The band gaps, band structure, and excited‐state (exciton) energies of CdS, GaAs, and GaP semiconductor clusters are calculated using pseudopotentials. In addition, the sensitivity of the exciton energies to the size, shape, crystal structure, and lattice constant of the unit cell are investigated. The calculated exciton energies of CdS clusters are in excellent agreement with experiment over a wide range of cluster sizes. Also, the exciton states of small CdS clusters are sensitive to whether their crystal structure is zinc blende or hexagonal. Such a sensitivity is absent in large CdS clusters. Furthermore, small GaAs clusters are shown to exhibit anomalous redshift of their absorption spectra, in sharp contrast to CdS and large GaAs clusters whose spectra always shift to blue with decreasing cluster size. Finally, the lowest‐energy non‐Franck–Condon transition in GaP clusters always shifts to blue with decreasing cluster size, whereas the higher‐energy Franck–Condon transition in small clusters exhibits the anomalous redshift. These novel findings reveal that (1) the optical spectroscopy of semiconductor clusters is strongly material and crystal structure dependent; (2) the spectroscopy of small clusters is dramatically different from those of large clusters and bulk; and (3) these effects cannot be explained, even qualitatively, using the effective‐mass approximation.

1.
E.
Corcoran
, Diminishing Dimensions,
Sci. Am.
263
(November),
122
(
1990
).
2.
W. D.
Knight
,
K.
Clemenger
,
W. A.
de Heer
,
W. A.
Saunders
,
M. Y.
Chou
, and
M. L.
Cohen
,
Phys. Rev. Lett.
52
,
2141
(
1984
);
H.
Göhlich
,
T.
Lange
,
T.
Bergmann
, and
T. P.
Martin
,
Phys. Rev. Lett.
65
,
748
(
1990
); ,
Phys. Rev. Lett.
S.
Bjorn-holm
,
J.
Borggreen
,
O.
Echt
,
K.
Hansen
,
J.
Pedersen
, and
H. D.
Rasmussen
,
Phys. Rev. Lett.
65
,
1627
(
1990
).,
Phys. Rev. Lett.
3.
M. V.
Rama Krishna
and
K. B.
Whaley
,
Phys. Rev. Lett.
64
,
1126
(
1990
);
M. V.
Rama Krishna
and
K. B.
Whaley
,
J. Chem. Phys.
93
,
746
(
1990
);
M. V.
Rama Krishna
and
K. B.
Whaley
,
93
,
6738
(
1990
); ,
J. Chem. Phys.
M. V.
Rama Krishna
and
K. B.
Whaley
,
Mod. Phys. Lett. B
4
,
895
(
1990
);
M. V.
Rama Krishna
and
K. B.
Whaley
,
Z. Phys. D
20
,
223
(
1991
);
M. V.
Rama Krishna
and
K. B.
Whaley
,
Phys. Rev. B
38
,
11
839
(
1988
).
4.
S.
Bjornholm
,
Contemp. Phys.
31
,
309
(
1990
).
5.
D.
Snoke
,
J. P.
Wolfe
, and
A.
Mysyrowicz
,
Phys. Rev. Lett.
59
,
827
(
1987
);
Y. Z.
Hu
,
S. W.
Koch
,
M.
Lindberg
,
N.
Peyghambarian
,
E. L.
Pollock
, and
F. F.
Abraham
,
Phys. Rev. Lett.
64
,
1805
(
1990
); ,
Phys. Rev. Lett.
Y. Z.
Hu
,
S. W.
Koch
, and
D. B. T.
Thoai
,
Mod. Phys. Lett. B
4
,
1009
(
1990
);
L.
Wang
,
L. P. F.
Chibante
,
F. K.
Tittel
,
R. F.
Curl
, and
R. E.
Smalley
,
Chem. Phys. Lett.
172
,
335
(
1990
).
6.
A. I.
Ekimov
and
A. A.
Onushchenko
,
Pis’ma Zh. Eksp. Teor. Fiz.
