Size effects on optical properties of self-assembled quantum dots are analyzed based on the theories of linear elasticity and of strain-dependent k-p with the aid of finite element analysis. The quantum dot is made of InGaAs with truncated pyramidal shape on GaAs substrate. The three-dimensional steady-state effective-mass Schro¨dinger equation is adopted to find confined energy levels as well as wave functions both for electrons and holes of the quantum-dot nanostructures. Strain-induced as well as piezoelectric effects are taken into account in the carrier confinement potential of Schro¨dinger equation. The optical transition energies of quantum dots, computed from confined energy levels for electrons and holes, are significantly different for several quantum dots with distinct sizes. It is found that for QDs with the the larger the volume of QD is, the smaller the values of the optical transition energy. Piezoelectric effect, on the other hand, splits the p-like degeneracy for the electron first excited state about 1~7 meV, and leads to anisotropy on the wave function.

Volume Subject Area:
Materials
Keywords:
quantum dot, induced strain, piezoelectric effect, optical property, finite element method
Topics:
Gallium arsenide, Piezoelectricity, Quantum dots, Self-assembly
1.
Bimberg, D., Grundmann, M. and Ledentsov N.N.: Quantum Dot Heterostructures (John Wiley and Sons, West Sussex, 1999)
2.
Chakraborty, T.: Quantum Dots: a survey of the properties of artificial atoms (Elsevier, Amsterdam, 1999)
3.
Grundmann, M.: Nano-Optoelectronics: concepts, physics and devices (Springer, Berlin, 2002)
4.
Shchukin, V.A., Ledentsov, N.N. and Bimberg, D.: Epitaxy of Nanostructures (Springer, Berlin, 2004)
5.
Johnson
H. T.
,
Freund
L. B.
,
Akyu¨z
C. D.
and
Zaslavsky
A.
:
J. Appl. Phys.
84
(
1998
)
3714
3714
.
6.
Freund
L. B.
and
Johnson
H. T.
:
J. Mech. Phys. Solids
49
(
2001
)
1925
1925
.
7.
Lin
T. R.
,
Liao
B. T.
and
Kuo
M. K.
:
WSEAS Transactions on Electronics
1
(
2004
)
284
284
.
8.
Lin
T. R.
,
Kuo
M. K.
,
Liao
B. T.
and
Hong
K. B.
:
Bulletin College Engineering NTU
91
(
2004
)
3
3
.
9.
Kuo
M. K.
,
Lin
T. R.
,
Liao
B. T.
and
Yu
C. H.
:
Physica E
26
(
2005
)
199
199
.
10.
Muralidharan, G.: Jpn. J. Appl. Phys. 39 (2000) L 658.
11.
Liu
G. R.
and
Jerry
S. S. Q.
:
Semicond. Sci. Technol.
17
(
2002
)
630
630
.
12.
Grundmann
M.
,
Stier
O.
and
Bimberg
D.
:
Phys. Rev. B.
52
(
1995
)
11969
11969
.
13.
Davies
J. H.
:
J. Appl. Phys.
84
(
1998
)
1358
1358
.
14.
Stier
O.
,
Grundmann
M.
and
Bimberg
D.
:
Phys. Rev. B.
59
(
1999
)
5688
5688
.
15.
Migliorato
M. A.
,
Cullis
A. G.
,
Fearn
M.
and
Jefferson
J. H.
:
Physica E
13
(
2002
)
1147
1147
.
16.
Migliorato
M. A.
,
Powell
D.
,
Zibik
E. A.
,
Wilson
L. R.
,
Fearn
M.
,
Jefferson
J. H.
,
Steer
M. J.
,
Hopkinson
M.
and
Cullis
A. G.
:
Physica E
26
(
2005
)
436
436
.
17.
Bahder
T. B.
:
Phys. Rev. B.
41
(
1990
)
11992
11992
.
18.
Singh, J.: Physics of Semiconductors and Their Heterostructures (McGraw-Hill, New York, 1993)
19.
Chuang, S.L.: Physics of Optoelectronic Devices (Wiley, New York, 1995)
20.
Wang
L. W.
,
Kim
J.
and
Zunger
A.
:
Phys. Rev. B.
59
(
1999
)
5678
5678
.
21.
Lee
S.
,
Jonsson
L.
,
Wilkins
J. W.
,
Bryant
G. W.
and
Klimeck
G.
:
Phys. Rev. B.
63
(
2001
)
195318
195318
.
22.
Landin
L.
,
Miller
M. S.
,
Pistol
M. E.
,
Pryor
C. E.
, and
Samuelson
L.
,
Science
280
(
1998
)
262
262
.
23.
Sheng
W.
,
Cheng
S. J.
and
Hawrylak
P.
:
Phys. Rev. B.
71
(
2005
)
035316
035316
.
24.
Sheng
W.
, and
Leburton
J. P.
,
Appl. Phys. Lette.
80
(
2002
)
2755
2755
.
25.
Cady, W.G.: Piezoelectricity (McGraw-Hill, New York, 1946)
26.
Adachi, S.: Physical Properties of III-V Semiconductor Compounds (Wiley, New York, 1992)
27.
Saito
T.
,
Nakaoka
T.
,
Kakitsuka
T.
,
Yoshikuni
Y.
and
Arakawa
Y.
:
Physica E
26
(
2005
)
217
217
.
28.
Patane`
A.
,
Hill
R. J. A.
,
Eaves
L.
,
Main
P. C.
,
Henini
M.
,
Zambrano
M. L.
,
Levin
A.
,
Mori
N.
,
Hamaguchi
C.
,
Dubrovskii
Y. V.
,
Vdovin
E. E.
,
Austing
D. G.
,
Tarucha
S.
and
Hill
G.
:
Phys. Rev. B.
65
(
2002
)
165308
165308
.
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