µm, W1 = 28 µm, and
224
R
α
Slot Antenna
3 µm microstrip feedline
Figure 6.11: The geometry of the radial stub design for devices of variation
THM4/THM5.
W2 = 5 µm. Sonnet simulations for the radial stub design’s input impedance when
terminating a 3 µm microstrip line for the THM4/THM5 design are shown in Figure
6.13 and show a broadband short to ground near 92 GHz.
6.1.5 Low-pass Filter
The low-pass filter design (shown in Figure 6.14) which blocks the high frequency
leaks from the slot antenna is based on a design by K. U-Yen [117]. The design
consists of three separate lumped element low-pass filters: two microstrip “stub” type
225
L1
L2
W1
W2Slot Line in ground plane
3 µm microstripline
Figure 6.12: The geometry of the rectangular stub design for devices of
variation us23/us25.
226
Figure 6.13: Input impedance for the THM4/THM5 radial stub design.
A very broad bandwidth at 92 GHz indicating a short to ground (with
impedance Z ≪ 20 Ω) is predicted.
227
Part 1 Part 2 Part 3
10 Ω
µstripline
10 Ω
µstripline
Figure 6.14: The geometry of the low-pass filter, consisting of three sub-
filters, indicated as “Part 1”, “Part 2”, and “Part 3”. “Part 1” and “Part
3” are “stub” type filters and “Part 2” is a “stepped impedance” type
filter.
filters and one microstrip “stepped impedance” type filter. These three filters combine
to block out frequencies from ∼ 150-600 GHz (at 600 GHz the microstrip becomes
non-superconducting and lossy). The design has a characteristic input and output
impedance of 10 Ω. An optical image of the low-pass filter on one of the test devices
of variation THM5 is shown in Figure 6.15. HFSS Ansoft Design simulations for the
us23/us25 design, showing the expected performance for the individual sub-filters and
the entire low-pass filter, are shown in Figures 6.16 & 6.17.
6.1.6 Couplers
The couplers in the microwave design for these test devices include either a direc-
tional coupled line coupler (in the case of the variation shown in Figure 6.4) or Wilkin-
son couplers [91]. The Wilkinson coupler geometry and design parameters are shown
in Figure 6.18. The Wilkinson coupler is used in the us23/us25 128 channel-splitting
network to isolate the detectors from each other; it rejects any out of phase signals
due to reflections in the circuit. The Wilkinson coupler is used in the THM4/THM5
microwave design to add the signals from the two slot antennas together. An optical
228
3 µm
Figure 6.15: Optical image of the low-pass filter from test device of varia-
tion THM5.
image of the Wilkinson coupler in a portion of the splitter network on a device of
variation us23 is shown in Figure 6.19. Simulations for the expected transmission be-
tween input and output ports for the Wilkinson Coupler design for the us23/us25 test
devices are shown in Figure 6.20. The directional coupler designs are not presented
here.
6.1.7 Termination Structure
The termination structure for the THM is perhaps the most important part
of the microwave circuit. It provides for the termination of microwave power in the
small THM absorber volume. The small volume of the absorber requires that the
incoming microwave radiation be absorbed over a short distance compared to the
effective wavelength of the radiation. The termination structure consists of two parallel
229
0 .0 0 1 0 0 .0 0 2 0 0 .0 0 3 0 0 .0 0 4 0 0 .0 0 5 0 0 .0 0 6 0 0 .0 0 7 0 0 .0 0F [GH z]
-8 7 .5 0
-7 7 .5 0
-6 7 .5 0
-5 7 .5 0
-4 7 .5 0
-3 7 .5 0
-2 7 .5 0
-1 7 .5 0
-7 .5 0
dB
(S(P
ort
1,P
ort
2))
Part “2”:
0 .0 0 1 0 0 .0 0 2 0 0 .0 0 3 0 0 .0 0 4 0 0 .0 0 5 0 0 .0 0 6 0 0 .0 0 7 0 0 .0 0F [GH z]
-7 5 .0 0
-6 5 .0 0
-5 5 .0 0
-4 5 .0 0
-3 5 .0 0
-2 5 .0 0
-1 5 .0 0
-5 .0 0
dB
(S(P
ort
1,P
ort
2))
Part “1”:
0 .0 0 1 0 0 .0 0 2 0 0 .0 0 3 0 0 .0 0 4 0 0 .0 0 5 0 0 .0 0 6 0 0 .0 0 7 0 0 .0 0F [GH z]
-7 0 .0 0
-6 0 .0 0
-5 0 .0 0
-4 0 .0 0
-3 0 .0 0
-2 0 .0 0
-1 0 .0 0
0 .0 0
dB
(S(P
ort
2,P
ort
1))
Part “3”:
Figure 6.16: Simulated transmission (S12) through the low-pass filter
parts. Part “2” defines the low frequency cut-off. Part “1” blocks the
higher frequency leaks from part “2”. Part “3” blocks the higher fre-
quency leaks from part “1”.
230
0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0-1 2 0
-1 0 0
-8 0
-6 0
-4 0
-2 0
0
Frequency (GHz)
S12
(dB
)
Figure 6.17: The simulated transmission (S12) through the low-pass filter
for the us23/us25 design. Note that “in-band” (∼ 75− 110 GHz) the loss
is < −3 dB while the out of band rejection at frequencies > 180 GHz is
excellent (< −20 dB transmission).
231
2Z0
Z0
Z0
Z0
e2 Z0
e2 Z0
l/4
Lumped Resistor
Microstrip line
Figure 6.18: The Wilkinson coupler design [91]. The design requirements
are shown in terms of the charateristic impedances of the input and output
microstripline, Z0, and the microwave wavelength in the dielectric, λ.
232
210 µm
Figure 6.19: An optical image of the Wilkinson couplers in part of the
128-channel splitter network on a test device of variation us23.