34
,
363
(
1981
)
[
A. I.
Ekimov
and
A. A.
Onushchenko
,
JETP Lett.
34
,
345
(
1981
)];
A. I.
Ekimov
and
A. A.
Onushchenko
,
Fiz. Tekh. Poluprovodn.
16
,
1215
(
1982
)
[
A. I.
Ekimov
and
A. A.
Onushchenko
,
Sov. Phys. Semicond.
16
,
775
(
1982
)].
7.
AI. L.
Éfros
and
A. L.
Éfros
,
Fiz. Tekh. Poluprovodn.
16
,
1209
(
1982
)
[
AI. L.
Éfros
and
A. L.
Éfros
,
Sov. Phys. Semicond.
16
,
772
(
1982
)].
8.
R.
Rosetti
and
L. E.
Brus
,
J. Phys. Chem.
86
,
4470
(
1982
).
9.
L. E.
Brus
,
J. Phys. Chem.
90
,
2555
(
1986
);
M. L.
Steigerwald
and
L. E.
Brus
,
Acc. Chem. Res.
23
,
183
(
1990
);
M. G.
Bawendi
,
M. L.
Steigerwald
, and
L. E.
Brus
,
Annu. Rev. Phys. Chem.
41
,
477
(
1990
).
10.
R.
Rosetti
,
S.
Nakahara
, and
L. E.
Brus
,
J. Chem. Phys.
79
,
1086
(
1983
).
11.
L. E.
Brus
,
J. Chem. Phys.
79
,
5566
(
1983
);
L. E.
Brus
,
80
,
4403
(
1984
).,
J. Chem. Phys.
12.
M. G.
Bawendi
,
A. R.
Kortan
,
M. L.
Steigerwald
, and
L. E.
Brus
,
J. Chem. Phys.
91
,
7282
(
1989
);
M. G.
Bawendi
,
W. L.
Wilson
,
L.
Rothberg
,
P. J.
Carroll
,
T. M.
Jedju
,
M. L.
Steigerwald
, and
L. E.
Brus
,
Phys. Rev. Lett.
65
,
1623
(
1990
);
J. J.
Shiahg
,
A. N.
Goldstein
, and
A. P.
Alivisatos
,
J. Chem. Phys.
92
,
3232
(
1990
);
V. L.
Colvin
,
A. P.
Alivisatos
, and
J. G.
Tobin
,
Phys. Rev. Lett.
66
,
2786
(
1991
).
13.
M. A.
Olshavsky
,
A. N.
Goldstein
, and
A. P.
Alivisatos
,
J. Am. Chem. Soc.
112
,
9438
(
1990
).
14.
Y.
Wang
,
A.
Suna
,
W.
Mahler
, and
R.
Kasowsky
,
J. Chem. Phys.
87
,
7315
(
1987
);
Y.
Wang
,
J. Phys. Chem.
95
,
1119
(
1991
).
15.
Y.
Wang
and
N.
Herron
,
Phys. Rev. B
42
,
7253
(
1990
).
16.
Y.
Kayanuma
,
Solid State Commun.
59
,
405
(
1986
).
17.
Y.
Kayanuma
,
Phys. Rev. B
38
,
9797
(
1988
).
18.
H.
Weller
,
H. M.
Schmidt
,
U.
Koch
,
A.
Fojtik
,
S.
Baral
,
A.
Henglein
,
W.
Kunath
,
K.
Weiss
, and
E.
Dieman
,
Chem. Phys. Lett.
124
,
557
(
1986
).
19.
P. V.
Kamat
,
K. R.
Gopidas
, and
D.
Weir
,
Chem. Phys. Lett.
149
,
491
(
1988
);
K. R.
Gopidas
and
P. V.
Kamat
,
J. Phys. Chem.
93
,
6428
(
1989
);
K. R.
Gopidas
and
P. V.
Kamat
,
Langmuir
5
,
22
(
1989
);
K. R.
Gopidas
and
P. V.
Kamat
,
Mater. Lett.
