Materials for CSQ

• PM: Karl Roenigk, IARPA

• PI: David P. Pappas, NIST

• Staff: Danielle Braje, Robert Erickson,

Fabio da Silva, Jeff Kline

• IC Postdoc - David Wisbey

• Collaboration :• CU Denver: H. Fardi, M. Huber

• Colorado School of Mines – Brian Gorman, Mike

Kaufman

ProgrammaticsMatrix management

Activity: Growth Fabrication Electronics Measurement Modeling& Thy

Personnel: J. Kline D. WisbeyF. da Silva

F. da SilvaD. WisbeyJ. Kline

H. FardiT. OsminerF. FarhoodiD. BrajeD. Pappas

D. BrajeD. WisbeyD. Pappas

R. EricksonH. FardiD. Braje

Outline• Ongoing theoretical work:

– Analyze junction response• DC and AC

– Simulate absorption of materials

• Potential work:– Atomistic calculations of interface structure

• Need cubic spinel sturctures as templates• Steve Helberg – NRL

– Q reference material ILC?• Q is a function of temperature and power• Q is high at high T & P, low at low T&P• Qubits operate at low T & P• RM is critical to define milestones of program

Technical Objectives TableObjective Figure of Merit End Goals Methods

Improve substrate loss tangent = 1/QMorphology

< 10-6 (Q~105)EpitaxialSmooth

Crystalline, possible buffer layers

Match bottom electrode to substrate

Loss tangentMorphology

<10-6

EpitaxialSmooth

CrystallineEpitaxy

Improve tunnel barriers

Subgap ConductanceRF QMorphologySplitting density

<10-3

<10-6

EpitaxialNo pinholes<0.01/GHz

Smooth,crystallineepitaxy

Improve top electrode Loss tangentMorphologySplitting density

<10-6

No pinholes<0.1/GHz/um2

Deposition

Improved wiring & insulators

Loss tangent < 8x10-6 Test candidates

Improved qubits Loss tangent = 1/QLong T1High Fidelity

<4x10-5 (Q=2x104)>5x10-6

>95%

ID Task Nam e

1 Task 1: Substrate Preparation

2 Sapphire s urface termination

3 Hom oepitaxy on Sapphire

4 Alternative substrates

5 Task 2: Bottom Electrode

6 Bottom electrode studies of roughness and crystallinity

7 Task 3: Epitaxial Barrier Development

8 Develop test platform for junction analys is

9 Study tunnel junction roughness

10 Develop new junction m aterials with sys tem atic s tudy of growth conditions

11 Develop s ingle junction res onator absorbers

12 Model I-V curves and feedback to materials and fabrication

13 Incorporate ideal zero splitting barriers into phase qubits and tes t

14 Task 4: Match Top Electrode to Tunnel Barrier

15 Vary multiple parameters to optim ize top electrode match

16 Task 5: Study and Optimize Insulators

17 Develop test platform for m easuring Q & loss at low T

18 Tes t a variety of m aterials using various growth conditions

19 Integrate low los s dielectrics in phase qubits

20 Task 6: Test Coherence Advances

21 Mid-term goal of T1 = 1 usec

22 Integrate and optimize all improvements

23 Final goal of T1 = 2.5 us ec

5/31

5/1

Qtr 1 Qtr 2 Qtr 3 Qtr 4 Qtr 1 Qtr 2 Qtr 3 Qtr 4 Qtr 1 Qtr 2 Qtr 3 Qtr 4 Qtr 1 Qtr 2 Qtr 3 Qtr 4 Qtr 1 Qtr 2 Qtr 32008 2009 2010 2011 2012

Work flowchart

Process junction

CAFMThy

RFIV

T1,T2Thy

Substrate

RF?RHEED?

AFM?

RHEED?AFM/STM?

RF?

RHEED?AFM?

CIPTTEM, AFM

Thy

Bottom Electrode

Tunnel Barrier

Top Electrode

Insulator, wiring

Example: sapphire/Al(111)/Al2O3/Al(111)

Need ADRTC Al <1.8 K

CIPT shows shorted junction

Need ADRFor TLS analysisT=1.8K

Trilayer flowchart

Epitaxial Junction Problem• Tunneling barrier interface defects:

– random roughness (O diffusion within Al overlayers), – terraces (epitaxially produced)– pinholes

Oxygen Diffusion Terraces Pinholes

S.C. Oxide Al S.C. S.C.Oxide S.C. Oxide S.C.