233
5 0 .0 0 7 0 .0 0 9 0 .0 0 1 1 0 .0 0 1 3 0 .0 0 1 5 0 .0 0F [GH z]
-3 5 .0 0
-3 0 .0 0
-2 5 .0 0
-2 0 .0 0
-1 5 .0 0
-1 0 .0 0
-5 .0 0
0 .0 0
dB
Curv e Inf o
dB(S(Por t1,Por t1) )
dB(S(Por t1,Por t2) )
dB(S(Por t1,Por t3) )
Figure 6.20: S-parameters showing transmission from port 1 (output of
coupler) to ports 2 and 3 (inputs to coupler) for the us23/us25 Wilkinson
coupler design. A 3 dB (equal) coupling/splitting is expected near 92
GHz.
234
shorts to ground made of lumped capacitive and inductive microstrip elements as
shown in Figure 6.21.
This termination design provides absorption over a very wide band as is shown
by the Ansoft Designer simulations in Figure 6.22. Here the reflection S-parameter
(S11) is the reflected power when an input signal is sent into a port at the microstrip
line transmission side of the termination structure, before the absorber. The very low
reflection indicates absorption in the THM Bi absorber. This simulation assumes an
exact impedance match between the microstrip line and the Bi absorber. However,
even a large mismatch in absorber resistance results in minimal loss to reflection. Here
one can assume the fraction of reflected power, Γ, is given by the relation [91]:
Γ = (RAbs − Z0
RAbs + Z0)2 (6.6)
where RAbs is the absorber resistance and Z0 is the characteristic impedance of the 3
µm wide microstrip line. Even an absorber resistance difference of 10 Ohms will result
in . 10% loss of the incoming power to reflection. The termination structure design
is also modifiable over a range of THM geometries.
6.1.8 DC Chokes
DC chokes are necessary in order to attach bias leads to the THM TES. DC
chokes can also can provide DC access to the THM absorber without interrupting the
microwave circuit of the THM detector. The absorber access allows a DC bias to be
applied in order to dissipate Joule power in the absorber to measure thermal conduc-
tance and compare DC to RF response. DC chokes are inserted at the microstrip
termination structure as bias leads the TES, and at the microstrip transmission line
235
Nb microstripline
Nb
Nb
Bi absorber
TES
L1
L2
W1
W2
RF signal
Figure 6.21: The THM microstrip termination structure geometry. The
large rectangular microstrip structures provide capacitive coupling to
ground. For the us23/us25 design optimal dimensions at 92 GHz were
W1 = 41 µm, W2 = 21 µm, L1 = 72 µm, and L2 = 29 µm. For the
THM4/THM5 design the optimal dimensions at 92 GHz were W1 = 54
µm, W2 = 10 µm, L1 = 90 µm and L2 = 30 µm.
236
0 2 0 4 0 6 0 8 0 1 0 0 12 0 1 4 0 1 6 0 1 8 0 2 0 0-4 0
-3 5
-3 0
-2 5
-2 0
-1 5
-1 0
-5
Frequency (GHz)
S1
1 (
dB
)
Figure 6.22: Simulated reflection (S11) for an input signal into the mi-
crostrip termination structure with matched THM absorber (Z0 = RAbs =
31 Ω) for the us23/us25 design.
237
DC Chokes for TES bias leads
DC Chokes for absorber access
THM and RF termination
W1
L1
L2
W2
Microstrip Termination Structure
RF signal
Figure 6.23: The geometry and placement of the DC chokes on the
us23/us25 devices in order to provide TES bias and absorber access. A
close up of the RF termination on the THM absorber is shown in Figure
6.21.
before the termination at the absorber for absorber access, as is shown in Figure 6.23.
The inductive and capacitive lumped elements of this choke design create a microwave
“open” at the input to the chokes, but allow for the transport of DC currents. In
Figure 6.24 the simulated microwave transmission in a microstrip line intersected by
a DC Choke is shown for the us23/us25 choke design.
6.1.9 Impedance Transformers
At various places in the THM microwave circuits for test devices us23/25 and
THM4/THM5, microstrip impedance transformers are necessary to impedance match
between microstrip components of different characteristic impedances and whose impedance
is constrained by geometry or other design constraints. For example, this is done in
238
Port1 Port2
5 0 .0 0 7 0 .0 0 9 0 .0 0 1 1 0 .0 0 1 3 0 .0 0 1 5 0 .0 0F [GH z]
-3 5 .0 0
-3 0 .0 0
-2 5 .0 0
-2 0 .0 0
-1 5 .0 0
-1 0 .0 0
-5 .0 0
0 .0 0
dB
Curv e Inf o
dB(S(Por t1,Por t1) )
dB(S(Por t1,Por t2) )
Figure 6.24: Simulated microwave transmission (S12) and reflection (S11)
through a microstripline (above) which is intersected by the DC choke
design used in test devices us23/us25. In the desired RF band of the
detector the presence of the DC connection has little effect on the RF
performance.
239
400 µm
3 µm 6 µm
Figure 6.25: The geometry of one of the stepped impedance transformers
from the us23/us25 test devices which transitions from a 19 Ω (6 µm wide)
to a 30 Ω (3 µm wide) microstrip line. Lengths/widths are not drawn to
scale.
the us23/25 design after microwave coupling to the slot antenna to convert from 30
Ω (3 µm wide) microstrip to the 10 Ω (14 µm wide) microstrip input to the low-pass
filter. Another impedance transformer is used to convert from the 19 Ω (6 µm wide)
Wilkinson coupler output to the 30 Ω microstrip line which terminates on the 3 µm
wide absorber. These impedance transformers are all stepped-impedance transform-
ers, an example of the geometry of which is shown in Figure 6.25. The simulated
performance of one of these transformer designs is also shown in Figure 6.26.
