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

1

2

3

4