the ideal electron gas thermometer lafe spietz, k.w. lehnert, i. siddiqi, r.j. schoelkopf department...
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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 kB
primary thermometer
• Demonstrate operation fromT=0.26 K to 300K
Fundamental Noise SourcesThermal(Johnson) Noise
• Frequency-independent• Temperature-dependent• Used for thermometry
• Frequency-independent • Temperature independent
( ) 2IS f eI
4( ) BI
k TS f
R
2A
Hz
2A
Hz
Shot(Schottky) Noise
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 dE
eG
I f f dEe
l r r lI I I GV Difference gives current:
M I M
Conductance (G) is constant
Fermi functions
Thermal-Shot Noise of a Tunnel Junction*
( ) 2 coth2I
B
eVS f eGV
k 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
Thermal-Shot Noise of a Tunnel Junction
( ) 2 coth2I
B
eVS f GV
k T
Thermal Noise
2eGV=2eIShot Noise
4kBTR
Johnson-SchottkyTransition Region eV~kBT
Johnson-Schottky Transition:Direct relationship between T and V
Tunnel Junction(AFM image)
Al-Al2O3-Al Junction
R=33 Area=10 m2
I+
I-
V+
V-
Experimental Setup:RF + DCMeasurement
Experimental Setup: Pumped He Cryostat
8
~ 10B Hz
42~ 10
noise
noise B
For = 1 second,
High bandwidth:hence fast
Noise power vs. bias voltage:
Self-Calibration Technique for Thermometry
P = Gain*B( SIAmp+SI(V,T) )
Noise Versus Voltage
Tnoise=5.128 K,
Gain=29.57 V/K
T=4.372 K
NOISE
B B
eV eVFit = Gain T + Coth
2k 2k T
Universal Functional Form: Agreement over three decades In temperature
Comparison With Secondary Thermometers
Temperature Measurements Over Time
6.0
5.5
5.0
4.5
4.0
T a
nd
Tno
ise(
K)
1086420Time [hours]
75.0
74.5
74.0
73.5
73.0
Ga
in [1
0-6V
/K]
Tfit
TRhFe
Tnoise
Gain
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
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
Diode NonlinearityVdiode = GP + G2P2
= -3.1 V-1 1mV => 3x10-3 fractional error
Conductance
R=31.22Ohms
More Conductance
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