The Shot Noise Thermometer

1
The Shot Noise Thermometer

• Lafe Spietz, K.W. Lehnert,
• I. Siddiqi, R.J. Schoelkopf
• Department of Applied Physics, Yale University
• Thanks to
• Michel Devoret, Daniel E. Prober, and Wes Tew

2
Introduction

• Johnson-Schottky transition of the noise in
  tunnel junctions
  
• Relates T and V using only e and kB
• ? primary thermometer
• Demonstrate operation from T0.02 K to 300 K

Lafe Spietz et al, Science 300, 1929 (2003)
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Thermometry
Desirable Characteristics for a Thermometer

• Wide Range
• Fast
• Primary
• Accurate
• Easy and simple to use
• Physically compact

Secondary Needs to be calibrated from some
outside standard, e.g. resistive thermometers
Primary Needs no outside calibrationbased on
understood physics, e.g. ideal gas thermometer
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Cryogenic Thermometry Overview
300 K
100 K
Johnson Noise
Resistance Thermometers
10 K
1 K
RuOx
50 mK
CBT
0.1 K
3He Melting Curve
0.01 K
Nuclear Orientation
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Fundamental Noise Sources

• Johnson-Nyquist Noise
• Frequency-independent
• Temperature-dependent
• Used for thermometry

Shot Noise

• Frequency-independent
• Temperature independent

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Conduction in Tunnel Junctions
Difference gives current
Fermi functions
Assume Tunneling amplitudes and
D.O.S. independent of energy Fermi
distribution of electrons
Conductance (G) is constant
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Thermal-Shot Noise of a Tunnel Junction
Sum gives noise
D. Rogovin and D.J. Scalpino, Ann Phys. 86,1
(1974)
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Thermal-Shot Noise of a Tunnel Junction
2eI Shot Noise
4kBT
Transition Region eVkBT
Johnson Noise
R
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Self-Calibration Technique
P(V) Gain( SIAmpSI(V,T) )
P(V)

V
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Experimental Setup RF DCMeasurement
P
5m
SEM
Al-Al2O3-Al Junction
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High-Bandwidth Measurement
t 1 second
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Noise Versus Voltage
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Universal Functional Form
Agreement over four decades in temperature
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Comparison With Secondary Thermometers
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High Precision Measurement
Residuals
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Uncertainty vs. Integration Time
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Thermodynamic Uncertainties of Temperature Scales
Thermodynamic Uncertainty of PLTS-2000
500 mK
SNT
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High Bias Nonidealities
High Bias
High T
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Nonlinear Current and Noise
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Modular SNT Package
Copper Tubing for DC lines
Copper Plumbing parts
Tunnel Junction
SMA Connectors for RF
Built-in Bias Tee (on-board SMT Components)
Total cost of package lt10
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Future Work

• Determine effect of nonlinearity on shot noise
• Measure heating effects with dirty film
• Improve room temperature results
• Measure hydrogen triple point
• Make SNT more modular and easy to use for use in
  other labs and for commercialization
• Push the lower temperature end with lower system
  noise temperature and more careful filtering

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Summary

• Demonstrate functional form of junction
  noise 0.02 - 300 Kelvin
• Use as fast, accurate thermometer
• As good as 200 ppm precision, 0.1 accuracy
• Relates T to V using only e and kB Possible
  kB determination?

Lafe Spietz et al, Science 300, 1929 (2003)
23
END
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Tien-Gordon Theory
Tucker and Feldman, 1985
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Tien-Gordon for Noise of Junction
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(No Transcript)
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Diode Nonlinearity
Vdiode GP bG2P2
b -3.1 V-1
1mV gt 3x10-3 fractional error
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Conductance
R31.22Ohms
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More Conductance
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Fano Factor Has No Effect
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Correlations of Fit Parameters
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Null-Balancing Noise Measurement for High
Precision
Noise Contours in Voltage-Space
Small range of noise keeps detector in linear
range
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Temperature Measurements Over Time
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Experimental SetupRF DCMeasurement and
Thermometry
RhFe Thermometer
capacitors
device
RuOx Thermometer
inductors
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Fit With Two Parameters
Residuals
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Merits Vs. Systematics
Merits

• Systematics
• I-V curve nonlinearities
• Amplifier and diode nonlinearities
• Frequency dependence
• Self-heating

• Fast and self-calibrating
• Primary

• Wide T range
• (mK to room temperature)

• No B-dependence

• Compact electronic sensor

• Possibility to relate T to frequency!

R. J. Schoelkopf et al., Phys Rev. Lett. 80,
2437 (1998)
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Tunnel Junction(AFM image)
R33 W Area10 mm2
Al-Al2O3-Al Junction
V
I
I-
V-