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 fromT=0.02 K to 300 K*

*Lafe Spietz et al, Science 300, 1929 (2003)

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

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

Fundamental Noise SourcesJohnson-Nyquist Noise

• Frequency-independent• Temperature-dependent• Used for thermometry

• Frequency-independent • Temperature independent

( ) 2IS f eI

4( ) B

I

k TS f

R

2A

Hz

2A

Hz

Shot 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:

Conductance (G) is constant

Fermi functions

Thermal-Shot Noise of a Tunnel Junction*

( ) 2 coth2I

B

eVS f eI

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 eI

k T

Johnson Noise

2eIShot Noise

4kBTR

Transition Region eV~kBT

Self-Calibration TechniqueP(V) = Gain( SI

Amp+SI(V,T) )

2 /Bk T e

4AmplifierI

BG Sk TR

P(V)

{

2eI

V

Al-Al2O3-Al Junction

Experimental Setup: RF + DCMeasurement

SEM

5

P

High-Bandwidth Measurement

8,~ 10 zB H

1PP B

= 1 second 410PP

Noise Versus Voltage

B B

eV eVFit = Gain Coth -T

2k 2k T

Universal Functional FormAgreement over four decades in temperature

Comparison With Secondary Thermometers

off off

B B

e(V - V ) e(V - V )Fit = Gain Coth - T

2k 2k T

High Precision Measurement

2 1.04

Re

sid

ual

s

502.5 .094T mK mK 51.0001 6.7 10Gain

18 4.2Offset nV nV

Uncertainty vs. Integration Time

Thermodynamic Uncertainties of Temperature Scales

500 mK

ThermodynamicUncertainty of PLTS-2000

SNT

High Bias Nonidealities~10max B

eV k THigh T High Bias

( ) 2 ( )IS V eI V

~ 6%R

R

~ 800R

ppmR

Nonlinear Current and Noise

( ) ( )

4

junctionjunctionI

junctionB

S V R VT

k

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

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

Summary

• Demonstrate functional form of junction noise0.02 - 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)

END

Tien-Gordon Theory

Tucker and Feldman, 1985

Tien-Gordon for Noise of Junction

Diode NonlinearityVdiode = GP + G2P2

= -3.1 V-1 1mV => 3x10-3 fractional error

Conductance

R=31.22Ohms

More Conductance

Fano Factor Has No Effect:

2 cothB

eVeI

k T

812 coth

3 3B

B

k TeVeI

k T R

Correlations of Fit Parameters

off off

B B

e(V -V ) e(V -V )Fit = Gain Coth -T

2k 2k T

Null-Balancing Noise Measurement for High Precision

Noise Contours in Voltage-Space

Small range of noise keepsdetector in linear range

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

Experimental Setup:RF + DCMeasurement and Thermometry

capacitors

inductors

RhFe Thermometer

RuOx Thermometer

device

B B

eV eVFit = Gain Coth -T

2k 2k T

2 1.49

Fit With Two ParametersR

esi

du

als

502.5 .094T mK mK 51.0001 6.7 10Gain

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

Tunnel Junction(AFM image)

Al-Al2O3-Al Junction

R=33 Area=10 m2

I+

I-

V+

V-