The Shot Noise Thermometer
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Transcript of The Shot Noise Thermometer
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The Shot Noise Thermometer
Lafe Spietz, K.W. Lehnert, I. Siddiqi, R.J. Schoelkopf
Department of Applied Physics, Yale UniversityThanks to:
Michel Devoret, Daniel E. Prober, and Wes Tew
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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*
*Lafe Spietz et al, Science 300, 1929 (2003)
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Thermometry
Secondary: Needs to be calibrated from some outside standard, e.g. resistive thermometers
Primary: Needs no outside calibration—based on understood physics, e.g. ideal gas thermometer
Desirable Characteristics for a Thermometer:
• Wide Range• Fast• Primary• Accurate• Easy and simple to use• Physically compact
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ResistanceThermometers
Cryogenic Thermometry: Overview
1 K
300 K
10 K
0.1 K
0.01 K
100 K
RuOx 50 mK
3He Melting CurveCBT
JohnsonNoise
Nuclear Orientation
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Fundamental Noise SourcesJohnson-Nyquist Noise
• Frequency-independent• Temperature-dependent• Used for thermometry
• Frequency-independent • Temperature independent
( ) 2IS f eI
4( ) BI
k TS fR
2A
Hz
2AHz
Shot 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:
Conductance (G) is constant
Fermi functions
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Thermal-Shot Noise of a Tunnel Junction*
( ) 2 coth2I
B
eVS f eIk 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 eIk T
Johnson Noise
2eIShot Noise
4kBTR
Transition Region eV~kBT
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Self-Calibration TechniqueP(V) = Gain( SI
Amp+SI(V,T) )
2 /Bk T e
4 AmplifierI
BG Sk TR
P(V)
{
2eI
V
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Al-Al2O3-Al Junction
Experimental Setup: RF + DCMeasurement
SEM
5
P
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High-Bandwidth Measurement
8,~ 10 zB H
1PP B
= 1 second 410PP
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Noise Versus Voltage
B B
eV eVFit = Gain Coth -T2k 2k T
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Universal Functional FormAgreement over four decades in temperature
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Comparison With Secondary Thermometers
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off off
B B
e(V - V ) e(V - V )Fit = Gain Coth - T
2k 2k T
High Precision Measurement
2 1.04
Res
idua
ls
502.5 .094T mK mK 51.0001 6.7 10Gain
18 4.2Offset nV nV
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Uncertainty vs. Integration Time
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Thermodynamic Uncertainties of Temperature Scales
500 mK
ThermodynamicUncertainty of PLTS-2000
SNT
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High Bias Nonidealities~10max BeV k T
High T High Bias
( ) 2 ( )IS V eI V
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~ 6%RR
~ 800R ppmR
Nonlinear Current and Noise
( ) ( )4
junctionjunctionI
junctionB
S V R VT
k
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Modular SNT Package
Total cost of package <10$
Tunnel Junction
Built-in Bias Tee(on-board SMTComponents)
Copper Plumbing parts
SMA Connectors for RF
Copper Tubing for DC lines
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Future Work• Determine effect of nonlinearity on shot noise• Measure heating effects with dirty film• Improve room temperature results• Measure hydrogen triple point• Make SNT more modular and easy to use for
use in other labs and for commercialization• Push the lower temperature end with lower
system noise temperature and more careful filtering
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Summary• Demonstrate functional form of junction noise
0.02 - 300 Kelvin*
• Use as fast, accurate thermometer
• As good as 200 ppm precision, 0.1% accuracy
• Relates T to V using only e and kB Possible kB determination?
*Lafe Spietz et al, Science 300, 1929 (2003)
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END
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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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Fano Factor Has No Effect:
2 cothB
eVeIk T
81 2 coth3 3
B
B
k TeVeIk T R
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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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Null-Balancing Noise Measurement for High Precision
Noise Contours in Voltage-Space
Small range of noise keepsdetector in linear range
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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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Experimental Setup:RF + DCMeasurement and Thermometry
capacitors
inductors
RhFe Thermometer
RuOx Thermometer
device
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B B
eV eVFit = Gain Coth -T2k 2k T
2 1.49
Fit With Two ParametersR
esid
uals
502.5 .094T mK mK 51.0001 6.7 10Gain
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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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Tunnel Junction(AFM image)
Al-Al2O3-Al JunctionR=33 Area=10 m2
I+
I-
V+
V-