Chapter 7
Superconducting Photon and
Particle Detectors
AS-Chap. 7 - 2
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3) detector
class range signal
frequency fs (Hz)
wavelength l (mm)
example detection mechanism
modulation low fre-quency – microwave
< 1012 >1000 heterodyne detector coherent
direct detector incoherent
thermal infrared 1011 – 1015
1 – 1000 bolometers, antenna-coupled microcalorimeters
incoherent
photon visible, UV, x-ray
> 1014 < 1 STJDs, micro-calorimeters
incoherent
7 Superconducting Photon and Particle Detectors
• already discussed: sensitive magnetic flux detectors: SQUIDs
• now: sensitive detectors for em radiation and particles
• detection principle for em radiation:
coherent incoherent
classification of detectors/sensors
AS-Chap. 7 - 3
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
1. modulation detector: - fast enough to follow the incoming electromagnetic signal directly low-freuqency up to microwave regime
2. thermal detector: - too slow to follow the incoming electromagnetic signal directly - measures absorbed power ∝ photon flux (photons/s) by sensitive thermometer - cannot resolve a single photon THz, far-infrared and infrared regime
3. single photon or particle detector: - is sensitive enough to measure the energy of a single absorbed photon/particle - does not measure absorbed power ∝ photon flux (photons/s) but the energy of a single photon/particle visible, UV and x-ray regime
transition between 2. and 3. depends on detector sensitivity and ranges between the near infrared and visible regime for the best detectors
7 Superconducting Photon and Particle Detectors
AS-Chap. 7 - 4
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7 Superconducting Photon and Particle Detectors
SIS-mixers HEMT transition edge sensor
(TES) bolometers, hot electron bolometers
superconducting tunnel junction detector (STJD)
limiting noise: quantum fluctuations:
𝑇𝑁𝑞= ℎ𝑓/2𝑘𝐵
limiting noise: phonon fluctuations:
NEP ∝ 4𝑘𝐵𝑇2𝐺
limiting noise: counting statistics:
NEP ∝ 2𝑒𝐼dark
detectors
coherent incoherent
mixers amplifiers bolometers, calorimeters
photo-conductors
direct detectors
AS-Chap. 7 - 6
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
• heterodyne receivers are modulation detector
7.1 Superconducting µw Detectors: Heterodyne Receivers
• broad field of applications: - telecommunication systems (radio, mobile phones, …..) - microwave instrumentation
- radio-astronomy: receivers based on superconducting mixers
• principle of operation: - microwave signal 𝑓𝑠 mixed with local oscillator signal 𝑓𝑙𝑜
- amplification of intermediate frequancy signal 𝑓𝐼𝐹 = 𝑓𝑠 − 𝑓𝑙𝑜
- heterodyne receiver: 𝑓𝑠 ≠ 𝑓𝑙𝑜
homodyne receiver: 𝑓𝑠 = 𝑓𝑙𝑜
AS-Chap. 7 - 7
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
• Noise Equivalent Power - NEP: - equivalent signal power resulting in a signal-to-noise ratio (SNR) of 1 - SNR > 1 required to detect a signal
NEP is the smallest signal power within bandwidth B of 1 Hz that can be detected
7.1.1 Noise Equivalent Power and Noise Temperature
• definition of important quantities:
• Noise Temperature TN:
𝑘𝐵𝑇𝑁 =𝑃
𝐵=
NEP
𝐵 ⇒ 𝑇𝑁 =
𝑃
𝑘𝐵 𝐵=
NEP
𝑘𝐵 𝐵 (𝑃 = power, 𝐵 = bandwidth)
example: - detector with incident power Ps generating a detector current Is
- current noise power spectral density: 𝑆𝐼 𝑓 = Δ𝐼2 /𝐵
noise current Δ𝐼 per 𝐵 power to current conversion
AS-Chap. 7 - 8
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
• Quantum Limit: - in the ideal case the noise temperature 𝑇𝑁 is limited only by quantum fluctuations
7.1.1 Noise Equivalent Power and Noise Temperature
- average energy of a harmonic oscillator at temperature T:
- at T = 0: ground state energy equivalent noise power
quantum limit of noise temperature
≈ 2.5 K @ 100 GHz
quantum fluctuations
AS-Chap. 7 - 9
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.1.2 Operation Principle of Mixers
• problem: - detect/amplify a signal at very high frequency 𝑓𝑠 - no low noise detector/amplifier available at this frequency
• solution: - down-convert the signal to a much lower frequency 𝑓𝐼𝐹 = 𝑓𝑠 − 𝑓𝑙𝑜 by superimposing it with a local oscillator signal on a nonlinear device/circuit mixer
• block diagram of a heterodyne receiver with a backend filter spectrometer
mixer = nonlinear circuit
AS-Chap. 7 - 10
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
• simplest mixer model: the switch
- signal at: 𝑓𝐼𝐹 = 𝑓𝑠 − 𝑓𝑙𝑜 - cf. stroboscopic illumination
• Josephson junction as fast switch:
nonlinear quasiparticle IVC SIS mixer
7.1.2 Operation Principle of Mixers
AS-Chap. 7 - 11
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3) - we assume two sinusoidal voltages at the mixer input (signal and local oscillator):
- we form product of 𝑉𝑠 and 𝑉𝑙𝑜:
- how to achieve the multiplication? use nonlinear IVC of mixer we develop current response into Taylor series:
for V 𝑡 ∝ cos𝜔𝑡:
𝑉2 ∝ cos2𝜔𝑠𝑡 =1
2(1 − cos 2𝜔𝑠𝑡), 𝑉
3 → 3𝜔𝑠-term, …
7.1.2 Operation Principle of Mixers
• mathematical description of a mixer:
usually not used since sum frequency is very high IF frequency
AS-Chap. 7 - 12
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.1.2 Operation Principle of Mixers
- mixer input: 𝑉 = 𝑉𝑠 + 𝑉𝑙𝑜 = 𝑎𝑠 cos𝜔𝑠𝑡 + 𝑎𝑙𝑜 cos𝜔𝑙𝑜𝑡 quadratic term 𝑉𝑠 + 𝑉𝑙𝑜2
AS-Chap. 7 - 13
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
prefactor of 𝑉2-term should be large large nonlinearity !
