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The Ideal Electron Gas Thermometer
R.J. Schoelkopf, Lafe Spietz, K.W. Lehnert, I. Siddiqi
Department of Applied Physics, Yale UniversityThanks 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 fromT=0.02 K to 300 K
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Fundamental Noise SourcesThermal(Johnson) Noise
• Frequency-independent• Temperature-dependent• Used for thermometry
• Frequency-independent • Temperature independent
( ) 2IS f eI
4( ) BI
k TS fR
2AHz
2AHz
Shot(Schottky) Noise
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Conduction in Tunnel Junctions
Assume: Tunneling amplitudes and D.O.S. independent of energy
Fermi distribution of electrons
V
I
(1 )
(1 )
l r l r
r l r l
GI f f dEeGI f f dEe
l r r lI I I GV Difference gives current:
M I M
Conductance (G) is constant
Fermi functions
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Thermal-Shot Noise of a Tunnel Junction*
( ) 2 coth2I
B
eVS f eGVk T
Sum gives noise:
( ) 2 ( )I l r r lS f e I I
*D. Rogovin and D.J. Scalpino, Ann Phys. 86,1 (1974)
I GV
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Thermal-Shot Noise of a Tunnel Junction
( ) 2 coth2I
B
eVS f GVk T
Thermal Noise
2eGV=2eIShot Noise
4kBTR
Johnson-SchottkyTransition Region eV~kBT
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Johnson-Schottky Transition:Direct relationship between T and V
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Tunnel Junction(AFM image)
Al-Al2O3-Al JunctionR=33 Area=10 m2
I+
I-
V+
V-
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Experimental Setup:RF + DCMeasurement
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Experimental Setup:RF + DCMeasurement and Thermometry
capacitors
inductors
RhFe Thermometer
RuOx Thermometer
device
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Experimental Setup: Pumped He Cryostat
8
~ 10B Hz42
~ 10noise
noise B
For = 1 second,
High bandwidth:hence fast
Noise power vs. bias voltage:
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Self-Calibration Technique for Thermometry
P = Gain*B( SIAmp+SI(V,T) )
Subtract offsets
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Self-Calibration Technique for Thermometry
-GB(4kBT/R)
Slope =2eGB/R
Intercept 2Slope
Bk Te
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Noise Versus Voltage
B B
eV eVFit = Gain Coth -T2k 2k T
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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
6.0
5.5
5.0
4.5
4.0
T an
d T n
oise
(K)
1086420Time [hours]
75.0
74.5
74.0
73.5
73.0
Gain [10
-6V/K
]Tfit TRhFe Tnoise Gain
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Uncertainty vs. Integration Time
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B B
eV eVFit = Gain Coth -T2k 2k T
2 1.49
Fit With Two ParametersR
esid
uals
500 .094T mK mK 51.0001 6.7 10Gain
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off off
B B
e(V -V ) e(V -V )Fit = Gain Coth -T2k 2k T
Fit With Three Parameters
2 1.04
Res
idua
ls
500 .094T mK mK 51.0001 6.7 10Gain
18 4.2Offset nV nV
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Correlations of Fit Parameters
off off
B B
e(V -V ) e(V -V )Fit = Gain Coth -T2k 2k T
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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
Merits Systematics
• I-V curve nonlinearities
• Amplifier and diode nonlinearities
• Frequency dependence*
• Self-heating
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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 NonlinearityVdiode = GP + G2P2
= -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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