1

Engineering of Disorder in MBE grown

Ultra-High Mobility 2D Electron System

Vladimir UmanskyBraun Center for Submicron Research

Weizmann Institute of Science, Rehovot, Israel

Collaborators:

Moty Heiblum & group (Braun Center for Submicron Research)

Jurgen Smet & group (Max-Planck-Institut für Festkörperforschung,

Stuttgart)

2

Preface: 2DEG and Mesoscopic Physics

Mobility: ~25,000 cm2/V∙s

3

Electron mobility progress

1980 1985 1990 1995 2000 2005 2010

1

10

Weizmann Inst. Bell Lab. Others

5

4030

20El

ectr

on M

obili

ty 1

06 cm

2 /Vs

m

e m

dQm

0

cos11

4

Outlook

2D Electron Gas - basics

DX centers – why we are lucky to have them?

How to observe 5/2 quasiparticles ?

New ideas for band gap engineering

Ultra – High Mobility. Is it enough ?

How to control disorder ?

Conclusions

5

2DEG in AlGaAs/GaAs 2DEG in AlGaAs/GaAs -scattering

0 20 40 60 80 100 120 140 160 1800.00

0.25

0.50

0.75

1.00

Total mobility

RI scatteting (=1)BG scattering

2DEG

Mob

ility

(ar

b. u

nits

)d (spacer thickness), nm

80708070 11 .... dN

CnN

CBG

BGsBG

BGBG

Background Impurities

sRIRIsRI

RIRI nNdCndN

C 525131 ..

Remote Ionized Impurities

NBG

2 <NBG

1Illumination

2DEGΔEc

EF

E0

Spacer (d)

AlGaAs(x~0.3)

Doping

GaAs

2DEG Total Depth (D)

RIBG 111

BGRI

T<1K

6

DX centers

Shallow donor

DX center

The “standard” 2DEG structure:

Pure GaAs

2DEG30-40% AlGaAs spacer

Delta or uniform doping

Gates

In the dark:

Pros: Frozen charge (in the dark) allows gating

Cons: Low doping efficiency (in the dark) → high RI

scattering

After Illumination in the dark:

Pros: Almost double density after illumination → high

mobility.

Cons: Parallel conduction/gate instability.

7

Applications

Gateable 2DEG:

QDs, QPC, Spin-pump,

Quantum shot noise, etc…

Deep structuresMeasurements after illumination

5/2

Shallow structuresMeasurements in the dark

8

5/2 in the “standard” 2DEG

“Standard” Al0.36Ga0.64As/GaAs

2DEG

Mobility: ~14 ×106 cm2/V∙s

Density: 2.2 ×1011 cm-3

Measurements: After illumination

Data from ~1998

5/2

9

How to Achieve Ultra-High Mobility ?

(*) background impurity density ~ 1×1014 cm-3 limits mobility by ~1÷2 ×106 cm2/V∙sec

MBE system design

Raw materials (i.e. Gallium (7N) → 2÷5×1015 cm-3 ) (*)

Optimal growth conditions (rate, temperature, III/V ratio,

etc…)

Optimal 2DEG structure design

Optimal growth sequence design

Background Impurity Scattering

10

Double – Side Doping

8.07.01~ s

BGBG n

N

5.131~ s

RIRI nd

N

Concern: Interface scattering in QW → Inverse interface

For the same spacer width:

EF

E0

2DEG Total Depth (D) W

d dns*

ss nn 2*

Used first by L. Pfeiffer to produce samples with > 30 ×106 cm2/Vsec

11

Doping in Short Period Super-Lattice

Γ

X

6ML AlAs

9ML GaAs

~250 meV 5 10 30 100 200

1011

1012

SPSL Doping

Doping in XAl

=35%

Density after illumination

Density in the dark

6

2

4

2DE

G d

ensi

ty (

cm-2)

Spacer (nm)

Higher transfer efficiency

Higher mobility due to better screening by X electrons

No parallel conductance due to ~3 times shorter Bohr

radiusShort Period Super-Lattice - SPSL

12

Results on Electron Mobility

Uniform Doping in Al0.35Ga0.65As

2DEGEFe

e

2DEG in QW

SPSL -doping

EF

SPSL -doping

1.0 1.5 2.0 2.5 3.0 3.5

10

15

20

25

30

35

40

45T = 0.36 Kin the dark

Single side doped DX

Elec

tron

Mob

ility

106 cm

2 /V·s

ec

Electron Density 1011 cm-2

Single side SPSL

Double side SPSL

~36x106cm2/V·s

RIBER MBE32 machine

13

Is Mobility a Relevant Parameter for FQHE ?