7.1.2 Operation Principle of Mixers
spectrum of I(t)
in most cases not used
• schematics of a mixer
I(w)
mixer
Vs
Vlo
I0
AS-Chap. 7 - 14
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.1.3 Noise Temperature of Heterodyne Receivers
• Dicke radiometer equation for minimal detectable input signal:
noise temperature of the receiver
observation time within bandwidth (signal averaging)
bandwidth
• example:
‐ Δ𝑓 = 1 Hz, 𝜏 = 1 𝑠 ⇒ 𝑇𝑠𝑚𝑖𝑛 = 𝑇𝑁
‐ Δ𝑓 = 1 Hz, 𝜏 < 1 𝑠 ⇒ 𝑇𝑠
𝑚𝑖𝑛 > 𝑇𝑁 we are loosing sensitivity, since Δ𝑓 ⋅ 𝜏 < 1 bandwidth is not large enough for short measuring time
‐ Δ𝑓 = 1 Hz, 𝜏 = 1 𝑠 ⇒ 𝑇𝑠𝑚𝑖𝑛 = 𝑇𝑁
we are gaining sensitivity, since Δ𝑓 ⋅ 𝜏 > 1 measuring time larger than 1/Δ𝑓 signal averaging
AS-Chap. 7 - 15
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.1.3 Noise Temperature of Heterodyne Receivers
• SNR of radiometer:
effective noise temperature 𝑇𝑁eff due
receiver, atmosphere, antenna, …
typically: Tatm + Tant ≈ 40 – 50 K @ 100 GHz
noise of Schottky diode mixers ≈ 2 000 K @ 690 - 830 GHz better mixers required SIS mixers
• important: gain of a factor two in noise temperature yields a reduction of measuring time by a factor of four
AS-Chap. 7 - 17
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.1.3 Noise Temperature of Heterodyne Receivers
• reduction of atmospheric transmission due to water vapor
atmospheric transmission at APEX, on the Llano de Chajnantor (Chile), for typical values of the precipitable water vapor (pwv).
spectral band passing through the set of filters used in SABOCA, measured at MPIfR, Bonn
AS-Chap. 7 - 18
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
The Chajnantor Observatory, a facility operated by the California Institute of Technology (Caltech) in collaboration with the University of Chile and the University of Concepción, is located at an elevation of 5080 meters (16700 feet) in the Andes mountains in northern Chile. The high, dry Chajnantor plateau is one of the best sites in the world for millimeter and submillimeter astronomy.
7.1.3 Noise Temperature of Heterodyne Receivers
AS-Chap. 7 - 19
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
atmospheric transmission of the 800 GHz window and the coverage of MPIRE
7.1.3 Noise Temperature of Heterodyne Receivers
• reduction of atmospheric transmission due to various molecules
AS-Chap. 7 - 20
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
photon assisted tunneling:
7.1.4 SIS Quasiparticle Mixers
steps in IVC
AS-Chap. 7 - 21
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
• IVCs of Nb/AlOx/Nb SIS mixer (two junctions in series) with the LO on and off - photon step corresponds to LO frequency of 332 GHz - inset: IF output power versus the bias voltage
7.1.4 SIS Quasiparticle Mixers
-8 -4 0 4 8-100
-50
0
50
100
curr
ent
(mA
)
voltage (mV)
0 4 80.0
0.2
0.4
0.6
0.8
1.0
IF o
utp
ut
po
wer
(m
W)
voltage (mV)with LO
without LO
77 K
290 K
LO off
photon step
AS-Chap. 7 - 22
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
SIS-mixers: • have conversion gain • can reach quantum limit 𝑇𝑁 = ℏ𝜔/2𝑘𝐵
• low LO power required
calculated optimum
noise temperature 𝑇𝑁𝑜𝑝𝑡
7.1.4 SIS Quasiparticle Mixers
quantum theory of SIS mixers: J.R. Tucker, Quantum limited detection in tunnel junction mixers, IEEE J. Quantum Electron 15, 1234-1258 (1979)
0.1 1 2
101
102
Top
t
N (
K)
fs / f
g
gap frequency: fg = 2𝚫/eh
AS-Chap. 7 - 23
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
100 500 1000
0.1
1
5
DSB
no
ise
tem
per
atu
re (
K/G
Hz)
frequency (GHz)
noise temperature of Nb based SIS quasiparticle mixers developed at different laboratories
3 − 5 ℏ𝜔𝑠/𝑘𝐵
7.1.4 SIS Quasiparticle Mixers
SRON Caltech Univ. of Cologne CFA&SMA IRAM NRO NRAO
3h/kB
AS-Chap. 7 - 24
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.1.4 SIS Quasiparticle Mixers
gap frequencies fg: Nb: 700 GHz NbN: 1.2 THz HTS: several THz ( problem: no sharp QP IVC!)
