an electronic primary thermometer based on thermal shot noise lafe spietz k.w. lehnert, r.j....
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![Page 1: An Electronic Primary Thermometer Based on Thermal Shot Noise Lafe Spietz K.W. Lehnert, R.J. Schoelkopf Department Of Applied Physics, Yale University](https://reader037.vdocuments.site/reader037/viewer/2022110207/56649d5e5503460f94a3e262/html5/thumbnails/1.jpg)
An Electronic Primary Thermometer Based on Thermal
Shot NoiseLafe Spietz
K.W. Lehnert, R.J. Schoelkopf
Department Of Applied Physics, Yale University
Thanks to:
Michel Devoret, Dan Prober, Irfan Siddiqi,
Ryan Held
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2ggC V
e0-0.5 0.5
n
300 mK400 mK500 mK600 mK
Coulomb Staircase T>T*
Motivation: Unfilled Need in Milikelvin Thermometry
Mystery kelvins!
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OutlineI. Motivation, overview of thermometry
- Limitations of cryogenic thermometry and temperature metrology
II. Thermal-shot noise of tunnel junctions- How it makes a thermometer
III. Fabrication of devices: - Dolan bridge junction fab at Yale
IV. Demonstration of the thermometer from 0.01K to 300 K
V. Future work, possible limitations
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Overview of low temperaturethermometry
• Johnson noise: Primary, slow, difficult, very wide range• Resistors: Secondary,can drift, can be field dependent, not good at very
low temperatures, cheap and fast• Nuclear orientation: Primary, expensive, very limited range, doesn’t work in
B field• 3He-4He vapor pressure: Primary, difficult, limited range• diodes: Secondary, not good below 1K• Capacitance: secondary, no B dependence, recalibrate on cycling• Paramagnetic salts: primary, limited range, B dependence
Primary vs. secondary
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ITS 90: The Modern Kelvin
Plank radiation law
Platinum resistance thermometer
He gas thermometer
3He 4He vapor pressure
?
.6K
961.78K25K5K3K
Below .6K
undefined!
T90 :
triple point of water = 273.16 K(T90 )
273.16K
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Fundamental Noise SourcesJohnson-Nyquist Noise
• Frequency-independent• Temperature-dependent• Used for thermometry
• Frequency-independent • Temperature independent
( ) 2IS f eI
4( ) bI
k TS f
R
2A
Hz
2A
Hz
Shot Noise
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Johnson Noise Thermometry
Limited by calibration of gain and bandwidth--very hard, limits bandwidth, and hence speed.
P = GB(SIamp + 4kT/R)
G B PR
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Conduction in Tunnel Junctions
Assume: Tunneling amplitudes and D.O.S. independent of Energy
V
I
~ (1 )
~ (1 )
l r l r
r l r l
I f f dE
I f f dE
l r r lI I I Difference gives current:
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Thermal-Shot Noise of a Tunnel Junction*
( ) 2 coth2I
b
eVS f eI
k T
Sum gives noise:
( ) 2 ( )I l r r lS f e I I
*D. Rogovin and D.J. Scalpino, Ann Phys. 86,1 (1974)
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Thermal-Shot Noise of a Tunnel Junction
( ) 2 coth2I
b
eVS f eI
k T
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Self-Calibration Technique
8
~ 10B Hz41
~ 10P
P B
( ( , ))
2,
( , )( , ) (2 )
AmpI IP GB S S V T
e
R
dS V TdP V T d eIIGBdV dVdV
For = 1 second
For eV>>kT
Hence can remove GB.
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Thermometer Demonstration
T is measured without reference to unknown system parameters
1/ 20.6126... / bT e k V
1/ 2V
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Silicon Substrate
PMMA
PMGI LOR
40 KeV Electrons
.7 m
1 m
E-Beam Lithography onBilayer
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Silicon Substrate
PMMA
PMGI LOR
Independent Developers Create Undercut
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SEM of Undercut
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Silicon Substrate
PMMA
PMGI LOR
Create Suspended Bridges!
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Device With Bridge
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Silicon Substrate
PMMA
PMGI LOR
AluminumAluminum
Double Angle: 1st Evaporation
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Silicon Substrate
PMMA
PMGI LOR
Aluminum +
Aluminum Oxide
Aluminum +
Aluminum Oxide
Oxidize to Create Barrier
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Silicon Substrate
PMMA
PMGI LOR
AluminumAluminum
Double Angle:2nd Evaporation
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Completed Junction Profile
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The Finished Product(AFM)
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The Measurement
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Linear I-V
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Good fit to theory:( ) 2 coth
2Ib
eVS f eI
k T
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Calibrate off of shotnoise
Pshot = GB(Samp+2eI)
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Comparison of normalized data to functional form
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Comparison of normalized data to functional form over
wide range
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Fit to extract temperature
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Preliminary Results:Comparison to Oxford
Thermometer
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Improvements, future work
Improve thermal contact to comparison thermometers
Compare against better thermometers
Investigate self-heating
Investigate precision limits—is this the new Kelvin?
4 wire measurement
Engineer for commercial distribution
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Advantages and Disadvantages
*R. J. Schoelkopf et al., Phys Rev. Lett. 80, 2437 (1998)
Advantages
Fast and self-calibrating
Primary
Wide T range
No B-dependence
Measures electron temperature
Possibility to relate T to frequency!*
Disadvantages
Lead heating
Frequency dependence*
I(V) nonlinearities from:
Density of states
Barrier shape
Weak localization, etc
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Summary
• Fundamental voltage and temperature dependent noise of a tunnel junction
(thermal-shot noise.)
• Makes fast, accurate thermometer which works over a wide temperature range
• Relates T to V using only e and kb implications for metrology