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

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

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

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

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

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

Johnson-Schottky Transition:Direct relationship between T and V

Tunnel Junction(AFM image)

Al-Al2O3-Al JunctionR=33 Area=10 m2

I+

I-

V+

V-

Experimental Setup:RF + DCMeasurement

Experimental Setup:RF + DCMeasurement and Thermometry

capacitors

inductors

RhFe Thermometer

RuOx Thermometer

device

Experimental Setup: Pumped He Cryostat

8

~ 10B Hz42

~ 10noise

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) )

Subtract offsets

Self-Calibration Technique for Thermometry

-GB(4kBT/R)

Slope =2eGB/R

Intercept 2Slope

Bk Te

Noise Versus Voltage

B B

eV eVFit = Gain Coth -T2k 2k T

Universal Functional Form: Agreement over four decades In temperature

Comparison With Secondary Thermometers

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

Uncertainty vs. Integration Time

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

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

Correlations of Fit Parameters

off off

B B

e(V -V ) e(V -V )Fit = Gain Coth -T2k 2k T

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

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

1

2

3

4