Bringing quantum Hall effect resistance standards closer to room temperature

S. P. Giblin, T. J. B. M. JanssenG. R. Nash, P. D. Buckle, L. Buckle, M. T. Emeny

Electromagnetics DayThursday 29th November 2007

2

Metrology = ratio measurements + absolute reference

R2 (Customer’s)

Instrument whichmeasures R1/R2

R1 = RQHR = RK-90/i RK-90 = 25812.807 Ω by definition

Monitoring the drift of a standard resistor

1995 2000 2005

-11.7

-11.6

-11.5

-11.4

-11.3

-11.210

6 (R/1

00Ω

- 1)

Year

Value of 100 Ω standard R100-2measured against QHR

0.1 parts per million

4

The Hall Effect

Vx

Magnetic Field B

VyI

I

Ordinary Resistance: Rx = Vx / IHall Resistance: Ry = Vy / IRy ∝ B / n

5

The quantum Hall effect

AlGaAs

GaAs

2-DEG

0 5 100

5

10

15

R (k

Ω)

B (T)

Ry

Rx

Plateaux in Ry (B) at 300 mKRy = RK/i, RK = h/e2

i=2

i=3i=4

Ry ∝B

Vx < 2 nV on plateau

How cold is Cold?

10 K 100 K1 K0.1 K

Outer Space2.8 K

Pluto50 K

Earth300 K

LiquidNitrogen

77 K

LiquidHelium-4

4 K£5000

PumpedHelium-3

0.3 K£100000

PumpedHelium-4

1.2 K

QHR operation

7

Quantum energy levels and temperature

EnergyTo see quantum effects, need to

operate atT << ΔE / kB

E0

E1

ΔE

kB×1 K kB×5 K

Energy

To increase T, need to increase ΔE

8

Why InSb?

Silicon GaAs In0.53Ga0.47As InAs InSb units

Energy gap 1.12 1.43 0.75 0.356 0.175 eV

Electron effective mass

0.19 0.072 0.041 0.027 0.013

Electron mobility in pure material

1,500 8,500 14,000 30,000 78,000 cm2 V-1 s-1

Electron mobility at 1x1012cm-2

600 4,600 7,800 20,000 30,000 ‘’

ΔE = heB / 2πm*For devices to exhibit QHE at higher temperatures, need a smaller effective electron mass

Compare 2 QHE devices at T = 4 K

We are looking for Rx < 10 nV

1007Mobilitym2 V-1 s-1

4.4 ×10156.1×1015Carrier densitym-2

120050Width

GaAs (PTB)InSb(Qineteq)

Scaling from QHR to a standard resistor

10 Ω 10 mA 8 μA Extreme turns ratio - problematic100 Ω 3 mA 23 μA OK1 k Ω 1 mA 77 μA Marginal - need robust QHR device10 k Ω 0.3 mA 232 μA QHR current too high

QHR (i=2)12906.4035 Ω

STDCCC

We are looking for Vx < 2 nV at I = 23 μA

CCC measurement time needed for 1 ppb

1 10 1000.01

0.1

1

10

100

1000Ti

me

(hou

rs)

Current (μA)

Resistor heats up

Measurement takes too long

OK

Need 25 μAIn QHR device

Rxx Plateaux at 4 K

4 6 8 10 12 14

0

10

20

30

40

50R

xx (Ω

)

B (T)

InSb GaAs

i=2i=4

ISD = 10 μAT = 4.2 K

Both samples quantised on i=2Neither sample quantised on i=4

Vxx of both samplesat 4 K

0 50 100 150 200

0

50

100

150 GaAs sample PTB-5: T = 4 K InSb sample Q-1: T = 4 K GaAs sample: T = 300 mK

Vxx

(nV

)

ISD (μA)25 μA

RK/2 - 100 Ohm using CCC bridge

10 15 20 25 30

-1.02

-1.01

-1.00

-0.99

-0.98

-0.97 InSb Q-1 at 4.2 K 27/6/06 PTB-5 at 4.2 K 28/6/06 PTB-5 at 300 mK 30/6/06

106 (R

/100

Ω -

1)

ISD (μA)

0.01 ppm

Error bars show 1 σ

Wide InSb Hall bar -problem with cracking

0.5 mm

Acknowledgements

• UK Department of Trade and Industry (as was)

• Royal Society Industrial Research Fellowship (GN)

• Catherine Bartlett for device processing