6.2 THM Microwave Testing Schemes & Preliminary Mea-
surements
6.2.1 CPW Probe Station Microwave Design & Measurements
For devices THM4/THM5 additional microwave designs were fabricated at 43
GHz in order to test microwave components independently of the THM detector re-
sponse, in a 4 K cryogenic probe station. This probe station allowed for two-port
transmission measurements and one-port reflection measurements on a variety of test
lines which included variations of scaled versions of the 92 GHz microwave compo-
240
0 .0 0 2 5 .0 0 5 0 .0 0 7 5 .0 0 1 0 0 .0 0 1 2 5 .0 0 1 5 0 .0 0 1 7 5 .0 0 2 0 0 .0 0F [GH z]
-5 0 .0 0
-4 0 .0 0
-3 0 .0 0
-2 0 .0 0
-1 0 .0 0
0 .0 0
Y1
Curv e Inf o
dB(S(Por t1,Por t2) )
dB(S(Por t1,Por t1) )
dB
Figure 6.26: The simulated transmission (S12) and reflection (S11) through
the microstrip impedance transformer shown in Figure 6.25.
241
nents, including microstrip throughlines, terminations, filters, transformers and DC
bias chokes. The layouts of two of these 43 GHz probe station test chips are shown in
Figures 6.27 and 6.28. The co-planar waveguide (CPW) pads at the edge of this design
transition to 3 µm wide Nb microstrip lines using a CPW-to-microstrip transformer.
The Sonnet simulated performance for this transformer is shown in Figure 6.29.
The CPW probe station consists of a cryostat chamber, with two probe arms.
These probe arms are cooled to temperatures between 5− 7 K. The cold stage where
the chip is mounted is cooled to temperatures of 3−4 K with a pumped 4He bath. The
microwave signal is brought into the cryogenic vacuum chamger via coaxial cable and
connects to a spectrum network analyzer and microwave source which sweeps from 20
to 48 GHz. An IR filtered window with a camera allows for a view into the cryostat.
The probe tip positions on the end of the probe arms are adjustable after cooldown.
Pictures of this setup are shown in Figure 6.30. Calibration must be done at room
and cryogenic temperatures.
Preliminary measurements of test devices of variation THM4/THM5 were com-
pleted. The Nb microstrip transition was observed as the devices were cooled. The
Nb superconducting transition occurred at probe and chip temperatures of 8-8.5 K
where the throughline microwave performance was observed to transition from a lossy
to near lossless state. Calibrated measurements of the microstrip transmission loss at
4 K (removing the loss due to the CPW-to-microstrip transition) are shown in Fig-
ure 6.31. Measurements of the Al2O3 relative dielectric constant and characteristic
impedance of the 3 µm wide microstrip line are also shown in Figures 6.32 and 6.33.
Unfortunately, due to shorting issues on some of the test devices and high fre-
242
CPW ground contacts
CPW center conductor which transitions to microstrip
Figure 6.27: One of the THM 43 GHz CPW test chip designs. Used mainly
for calibration purposes, it includes microstrip throughlines of various
length as well as two microstrip line “opens”. Contact to each lines is
made by 3 CPW probe tip pads at the edges of the chip.
243
CPW ground contacts
CPW center conductor which transitions to microstrip
Figure 6.28: Another of the THM CPW designs, with test lines to test the
low-pass filter, termination structure, and impedance transformer perfor-
mances.
244
Figure 6.29: The predicted transmission (S11) and reflection (S12) through
the coplaner waveguide to microstrip transformer for the 43 GHz
THM4/THM5 CPW test chip design.
245
Probe Arms
Camera
Cable to Network Analyzer
and Source
Test Chamber
Window
Test chips
Probe tip
Figure 6.30: The CPW cryogenic probe station measurement setup.
246
Figure 6.31: Measured loss per millimeter of 3 µm wide microstrip
throughline on a test device of variation THM5. This measured loss is
within the measurement noise (∼ ±0.01 dB).
247
Figure 6.32: Measured relative dielectric constant of Al2O3 dielectric found
via calibration measurement of the microstrip throughlines and opens on
a test device of variation THM5. Expected ǫr ≈ 10.
248
Figure 6.33: Measured characteristic impedance of a 3 µm wide microstrip
line, found via calibration measurements of microstrip throughlines and
open lines on a test device of variation THM5. The measured impedance
is close to the 20 Ω design impedance.
249
quency calibration issues, we were unable to recover calibrated measurements of mi-
crowave absorption in the microstrip termination structure, or to measure other mi-
crowave components during these preliminary measurements of devices THM4/THM5.
Uncalibrated measurements of absorption were seen above the measurement noise
level at frequencies >35 GHz for a few of the CPW THM microstrip termination
structures. In the future, however, the probe station measurement setup may be a
very useful method for investigating the individual components necessary for coupling
microwaves to the THM detector.
6.2.2 Optical Coupling Schemes
To illuminate the devices with calibrated RF signals in the laboratory cryostat
we have devised two basic optical coupling schemes. These two schemes are depicted in
Figure 6.34 and are: 1) a black body microwave source placed inside the cryostat near
the THM detector chip; 2) an external variable frequency microwave source which is
brought into the cryostat via coaxial cable. In both of these cases the optical coupling
in the dewar is accomplished via the setup shown in Figure 6.34, in which the black
body source or the external source is coupled to a waveguide mount which feeds a
horn antenna mounted on the 4 K stage of the cryostat.
These optics are designed following quasi-optical Gaussian beam theory [41].
Contrary to how light behaves in geometrical optics, when the wavelength of the
light is much smaller than the optical components, with microwave light, where the
wavelength is macroscopic compared to the optical components, a beam never focuses
to a single point. Instead, the light is described as a Gaussian beam which focuses to
a beam of minimum spread, where this minimum beam size is defined as the Gaussian
250
beam “waist” radius, w0. The Gaussian beam waist is described in terms of a beam
width radius, w, and beam radius of curvature, R, at any location along the beam by
[41]:
w0 =w
√
1 + (πw2
λR)2
(6.7)
The location of this beam waist relative to the location of the beam at width, w, is
found using the relation [41]:
z =πw0
λ
√
w2 − w20 (6.8)
Optical coupling between two different Gaussian beams is done by matching the two
beam waist sizes and locations.