• frequency limitations:
junction capacitance 𝑪𝑱: tends to short out the high-frequency signal current
embed junctions into tuning circuit compensating for 𝐶𝐽
optimum situation (empirically): 𝜔𝑠𝑅𝑁𝐶𝐽 ≃ 2 − 4
with BCS expression: 𝐽𝑐 =𝜋
4
2Δ
e
1
RNA we obtain (Nb/AlOx/Nb)
𝐽𝑐 ≃𝜋
16
2Δ
𝑒
𝐶
𝐴 𝜔𝑠 ≃ 8 000
A
cm2
50 fF/µm² 500 GHz
small junctions with high Jc
2.9 meV 𝐴 ≃ 1 𝜇𝑚2
𝜔𝑠𝑅𝑁𝐶𝐽 ≃ 2 − 4
AS-Chap. 7 - 25
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
high frequency design: - junction size « free-space wavelength, 3 mm @ 100 GHz) - lumped element circuit
7.1.4 SIS Quasiparticle Mixers
AS-Chap. 7 - 26
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.1.4 SIS Quasiparticle Mixers
AS-Chap. 7 - 27
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
The integrated MPIfR/SRON 800 GHz system in the Cassegrain focus cabin of the JCMT.
“With a diameter of 15 m the James Clerk Maxwell Telescope (JCMT) is the largest astronomical telescope in the world designed specifically to operate in the submillimeter wavelength region of the spectrum. The JCMT is used to study our Solar System, interstellar dust and gas, and distant galaxies. It is situated close to the summit of Mauna Kea, Hawaii, at an altitude of 4092m.”
7.1.4 SIS Quasiparticle Mixers
AS-Chap. 7 - 28
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
Cologne Observatorium for Submillimeter Astronomy Gornergrat, Zermatt
7.1.4 SIS Quasiparticle Mixers
AS-Chap. 7 - 29
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
Fully assembled flight model of the HIFI (Heterodyne Instrument for the Far Infrared: 480-1280 GHz and 1410-1910 GHz) focal plain unit: for each frequency band one mixer for horizontal and one mixer for vertical
polarization processes the signal. One mixer band will operate at a time selected by switching the respective IF-amplifiers to operation (source: SRON, NL, April 2006)
7.1.4 SIS Quasiparticle Mixers
AS-Chap. 7 - 30
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
Noise temperature data for HIFI frequency bands (Heterodyne Instrument for the Far Infrared (480-1280 GHz and 1410-1910 GHz). The lower five bands are realized as SIS-mixers. Frequency bands 6L and 6H use HEB devices as mixers. The green line shows the mixer performance baseline. For band 2 the data, acquired in the FPU (filled points) confirm the data, presented in this thesis (open points, compare Fig. 4.29). Source: G. de Lange, SRON, NL
7.1.4 SIS Quasiparticle Mixers
AS-Chap. 7 - 31
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
square-law detector: - convert incoming signal power into change of dc current Δ𝐼 - use of QP nonlinearity of SIS junction to rectify the signal
7.2 Superconducting µw Detectors: Direct Detectors
AS-Chap. 7 - 32
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.2 Superconducting µw Detectors: Direct Detectors
• principle of operation:
- Taylor series:
- input signal:
- dc current response corresponds to time average (classical treatment):
- time average of input power:
Rd = diff. resistance at I0
= numerical factor ≤ 1 (finite absorption thickness, reflectivity, etc.)
- detector efficiency: (power-to-current conversion)
AS-Chap. 7 - 33
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.2 Superconducting µw Detectors: Direct Detectors
- quantum mechanical treatment:
- sharp onset of qp tunneling current @ 𝑉 = 2Δ/𝑒 for 𝑉0 < 2Δ/𝑒
each photon is transformed into an additional electron tunneling across the barrier
J.R. Tucker and M.J. Feldman, Quantum detection at millimeter wavelength, Rev. Mod. Phys. 57, 1055 (1985).