2.0 2.5 3.0

0.0

0.4

0.8

0.0

0.28/35/27/3

T~10 mK

n = 2.6·1011

cm-2 = 29·10

6cm

2/V·s

Filling factor

7/3 8/35/2

T~10 mK

Rxx (k

)

n = 2.75·1011

cm-2 = 32·10

6cm

2/V·s

Rxx (k

)

14

BG scattering vs RI scattering

0 2 4 6 8 10 12 14

0.6

0.7

0.8

0.9

1.0

1.1

10.5·106 cm2/V·s

13.2·106 cm2/V·s

14.4·106 cm2/V·s

T=0.36 K

Inve

rse

mob

ility

(10-7

V·s/c

m2 )

-doping areal denstity (1011 cm-2)

uniformdoping

SPSL -doping

2DEGEF

EF

EF

BG limited mobility ~ 16 ×106 cm2/V∙s

Spacer 80 nm

For spacer > 80 nm contribution of RI scattering < 13÷15 %

15

Mobility, Disorder & FQHE

In high mobility 2DEG the main scattering mechanism – BG

scattering

BG impurities ~1013 cm-3 in 30 nm QW→ average distance ~2 m

RI disorder potential characteristic length → spacer → ~80÷100

nm

RI Disorder

BG

BG

BG

16

How to control the RI disorder?

Introduce Spatial Correlations between Ionized Donors!!!

mind

d

N

N

Over-doping:

Freeze-out temperature:

de

TN RIeff 2

0

4~

)Efros A.L. 1988(

17

Over-doping & FQHE

Concern: Over-doping leads to “Parallel” conductance

Minimal Doping ~2×1011 cm-2

Average distance between donors ~200 Ǻ

Bohr Radius for X-electron 20÷30 Ǻ → over-doping of ~ 2÷5 times looks

feasible

Uniform Doping in Al0.35Ga0.65As

2DEGEFe

e

SPSL -doping

0.4 0.6 0.8 1.0 1.2

0.0

0.5

1.0

0.0

0.5

1.0

0.0

0.5

1.0

Rxx

(kO

hm)

180

215

402 mbe8-269Doping 100%=12e6 (300 mK)

Rxx

(kO

hm)

mbe8-273Doping 220%=18e6 (300 mK)

mbe8-270Doping 160%=14e6 (300 mK)

Rxx

(kO

hm)

18

Application for 5/2

mind

d

N

N

SPSL -doping

EF

2.0 2.5 3.0

0.0

0.2

0.4

0.6

0.8

1.0 1.5 2.0 2.5 3.0

0.0

0.1

0.2

T~10 mK

(over-doping factor)

Rxx

(k

) a

t 5

/2

0

10

20

30 q (p

sec)

5/2

Rxx

(k)

Filling factor,

19

Measurements of ¼ electrons charge

20

There’s no such thing as a free lunch

≈ 2 ≈ 2.3 ≈ 2.5

0 1 2 3 4 5 6 7

0.0

0.2

0.4

0.6

B (T)

0

4

8

12 T=10 mK

0 1 2 3 4 5 6 7

0.0

0.2

0.4

0.6

T=10 mK

B (T)

0

4

8

12

Double side doped 2DEG n~(3.0÷3.3)×1011 cm-2, ~(29÷33)×106 cm2/V∙s

0 1 2 3 4 5 6 7

0.0

0.2

0.4

0.6

Rxx

(k

)

B (T)

0

4

8

12 T=10 mK

Rxy (

k)

5/2

21

Phase transition in Donor layer (s)

0 1 2 3 4 5 6 70

4

8

12 T=10 mK

B (T)

Rxy (

k)

1 2 3 4 5 6 7 8 9 10 11 12 131

2

3

4

5

6

7

8

9

10

11

12

13

heB

ne

hexy

2

0 2 4 60

4

8

12 T=10 mK

B(T)

Rxy (

k)

1 2 3 4 5 6 7 8 9 10 11 12 131

2

3

4

5

6

7

8

9

10

11

12

130+2+10

~2.3

~1.1

B

≈ 2

≈ 2.3

22

Phase Transition in Disordered 2DES

QPC

23

Ideal 2D system for mesoscopic device

Ultra-high purity 2DEGSpatially correlated 2D electron

system

However, frozen at low T

24

Engineering of Disorder: Doping Schemes

Shallow donor

DX center

Using another AlAs-GaAs SPSL for doping

Using multiple doping layers in SPSL

Using “shallow” DX centers in AlGaAs

25

Conclusions

High mobility (low total scattering rate) is just a precondition

to obtain very low disordered 2D systems.

FQHE is governed by RI induced disorder

Spatial Correlations of Remote Ionized Donors are necessary

to obtain perfect 5/2 FQHE