In the setup for coupling microwaves to the THM detector, the beam waist from
the horn antenna is matched via a Rexolite lens to the beam waist formed by an
extended hemispherical lens mounted to the slot antenna chip. The geometry of this
optical coupling method is shown in Figure 6.35. In the following sections the optimal
geometry for this optical coupling is derived. These optimal dimensions are listed in
Figure 6.35. In Section 6.2.3 and 6.2.4 the black body source design and the specifics
of routing the external source into the cold dewar are described.
6.2.2.1 The Horn Antenna
The horn antenna used is a pyramidal horn antenna with 15 dB gain attached
to a WR-10 waveguide mount. The horn antenna geometry is shown in Figure 6.36.
The beam waist and location for this pyramidal horn was determined by the following
procedure. First, the beam size and radius of curvature at the aperture is give by
251
200 mK
THM detector Chip
Slot antenna aperture
Extended hemispherical lens
4 K
Rexolite lens
Waveguide w/ horn antenna
Scheme 1: 4-20 K Blackbody source
embedded in waveguide
RF Source
300 K
Scheme 2:
External RF source
Figure 6.34: The two optical coupling schemes for testing the microwave
components and microwave response of the THM in the laboratory cryo-
stat. Components are not drawn to scale.
[124]:
wA =0.35wH + 0.5wE
2(6.9)
RA =SH + SE
2(6.10)
where wA is the average beam width at the aperture and RA is the average wavefront
radius of curvature at the aperture. These quantities can be calculated from the horn
geometry shown in Figure 6.36.
Using w = wA and R = RA the beam waist of this horn antenna, w0,in, is found
using Equation 6.7, assuming a 92 GHz center band frequency:
w0,in =wA
√
1 + (πw2
A
λRA)2
(6.11)
Using w = wa and Equation 6.8 one can solve for the beam waist location, zA, relative
252
Si Extended hemispherical Lens:
R=7 mm
L=2.8 mm
Rexolite Lens:
Radius of curvature= 12.0 mm
Diameter= 12.6 mm
Index of refraction=1.6
Horn Antenna:
Aperature width=6.3 mm
Aperature height=4.3 mm
w0,in= 2.0 mm w0,out= 5.1 mm
din=16.5 mm dout=8.8 mm
d0=1.7 mm
L
R
Figure 6.35: Dimensions of the optical components, separation distances
and beam waists. Figures are not drawn to scale.
253
to this aperture:
zA =πw0,in
λ
√
w2A − w2
0,in. (6.12)
Following this procedure for the horn antenna we calculate a beam waist radius of
w0,in = 2.0 mm, a distance of 1.65 mm behind the aperture plane of the horn an-
tenna, as shown in Figure 6.35. The beam pattern of the horn antenna was simulated
with CST Microwave Studio. The measurement of this beam pattern as well as the
simulation are shown in Figure 6.37.
6.2.2.2 The Extended Hemispherical Lens
The extended hemispherical lens geometry is shown in Figure 6.38. The optimal
dimensions for optical coupling to the THM slot antenna were chosen based on simula-
tions by Filopovic et al. [27] for an extended hemispherical lens coupling a similar slot
antenna design to free space, as our own simulations with HFSS and CST Microwave
studio of this coupling have been unsuccessful so far. We chose to use an extended
hemispherical lens characterized by the geometrical relation RL
= 0.39 for a Si lens
with ǫR = 11.7. This geometrical relation creates an approximate elliptical lens from
the extended hemispherical lens geometry. Filopovic et al. claim that this elliptical
lens design produces a beam waist at the curved surface of the hemispherical lens.
Another possible lens geometry for this design, which is also discussed in Filopovic et
al., is a hyper-hemispherical lens characterized by the geometrical relation RL= 0.27
for a Si lens. With the chosen elliptical lens we chose R = 7 mm to match to the
THM chip dimensions (15 mm x 15 mm) resulting in an extension length of L = 2.7
mm, with a predicted beam waist at the edge of the lens of w0,out =5.1 mm based on
Filipovic et al. simulations at 92 GHz. The elliptical lens is mounted directly to the
254
Horn Aperture
x=10.8 mm
Horn Aperture (face on)
wH= 6.3 mm
wE =
4.3
mm
Horn Throat
Horn Throat (face on)
lE =
1.3
mm
lH= 2.5 mm
SE = 10.9 mm
wE =
4.3
mm
Horn Aperture
x=10.8 mm
Horn Throat
SH = 11.0 mm
wH
= 6
.3 m
m
Cross-sectional view in E-plane
lE =
1.3
mm
lH =
2.5
mm
Cross-sectional view in H-plane
Figure 6.36: The horn antenna geometry and dimensions. Here SE and SH
are the pyramidal horn dimensions projected into the E-field and H-field
planes.
255
Figure 6.37: The simulated (above) and measured (below) beam pattern
from the pyramidal horn antenna at 92 GHz. Courtesy Sara Stanchfield.
256
L
R
Figure 6.38: The extended hemispherical lens geometry. R is the spherical
radius, L is the cylindrical extension length.
backside of the THM chip via a copper L-bracket mount and beryllium-copper spring
clamps to provide mechanical and thermal contact to the mount and coldstage.
6.2.2.3 The Rexolite Lens
The Rexolite lens dimensions and location (labelled as dout and din in Figure 6.35)
were determined by the available space in the dewar and requiring a match between
the horn antenna beam waist w0,in and the beam waist at the elliptical lens w0,out.
