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 Johnson-Schottky transition of the noise in tunnel junctions Relates T and V using only e and k B  primary thermometer Demonstrate operation from T=0.26 K to 300K

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

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

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 Thermal Noise 2eGV=2eI Shot Noise 4k B T R Johnson-Schottky Transition Region eV~k B T

Johnson-Schottky Transition: Direct relationship between T and V

Tunnel Junction (AFM image) Al-Al 2 O 3 -Al Junction R=33  Area=10  m 2 I+I+ I-I- V+V+ V-V-

Experimental Setup:RF + DC Measurement

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

Self-Calibration Technique for Thermometry P = Gain*B( S I Amp +S I (V,T) )

Noise Versus Voltage T noise =5.128 K, Gain=29.57  V/K T=4.372 K

Universal Functional Form: Agreement over three decades In temperature

Comparison With Secondary Thermometers

Temperature Measurements Over Time

Merits Vs. Systematics *R. J. Schoelkopf et al., Phys Rev. Lett. 80, 2437 (1998) Possibility to relate T to frequency!* Compact electronic sensor No B-dependence Wide T range (mK to room temperature) Fast and self-calibrating Primary MeritsSystematics I-V curve nonlinearities Amplifier and diode nonlinearities Frequency dependence* Self-heating

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 k b applications for metrology

Diode Nonlinearity V diode = GP +  G 2 P 2  = -3.1 V -1 1mV => 3x10 -3 fractional error

Conductance R=31.22Ohms

More Conductance