Local-field and excitonic effects in the calculated optical properties of semiconductors
from first-principles
B. Arnaud and M. Alouani
Institut de Physique et Chimie des Mate ´riaux (IPCMS), UMR 7504 du CNRS, Universite ´ Louis Pasteur, 23 rue du Loess,
67037 Strasbourg, Cedex, France
Received 11 September 2000; published 7 February 2001
The recently developed GW approximation GWA based on the all-electron full-potential projector aug-
mented wave method is used to study the local-field LF and electron-hole excitation effects in the optical
properties of small-, medium-, and large-band-gap semiconductors: Si, InP, AlAs, GaAs, and diamond. It is
found that while the use of the GWA energies instead of local-density approximation LDA eigenvalues has
a tendency to align the calculated structures in the optical spectra with their experimental counterparts, the LF
effects do not change these peak positions but systematically reduce the intensities of the so-called E
1
and E
2
structures in all the optical spectra. Taking into account the electron-hole interaction, shifts the theoretical
oscillator strength towards lower photon energies and thereby improves considerably the comparison with
experiment. It is also shown that the LDA static dielectric constant, a ground-state property, is considerably
improved when the LF effects are included. On the other hand, as expected, the static dielectric function
obtained using the GW quasiparticle energies, and including the LF effects, is underestimated for all the
semiconductors. Including the excitonic effects in the theory is expected to correct this discrepancy with
experiment.
DOI: 10.1103/PhysRevB.63.085208 PACS numbers: 71.10.-w, 71.15.Mb, 71.20.Nr
I. INTRODUCTION
The electronic structures of semiconductors and insulators
are now well described by means of ab initio methods based
on the density-functional theory within the local-density
approximation
1
in conjunction with the so-called GW ap-
proximation of Hedin.
2
In this approximation the self-energy
operator is given as a product of the Green’s function G
times the screened Coulmb interaction W. The excited states
obtained with this approach are in good agreement with
angle-resolved photoemission experiments.
3–5
However, the
one-electron description of the optical properties of materials
based on the knowledge of the GW electronic structure is not
satisfactory. In particular, 1 when the GW energies are
used the peak positions are much higher in energy than the
experimental ones, 2 the relative intensity of the so-called
E
1
and E
2
peaks is not reproduced with the one-electron
theory, i.e., the E
1
peak is underestimated by as much as
50% of the observed value and the E
2
peak is somewhat
larger, and 3 calculations ignoring excitonic effects, but
including local-field LF effects, reduce the intensities of
both E
1
and E
2
peaks.
6
On the other hand, the local-density approximation LDA
description of the optical spectra is not satisfactory either,
since 1 the peak positions are much lower in energy than
the experimental ones due to the underestimation of the en-
ergy band gap and 2 the static dielectric constant, which
can be obtained from a functional derivative of the electron
density with respect to the total Kohn-Sham potential evalu-
ated at the ground state, hence a ground-state property, is
overestimated by the LDA calculation.
7–13
However, some
of this overestimation is primarily due to the neglect of the
local-field effects, and as it can be seen in this paper, the
inclusion of the LF effects improves somewhat the agree-
ment with experiment.
It was always assumed that the inclusion of the electron-
hole excitations in the interaction of light and matter is the
missing ingredient for an adequate comparison of the theo-
retical and experimental optical spectra. Model calculations
have somehow qualitatively confirmed this assumption.
14,15
However, it is only recently that ab initio pseudopotential
PP calculations,
16–18
incorporating the electron-hole inter-
action into the dielectric function, have been able to deter-
mine the importance of this interaction and make a realistic
comparison with experiment. To achieve this goal, the so-
called Bethe-Salpeter equation has been solved for a range of
semiconductors and insulators using the same approach as
for the model calculations.
14
The outcome of this hard work
was quite an achievement, and led to a good agreement of
the optical spectra of Si, Ge, GaAs, diamond, and LiF with
experiment.
16–18
Those calculations clearly show that the in-
clusion of the two-particle effects in the dielectric function,
i.e., the interaction of the electron, promoted from a valence
band to a conduction band, with the hole left behind, is in-
deed an important ingredient for the description of the opti-
cal spectra.
In this paper, we are also motivated by the same old prob-
lem, i.e., computing correctly the optical spectra without any
adjustable parameter. But, instead of using the most popular
ab initio pseudopotential method, we use an all-electron
method. The calculation becomes, of course, much more
complicated due to the complexity of the basis set; neverthe-
less, the advantages are well worth the effort. We do not
have to pseudoize the valence electron in the atomic region.
This is a plus over the PP method, since for localized d
electrons the optical matrix elements can be computed with-
out any approximation. Even, for semiconductors, it is not
clear whether the matrix elements calculated using a PP ap-
proach are not necessarily as accurate as those obtained us-
ing an all-electron theory. As it can be seen later, the dielec-
tric functions of Si and GaAs are reproduced by two different
PHYSICAL REVIEW B, VOLUME 63, 085208
0163-1829/2001/638/08520814/$15.00 ©2001 The American Physical Society 63 085208-1