2 500 A/W @ 100 GHz
replace derivatives in the classical expression by the second difference of the unpumped IVC computed for the three points 𝑉 = 𝑉0 and 𝑉 = 𝑉0 ± ℏ𝜔𝑠/𝑒, divided by the first difference computed between and 𝑉 = 𝑉0 ± ℏ𝜔𝑠/𝑒
AS-Chap. 7 - 34
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.2.1 NEP of Direct Detectors
• example: SIS direct detector operated at low T Nyquist noise:
shot noise: dominates due to low T and high R
- for 𝐼0 → 0: ≈ 10-22 W/ Hz @ 100 GHz, Ns = 1 and B = 1Hz
𝐼 = 𝑁𝑒𝐵: number of electrons tunneling through barrier per time
- measured values: 10-16 W/ Hz @ few 10 GHz corresponds to Ns ≈ 1014 @ B = 1Hz equivalently ≈ 1014 ph/s for SNR = 1
far from single photon detection
AS-Chap. 7 - 35
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
• infrared regime:
detector cannot follow the em signal directly measure average power dissipated by signal: photon flux (photons/s) thermal detector: measure T due to absorbed power
- sensitive thermometer required, eg. transition edge sensor (TES) TES bolometers
7.3 Thermal Detectors
• quasi-thermal detectors:
sometimes thermal equilibrium is not strictly achieved (e.g. electrons not in equilibrium with phonons - use of effective temperature T* (e.g. for electrons)
AS-Chap. 7 - 36
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
• incoming radiation power 𝑃𝑠 + thermal background radiation 𝑃𝑏 ≃ 𝑏 𝐴 𝜎 𝑇𝑏4
A = absorber area, b = geometry factor s = 5.67 x 10-8 W/m²K4: Stefan-Boltzmann constant) Tb = background temperature
heat up sensor with heat capacity C and mass M measure 𝛿𝑇 by thermometer
7.3.1 Principle of Thermal Detectors
• loss of absorbed power by radiative emission ≃ 𝑎 𝜖𝐴 𝜎 𝑇4 𝜖 = emissivity, a = geometry factor
direct thermal coupling to heat sink, transferred heat ∝ 𝐺 𝑇 ⋅ 𝛿𝑇 G = thermal conductance [W/K]
fs
incident power Ps
C(T) M
thermometer: T absorber: e
heat sink: TS
G(T)
T0 T0 G(T)
TS
fs
C(T) M
heat sink
AS-Chap. 7 - 37
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
𝜏𝑡ℎ = 𝐶/𝐺: thermal time constant large 𝛿𝑇/𝑃𝑠 small G fast detector small C (thin membrane)
T
7.3.1 Principle of Thermal Detectors
• heat balance equation:
can be neglected for large Ps
• for time varying field: Ps = P0 + Ps eiwt dc + ac detector response
dc
ac
(Pb and radiative loss neglected)
AS-Chap. 7 - 38
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
• antenna-coupled micro-bolometer: - radiation wavelength > absorber size
- collect radiation power by antenna - electric power is dissipated in a few µm- sized thermally active element
7.3.1 Principle of Thermal Detectors
Two detector types:
• bolometer: - radiation wavelength << absorber size
- absorbed radiation power is determined by 𝛿𝑇 measurement
- thermometer is a T-dependent resistance
AS-Chap. 7 - 39
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.3.2 Bolometers: the thermometer
• irradiation temperature rise 𝛿𝑇 resistance change 𝛿𝑅 =𝑑𝑅
𝑑𝑇𝛿𝑇
increase of heat dissipation due to bias current
𝐼2𝛿𝑅 𝑒𝑖𝜔𝑡
• time varying part of heat balance equation (Pb and radiative loss neglected):
R(T) I
Ps
T0
R0
R
T
2DT
2R
0
T0
dR
T Tc0
• Transition Edge Sensor (TES): make use of narrow sc transition large 𝑑𝑅/𝑑𝑇
AS-Chap. 7 - 40
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3) • responsivity S (V/W):
large dR/dT small G and C are required
7.3.2 Bolometers
AS-Chap. 7 - 41
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.3.2 Bolometers
NEP of 1.6 × 10−16 W/ Hz @ 0.45 K
Transition Edge Sensors (TES) consisting of bilayers of Mo and a Au/Pd alloy, deposited on a SiN membrane
SABOCA ( Submillimeter APEX Bolometer Camera) Max-Planck-Institut für Radioastronomie (MPIfR), Bonn
AS-Chap. 7 - 42
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
The Large APEX BOlometer CAmera (LABOCA)
7.3.2 Bolometers
NTD thermistor
AS-Chap. 7 - 43
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
Transition edge sensor (TES) bolometers sense small temperature changes that occur when photons are absorbed and converted to heat. The use of TESs enables
arrays with a much larger number of pixels than is practical with spider-web bolometers. Sustaining its leading role in superconducting TES array technology,
MDL developed and continues to improve a process to create arrays of thousands of TESs with high yield (>90 percent). These arrays are being employed on three
major astrophysics projects, all with the same goal: generating detailed maps of the polarization of the cosmic microwave background (CMB).