These parameters for the Rexolite lens can be calculated following the quasi-optical
thin lens approximation described here. First, dout and din are given by [41]:
din = f +M−1√
f 2 − f 20 (6.13)
dout = f +M√
f 2 − f 20 (6.14)
where M ≡ w0,out
w0,inand f0 =
πw0,outw0,in
λ. f ≡ the focal length of the Rexolite lens.
Assuming a thin lens approximation this focal length is given by [41]:
1
f=n2 − n1
n1
2
R(6.15)
257
where n2 = 1.59 is the index of refraction of Rexolite and n1 = 1.0 is the index of
refraction of air. R is the radius of curvature of both sides of the Rexolite lens. For
a focal length chosen to fit within the dewar space, the Rexolite curvature can be
determined, and the din and dout values found.
CST Microwave Studio simulations of the beam profile of the horn antenna Rex-
olite lens combination with optimal dimensions calculated from this method indicated
slight deviations of w0,out and dout from the values predicted by these calculations,
probably due to deviations of the Rexolite lens from the thin lens approximation.
Thus modifications to the Rexolite dimensions and placement were made via CST
studio simulations to find the optimal lens dimension and locations. These final di-
mensions are listed in Figure 6.35. Measurements and simulations of the horn antenna
beam pattern after refocusing by this Rexolite lens are shown in Figure 6.39.
6.2.3 Black Body Source
We have constructed and measured the characteristics of two cryogenic black
body microwave source designs. These black body sources are inserted into a waveg-
uide mount attached to the horn antenna on the 4 K stage of the dewar, and allow
testing of the response of the THM detector to a CMB-like source internal to the
cryostat. The black body source consists either of a distributed resistive element or a
lumped chip resistor which terminate a W-band waveguide. The termination can be
heated from 4 K to ∼ 20 K by Joule heating. At 4 K the black body source mimics
the 3 K black body loading from the CMB seen from a space-based instrument. At
20 K the black body source mimics the equivalent power loading from the CMB with
sky background for a ground-based instrument. A chip thermometer is mounted to
258
Figure 6.39: The simulated and measured beam pattern at 92 GHz from
the horn antenna after focusing by the Rexolite lens. Courtesy Sara
Stanchfield. Measurements are consistent with the simulated beam pat-
tern.
259
the black body source to monitor the black body temperature.
The black body source is thermally isolated from the waveguide and 4 K bath
via a thermal link which is characterised by a thermal conductance, Gbb. The black
body source also has a heat capacity, Cbb, consisting of the resistor heat capacity,
thermometer heat capacity, the heat capacity of any additional heater, as well as
the heat capacity of the adhesives used to mount these components and the insulating
substrate they are mounted on. The thermal time constant is τbb ≃ Cbb
Gbband determines
how fast the source power level can be chopped. The power, PJ , to heat the black
body is also determined by the thermal conductance where PJ ∼ Gbb(Tbb − Tbath).
A black body with near perfect emissivity (& 95%) is desired. In the following two
sections we describe and present thermal and microwave measurements of two black
body source designs, which fulfil these basic requirements.
6.2.3.1 Nichrome Black Body Source
The nichrome black body design is based on a similar black body source design
by McGrath et al. [85] for longer wavelengths. For our design a thin Nichrome film
(∼ 20 nm thick) with measured surface resistivity of ρ ∼ 200 Ω
is deposited on a
quartz wafer. A sliver of this quartz wafer is then inserted into the waveguide cavity
via a thin slot cut in the broad wall of the WR-10 waveguide. Outside of the waveguide
slot area, a 5 kΩ (∼ 8 kΩ at 4 K) resistor heater is mounted with silver epoxy. The
lead wires are Stycast to the quartz wafer. A ruthenium oxide chip thermometer is
mounted in a similar manner. This nichrome black body layout and the arrangement
of this black body source in the waveguide are shown in Figure 6.40.
The thermal link to the waveguide mount and 4K stage is provided by a copper
260
Waveguide Copper Block Mount
Heat Sink to 4K
Copper wire thermal linkThermometer
Resistor Heater
NichromePortion in waveguide
Figure 6.40: The nichrome blackbody source.
261
wire, the diameter and length of which can be adjusted. One end of this wire is glued
to the nichrome film with Ge varnish and the other end is soldered directly to a copper
plate which is clamped down to the copper waveguide mount. An additional thermal
link is provided by the thermal boundary conductance where the nichrome film and
the Quartz wafer come into contact with the copper waveguide mount as the wafer
is inserted into the waveguide. This boundary conductance was found to be quite
low, and did not dominate the thermal characteristics of the device. The thermal
conductance of the copper wire was adjusted to find the optimal Gbb which provided
a fast response, but still allowed for low power dissipation (< 100 mW) when heating
the source to 20 K. The heat capacity was also minimized as much as possible to
decrease the thermal response time.
The black body source design was cooled to 4 K in vacuum in an IR-shielded
laboratory cryostat and Joule power was applied to heat the device up to temperatures
of ∼ 20 K, while the bath temperature was held constant at 4 K. PJ vs. Tbb was
measured, as well as the thermal rise and fall time as the power was switched on
and off, allowing τbb, Gbb and Cbb to be determined. The maximum power needed
to raise the black body temperature to 20 K, PJ,max, was also determined. These
measurements of Gbb, Cbb, Pbb,max and τbb are listed in Table 6.1.
The microwave emissivity of the nichrome black body mounted inside the waveg-
uide was also measured via transmission and reflection measurements using a scalar
network analyzer with a microwave sweeper and external multipliers from 75 to 110
GHz. These measurements are shown in 6.41. We measure a thermal time constant
of 90 seconds, maximum power of 0.86 mW, and emissivity of 90 − 99%. Although
262
Table 6.1: The measured thermal characteristics of the nichrome black
body source.
Cbb (JK) Gbb (
WK) τbb (s) PJ,max (mW)
4.32 ·10−3 4.8 ·10−5 90 0.86
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
76 80 84 88 92
Frequency (GHz)
Em
issiv
ity
Figure 6.41: The measured emissivity of the nichrome black body source.
these thermal and microwave characteristics for this nichrome black body design are
acceptable, improvements are possible with the “finline” black body source design,
described in the following section.