Example:Al(111)/epi-Al2O3/Al(111) structure on sapphire

Sapphire Substrate

Epitaxial Al

FIB Pt

Oxide / Al / Re

TEMBrian Gorman

CSM

HRTEM of Oxide Layer

0.23nm

0.37nm

<111> Al <111>Al<0001> Al2O3

Epi Al(111)

Oxide Al2O3

Top Al(111)

Approach• Development of quick and efficient procedure for

detecting junction interface defects

• Electrical IV measurements (DC)– Barrier tunneling model

• account for subharmonic energy-gap structure• assess interface defects, particularly pinholes

• Electric RF absorption (AC)– Engineered Fe+3 magnetic impurities – Probes of terracing & thickness deviations

• Applicable to S-I-S geometry [Arnold]

Barrier Tunneling Model

xdxdxdxdxm

xHT ),()()()(2

)( 22113

2

• Non-transfer Hamiltonian—transmission probability T2 included to all orders [Feuchtwang]

d1 d2

S SI x

• Tunneling current formalized using non-equilibrium single-particle Green functions [Keldysh]

(first principles equivalent)

Barrier Tunneling Model

-

2 = 0

CP

CP

h

e

e

SS I

Multiple Andreev Reflection (eV = - )

(evanescent)

-

1 = -

2 - 2 - 3

• MAR accounts for voltages below threshold /e, which are not addressed by MPT

• Subharmonic gap structure (barrier contribution)– MAR: Multiple Andreev Reflection [KBT]– MPT: Multi-Particle Tunneling [Shrieffer and Wilkins]

Barrier Tunneling Model• Voltages above threshold /e

-

2 = 0

CP

h

e

e

SS I

Multiple Andreev Reflection (eV = + )

(evanescent)

1 = +

2 +

2 +3

-

• Example applied to Nb/AlOx/Nb tunnel junctions [Kleinsasser]

Barrier Model and Pinholes

– Subgap current attributable to multiple Andreev reflection

– Extended to account for pinholes via parameters:

• Pinhole transmission probability T2 (near unity, by definition)

• Ratio of pinhole conductance to that of barrier

4% of current due to pinholes (T2 ~ 1)

Al-O

Al

Al

(x,y)(x,y)=d

z

xFe3+

• Fe3+ impurities can be used as probes of junction interface roughness when microwaves are applied

2

0

22

02221

20

20

22

0 )(2)(;)(1

2/)(

Bg

TTT

TnP Babs

Fe3+ Probes of Roughness

• For example, Fe3+ power absorption depends on the variance of this induction (ħ0 ~ 12 GHz)

• By Faraday’s law, roughness induces a driving magnetic induction that couples to Fe3+ impurities

),(ˆ),(

sin),,(

20 yxz

yx

tVtyxB

,V0

16

How Fe3+ Impurities Couple to Junction Phase Qubit

0

)(2)(

mi

N

nn

nyn

nx

nmi mmI

RK

R 1

)()(11

0 cossin222

)(

N

nmn

nyn

nxm

mym

mx

nmmi

N

nn

nyn

nx

nbiasmimiqb

SSSSIII

SSIII

1,

)()()()(110

0221

1

)()(10

0

cossincossin22

cos2

)(

cossin2

sin2

)(

H

2

)( 10

0

RK

R

g Bmi

R

Fe3+

z

d

d<<R

JJ

* R.P. Erickson and D.P. Pappas, “Model of magnetic impurities within the Josephson junction of a phase qubit”, Submitted to PRB Rapid Comm.

• Phase of Cooper-pair wave function is shifted by Fe3+ impurities in single-crystal sapphire junction*

• This introduces time-independent interaction terms in the washboard potential of the Hamiltonian

• Provides mechanism for decoherence and 1/f noise

Progress• Barrier tunneling model

– Correspondence with G. Arnold; source code provided– Initial implementation to be completed June 1, 2009– Next step: application to NIST I-V measurements– Then extend model to include terrace-induced channels

• Fe3+ probes of roughness– Initial theory development completed April 1, 2009– Next step: application to NIST measurements– Then extend model to self-consistency within London gauge

Nature of the faults in Al(111) on sapphire

Faults in epi Al initiate at substrate, are transferred vertically through the Al to the oxide layer, near where the growth abnormalities seem to form in most cases

Dark Field Imaging of Faults in Al(111) on sapphire

Left: 2-beam bright field image using the 006 reflection shown in the inset SADPRight: CDF image using the same 006 reflection as in the left imageNote that the top layer of Al are not illuminated using this reflection, indicating that the bright areas in the CDF image are slightly misoriented in-plane

Slightly tilt sample:

Left: 2-beam bright field image using the 006 reflection shown in the inset SADPRight: CDF image using the 006 reflection as in the left image, Note the top layer of Al are not illuminated, indicating that the bright areas in the CDF image are slightly misoriented in-plane with respect to the previous 006 CDF image

Basal Plane Sapphire Atomic Placement

Atomic positions of the Al (pink) and O (gray) for sapphire oriented down the basal plane.