7.3.2 Bolometers
AS-Chap. 7 - 44
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
Next-Generation CERES Instrument Will Enhance Climate Forecasts MDL is furthering development of the next-generation CERES-C, a continuation of the Earth Radiation Budget Experiment/Clouds and the Earth’s Radiant Energy System (ERBE/CERES)
climatological experiment, to measure both solar-reflected and Earth-emitted radiation from the top of the atmosphere to Earth’s surface. CERES-C requires detectors that are broadband
(absorptivity >90 percent between 0.3–50 µm) with an absorber area of 1.5x1.5 mm, a baseline noise equivalent power (NEP) below 7x10–9 W (goal: 2x10–9 W) between 0.3–30 Hz bandwidth, a
response time between 8–9 ms, a responsivity of at least 65 V/W, and a dynamic range of 0–60 µW. We recently completed a wafer of thermopile detectors and demonstrated that the detectors
exceed all the requirements of CERES-C.
7.3.2 Bolometers
AS-Chap. 7 - 45
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
Noise Equivalent Power (NEP) determined by:
7.3.2 Bolometers
• phonon noise (thermal fluctuations): thermodynamic energy fluctuations in the detector due to the random exchange of phonons (or electrons) through the thermal link
• photon noise (random emission of photons) NEPBLIP (background limited infrared detectors)
plausibility:
- number of phonons in absorber ∼𝐶
𝑘𝐵, phonon energy ∼ 𝑘𝐵𝑇0 Δ𝐸𝑟𝑚𝑠
2 ∼ 𝑘𝐵2𝑇0
2𝑁 = 𝑘𝐵𝑇02𝐶
- ⟨Δ𝑇⟩ =Δ𝐸𝑟𝑚𝑠
𝐶 Δ𝑇2 =
𝑘𝐵𝑇02
𝐶= 𝑆𝑇 𝜔 𝑑𝜔 (𝑆𝑇 𝑓 = Δ𝑇2 𝑓 /𝐵)
AS-Chap. 7 - 46
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
• 1/f noise (various sources)
7.3.2 Bolometers
thermal noise dominates for large S, T0, and G
• Nyquist noise (voltage fluctuations in resistor)
- voltage noise power spectral density 𝑆𝑉 = 4𝑘𝐵𝑇𝑅0 V2
Hz
- responsivity 𝑆 𝑉
𝑊
ratio of thermal noise and Nyquist noise
• amplifier noise
AS-Chap. 7 - 47
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
T0 , G should be small make response time small, t = C/G C as small as possible
7.3.2 Bolometers
BILP: Background Limited Infrared Photodetector
AS-Chap. 7 - 48
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
high temperature superconductor bolometer
7.3.2 Bolometers
Si
Si3N4
absorber
YBa2Cu3O7 film
• small mass (C), • small thermal coupling to heat sink (G), • sensitive temperature sensor (TES) • broad band absorption (advantage compared to semiconducting sensors)
AS-Chap. 7 - 49
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
100
101
102
103
108
109
1010
1011
1012
D*
(cm
Hz1
/2/W
)
wavelength (mm)
HgCdTe
HgCdTe 77 K
InSb PtSi
YBCO/YSZ/Si3N4
YBCO/YSZ/Si
photon noise (300 K, 0.02 sr)
PC PV
specific detectivity 𝐷∗ = 𝐴/NEP vs. Wavelength (𝐴 = detector area)
7.3.2 Bolometers
1012 Hz 1014 Hz
AS-Chap. 7 - 50
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
Nonequilibrium Effects: relaxation processes in a superconducting film after absorption of em radiation
𝐺𝑖 = 𝐶𝑖/𝜏𝑖
𝑇𝑒𝑓𝑓𝑒𝑙 depends on PS and Cel
𝑇0 depends on C
7.3.2 Bolometers
• not discussed so far: physics of absorption process and relaxation to thermal equilibrium complex process, only brief qualitative discussion
AS-Chap. 7 - 51
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
• far infrared to millimeter radiation long wavelength - radiation collected via antenna
- induced electrical power dissipated in absorber ≪ wave length - keep absorber mass/heat capacity small
- measure 𝛿𝑇 by µm-sized thermometer
7.3.3 Antenna-Coupled Micro-Bolometers
(a) Transition-Edge Micro-bolometers (b) Hot Electron Microbolometer (c) Hot Electron Bolometer Mixer
• main detector types:
absorber/thermometer
AS-Chap. 7 - 52
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
(a) Transition-Edge Micro-bolometers
7.3.3 Antenna-Coupled Micro-bolometers
• example: YBCO transition edge sensor on YSZ membrane - S > 1000 V/W @ 85 K
- NEP ≈ 3 x 10-12 W / Hz - t = 2 µs
AS-Chap. 7 - 53
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
Left: 2" silicon wafer after microfabrication of more than a hundered antenna-coupled bolometer devices. Top right: Optical micrograph of niobium bolometer with log spiral antenna for terahertz detection. Bottom right: Measured frequency response of device with log spiral antenna (source: Yale University).