263
Waveguide 1.5mm Kapton
Kapton film/circuit board
Figure 6.42: The geometry and layout of the finline black body source.
6.2.3.2 Finline Black Body Source
The second black body design is a modification of the nichrome black body
design and was developed to simplify the fabrication and shorten the time constant.
In this design a copper finline structure on a Kapton dielectric PC board (fabricated
by Brigitflex) is inserted in the E-plane of the WR-10 waveguide. The geometry of
this finline is shown in Figure 6.42 and a photo of the actual finline device is shown
in Figure 6.43. The finline structure provides a microwave transition from the 3-D
WR-10 waveguide to a 2-D slot line transmission line with characteristic impedance
of ∼100 Ω. A chip resistor of 100 Ω is soldered across the slot line to terminate the
microwaves and serve as the black body emitter/absorber. This resistor also serves
as the heating element for the black body as DC current can be passed through the
resistor.
264
Figure 6.43: The finline black body source.
265
Table 6.2: The measured thermal characteristics of the finline black body
source.
Cbb (JK) Gbb (
WK) τbb (s) PJ,max (mW)
9.7 ·10−3 2.9 ·10−3 3.3 34
As with the nichrome design a ruthenium oxide thermometer is soldered to the
finline structure to monitor the temperature of the source. One end of a copper wire
is soldiered to the copper layer of the PC board and the other end is clamped to the
copper waveguide mount which is heat sunk to 4 K. This copper wire controls the
thermal conductance between the finline black body source and the copper waveguide
mount in a similar manner to the nichrome black body.
Measurements of the thermal time constant, τbb, thermal conductance Gbb, heat
capacity Cbb, and Pmax,bb were taken while the device was cooled to 4 K and Joule
power was dissipated in the chip resistor. These measurements are shown in Table
6.2. Microwave emissivity measurements are shown in Figure 6.44. We measure a
thermal time constant of 3 seconds, maximum power of 34 mW, and emissivity of 60-
99%. These characteristics are acceptable, and the increase in the time constant is an
improvement over the nichrome design. A higher emissivity is possible (ǫ ∼ 90−98%)
for this design if an extended resistor is used in place of the chip resistor. The simulated
emissivity for an extended resistive film of length ∼ 0.22 inches, R = 250 Ωdeposited
along the finline for termination is shown in Figure 6.45.
266
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
75 80 85 90 95 100 105 110
Frequency (GHz)
Em
iss
ivit
y
Figure 6.44: The measured emissivity of the finline black body source.
Courtesy Sara Stanchfield.
267
Figure 6.45: The simulated emissivity of the finline black body source
with a 0.22 inch long extended resistor with resistivity of 250 Ωand total
terminating resistance of 28.5 Ω. Courtesy Sara Stanchfield.
268
6.2.4 External RF Source Coupling
The source in the external scheme is a HP model 83751A sweeper with external
active multipliers. It can be swept from 75−110 GHz. This signal is transmitted into
the dewar by a coaxial cable. This cable consists of an outer conductor of beryllium
copper (diameter of 1.19 mm) and inner conductor of silver plated beryllium copper
(diameter of 0.287 mm), separated by a PTFE dielectric (diameter of 0.94 mm). The
coaxial cable has characteristic impedance of 50 Ω. Room temperature loss in the
cable is ∼7 dBm
at 20 GHz. We use ∼ 0.5 m of cable to make the transition through
the dewar to the waveguide mount. This cable passes through a vacuum feed-through
at room temperature into the cryostat and is heat sunk as it travels through the 77
K and then 4 K stages. The coaxial cable connects to the copper waveguide mount
at the 4 K stage. Measurements of the performance of the us23/us25 test devices
are currently under way using the thermometry of the gradual transition from 4K
to 200 mK on these devices to make measurements of the total optical and on-chip
transmission efficiency. RF test on THMs with actual low temperature TES transitions
with Tc ∼ 200 mK will have to wait until we fabricate a working THM device in an
RF circuit. The design of such a device is described in the concluding Chapter 7.
269
Chapter 7
Conclusion
7.1 Summary of Understanding of the THM Design
In this thesis measurements of a variety of THM test devices have been presented.
A thermal model based on our understanding of TES and bolometer theory and the
theory of the physical processes in the THM detector (Chapters 2 and 3) for both an
ideal and a non-ideal THM detector has been developed and applied. These thermal
models make an understanding of thermal measurements and DC electrical measure-
ments of THM test devices possible. These measurements include I-V measurements,
thermal conductance measurements, responsivity, and dark noise measurements of
THM test devices (Chapter 5).
These models also allow the optimal THM design and performance (Chapter 4)
to be constrained while considering the very specific loading conditions for observing
the CMB from the ground or from space. Comparison to the THM performance un-
der FIR spectral loading conditions was also discussed in this thesis, as hot-electron
type bolometers have a unique advantage in FIR applications, but perform very dif-
ferently under these relatively low power loading conditions. In this discussion of the
270
THM optimization (Chapter 4), some time was also devoted to discussing the general
optimization of any bolometeric CMB detector, in order to further place the THM
performance in context.
Specifically, the investigations of the THM detector design presented in this
thesis have included measurements of the magnitude (κep and Σep) and temperature
dependence (n = 5− 6) of the hot-electron effect in a composite Au and Bi bolometer
(Section 5.4). These measurements confirm our understanding that the dominant
thermal process within the THM detector is due to scattering between electrons and
phonons. In addition, measurements of Mo/Au bilayer THM devices on the micron
size scale with Nb superconducting leads indicate the current geometrical limits on the
THM model and design due to the lateral proximity effect (Section 5.5). A relatively
simple procedure (described in Section 5.1) to fabricate optimal THM designs using
standard photolithography has also been demonstrated.
