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)
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,
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
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
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