(a) Transition-Edge Micro-bolometers
7.3.3 Antenna-Coupled Micro-bolometers
AS-Chap. 7 - 54
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
(b) Hot Electron Micro-bolometer - superconducting antenna + normal metal load of antenna + thermometer - thermometer measures effective T of electron system of normal metal
7.3.3 Antenna-Coupled Micro-bolometers
• very low T operation is advantageous:
efficient thermal decoupling of absorber from environment (thermal conductivity of insulator T3)
e-p scattering time increases 1/T3
electron system decoupled from lattice hot electrons (trapped for long time)
• thermometer: S/I/N junction (N: absorber) - magnitude of QP tunneling current electron T - low NEP and high sensitivity for T ≈ 0.1 K and N volume ≈ 1 µm³
NEP ≈ few 10-18 W / Hz S ≈ few 109 V/W
AS-Chap. 7 - 55
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.3.3 Antenna-Coupled Micro-bolometers
A scanning electron micrograph of the antenna-coupled Nb bridge bolometer. The inset at upper right shows a detailed image of the feed region taken at a steep angle to show the separation between the bridge and the substrate. The diagram at lower left shows the model used in the theoretical treatment with S indicating the superconducting regions, and the shaded area in the middle of the bridge marking the normal region extending from −𝑙𝑛/2 to +𝑙𝑛/2.
A superconducting antenna-coupled hot-spot microbolometer A. Luukanen and J. P. Pekola, Appl. Phys. Lett. 82, 3970 (2003)
𝑆 = −1430 A/W
NEP = 1.4 × 10−14 W/ Hz @ 4.2 K
AS-Chap. 7 - 56
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.3.3 Antenna-Coupled Micro-bolometers
Superconducting Hot Spot Micro-bolometer
AS-Chap. 7 - 57
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
A superconducting hot-spot air-bridge bolometer (SHAB) consisting of a niobium (Nb) air bridge (1 μm wide and 15 μm long) suspended between the feed points of a logarithmic spiral antenna. Below the superconducting critical temperature Tc ≈ 8.2 K, a DC current bias produces a normal-state region (called a hot spot), where the local temperature is higher than Tc at the center of the bridge.
7.3.3 Antenna-Coupled Micro-bolometers
M.S. Vitiello et al., "Terahertz quantum cascade lasers with large wall-plug efficiency," Appl. Phys. Lett., 90, 191115 (2007).
AS-Chap. 7 - 58
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
(c) Hot Electron Bolometer Mixer
small heat capacity, good thermal coupling short thermal time constant 𝜏𝑡ℎ = 𝐶/𝐺 large 𝑓𝐼𝐹 ∼ 1/𝜏𝑡ℎ possible
mixing up to 𝑓𝑠 > 2Δ/𝑒, i.e. several THz possible low LO power required for 𝑓𝑠 > 2Δ 𝑇 /ℎ no harmonics of signal and LO no magnetic field to suppress SC
7.3.3 Antenna-Coupled Microbolometers
V
I
antenna
phonon escape
superconducting microbridge
quasiparticle diffusion
Ps Plo
AS-Chap. 7 - 59
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
• power coupled into the microbridge:
• bolometer cannot follow the fast power variation at 𝑓𝑠 or 𝑓𝑙𝑜, but at 𝑓𝐼𝐹 = 𝑓𝑙𝑜 − 𝑓𝑠 :
• IF voltage amplitude:
S: responsivity
• absorption of photons heating measure 𝜹𝑻 at 𝒇𝑰𝑭 by fast thermometer (𝝉𝒕𝒉 < 𝟏𝒏𝒔) no upper frequency limit by energy gap as for SIS mixers!
• cooling down by: phonon emission (phonon cooling) diffusion of hot electrons (diffusion cooling)
7.3.3 Antenna-Coupled Microbolometers
AS-Chap. 7 - 60
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
NbN hot electron bolometer mixer (SRON, The Netherlands)
7.3.3 Antenna-Coupled Microbolometers
AS-Chap. 7 - 61
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
• with increasing quantum energy, the signal due to individual photons may become detectable (e.g. in visible to UV range)
• time interval between single photon events must be larger than detector response time single photon counting possible (photon counting mode) averaging over long time (photon integrating mode)
• if we can resolve the signal height as a function of the photon energy single photon spectroscopy
7.4 SC Particle and Single Photon Detectors
• detector types:
(a) superconducting tunnel junction detector (STJD): non-thermal detector (counting of excess qp generated by single photon)
(b) micro-calorimeter: thermal detector (bolometer with single photon resolution)
• applications:
- e.g. superconducting spectrometers for astronomical imaging (optical to soft x-ray) - particle detectors (electrons, -particles, …
AS-Chap. 7 - 62
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.4.1 Thermal Photon and Particle Detectors: Micro-calorimeters
• energy resolution of a detector can be derived from NEP
example: NEP of thermal detectors can be as low as 10-18 W/ Hz if thermal time constant 𝜏 ≈ 1 ms corresponding to B ≈ 1 kHz Δ𝐸 = NEP ⋅ 𝜏 ≈ 10−19 J ≈ 1 eV corresponds to energy of single photon of visible light !!
