Electron Transport of Metal Gated Devices in GaAs/AlGaAs Heterostructure

K. M. Liu(劉凱銘 ) , W. R. Chen(陳偉仁 ), Y. M. Lin (林玉敏 ), and S. Y. Hsu (許世英 )

Low Temperature Laboratory, Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan, R.O.C.

Outline

• Introduction– GaAs/AlGaAs Heterostructure– Transport in mesoscopic system– Quantum Point Contact– Gate Defined Quantum Dot

• Fabrication• Double quantum point contacts in series• Electron Pumping

– Adiabatic Quantum Pumping• Summary

Introduction-GaAs/AlGaAs Heterostructure

There is a very thin layer called 2-Dimensional Electron Gas(2DEG) at the interface of GaAs and AlGaAs. Which is a conducting layer.

GaAs/AlGaAs 0.3K(5-70)

carrier density ns 1.88x1011 cm-2

mobility μ 0.8x106 cm2/Vs

Fermi wavelength λf 57.8 nm

mean free path le 5.9m

2DEGE1

energy

Ec

Ef

0.2eV

Structure of GaAs/AlGaAs grown by MBE

10 nm, GaAs Cap

15 nm, δ- doping layer, Si, 2.6x1018 cm-2

60 nm, spacerAlGaAs, x=0.37

1500 nm, buffer layer GaAs

0.3mm GaAs substrate

8 nm, spacer AlGaAs

The mean free path is much larger than the limit length scale of modern technology. Thus we can obtain a system where the transport of electron is coherent and ballistic through lithographic fabrications.

Transport in Mesoscopic System –A Theoretical Description

For an Ideal 1D system with one conducting channel

]')'()'()'()()()([2

20

0

21

dkETkfkvdkETkfkve

I

Current passing through a conductor can be expressed as

v(k): electron velocityf(k): distribution functionT(E): Transmission

In the limit of low temperature, small (μ1- μ2), and assume T(E) independent with E

)(2

)( 21

1

2

T

h

edEET

eI

μ2

reservoir

μ1TR

T

e-

conductor

Transport is conductance!

2. Multi-Channel Conductor

Th

eG

22

)(2 2

ttTrh

eG

-Landauer Formula

1. Conductor with one channel

Quantum Point Contact

Applying a negative voltage on the metal split-gates fabricated above a 2DEG, depleting the electron gas, a quasi-1D quantum wire is formed. And the electron state in the conductor is quantized.

e-Source Drain

Vg

Ef

E(kx)

kx

x

y

-1.6 -1.4 -1.2 -1.0 -0.80

1

2

3

4

5

6

7

8

9

10

11

12

G(2

e2 /h)

Vg (volt)

Each plateau corresponds to an additional mode as integer multiples of half the Fermi wavelength.

Gate Defined Quantum Dot

e-

source

drain

The modeled circuit:

Vg

Vsd

Rl

Cl

Rr

Cr

ΣCg

- +

-+

dot

The energy is quantized as soon as the quasi-0D dot is formed. And the transport is blocked as shown:

The energy potential of QD can be tuned by varying Vg, and electron tunneling occurs when there is a state aligning with the Fermi level at source or drain.

Coulomb Blockade

0.5μm

e2/Ceq charging energyN

N+1

Vg

μs

μD

-100.0m 0.0 100.0m2.4

2.6

2.8

3.0

Open Dot

G

(2e2

/h)

H(T)

4.2K

PRL. 80, 4522(1998)Coulomb Staircase For the I-V curve of the QD, the value of current corresponds to the number of states in the energy window Vsd and is quantized.