Concerning the coupling of microwave radiation to the small volume of the THM
detector a microwave design has been developed which provides polarization-selective
RF coupling to the THM detector via a planar slot antenna design, using planar
microstrip technology (Section 6.1). This development has included E-M simulations
of all components. Additionally, work has been done towards developing the necessary
off-chip optical components for coupling microwaves to the THM detector (Section
6.2.2), both for calibration in the laboratory cryostat, and in some modified form, for
actual observation of the CMB sky.
271
7.2 Future Work Involving The Lateral Proximity Effect
As was demonstrated by the measurements presented in Section 5.5, the obtain-
able NEP of THM devices with micron-size TES devices, in which the bilayer TES
forms a S-S’-S junction with the Nb superconducting leads, is limited due to shifting of
the effective Tc of these devices to higher temperatures. Based on these measurements
bilayer THM devices with lead-to-lead lengths of L ≥ 12 µm are necessary to avoid
large shifts in the transition temperature of the TES on the order of 500 mK-1 K for
a bulk TcN of ∼200 mK. These measurements confirm results by Sadleir et al. [97],
in which lead-to-lead lengths of L ≥ 16 µm are necessary to avoid large shifts in the
transition temperature of the TES on order of 100 mK for a bulk TcN of 170 mK. There
is still much irreproducibility and variation in this effect in bilayer devices, however,
possibly due to variations inherent in the fabrication process and due to the purity of
the deposited film and/or the contact resistance between the superconducting leads
and the TES.
To overcome the size constraints imposed by this lateral proximity effect, future
work on micron-sized THMs with bilayer TES devices might focus on developing
techniques to weaken this proximity effect. Possible techniques include inserting a thin
ferromagnetic layer (such as Ni, Fe, or Co) between the superconducting leads and the
superconducting bilayer TES. The phase coherence of a Cooper pair is very quickly
disrupted when travelling from a superconductor into a nearby ferromagnetic layer
and the coherence length in a ferromagnetic material is substantially shorter (by 1-3
orders of magnitude) than the coherence length in a normal metal due to interactions
with the opposing spins of each of the electrons in the Cooper pair [13] [19]. A similar
272
technique would be to purposely create or deposit an insulating contact resistance
layer between the superconducting lead and superconducting TES which would also
attenuate this lateral proximity effect.
Another avenue for developing a low Tc micron-sized TES device for the THM
was explored preliminarily in this thesis in Section 5.5. This idea is to create a new
type of TES made not of a bilayer, but of a normal monolayer, in which the lateral
proximity effect creates a S-N-S TES. In addition to the practical reasons of achieving a
micron-sized TES which can reach the optimal NEP for the THM detector, pursuing
the development of this type of TES is interesting simply from a novel technology
standpoint. Although this preliminary investigation resulted in no observation of a
superconducting transition, even in THM designs in which transitions are predicted
by simple S-N-S theories (see Section 3.3.9), we do not believe this method has been
ruled out. However, this technique may be more difficult to achieve than was originally
anticipated based on the strong lateral proximity effect observed in bilayer S-S’-S
devices.
Future exploration of this S-N-S TES idea might focus on a single deposition
procedure where the Au and Nb layers are deposited without breaking vacuum, as
was done by van Dover et al. [119], in order to take further precautions to avoid a
dirty interface. Another direction to explore in the development of an S-N-S TES
device would be the use of novel photolithography techniques or e-beam lithography
in order to reduce the lead-to-lead length of the devices below 3 µm.
All of these ideas for fabricating S-N-S or S-S’-S micron size THM devices are
especially worth pursuing for far-infrared hot-electron bolometers, where the advan-
273
tages provided by low thermal conductance and small volume are necessary to reach
background limited levels. However, for a CMB-observing THM detector this per-
formance is already achievable without pursuing these designs (as is presented in the
final section of this thesis, Section 7.5), and it will not be necessary, or arguably worth
the effort to follow these ideas further. This is because the optimal size for the THM
detector TES at low bath temperatures occurs at size scales above those which are
strongly affected by the lateral proximity effect (as shown in Chapter 4).
7.3 Future Microwave Work
The complete testing of the 92 GHz THM microwave design should include
measurements of transmission and reflection of the individual microwave components,
focusing on testing the microwave termination structure (Section 6.1.7), and low-pass
filter (Section 6.1.5) in order to test the frequency dependent microwave performance
of these components which have been predicted by E-M simulations. This type of
testing of individual components scaled to 43 GHz could be done in a cryogenic CPW
probe station measurement system as described in Section 6.2.1.
In addition, it is important to confirm the performance and efficiency of the
slot antenna design as it is coupled via the optical setup described in Section 6.2.2
in the laboratory cryostat. These tests would provide further confirmation of the
agreement between the E-M simulation and the actual performance via a measurement
of total optical efficiency from the RF source to the THM detector. More complete
simulations of the optical coupling efficiencies involved would also allow disentangling
of the optical efficiency of off-chip components and provide for on-chip microwave
efficiency measurements. These microwave measurements will also demonstrate and
274
provide a calibrated measurement of the THM RF responsivity and NEP under CMB-
loading conditions.
7.4 Future Work for Scaling to Large Arrays
Other future challenges that have not been addressed by this thesis occur with
the scaling from a single pixel THM detector to a large array of THM detectors. These
issues include uniformity concerns, and the design of optical coupling and SQUID
readout for an array of THMs. However, much work has been done and is in progress
in this area for membrane-isolated CMB bolometeric detectors, with current arrays of
1000s of detectors with multiplexed SQUID schemes obtainable (Section 1.2.1). As was
stated in Section 1.2, the THM detector has many advantages which may make array
scaling simpler, including the fact that no delicate thermal isolation legs or membranes
are required. One area of difference in the THM read out, however, is the high-speed
of these THM devices (τ . 1− 100 µs) compared to typical TES bolometers. Due to
the speed of these detectors, hot-electron type bolometers will likely need to be read
out with a microwave SQUID multiplexing scheme [57]. Although this topic of array
scalability is beyond the scope of this thesis, these issues will need to be considered
for the THM to prove applicable to the future science needs of CMB telescopes, and
specifically, the detection of B-mode polarization in the CMB.
