We present a comprehensive approach to modeling the photoreflectance (PR) spectra of semiconductor quantum wells embedded in layered heterostructures. Near-gap PR spectra are obtained directly from the calculated variation of surface reflectance spectra induced by modulation of an internal electric field. The field-dependent reflectance spectra are themselves obtained from a transfer matrix model of a quantum well heterostructure (QWH) in which the quantum well layer is treated in detail using electric-field-dependent optical absorption calculations and all surrounding higher-gap layers are treated as lossless dielectric slabs. The model is described in detail and is applied to unstrained GaAs/AlGaAs and compressively strained InGaAs/GaAs single-well QWHs for which both experimental data and other calculations are available for comparison. This model can serve as a tool for interpretation of experimental PR spectra, and should be particularly useful for analysis of dense spectra with overlapping features that would be difficult to analyze using empirical fitting schemes. The approach can be used to model electroreflectance without modification.

1.
M.
Cardona
,
Modulation Spectroscopy, Solid State Physics, Advances in Research and Applications
(
Academic
,
New York
,
1969
), Vol.
11
, pp.
1
301
.
3.
D. E.
Aspnes
, “
Modulation Spectroscopy/Electric Field Effects on the Dielectric Function of Semiconductors
,” in
Handbook on Semiconductors
, edited by
T. S.
Moss
and
M.
Balkanski
(
North Holland
,
Amsterdam
,
1980
), Vol.
2
, pp.
109
154
.
4.
F. H.
Pollak
and
O. J.
Glembocki
,
Proc. SPIE
946
,
2
(
1988
).
5.
F. H.
Pollak
and
H.
Shen
,
J. Electron. Mater.
19
,
399
(
1990
).
6.
F. H.
Pollak
,
Mater. Sci. Eng., B
80
,
178
(
2001
).
7.
J.
Misiewicz
,
G.
Sek
,
R.
Kudrawiec
, and
P.
Sitarek
,
Thin Solid Films
450
,
14
(
2004
).
8.
Y. S.
Huang
and
F. H.
Pollak
,
Phys. Status Solidi A
202
,
1193
(
2005
)
9.
T. J.
Ochalski
,
B.
Gil
,
P.
Lefebvre
,
N.
Grandjean
,
J.
Massies
, and
M.
Leroux
,
Solid State Commun.
109
,
567
(
1999
).
10.
M. Y.
Ryu
,
P. W.
Yu
,
J. S.
Kim
,
J. I.
Lee
,
S. K.
Yu
,
E. S.
Yu
,
Y. J.
Park
,
H. S.
Park
, and
T. I.
Kim
,
J. Korean Phys. Soc.
37
,
300
(
2000
).
11.
J. B.
Héroux
,
X.
Yang
, and
W. I.
Wang
,
J. Appl. Phys.
92
,
4361
(
2002
).
12.
S.
Shirakata
,
M.
Kondow
, and
T.
Kitatani
,
J. Phys. Chem. Solids
64
,
1533
(
2003
).
13.
C.
Bru-Chevallier
,
S.
Fanget
,
G.
Guillot
,
S.
Ruffenach
, and
O.
Briot
,
Thin Solid Films
450
,
75
(
2004
).
14.
C.
Bru-Chevallier
,
S.
Fanget
, and
A.
Philippe
,
Phys. Status Solidi A
202
,
1292
(
2005
)
15.
T. J. C.
Hosea
,
Thin Solid Films
450
,
3
(
2004
).
16.
M. E.
Murtagh
,
V.
Guenebaut
,
S.
Ward
,
D.
Nee
,
P. V.
Kelly
,
B.
O’Looney
,
F.
Murphy
,
M.
Modreanu
,
S.
Westwater
,
R.
Blunt
, and
S. W.
Bland
,
Thin Solid Films
450
,
148
(
2004
).
17.
M. E.
Murtagh
,
S.
Ward
, and
P. V.
Kelly
,
Phys. Status Solidi A
202
,
516
(
2005
)
18.
P. J.
Klar
,
C.
Karcher
,
B.
Metzger
, and
T. J. C.
Hosea
,
Phys. Status Solidi A
202
,
1208
(
2005
)
19.
T. H.
Chen
,
Y. S.
Huang
,
T. S.
Shou
,
K. K.
Tiong
,
D. Y.
Lin
,
F. H.
Pollak
,
M. S.
Goorsky
, and
D. C.
Streit
,
Physica E
8
,
297
(
2000
).
20.
L. G.
Mourokh
,
L.