Z. Phys. 85, 367(1991)

Weak Localization

Coulomb Oscillation

e-

-55.0m -50.0m -45.0m -40.0m -35.0m -30.0m0.40

0.42

0.44

0.46

0.48

0.50

G(2

e2/h

)

Vg(volt)

6-102a-I2

Number of electrons~1500

FabricationsPart I. Photolithography

Hot plate 90°C

sample

PR

Coating & Prebake

UV Light Exposure

sample

PR

mask

Develop

sample

Mesa Etch the wafer with solution H2SO4:H2O2:H2O=1:8:160

Ohmic Contact

Deposit Ni/Au/Ge/Ni=100Å/2000Å/1000Å/700Å

Annealing:450o for 13min

Gate Deposit Au/Ti =1200Å/100Å

mesa

contact pads

metal gates

Part II. E-beam lithography

sample

Develop (MIBK:IPA=1:3)

sample

Metal Deposition (Ti/Au)

metal

sample

metal

Lift off in the Acetone

sample

PMMA

Coating & Prebake

sample

PMMA

Electron Beam Exposure

electron beam

-J. Phys. C 21, L887 (1988)

g1 g2

(a)Vg2=-1V(b)Vg2=0V

The second channel must impose a more severe constriction on the transverse momentum (Collimation) additional geometry resistance

As both QPCs are confined, the plateau index start from the smallest number among themthe resistance through two QPCs is determined by the narrowest of the two constrictions.

Double QPCs in Series

Channel length:0.3μm

1 μm

Remove the anomalous resistance

Preliminary Summary

Transport through single QPC demonstrates quantized conductance in units of 2e2/h.

If the transport is ballistic, the total conductance across double QPCs is determined by the smallest one. The values are also integer multiples of 2e2/h.It is theoretically predicted that:

When one of the QPC is in the tunneling regime (N<1), the transport should behave ohmic addition.

Sourcee-

V2L

V1

Drain

qpc2qpc1

-1.3 -1.2 -1.1 -1.0 -0.9 -0.80

1

2

3

4

5

6

7

8

V1(volt)V

1(volt)

G2(2e2/h)

6 5 4 3 2 0.9

G (

2e2 /h

)

-1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5

212

1*

RRG

12

1

RG L=0.8μm

The traces have fewer plateaus with narrower qpc2.

It has only 1 plateaus with qpc2 set in N=2. It’s ballistic when L=0.8μm.

Destruction of coherence in double quantum point contacts (QPCs) in series

-1.1 -1.0 -0.9 -0.8 -0.7 -0.60

1

2

3

4

5

6

7

8

-1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4

G(2

e2 /h)

V1(volt) V

1(volt)

G2(2e2/h)

5 4 3 2 1 0.8

For larger L, subtracting the contribution from qpc2,

the single QPC’s conductance quantization is restored. These two QPCs are almost independent with each other.

212

1*

RRG

12

1

RG L=2.9μm

-0.2 -0.1 0.0 0.1 0.20

1

2

3

4

5

6

7

8

-0.2 -0.1 0.0 0.1 0.2

G(2

e2 /h)

V1(volt)

R2=0

G2(2e2/h)

13 6 3 0.9 0.7

V1(volt)

R2=0

When the separation L is much larger than the mean free path, identical traces were obtained. These two QPCs are completely independent with each other.

212

1*

RRG

12

1

RG L=20μm

As the transmission mode is set to zero (N<1) and L small, we can regard qpc2 as a barrier, and there’s no coherence between QPCs.Plateaus completely vanish.

-1.0 -0.8 -0.60

1

2

3

4

5

6

7

8

-1.4 -1.2 -1.0 -0.8 -0.6 -0.4

G

* (2

e2 /h

)

1.9m

2.9mL=2.9m

1.8m

1m

1.1m

G2=0.8(2e2/h)

m

G2=0.9(2e2/h)

V1 (volt)

Summary

Transport through double QPCs in series :•The transport behaviors are determined by two factors: (a) separation between two QPCs, L. (b) number of transmission modes N.

• As L is larger than a specific length, order of e,

the transport behaves completely as that of two independent QPCs.

• As L is less than e and N is less than one ,

the quantized conductance vanishes. Coherence between QPCs can be destroyed.

Adiabatic Quantum Pumping

System:

qpc1 qpc2

•Electron reservoirs are held at same voltage.(zero bias)

•Each QPC have N channels at the Fermi level EF.