7.5 A Last Word: The Recommended THM Design
As the last word of this thesis the recommended design for the THM detector
for CMB applications will now be presented. Although this design has not yet been
implemented in the form of a THM test device embedded in an RF circuit, the un-
275
derstanding of the THM thermal model and the physical effects in the model based
on the DC and “dark” measurements of similarly sized test devices presented in this
thesis give high confidence that this design will meet the requirements for a CMB
background-limited detector, and that in fact no, or very little further development is
necessary to provide a “working” CMB detector which might be inserted into a CMB
ground- or space-based telescope. In addition to this understanding of the THM phys-
ical processes, and the development of reliable and fairly straightforward fabrication
methods for the THM design, our investigation into the microwave design via E-M
simulations is to be complemented by impending microwave measurements, using the
test setup described in Section 6.2.2.
The recommended CMB THM design consists of a Mo/Au bilayer TES with a
Au thickness of ∼300 nm, and with a Mo/Au thermal area of ∼ 20 x 20 µm2 and with
a bilayer Tc = 80− 300 mK, depending on the precise bath temperature and whether
the detector is designed for ground- or space-based observing. This choice of TES
area provides for a lead-to-lead length significantly above the size scale where lateral
proximity effects from the superconducting Nb leads have been observed to have a
strong influence. The absorber for this recommended design consists of a ∼800 nm
thick Bi film, with total thermal area 3 µm x 12 µm, with a 3 µm x 3 µm terminating
resistive area and a 3 µm x 3 µm contact area overlapping the center of the Mo/Au
TES. This design is illustrated in Figures 7.1 and 7.2.
The recommended THM device would have the optimal thermal design following
the ideal thermal model. The predicted detector noise, as well as other important de-
tector characteristics, for this recommended THM detector design are listed in Tables
276
Table 7.1: Predicted thermal characteristics, including detector NEP for
the recommended CMB THM design for a ground-based instrument with
bath temperature of 240 mK. Mo/Au TES dimensions are 300 nm x 20
µm x 20 µm, with RTES ∼ 0.1 Ω. Bi absorber dimensions are 800 nm
x 3 µm x 12 µm with a terminating resistance of RAbs ∼30 Ω. Photon
background noise from the ground is NEPphoton = 3.6 · 10−17 W√Hz
. A
50% optical efficiency and bias power of twice the sky loading has been
assumed. The ‘measured n = 5’ and ‘measured n = 6’ design assumptions
are described in Section 4.2.1.Design Assumptions C ( J
K) G (W
K) τ (µs) Tc (mK) NEP ( W√
Hz)
measured n = 6 2.5·10−15 2.5·10−10 < 10 300 2.7·10−17
measured n = 5 2.1·10−15 2.3·10−9 < 1 244 8.5·10−17
7.1 and 7.2 for ground-based observing and in Table 7.3 for space-based observing. A
low bath temperature of 50 mK is necessary for space-based observing, and recom-
mended for ground-based observing as well. In both cases, photon-limited performance
is obtainable with this detector design.
277
Table 7.2: Predicted thermal characteristics, including detector NEP for
the recommended CMB THM design for a ground-based instrument with
bath temperature of 50 mK. Mo/Au TES dimensions are 300 nm x 20 µm
x 20 µm, with RTES ∼ 0.1 Ω. Bi absorber dimensions are 800 nm x 3 µm x
12 µm with a terminating resistance of RAbs ∼30 Ω. Photon background
noise from the ground is NEPphoton = 3.6 · 10−17 W√Hz
. A 50% optical
efficiency and bias power of twice the sky loading has been assumed. The
‘measured n = 5’ and ‘measured n = 6’ design assumptions are described
in Section 4.2.1.Design Assumptions C ( J
K) G (W
K) τ (µs) Tc (mK) NEP ( W√
Hz)
measured n = 6 2.4·10−15 1.9·10−10 < 13 280 2.0·10−17
measured n = 5 1.3·10−15 3.0·10−10 < 4 150 1.3·10−17
Table 7.3: Predicted thermal characteristics, including detector NEP for
the recommended CMB THM design for a space-based instrument for bath
temperature of 50 mK. Mo/Au TES dimensions are 300 nm x 20 µm x 20
µm, with RTES ∼ 0.1 Ω . Bi absorber dimensions are 800 nm x 3 µm x
12 µm with a terminating resistance of RAbs ∼30 Ω. Photon background
noise from a space-based instrument is NEPphoton = 4.3 · 10−18 W√Hz
. A
50% optical efficiency and bias power of twice the sky loading has been
assumed. The ‘measured n = 5’ and ‘measured n = 6’ design assumptions
are described in Section 4.2.1.Design Assumptions C ( J
K) G (W
K) τ (µs) Tc (mK) NEP ( W√
Hz)
measured n = 6 1.4·10−15 1.5·10−11 < 100 170 3.4·10−18
measured n = 5 7.0·10−16 2.8·10−11 < 30 80 2.3·10−18
278
Slot Antenna
Low-pass Filter
THM, Microstrip Termination and Bias Leads
Figure 7.1: The basic microwave circuit for the recommended THM design.
A close-up of the THM detector is shown in Figure 7.2.
279
Bi
AbsorberNb µstripMo/Au TES
Nb
Nb
20 µm
20 µm
RF Power
DC bias leads and
µstrip termination structure
3 µm
Au overlap on Nb for contact
Bi overlap on Nb for contact
Figure 7.2: The geometry of the recommended THM design for CMB ap-
plications.
280
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