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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
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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
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Fundamental Noise Sources
Thermal(Johnson) Noise Frequency-independent Temperature-dependent Used for thermometry Shot(Schottky) Noise Frequency-independent Temperature independent
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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
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Thermal-Shot Noise of a Tunnel Junction*
Sum gives noise: *D. Rogovin and D.J. Scalpino, Ann Phys. 86,1 (1974)
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Thermal-Shot Noise of a Tunnel Junction
2eGV=2eI Shot Noise Johnson-Schottky Transition Region eV~kBT 4kBT Thermal Noise R
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Johnson-Schottky Transition:
Direct relationship between T and V
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Tunnel Junction (AFM image)
R=33 W Area=10 mm2 Al-Al2O3-Al Junction V+ I+ I- V-
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Experimental Setup:RF + DC Measurement
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Experimental Setup:RF + DC Measurement and Thermometry
RhFe Thermometer capacitors device RuOx Thermometer inductors
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Experimental Setup: Pumped He Cryostat
Noise power vs. bias voltage: High bandwidth: hence fast For t = 1 second,
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Self-Calibration Technique for Thermometry
Subtract offsets P = Gain*B( SIAmp+SI(V,T) )
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Self-Calibration Technique for Thermometry
Slope = 2eGB/R -GB(4kBT/R)
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Noise Versus Voltage
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Universal Functional Form: Agreement over four decades In temperature
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Comparison With Secondary Thermometers
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Temperature Measurements Over Time
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Uncertainty vs. Integration Time
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Fit With Two Parameters
Residuals
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Fit With Three Parameters
Residuals
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Correlations of Fit Parameters
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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)
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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
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Tien-Gordon Theory Tucker and Feldman, 1985
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Tien-Gordon for Noise of Junction
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Diode Nonlinearity Vdiode = GP + bG2P2 b= -3.1 V-1
1mV => 3x10-3 fractional error
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Conductance R=31.22Ohms
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More Conductance
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