•The scattering matrix of the system has dimension 2N×2N and is a function of X1 and X2

X1 and X2 are two parameters modifying the wavefunction of the open dots. Which may be magnetic field or gate voltage.

tieXXtX 0)(

Small harmonic variation:

The charge δ Q(m) entering or leaving the cavity through contact m(m=1,2) in an infinitesimal time:

*Im2

1)(

,)(

),(

SX

S

dX

mdn

XdX

mdnemQ

m

For two parameters X1 and X2

)()(

)()(

),( 22

11

tXdX

mdnetX

dX

mdnetmQ

Integrate over one period and use Green’s Theorem

1221

21

)()(),(

dX

mdn

XdX

mdn

XdXdXemQ

A

SX

SiRRRdXdX

eiI XXX

m A

m ,,4 212 21

21 1

*21 Im

2

sin

X

S

X

SXXeIm

or

PRB, 58, 10135(1998)

emissivity

tieXXtX 101 )( tieXXtX 202 )(

a. For a phase coherent quantum system, the out-of-phase variation will give rise to a dc current.

b. The current scales as the area enclosed by X1 and X2 in phase space or say the current varies as sinφ.

Science 283, 1905(1999)Experiments:

Isd=0

V

0 100 200 300 400 500 600 700-300.0p

-200.0p

-100.0p

0.0

100.0p

200.0p

300.0p

Vpp

=130mV; T=0.3K; f=20MHz

I(A

mp

)

deg)

Pumped current in different dot size

0 100 200 300 400 500 600 700-3.0p

-2.0p

-1.0p

0.0

1.0p

2.0p

3.0p

Vpp

=130mV; T=0.3K; f=20MHz

I(A

mp

)

deg)

Open dot

Closed dot

)sin(0 tV

)sin(0 tV

II: N=(2,2),V=(-1.803,-1.98)

III:N=(1,1),V=(-1.209,-2.19)

IV:N=(0,1),V=(-1.23,-2.19)

V:N=(0,0),V=(-1.35,-2.25)

VII:N=(0,0),V=(-1.4,-2.25)

VIII:N=(0,0),V=(-1.4,-2.35)

IX:N=(0,0),V=(-1.4,-2.4)

qpc3 qpc4

The pumped current reduces with increasing barrier height between dot and reservoirs.

Vpp

(peak to peak)

10mV

40mV

50mV

60mV

70mV

80mV

100mV

120mV

0 100 200 300 400 500 600 700-20.0u

-10.0u

0.0

10.0u

20.0u

Vd

ot(v

olt)

(deg)

Vpqc3,Vqpc4=(-1.602,-1.599); Rdot~10k; 0.3K; f=5MHz

0 100 200 300 400 500 600 700

-30.0u

-20.0u

-10.0u

0.0

10.0u

20.0u

30.0u

Vd

ot(v

olt)

(deg)

Vpqc3,Vqpc4=(-1.602,-1.599); Rdot~10k; 0.3K; f=5MHz

Pumped current with different excitation amplitude

The pumped current enhances with increasing excitation amplitude. Non-sinusoidal form when Vpp becomes too large.

0 100 200 300 400 500 600-10.0u

-8.0u

-6.0u

-4.0u

-2.0u

0.0

2.0u

4.0u

6.0u

8.0u

10.0u

Vd

ot(v

olt)

(deg)

7.5MHz

5MHz

2.5MHz

1MHz

Vpqc3

,Vqpc4

=(-1.605,-1.603);Rdot

~10k;1.8K;Vpp=40mV

Pumped current with different frequency

The pumped current is roughly linear with frequency.

Summary

A mesoscopic system is easily achieved through GaAs/AlGaAs heterostructures due to it’s long mean free path.

The transport of electrons in such systems is characterized by transmission or conductance.

Quantum phenomenon: Quantized Conductance in QPC, periodic Coulomb Oscillations, Weak Localization.

Double QPCs in series is also studied, where the behavior is characterized by distance between QPCs.

Adiabatic Pumping can generate a DC voltage or current without external bias.