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 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

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

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

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

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

Johnson-Schottky Transition: Direct relationship between T and V

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

Experimental Setup:RF + DC Measurement

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

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

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

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

Noise Versus Voltage

Universal Functional Form: Agreement over four decades In temperature

Comparison With Secondary Thermometers

Temperature Measurements Over Time

Uncertainty vs. Integration Time

Fit With Two Parameters Residuals

Fit With Three Parameters Residuals

Correlations of Fit Parameters

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)

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

Tien-Gordon Theory Tucker and Feldman, 1985

Tien-Gordon for Noise of Junction

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

Conductance R=31.22Ohms

More Conductance

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