Transcript The Shot Noise Thermometer

The Shot Noise Thermometer
Lafe Spietz, K.W. Lehnert,
I. Siddiqi, R.J. Schoelkopf
Department of Applied Physics, Yale University
Thanks to:
Michel Devoret, Daniel E. Prober, and Wes Tew
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*
*Lafe Spietz et al, Science 300, 1929 (2003)
Thermometry
Desirable Characteristics for a Thermometer:
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Wide Range
Fast
Primary
Accurate
Easy and simple to use
Physically compact
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
Cryogenic Thermometry: Overview
300 K
100 K
Johnson
Noise
10 K
1K
CBT
0.1 K
0.01 K
Nuclear
Orientation
Resistance
Thermometers
RuOx
50 mK
3He
Melting Curve
Fundamental Noise Sources
Johnson-Nyquist Noise
4 k BT  A2 
SI ( f ) 
 Hz 
R  
• Frequency-independent
• Temperature-dependent
• Used for thermometry
Shot Noise
SI ( f )  2eI
 A2 
 Hz 


• Frequency-independent
• Temperature independent
Conduction in Tunnel Junctions
I
V
G
I L  R   f L (1  f R )dE
e
G
I R  L   f R (1  f L )dE
e
Difference gives current:
I  I LR  I RL  GV
Fermi functions
Assume: Tunneling amplitudes and
D.O.S. independent of energy Conductance (G)
is constant
Fermi distribution of electrons
Thermal-Shot Noise of a Tunnel
Junction*
Sum gives noise:
SI ( f )  2e( I LR  I RL )
 eV 
S I ( f )  2eI coth 

 2k BT 
I  GV
*D. Rogovin and D.J. Scalpino, Ann Phys. 86,1 (1974)
Thermal-Shot Noise of a Tunnel
Junction
2eI
Shot Noise
Transition Region
eV~kBT
4kBTJohnson Noise
R
 eV 
S I ( f )  2eI coth 

 2k BT 
Self-Calibration Technique
P(V) = Gain( SIAmp+SI(V,T) )
P(V)
2eI
{
 4k T

G  B  S IAmplifier 
 R



2kBT / e
V
Experimental Setup: RF + DC
Measurement
P
5m
SEM
Al-Al2O3-Al Junction
High-Bandwidth Measurement
P 1
P
B
8
B ~ 10 Hz ,  = 1 second
 P 104
P
Noise Versus Voltage
 eV
 eV  
Fit = Gain 
Coth 
 - T
 2k B T  
 2k B
Universal Functional Form
Agreement over four decades in temperature
Comparison With Secondary
Thermometers
High Precision Measurement
 e(V - V
Fit = Gain 
 2k
off
Residuals
B
)
 e(V - V )  
Coth 
-T

 2k T  
 2  1.04
off
B
T  502.5mK  .094mK
Gain  1.0001  6.7 105
Offset  18nV  4.2nV
Uncertainty vs. Integration Time
Thermodynamic Uncertainties
of Temperature Scales
Thermodynamic
Uncertainty of
PLTS-2000
500 mK
SNT
High Bias Nonidealities
eVmax ~10kBT
High T
High Bias
SI (V )  2eI (V )
Nonlinear Current and Noise
R
R
R
R
~ 800 ppm
~ 6%
SIjunction (V ) R junction (V )
T junction 
4kB
Modular SNT Package
Copper Tubing for DC lines
SMA Connectors for RF
Copper Plumbing parts
Tunnel Junction
Built-in Bias Tee
(on-board SMT
Components)
Total cost of package <10$
Future Work
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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
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)
Tien-Gordon Theory
Tucker and Feldman, 1985
Tien-Gordon for Noise of Junction
Diode Nonlinearity
Vdiode = GP + bG2P2
b= -3.1 V-1
1mV => 3x10-3 fractional error
Conductance
R=31.22Ohms
More Conductance
Fano Factor Has No Effect:
 eV 
2eI coth 

k
T
 B 
 eV  8k BT
1
2eI coth 

3
 k BT  3R
Correlations of Fit Parameters
 e(V - Voff )
 e(V - Voff )  
Fit = Gain 
Coth 
 - T
 2k B T  
 2k B
Null-Balancing Noise
Measurement for High Precision
Noise Contours in Voltage-Space
Small range of noise keeps
detector in linear range
Temperature Measurements
Over Time
Tfit
TRhFe
Tnoise
Gain
5.5
75.0
74.5
5.0
4.5
73.5
4.0
73.0
0
2
4
6
8
Time [hours]
10
-6
74.0
Gain [10 V/K]
T and Tnoise(K)
6.0
Experimental Setup:RF + DC
Measurement and Thermometry
capacitors
device
inductors
RhFe
Thermometer
RuOx
Thermometer
Fit With Two Parameters
Residuals
 eV
 eV  
Fit = Gain 
Coth 
 - T
 2k B T  
 2k B
 2  1.49
T  502.5mK  .094mK
Gain  1.0001  6.7 105
Merits Vs. Systematics
Merits
Systematics
• Fast and self-calibrating
• I-V curve nonlinearities
• Primary
• Amplifier and diode
• Wide T range
nonlinearities
(mK to room temperature)
• No B-dependence
• Compact electronic sensor
• Frequency dependence*
• Self-heating
• Possibility to relate T to
frequency!*
*R. J. Schoelkopf et al., Phys Rev. Lett. 80, 2437 (1998)
Tunnel Junction
(AFM image)
R=33 W
Area=10 mm2
Al-Al2O3-Al Junction
V+
I+
I-
V-