Malikova
,
F. H.
Pollak
,
B. Q.
Shi
, and
C.
Nguyen
,
J. Appl. Phys.
89
,
2500
(
2001
).
21.
D. Y.
Lee
,
J. Y.
Leem
,
S. K.
Kang
,
J. S.
Kim
,
J. S.
Son
, and
I. H.
Bae
,
Physica E
19
,
349
(
2003
).
22.
L.
Zamora-Peredo
,
M.
Lopez-Lopez
,
A.
Lastras-Martinez
, and
V. H.
Mendez-Garcia
,
J. Cryst. Growth
278
,
591
(
2005
).
23.
J.
Misiewicz
,
R.
Kudrawiec
,
M.
Syperek
,
R.
Paszkiewicz
,
B.
Paszkiewicz
, and
M.
Tlaczala
,
Microelectron. J.
36
,
442
(
2005
).
24.
T. J.
Ochalski
,
A.
Grzegorczyk
,
M.
Rudzinski
,
P. K.
Larsen
,
P. O.
Holtz
,
P.
Bergman
, and
P. P.
Paskov
,
Phys. Status Solidi A
202
,
1300
(
2005
).
25.
J.
Misiewicz
,
J. G.
Sek
,
R.
Kudrawiec
,
K.
Ryczko
,
D.
Gollub
,
J. P.
Reithmaier
, and
A.
Forchel
,
Microelectron. J.
34
,
351
(
2003
).
26.
J. S.
Hwang
,
M. F.
Chen
,
K. I.
Lin
,
C. N.
Tsai
,
W. C.
Hwang
,
W. Y.
Chou
,
H. H.
Lin
, and
M. C.
Chen
,
Jpn. J. Appl. Phys., Part 1
42
,
5876
(
2003
).
27.
G.
Rowland
and
T. J. C.
Hosea
,
J. Appl. Phys.
83
,
4909
(
1998
).
28.
E.
Hecht
and
A.
Zajac
,
Optics
(
Addison-Wesley
,
Reading, MA
,
1979
), pp.
71
80
.
29.
A.
Baliga
,
D.
Trivedi
, and
N. G.
Anderson
,
Phys. Rev. B
49
,
10402
(
1994
).
30.
Quantum Well Lasers
, edited by
P. S.
Zory
(
Academic
,
New York
, (
1993
), pp.
17
96
.
31.
C. Y. P.
Chao
and
S. L.
Chuang
,
Phys. Rev. B
48
,
8210
(
1993
).
32.
See, for example,
C. P.
Hilton
,
W. E.
Hagston
, and
J. E.
Nicholls
,
J. Phys. A
25
,
2395
(
1992
). We assume the form exp[δ(r2+(zezh)2)12] for the relative component R(|zezh|,r) of the exciton wave function, where δ is the variational parameter. In-plane effective hole masses, required for calculation of the in-plane reduced effective masses appearing in the Hamiltonians for light and heavy-hole excitons, are obtained as mlh*=m0(γ1+γ2) and mhh*=m0(γ1γ2), where γ1 and γ2 are Luttinger parameters. Values of the Luttinger parameters are obtained as in Ref. 29.
33.
P. C.
Klipstein
and
N.
Apsley
,
J. Phys. C
19
,
6461
(
1986
).
34.
W. M.
Theis
,
G. D.
Sanders
,
C. E.
Leak
,
K. K.
Bajaj
, and
H.
Morkoc
,
Phys. Rev. B
37
,
3042
(
1988
).
35.
D. C.
Bertolet
,
J. K.
Hsu
,
S. H.
Jones
, and
K. M.
Lau
,
Appl. Phys. Lett.
52
,
293
(
1988
).
36.
Calculated oscillator strengths for the 22H and 32H transitions, normalized to the oscillator strength of the 11H transition, are 0.34 and 0, respectively, at zero electric field. These oscillator strengths exhibit a weak field dependence up to a field of 5kVcm, above which the dependence is strong. At a field of 10.5 kV/cm, the normalized oscillator strengths for the 22H and 32H transitions are 0.03 and 0.29, respectively. The calculated oscillator strength for the 11H transition, by contrast, decreases by less than ten percent over the entire field range 0–10.5 kV/cm.
37.
A.
Ksendzov
,
H.
Shen
,
F. H.
Pollak
, and
D. P.
Bour
,
Surf. Sci.
228
,
326
(
1990
).
38.
A. N.
Pikhtin
,
O. S.
Komkov
, and
F.
Bugge
,
Phys. Status Solidi A
202
,
1270
(
2005
).
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