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

Surface Science 507–510 (2002) 406–410
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Structure and energetics of Ga-rich GaAs(001) surfaces
K. Seino a, *
, W.G. Schmidt a , F. Bechstedt a , J. Bernholc b
a Institut f€ur Festk€orpertheorie und Theoretische Optik, Friedrich-Schiller-Universit€at, Max-Wien-Platz 1, 07743 Jena, Germany
b Department of Physics, North Carolina State University, Raleigh, NC 27695-8202, USA
Abstract
The atomic structures and energies of Ga-rich GaAs(0 0 1) surface reconstructions are examined by means of firstprinciples
total-energy calculations based on a real-space multigrid method. Our calculations confirm the existence of
the novel f(4 2) structure suggested by Lee et al. [Phys. Rev. Lett. 85 (2000) 3890]. (4 6) surface reconstructions
suggested to explain STM experiments are found to be unstable. The calculations indicate that the adsorption of Ga
adatoms in the trenches of the f(4 2) surface could possibly explain the observed structures. The diffusion of Ga/As
adatoms on the Ga-rich GaAs surface is predicted to be anisotropic and should preferably take place parallel to the
[1 1 0]/[1 1 0] direction, respectively. Ó 2002 Elsevier Science B.V. All rights reserved.
Keywords: Gallium arsenide; Single crystal surfaces; Density functional calculations; Surface diffusion
1. Introduction
The GaAs(0 0 1) surface belongs to the most
intensively investigated compound semiconductor
surfaces. Its stoichiometry-dependent geometries
seemed to be well established from both experiment
and theory [1]. These geometries were used as
starting points for further calculations such as kinetic
Monte Carlo studies on the GaAs surface
growth (see, e.g., Ref. [2]). Recent computational
studies [3,4], however, provided new insight into
the microscopic structure of the stoichiometric
(2 4) and the Ga-rich ð4 2Þ=cð8 2Þ surface. A
more uniform arrangement of the surface As dimers
in case of the a2ð2 4Þ surface as compared
to the previously accepted að2 4Þ structure lowers
the electrostatic energy of the surface and leads
* Corresponding author.
E-mail address: seino@ifto.physik.uni-jena.de (K. Seino).
to an overall lower surface energy [3]. STM images
of the GaAs(0 0 1)(2 4) surface (see, e.g., Ref. [5])
seem to confirm the existence of the a2ð2 4Þ
geometry. Similarly, in case of the Ga-rich ð4
2Þ=cð8 2Þ surface a theoreticalstudy [4] has
shown that a re-arrangement of the Ga dimers
lowers the electrostatic as well as the total energy
compared to the previously postulated b2ð4 2Þ
structure [6]. The fð4 2Þ geometry predicted instead
(cf. Fig. 1) is characterized by surface and
subsurface Ga dimers as well as threefold coordinated
Ga and As surface atoms in the uppermost
layer. Given the complexity of this structure,
however, the existence of further atomic models
with low surface energies seems likely. Thus the
comparison with experimentaldata becomes particularly
important. The fð4 2Þ structure explains
well LEED [4] and X-ray diffraction data
[7,8]. There remain open questions, however. The
relatively bad agreement between surface optical
spectra calculated and measured for Ga-rich
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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).

408 K. Seino et al. / Surface Science 507–510 (2002) 406–410
Table 1
Calculated atomic coordinates (in A, normalized to the experimentallattice
constant) of the GaAs(0 0 1)fð4 2Þ surface
x y z
First
layer
Ga(1) 7.943 2.770 2.882
As(2) 5.745 2.054 3.797
Ga(3) 4.423 0.002 3.375
Ga(4) 4.335 3.991 3.276
As(5) 1.982 3.996 3.043
As(6) 2.049 0.006 3.072
Second
layer
Ga(7) 2.013 1.990 1.603
Ga(8) 5.829 1.270 1.288
Fig. 2. Relative formation energy per (1 1) unit cell for GaAs
surface reconstructions vs. the Ga chemicalpotential. Dashed
lines mark the approximate anion- and cation-rich limits of the
thermodynamically allowed range of Dl(Ga).
Structural details of the calculated f modelare
given in Table 1. They are in excellent agreement
with the X-ray diffraction data by Paget and coworkers
[7]. Another X-ray diffraction study [8]
suggests a slightly modified f structure, with additionalGa
adatoms.
The most favourable sites for the adsorption of
single Ga or As atoms are given by the global
minima of the respective PES. The calculated PES
for Ga and As adsorption on top of the (4 2)
reconstructed GaAs(0 0 1) surface is shown in Fig.
3. We find the adsorption behaviour for ad-cations
to be very different from that of adsorbed anions.
The preferred bonding position for single Ga adatoms
(AC in Fig. 3) is located in the trenches,
Third
layer
As(9) 3.904 2.000 0.012
As(10) 7.982 1.977 0.198
As(11) 0.022 1.974 0.198
The notation of the atoms corresponds to Fig. 1.
fourfold coordinated between the doubly occupied
dangling bonds of the first layer As atoms (see Ref.
[9] for a discussion of the surface electronic properties
of GaAs(0 0 1)fð4 2Þ). That position seems
to agree with a recent X-ray analysis [7], which was
interpreted to indicate that about 19% of the AC
positions are occupied by Ga adatoms. However,
even at extreme Ga-rich surface preparation conditions
we find the adsorption of additionalGa
atoms in AC position to increase the surface
energy per (1 1) surface unit cell by 0.1 eV. It
does therefore not constitute an equilibrium surface
structure.
Fig. 3 shows also the PES as experienced by As
adatoms on top of the GaAs(0 0 1)fð4 2Þ surface.
In this case the most favourable adsorption position
(denoted AA) allows a threefold coordination
of the As adatom with three empty Ga dangling
bonds. However, occupation of the AA site
Fig. 3. Potential-energy surface for the adsorption of As (left panel) and Ga (right panel) on the Ga-rich GaAs(0 0 1)fð4 2Þ surface.
The contour spacing is 0.15 eV. Light regions indicate low-energy adsorption positions.