AS-Chap. 7 - 63
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
• incident single photon/particle heats up sensor - thermometer: transition edge bolometer transition edge sensor (TES)
• energy resolution:
with 𝜖 = 1, 𝜏 = 𝐶/𝐺, 𝐵 =1
𝜏 ⇒ Δ𝐸 = NEP ⋅ 𝜏
7.4.1 Thermal Photon and Particle Detectors: Micro-calorimeters
• dominating NEP at low T: thermal noise
low T0, low C required
example: reduce heat capacity by fabricating thin absorber layers (e.g. Bi, Au) on Si3N4 membrane
AS-Chap. 7 - 65
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
- SC: Mo/Cu or Ti/Au: Tc < 1 K - energy resolution few eV - counting rate 1000/s at 1 keV photon energy - collecting area 4 mm2 at T = 0.1K
7.4.1 Thermal Photon and Particle Detectors: Micro-calorimeters
micrographs curtesy of SRON, The Netherlands
AS-Chap. 7 - 66
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.4.1 Thermal Photon and Particle Detectors: Micro-calorimeters
example: - 𝑇0 = 0.1 K - 𝐶 = 10−12 J/K - 𝑉 = 100 µm³ - 𝑐𝑉 = 1 J/m³K
Δ𝐸FWHM ≈ 10 eV
converts from one standard deviation to FWHM
AS-Chap. 7 - 67
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
x-ray spectrum of a 55Fe source recorded by Mo/Cu TES energy resolution of 4.5 0.1 eV FWHM @ 5.9 keV photon energy
7.4.1 Thermal Photon and Particle Detectors: Micro-calorimeters
improved sensors: 2.4 eV FWHM @ 5.9 keV photon energy, 30 times better than Si(Li) semiconductor sensors
AS-Chap. 7 - 68
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
• Principle of operation: - incoming radiation generates excess number N of QPs:
measure 𝛿𝐼 of excess QP tunneling current
𝛿𝑄 = 𝛿𝐼 𝑑𝑡 ∝ 𝑁 ∝ 𝐸
• electronic readout:
FET-based charge amplifier
7.4.2 Superconducting Tunnel Junction Photon and Particle Detectors
AS-Chap. 7 - 69
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
• energy resolution:
limited by statistical fluctuations of N given by 𝐹 ⋅ 𝑁 (F = Fano factor)
7.4.2 Superconducting Tunnel Junction Photon and Particle Detectors
𝜖 = average energy required for a single excess qp F = 1 for Poisson process, Monte Carlo simulations yield F ≈ 0.2
• other noise contributions:
tunneling is statistical
process
inhomogeneities diffusion losses of
qp
amplifier noise
*2.355 = 2 2 ln 2 converts from one standard deviation to FWHM
AS-Chap. 7 - 70
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
detector type excitation e
gas proportional counter electron-hole pair 25-35 eV
scintillator photon ~ 3 eV
semiconductor detector electron-hole pair 3.65 eV (Si), 2.85 eV (Ge)
STJD quasiparticle 2.6 meV (Nb), 1.3 meV (Ta)
superfluid 4He roton 0.75 meV
superfluid 3He quasiparticle 0.14 meV
7.4.2 Superconducting Tunnel Junction Photon and Particle Detectors
energy 𝜖 required for generating elementary excitations should be as small as possible
AS-Chap. 7 - 71
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
calculated energy resolving power 𝑹 = 𝑬/𝚫𝑬
7.4.2 Superconducting Tunnel Junction Photon and Particle Detectors
AS-Chap. 7 - 72
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
• QP counting by tunneling STJD count excess QPs
7.4.2 Superconducting Tunnel Junction Photon and Particle Detectors
DOS electrode 1
DOS electrode 2
Fermi distribution in electrode 1 and 2
density of states: 𝑑𝐹 = 𝐷𝐹/𝑉
AS-Chap. 7 - 73
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
• main tunneling processes:
Note: once qp has tunneled to SC2 (process A), it can tunnel back again to SC1 (process B) QPs can be counted several times increase of signal !!!