9
,
372
(
1990
);
K. R.
Gopidas
,
M.
Boborquez
, and
P. V.
Kamat
,
J. Phys. Chem.
94
,
6435
(
1990
);
P. V.
Kamat
and
K. R.
Gopidas
,
SPIE Proc.
1209
,
115
(
1990
);
H. M.
Schmidt
and
H.
Weller
,
Chem. Phys. Lett.
129
,
615
(
1986
);
S. V.
Nair
,
S.
Sinha
, and
K. C.
Rustagi
,
Phys. Rev. B
35
,
4098
(
1987
).
20.
T.
Takagahara
,
Phys. Rev. B
36
,
9293
(
1987
);
T.
Takagahara
,
39
,
10
206
(
1989
).,
Phys. Rev. B
21.
E.
Hanamura
,
Phys. Rev. B
37
,
1273
(
1988
).
22.
P. E.
Lippens
and
M.
Lannoo
,
Phys. Rev. B
39
,
10
935
(
1989
).
23.
H. Haken, Quantum Field Theory of Solids (North-Holland, Amsterdam, 1976), Chap. 4.
24.
D.
Brust
,
J. C.
Phillips
, and
F.
Bassani
,
Phys. Rev. Lett.
9
,
94
(
1962
);
D. Brust, in Methods in Computational Physics, edited by B. J. Alder, S. Fernbach, and M. Rotenberg (Academic, New York, 1968), Vol. 8.
25.
T. K.
Bergstresser
and
M. L.
Cohen
,
Phys. Rev.
164
,
1069
(
1967
);
M. L. Cohen and J. R. Chelikowsky, Electronic Structure and Optical Properties of Semiconductors (Springer, Berlin, 1989).
26.
H. J. Emeléus and A. G. Sharpe, Modern Aspects of Inorganic Chemistry, 4th ed. (Routledge and Kagan Paul, London, 1973), p. 53.
27.
R. W. G. Wyckoff, Crystal Structures (Interscience, New York, 1963), pp. 108 and 111.
28.
S. Flügge, Practical Quantum Mechanics (Springer, Berlin, 1971).
29.
K. J.
Chang
,
S.
Froyen
, and
M. L.
Cohen
,
Phys. Rev. B
28
,
4736
(
1983
).
30.
C. S.
Wang
and
B. M.
Klein
,
Phys. Rev. B
24
,
3393
(
1981
).
31.
C. Kittel, Introduction to Solid State Physics, 6th ed. (Wiley, New York, 1986).
32.
Y. Wang (private communication).
33.
Y.
Wang
and
N.
Herron
,
J. Phys. Chem.
95
,
525
(
1991
), Fig. 3.
34.
A.
Kobayashi
,
O. F.
Sankey
,
S. M.
Volz
, and
J. D.
Dow
,
Phys. Rev. B
28
,
935
(
1983
).
35.
We used Vs(8/3) = −0.145,VS(3) = −0.10, and Vs(17/3) = −0.012 a.u. instead of −0.13,−0.12, and −0.015 a.u., respectively, given in Ref. 25. All other form factors are identical to those in Ref. 25. The cluster calculations were carried out without any additional changes.
36.
V.
Mohan
and
J. B.
Anderson
,
Chem. Phys. Lett.
156
,
520
(
1989
).
37.
M. V.
Rama Krishna
and
R. A.
Friesner
,
Phys. Rev. Lett.
67
,
629
(
1991
);
M. V.
Rama Krishna
and
R. A.
Friesner
,
SPIE Proc.
1599
(
1991
).
38.
C. V.
de Alvarez
,
J. P.
Walter
,
M. L.
Cohen
,
J.
Stokes
, and
Y. R.
Shen
,
Phys. Rev. B
6
,
1412
(
1972
).
39.
J. P.
Walter
and
M. L.
Cohen
,
Phys. Rev.
183
,
763
(
1969
).
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