1. The Ideal Electron Gas Thermometer
R.J. Schoelkopf, Lafe Spietz, K.W. Lehnert,
I. Siddiqi
Department of Applied Physics, Yale University
Thanks to:
Michel Devoret and Daniel E. Prober

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

3. Fundamental Noise Sources
Thermal(Johnson) Noise
Frequency-independent
Temperature-dependent
Used for thermometry
Shot(Schottky) Noise
Frequency-independent
Temperature independent

4. Conduction in Tunnel Junctions
M I M
Difference gives current:
Fermi functions
Assume: Tunneling amplitudes and
D.O.S. independent of energy
Fermi distribution of electrons
Conductance (G)
is constant

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

6. Thermal-Shot Noise of a Tunnel Junction
2eGV=2eI
Shot Noise
Johnson-Schottky
Transition Region
eV~kBT
4kBT
Thermal Noise R

7. Johnson-Schottky Transition:
Direct relationship between T and V

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

9. Experimental Setup:RF + DC Measurement

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

11. Experimental Setup: Pumped He Cryostat
Noise power vs. bias voltage:
High bandwidth:
hence fast
For t = 1 second,

12. Self-Calibration Technique for Thermometry
Subtract offsets
P = Gain*B( SIAmp+SI(V,T) )

13. Self-Calibration Technique for Thermometry
Slope =
2eGB/R
-GB(4kBT/R)

14. Noise Versus Voltage

15. Universal Functional Form: Agreement over four decades In temperature

16. Comparison With Secondary Thermometers

17. Temperature Measurements Over Time

18. Uncertainty vs. Integration Time

19. Fit With Two Parameters
Residuals

20. Fit With Three Parameters
Residuals

21. Correlations of Fit Parameters

22. 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)

23. Summary
Ideal Electron Gas Thermometer based on Johnson-Schottky transition of noise in a tunnel junction (thermal-shot noise.)
Fast, accurate, primary thermometer
Works over a wide temperature range
Relates T to V using only e and kb applications for metrology

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. 2 3 1 4