7.4.2 Superconducting Tunnel Junction Photon and Particle Detectors
• process A: qp tunnels from SC1 to SC2, large probability due to large DOS of empty states in SC2
• process B: CP in SC 1 is broken up, one qp tunnels to SC2 and recombines with qp of SC2, effectively charge e is transferred from SC2 to SC1 tunneling of hole from SC1 to SC2
• process C and D are analogue to A and B but with much smaller probabilities
AS-Chap. 7 - 74
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.4.2 Superconducting Tunnel Junction Photon and Particle Detectors
• tunneling current:
with
• extra tunneling current due to photon/particle absorption:
𝜏𝐷: signal decay time
• first order approximation of collected charge:
𝜏𝐷 ≫ 𝜏tun to maximize 𝛿𝑄𝑠
make 𝜏tun ∝ 𝑑, 𝐽𝑐−1
small JJs with high 𝐽𝑐 and small 𝑑
AS-Chap. 7 - 75
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
QP trapping
QP trapping close to tunneling barrier makes tunneling time shorter total collected charge increases significantly improving the energy resolution
7.4.2 Superconducting Tunnel Junction Photon and Particle Detectors
S1 I eV
µ1
(i)
(ii)
(iii)
(iv)
ħW
= D
-D´
ħW
= 2D´
tR
tep
(v)
E
𝑺𝟏′
𝚫′
𝚫
absorber layer trapping layer trapping layer
ba
rrier
𝑺𝟐′
µ1
AS-Chap. 7 - 76
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3) lateral QP trapping
no QP diffusion into leads
large-gap absorber
7.4.2 Superconducting Tunnel Junction Photon and Particle Detectors
lead
𝚫𝟑
tunnel junction
𝚫𝟏 lead
𝚫𝟑
tunnel junction
𝚫𝟏
absorber
𝚫𝟐
qp diffusion
lead
𝚫𝟑
𝚫𝟑 > 𝚫𝟐 > 𝚫𝟏
tunnel junction
𝚫𝟏
AS-Chap. 7 - 77
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.4.2 Superconducting Tunnel Junction Photon and Particle Detectors
AS-Chap. 7 - 78
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
energy resolution of a Nb/Al/AlOx/Al/Nb STJD vs photon energy
counting rates up to 104/s per pixel operation at 0.1 K
7.4.2 Superconducting Tunnel Junction Photon and Particle Detectors
S. Friedrich et al., IEEE Trans. Appl. Supercond. AS-9, 3330 (1999)).
AS-Chap. 7 - 79
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
Close-up of the 100 pixel array detector with 200-µm-square superconducting-tunnel-junctions (STJs). Because of the better energy resolution (ΔE), an array detector of 100-µm-square pixels with the same arrangement was used to measure XANES of N in SiC. (b) Histogram of ΔE values for the 80 operating 100-µm-square STJs. The solid line shows a Gaussian fit with a mean value of 14.2 eV and a standard deviation of 2.8 eV.
X-ray absorption near edge spectroscopy with a superconducting detector for nitrogen dopants in SiC M. Okubo et al., Scientific Reports 2, 831 (2012)
7.4.2 Superconducting Tunnel Junction Photon and Particle Detectors
resolution: 2.8 eV @ 14.2 keV
AS-Chap. 7 - 80
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
single photon charge spectrum at (a) 350 nm and (b) 250 nm wavelength
7.4.2 Superconducting Tunnel Junction Photon and Particle Detectors
A. Peacock et al., Nature 381, 135 - 137 (09 May 1996) Single optical photon detection with a superconducting tunnel junction
AS-Chap. 7 - 81
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.4.2 Superconducting Tunnel Junction Photon and Particle Detectors
• antenna coupled STJD for sub-millimeter-wave single photons
R.J. Schoelkopf et al., IEEE Trans. Appl. Supercond. 9, 2935 (1999)
AS-Chap. 7 - 82
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
7.4.2 Superconducting Tunnel Junction Photon and Particle Detectors
(a) Microscope photograph of a transmission-line STJ detector. The long junctions of 4 µm x 27 µm in size are symmetrically integrated on both wings of a Nb log-periodic antenna. A Nb antenna and an impedance transformer were used in this prototype fabrication, although Nb is a high-loss material above 𝑓𝑔 ≃ 0.7 THz. (b) Typical I–V curve of the STJ
detector at 4.2 K.
S. Ariyoshi et al., Supercond. Sci. Technol. 25, 075011 (2012) Terahertz detector with transmission-line type superconducting tunnel junctions
AS-Chap. 7 - 83
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
Detector types: (i) modulation detectors: heterodyne receivers, direct detectors (ii) thermal detectors: without antenna for absorber mass > wave length with antenna for absorber mass < wave length (iii) single photon/particle detectors:
Summary
Noise equivalent power (NEP):
Noise temperature: 𝑇𝑁 =𝑃
𝑘𝐵 𝐵=
NEP
𝑘𝐵 𝐵 (𝑃 = power, 𝐵 = bandwidth)
quantum limit:
Dicke radiometer equation for minimal detectable input signal:
Heterodyne receiver: frequency down-conversion by nonlinear element –> SIS tunnel junction
mixer input: 𝑉(𝑡) = 𝑎𝑠 cos𝜔𝑠𝑡 + 𝑎𝑙𝑜 cos𝜔𝑙𝑜𝑡
AS-Chap. 7 - 84
R. G
ross
, A. M
arx
and
F.
De
pp
e ©
Wal
the
r-M
eiß
ne
r-In
stit
ut
(20
01
- 2
01
3)
Summary (2)
Direct detector: „rectification“ by nonlinear element (SIS tunnel junction
(quantum limit) detector efficiency:
thermal detector: responsivity
Hot electron bolometer mixer:
make T0 , G small, make C small for short response time t = C/G
small 𝜏eff ∼ 𝐶/𝐺eff to allow for large IF bandwidth, large 𝑑𝑅/𝑑𝑇, small 𝐺eff
Micro-calorimeter:
small T, G and C, 𝜖 ≃ 1
STJ photon detector:
small average energy 𝜖 per excess quasiparticle