materials for csq pm: karl roenigk, iarpa pi: david p. pappas, nist staff: danielle braje, robert...
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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
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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
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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
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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%
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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
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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
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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.
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Example:Al(111)/epi-Al2O3/Al(111) structure on sapphire
Sapphire Substrate
Epitaxial Al
FIB Pt
Oxide / Al / Re
TEMBrian Gorman
CSM
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HRTEM of Oxide Layer
0.23nm
0.37nm
<111> Al <111>Al<0001> Al2O3
Epi Al(111)
Oxide Al2O3
Top Al(111)
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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
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• 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)
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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]
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Barrier Tunneling Model• Voltages above threshold /e
-
2 = 0
CP
h
e
e
SS I
Multiple Andreev Reflection (eV = + )
(evanescent)
1 = +
2 +
2 +3
-
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• 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)
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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
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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
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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
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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
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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
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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
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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)
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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
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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
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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)
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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
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Saturation of TLSs at low T & P
RFg
e
g
e
PPMSADR
10% effect @ 1.8 K80% effect @ 0.1 K
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1/Q
=
Increasing P
Increasing T
Quality factor can appear higher due to poor T and Pwr control
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“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
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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
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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
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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
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Capres CIPT – NIST12-tip probe
Re(10 nm)Al(10)
BarrierRe or Al(150)
Top surface must be conductive(Au, RuO, Re)
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Percent of total energy in dielectric(50 micron trench depth )
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Prelim Data 1.8 K
Model: Ideal CPW – lossless
Qc L(C 2Cc )
2CcRoZo
1
Qmeas
1
Qo
1
Qc
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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