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The Ideal Electron Gas Thermometer

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. Introduction.

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The Ideal Electron Gas Thermometer

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  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 + DCMeasurement

  10. Experimental Setup:RF + DCMeasurement 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

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

  27. Conductance R=31.22Ohms

  28. More Conductance

  29. 2 3 1 4

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