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The Ideal Electron Gas Thermometer

The Ideal Electron Gas Thermometer. Lafe Spietz, K.W. Lehnert, I. Siddiqi, R.J. Schoelkopf 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 Lafe Spietz, K.W. Lehnert, I. Siddiqi, R.J. Schoelkopf 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=0.26 K to 300K

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

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

  12. Noise Versus Voltage T=4.372 K Tnoise=5.128 K, Gain=29.57 mV/K

  13. Universal Functional Form: Agreement over three decades In temperature

  14. Comparison With Secondary Thermometers

  15. Temperature Measurements Over Time

  16. 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)

  17. 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

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

  19. Conductance R=31.22Ohms

  20. More Conductance

  21. 2 3 1 4

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