Bringing quantum Hall effect resistance standards closer...
Transcript of Bringing quantum Hall effect resistance standards closer...
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
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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
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-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
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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
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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