K. Seino et al. / Surface Science 507–510 (2002) 406–410 409
increases the surface energy by 0.3 eV at Ga-rich
preparation conditions. The large energy difference
indicates that this ad-structure is only a transient
state.
The PES allows furthermore to predict the diffusion
characteristics of adatoms. We find the
diffusion for Ga and As atoms to be rather different.
Ga atoms will preferably migrate in the
trenches along the [1 1 0] direction, where energy
barriers of only 0.2 eV need to be overcome. The
minimum energy barrier for diffusion along the
[1 1 0] direction is 0.6 eV. The motion of As adatoms
will be somewhat less anisotropically. It will
preferably occur along the [1 1 0] direction. The
minimum energy barrier along [1 1 0] is 0.5 eV
compared to about 0.7 eV in [1 1 0] direction. We
mention that the diffusion behaviour predicted
here for As and Ga adatoms is very different from
earlier findings [16], where the formerly accepted
b2ð4 2Þ structure has been used as starting point
for the calculation.
The calculated phase diagram in Fig. 2 predicts
the formation of a (2 4) mixed-dimer structure
for surfaces which are even more cation-rich than
the fð4 2Þ structure. While such mixed-dimer
structures occur for cation-rich InP and GaP surfaces
[17], they are not observed for GaAs. Rather
the formation of (4 6) symmetries is reported
for extreme Ga-rich GaAs surfaces [1]. Xue et al.
discriminate between a genuine (4 6) reconstruction
which is more Ga-rich than the Ga-rich
(4 2) reconstruction, and a pseudo (4 6) phase,
which actually consists of a mixture of the (2 6),
the (4 2), and the genuine (4 6) phase. More
recent STM works indicate, however, that also the
genuine (4 6) symmetries occur only locally and
have no long-range order [12,13].
The PES for Ga adatoms may be used as a
starting point to explore possible surface structures
explaining the locally occurring GaAs-(0 0 1)
(4 6) surface symmetries. We start from the AC
Fig. 4. Top view of the investigated GaAs(0 0 1)(4 6) surface
structures described in the text.
adsorption site, but consider now the (4 6) surface
unit cell shown in Fig. 4. The resulting C1
adsorption geometry is lower in energy than the
AC position (cf. Table 2). From that we can conclude
on a repulsive interaction between the Ga
adatoms. However, the C1 geometry is still higher
in energy than the clean GaAs-(0 0 1)fð4 2Þ surface.
In order to find favourable surface structures
we therefore investigated further models. These
include the formation of Ga dimers (C2), Ga
clusters of various shapes ranging in size from
four to eight atoms (C4 ...C8) as well as exchange
geometries, where one (S1) or four (S4) of the
surface anions marked gray in Fig. 4 are replaced
by Ga. The energies for the most favourable configuration
of each structure class are compiled in
Table 2. None of the structures investigated is
stable. It has been suggested that Ga clusters on
GaAs may be particularly stable, if they contain a
‘‘magic’’ number of electrons [18]. The trend of
the energies given in Table 2 does not support
this hypothesis. Instead, we find that the surface
energy increases nearly linearly with the cluster
size.
Given the fact that single Ga adatoms lead still
to the smallest increase in energy, they may be the
Table 2
Relative surface energies for the (4 6) and (4 2) surface structures described in the text
Structure C1 C2 C4 C5 C6 C8 S1 S4 AC AA
DE (meV) 28 48 119 161 153 225 29 121 104 295
The energies refer to a (1 1) surface unit cell and are given with respect the Ga-rich GaAs(0 0 1)fð4 2Þ surface under extreme
Ga-rich conditions (l(Ga)¼ l(Ga) bulk ).

410 K. Seino et al. / Surface Science 507–510 (2002) 406–410
most likely candidates for surface defects. Their
occurrence seems to be confirmed by X-ray diffraction
[7] and their repulsive interaction would
explain the local ordering observed by STM [11–
13]. Also the anisotropic motion of the defects in
the trenches along the [1 1 0] direction [13] is in
agreement with the PES calculated for Ga adatoms.
We have to mention, however, that the
occurrence of Ga adatoms can hardly explain the
outcome of the chemicaltitration experiment by
Kruse et al. [12]. They observed the disappearance
of the ‘‘surface defects’’ upon adsorption of just
7:5 10 4 ML of molecular oxygen. Their interpretation
of the ‘‘surface defects’’ as surface excess
charge localized in Ga-dangling bonds is not
plausible, however, since the defect positions do
not coincide with surface Ga atoms.
4. Conclusion
We presented first-principles total-energy calculations
on Ga-rich GaAs(0 0 1) surfaces. Our
results confirm the occurrence of the (4 2) reconstructed
f surface under Ga-rich conditions.
This structure was used to calculate the PES for
single As and Ga adatoms on top of the Ga-rich
GaAs surface. We find marked differences between
the adsorption of cation and anions both with
respect to their favourite adsorption sites as well
as with respect to their diffusivities. The existence
of repulsive forces between single Ga adatoms may
be considered as one reason for the local (4 6)
ordering on extreme Ga-rich GaAs(0 0 1) surfaces.
Acknowledgements
Grants of computer time from the H€ochstleistungsrechenzentrum
Stuttgart, the Leibniz Rechenzentrum
M€unchen, the John von Neumann-
Institut J€ulich, and the DoD Challenge Program
are gratefully acknowledged.
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