Note the rotation of the oxygen atoms in the c-direction of the crystal

Sapphire

Al(111)

Potential solution

• Change substrate to cubic spinel

– e.g. MgAl2O4 (111)

– Lattice matched between Al & Al2O3

– No staggered O atom sub-lattices– High T material

• Suggest simulating superconductor-spinel interface

• Potential NRL contribution

LCR electrical model for phase qubit

=

CJ~1-100 x10-12LJ~sin

JJCL1

0

Inte

nsi

ty

JCVG )(T :state 1 of Lifetime 1

G(V)

• Quality factor – Energy stored/Energy lost/cycle

• Q = 0/

Q/

• Delectric loss tangent = 1/Q

• tan = Im()/Re()

Rjunction – non-linear QP tunneling

Rdielectric – bound dipole relaxation

Junction & insulators

What can be quantified?

frequency

Test dielectrics with simple LC & CPW circuits

L

C

LC – parallel plate C CPW

Material Q=1/tanSi(111) 200,000

Sapphire – Al2O3 160,000

a-Si:H 45,000

a-SiN 10,000

a-SiOX 3,300

O’Connell, APL (2008)

Electric Field around CPW

CPW simulations Model field around center conductor

• Absorption in dielectric reduces Q

• Primary absorption due to two-level fluctuators

• Active at low T & Pwr

Saturation of TLSs at low T & P

RFg

e

g

e

PPMSADR

10% effect @ 1.8 K80% effect @ 0.1 K

1/Q

=

Increasing P

Increasing T

Quality factor can appear higher due to poor T and Pwr control

“To provide for the dissemination of an internationally consistent, accurate, reproducible, and measurable cryogenic measurement standard”

Q =

Cryogenic Measurement Standard

• Objectives:– Standardize inter-laboratory results– Set the bar for superconducting coherent measurements

• Approach– Design test samples, which are relevant to the field

• High Q CPWs for single frequencies– T & Pwr dependence

• RF resonator combs for full transfer function– Fabricate AND measure samples at NIST– Conduct Inter-laboratory Comparison (ILC)– Generate SRM for community

• Methods– State-of-the-art superconducting circuit test facility– Perfect Quality Factor measurements– Traceable to NIST standards (frequency and voltage)

• Vision– Give researchers SMA box with calibration standard

Measurements of all labs are not created equalQ appears higher for high Temperature & Power

Summary• Ongoing theoretical work:

– Analyze junction response• DC and AC

– Simulate absorption of materials

• Potential work:– Atomistic calculations of interface structure

• Need cubic spinel sturctures as templates• Steve Helberg – NRL

– NIST Q-factor SRM• Q is a function of temperature and power• Q is high at high T & P, low at low T&P• Qubits operate at low T & P• RM is critical to define milestones of program

HPD ADR delivered & cooled• Agilent 20 GHz VNA ordered

• Wiring for

• 32 test junctions (4x25 pin)

• 1 resonator (2 SMA)

• Demonstrated T < 50 mK

• Will enable in-house:

• Sub-gap structure in epitaxial tunnel junctions

• Process controll

• Q-measurements at Low T, P to measure TLS’s

Opportunities & Issues• NIST Leverage

– B1E Cleanroom B1E being installed• Can get significant space & leverage

• Deposition systems, low noise space

• Chlorine etch coming on line

– Quantum information high priority

Action Items• New techniques

– Ellipsometry– Fe impurities at barriers to evaluate roughness– ADR – Lower temperature & TLS evaluation

• Flip chip – Design SQUID & qubits

• Stay on track with GANTT chart

Capres CIPT – NIST12-tip probe

Re(10 nm)Al(10)

BarrierRe or Al(150)

Top surface must be conductive(Au, RuO, Re)

Percent of total energy in dielectric(50 micron trench depth )

Prelim Data 1.8 K

Model: Ideal CPW – lossless

Qc L(C 2Cc )

2CcRoZo

1

Qmeas

1

Qo

1

Qc

RF Substrate Evaluation Through Q

• Q ~ 105 for Si, sapphire •Q decreases at lower RF power (~ 103 photons)

Influence of two-level systems

Next step: go to low temp & power with Al, Re in ADR

Substrate Material Qmax

SiOX 100,000

Sapphire 60,000

Si(100) 45,000

25% diamond 10,000

50% diamond 3,000T = 1.8 K