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 T=0.02 K to 300 K*
*Lafe Spietz et al, Science 300, 1929 (2003)

3. 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 calibration—based on understood physics, e.g. ideal gas thermometer

4. 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

5. Fundamental Noise Sources
Johnson-Nyquist Noise
Frequency-independent
Temperature-dependent
Used for thermometry
Shot Noise
Frequency-independent
Temperature independent

6. 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

7. Thermal-Shot Noise of a Tunnel Junction*
Sum gives noise:
*D. Rogovin and D.J. Scalpino, Ann Phys. 86,1 (1974)

8. Thermal-Shot Noise of a Tunnel Junction
2eI
Shot Noise
Transition Region
eV~kBT
4kBT
Johnson Noise R

9. Self-Calibration Technique
P(V) = Gain( SIAmp+SI(V,T) )
P(V) { V

10. Experimental Setup: RF + DC Measurement
SEM
Al-Al2O3-Al Junction

11. High-Bandwidth Measurement
t = 1 second

12. Noise Versus Voltage

13. Universal Functional Form
Agreement over four decades in temperature

14. Comparison With Secondary Thermometers

15. High Precision Measurement
Residuals

16. Uncertainty vs. Integration Time

17. Thermodynamic Uncertainties of Temperature Scales
Uncertainty of
PLTS-2000
500 mK
SNT

18. High Bias Nonidealities
High T
High Bias

19. Nonlinear Current and Noise

20. Modular SNT Package Total cost of package <10$
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 <10$

21. 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

22. Summary
Demonstrate functional form of junction noise 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

24. Tien-Gordon Theory
Tucker and Feldman, 1985

25. Tien-Gordon for Noise of Junction

27. Diode Nonlinearity Vdiode = GP + bG2P2 b= -3.1 V-1
1mV => 3x10-3 fractional error

28. Conductance
R=31.22Ohms

29. More Conductance

30. Fano Factor Has No Effect:

31. Correlations of Fit Parameters

32. Null-Balancing Noise Measurement for High Precision
Noise Contours in Voltage-Space
Small range of noise keeps
detector in linear range

33. Temperature Measurements Over Time

34. Experimental Setup:RF + DC Measurement and Thermometry
RhFe
Thermometer
capacitors
device
RuOx
Thermometer
inductors

35. Fit With Two Parameters
Residuals

36. 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)

37. Tunnel Junction (AFM image)
R=33 W
Area=10 mm2
Al-Al2O3-Al Junction V+ I+ I- V-