An Electronic Primary Thermometer Based on Thermal

Shot NoiseLafe Spietz

K.W. Lehnert, R.J. Schoelkopf

Department Of Applied Physics, Yale University

Thanks to:

Michel Devoret, Dan Prober, Irfan Siddiqi,

Ryan Held

2ggC V

e0-0.5 0.5

n

300 mK400 mK500 mK600 mK

Coulomb Staircase T>T*

Motivation: Unfilled Need in Milikelvin Thermometry

Mystery kelvins!

OutlineI. Motivation, overview of thermometry

- Limitations of cryogenic thermometry and temperature metrology

II. Thermal-shot noise of tunnel junctions- How it makes a thermometer

III. Fabrication of devices: - Dolan bridge junction fab at Yale

IV. Demonstration of the thermometer from 0.01K to 300 K

V. Future work, possible limitations

Overview of low temperaturethermometry

• Johnson noise: Primary, slow, difficult, very wide range• Resistors: Secondary,can drift, can be field dependent, not good at very

low temperatures, cheap and fast• Nuclear orientation: Primary, expensive, very limited range, doesn’t work in

B field• 3He-4He vapor pressure: Primary, difficult, limited range• diodes: Secondary, not good below 1K• Capacitance: secondary, no B dependence, recalibrate on cycling• Paramagnetic salts: primary, limited range, B dependence

Primary vs. secondary

ITS 90: The Modern Kelvin

Plank radiation law

Platinum resistance thermometer

He gas thermometer

3He 4He vapor pressure

?

.6K

961.78K25K5K3K

Below .6K

undefined!

T90 :

triple point of water = 273.16 K(T90 )

273.16K

Fundamental Noise SourcesJohnson-Nyquist 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 Noise

Johnson Noise Thermometry

Limited by calibration of gain and bandwidth--very hard, limits bandwidth, and hence speed.

P = GB(SIamp + 4kT/R)

G B PR

Conduction in Tunnel Junctions

Assume: Tunneling amplitudes and D.O.S. independent of Energy

V

I

~ (1 )

~ (1 )

l r l r

r l r l

I f f dE

I f f dE

l r r lI I I Difference gives current:

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)

Thermal-Shot Noise of a Tunnel Junction

( ) 2 coth2I

b

eVS f eI

k T

Self-Calibration Technique

8

~ 10B Hz41

~ 10P

P B

( ( , ))

2,

( , )( , ) (2 )

AmpI IP GB S S V T

e

R

dS V TdP V T d eIIGBdV dVdV

For = 1 second

For eV>>kT

Hence can remove GB.

Thermometer Demonstration

T is measured without reference to unknown system parameters

1/ 20.6126... / bT e k V

1/ 2V

Silicon Substrate

PMMA

PMGI LOR

40 KeV Electrons

.7 m

1 m

E-Beam Lithography onBilayer

Silicon Substrate

PMMA

PMGI LOR

Independent Developers Create Undercut

SEM of Undercut

Silicon Substrate

PMMA

PMGI LOR

Create Suspended Bridges!

Device With Bridge

Silicon Substrate

PMMA

PMGI LOR

AluminumAluminum

Double Angle: 1st Evaporation

Silicon Substrate

PMMA

PMGI LOR

Aluminum +

Aluminum Oxide

Aluminum +

Aluminum Oxide

Oxidize to Create Barrier

Silicon Substrate

PMMA

PMGI LOR

AluminumAluminum

Double Angle:2nd Evaporation

Completed Junction Profile

The Finished Product(AFM)

The Measurement

Linear I-V

Good fit to theory:( ) 2 coth

2Ib

eVS f eI

k T

Calibrate off of shotnoise

Pshot = GB(Samp+2eI)

Comparison of normalized data to functional form

Comparison of normalized data to functional form over

wide range

Fit to extract temperature

Preliminary Results:Comparison to Oxford

Thermometer

Improvements, future work

Improve thermal contact to comparison thermometers

Compare against better thermometers

Investigate self-heating

Investigate precision limits—is this the new Kelvin?

4 wire measurement

Engineer for commercial distribution

Advantages and Disadvantages

*R. J. Schoelkopf et al., Phys Rev. Lett. 80, 2437 (1998)

Advantages

Fast and self-calibrating

Primary

Wide T range

No B-dependence

Measures electron temperature

Possibility to relate T to frequency!*

Disadvantages

Lead heating

Frequency dependence*

I(V) nonlinearities from:

Density of states

Barrier shape

Weak localization, etc

Summary

• Fundamental voltage and temperature dependent noise of a tunnel junction

(thermal-shot noise.)

• Makes fast, accurate thermometer which works over a wide temperature range

• Relates T to V using only e and kb implications for metrology