Structure and energetics of Ga-rich GaAs(001) surfaces - Institut für ...

K. Seino et al. / Surface Science 507–510 (2002) 406–410 407
calculated in order to identify the most favourable
adsorption sites and to study the diffusion characteristics.
Based on these data possible configurations
for a (4 6) reconstructed GaAs surface
are probed.
2. Computational method
Fig. 1. Top and side view of the relaxed GaAs(0 0 1)fð4 2Þ
surface. Light (dark) balls represent Ga (As) atoms. The notation
of the atoms corresponds to Table 1.
GaAs(0 0 1)(4 2) surfaces [9,10] indicates that
either the surface has many defects or that structuralmodels
different from the f structure need to
be considered. Under certain preparation conditions
the STM images of the Ga-rich GaAs(4 2)
surface show additionalcorrugations [11–13]. Xue
and co-workers [1,11] interprete these corrugations
as clusters consisting of 6–8 Ga atoms. According
to their studies these Ga clusters are responsible
for the observation of the (4 6) surface reconstruction.
A more recent study by Kruse et al., on
the other hand, associates the corrugations seen in
similar STM images to surface excess charge localized
in Ga dangling bonds of the GaAs(4 2)
surface [12]. As or Ga adatoms could be another
explanation for STM observations: fourfold coordinated
Ga adatoms in the trenches of the
(4 2) surface are seemingly observed in X-ray
diffraction experiments [7].
We perform first-principles total-energy calculations
in order to contribute to a better understanding
of the Ga-rich GaAs(0 0 1) surface. The
potential-energy surface (PES) for Ga and As adsorbed
on the GaAs(0 0 1)fð4 2Þ geometry is
The calculations are based on a real-space
finite-difference implementation [14] of the densityfunctionaltheory
in local-density approximation
(DFT-LDA). Nonlocal norm-conserving pseudopotentials
[15] are used for the description of the
electron-ion interaction. Ga 3d electrons are partially
taken into account by means of a nonlinear
core correction to the exchange and correlation
energy. The spacing of the finest grid used to
represent the electronic wave functions and charge
density was determined through a series of bulk
calculations. We find that structural and electronic
properties are converged for a spacing corresponding
to 4% of the bulk lattice constant. The
calculations were performed using the theoretical
equilibrium lattice constants of 5.57 A for GaAs.
Integrations in the surface Brillouin zone are performed
over four special k points in its irreducible
part. We modelthe surfaces by using periodic supercells
containing material slabs which are about
12 A thick. They are separated by 12 A of vacuum.
The dangling bonds at the bottom layer are saturated
with fractionally charged pseudohydrogens.
The atoms in the lowest bilayer are kept frozen in
their idealbulk positions. In order to map the PES
the [0 0 1] coordinate of the respective adatom is
allowed to relax, while its lateral position is fixed.
3. Results and discussion
In Fig. 2 the calculated phase diagram for the
GaAs(0 0 1) surface is shown. Extreme and moderately
As-rich surfaces are characterized by cð4
4Þ and b2ð2 4Þ reconstructions, respectively [6].
For a very narrow range of surface preparation
conditions the a2ð2 4Þ surface [3] may be observed.
Under Ga-rich conditions the fð4 2Þ
structure due to Lee et al. [4] forms (cf. Fig. 1).