Full text of DOI:10.1051/epjap:2001131

Eur. Phys. J. AP 13, 171–176 (2001)
THE EUROPEAN
PHYSICAL JOURNAL
APPLIED PHYSICS
c
ꢀ EDP Sciences 2001
Simulation of surface morphology and defects in heteroepitaxied
thin films
M. Sahlaoui1,2,a, A. Ayadi1, N. Fazouan3, M. Addou3, M. Djafari Rouhani4,5, and D. Est`eve5
1
LPMC, D´epartement de Physique, Facult´e des Sciences, Universit´e Choua¨ıb Doukkali, BP 20, El jadida, Morocco
LPC, D´epartement de Physique, Facult´e des Sciences et Techniques, BP 523, B´eni Mellal, Morocco
D´epartement de Physique, Facult´e des Sciences, Universit´e ibn Tofl, K´enitra, Morocco
Laboratoire de Physique des Solides, Universit´e Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France
LAAS, CNRS, 7 avenue Colonel Roche, 31077 Toulouse Cedex, France
2
3
4
5
Received: 7 February 2000 / Revised and Accepted: 17 November 2000
Abstract. We have performed atomic scale simulations of heteroepitaxial growth of thin films using the
valence force field approximation and Monte Carlo techniques. The case of CdTe/(001)GaAs is considered.
Our simulations indicate valley formation presenting (111) facets with unstable bottoms in the early stages
of the growth. This roughening is a source of dislocation, as it appears to relax the elastic energy of the
deposited layers by formation of V-grooves. We have used a calculated RHEED as an in situ control
of deposited layers. Finally, we present the influence of an imperfect surface in the morphology of the
deposited films.
PACS. 68.35.Ct Interface structure and roughness – 68.35.Fx Diffusion, interface formation – 61.72.Bb
Theories and models of crystal defects
1 Introduction
subject. Molecular dynamics simulation is used within a
potential energy [6]. Nevertheless, this approach suffers
some restriction, because of the computational limitations,
and calculations are generally made in a two-dimensional
lattice.
Heteroepitaxial growth of semiconductors has increas-
ingly been studied for many years. The main reason
being the technological importance of these structures
in the optoelectronics field. An interesting example is
CdTe/(001)GaAs. This system with a large mismatch
(14.6%) is characterized by dislocation formation at the
interface [1]. These defects can be detrimental to the elec-
trical properties of devices by acting as electron-hole re-
combination centers or causing problems in subsequent
processing steps such as lithography [2].
Atomic scale simulation has proved useful in the un-
derstanding of strain and stress effects during growth and
the description of defect nucleation mechanisms. Two ap-
proaches have been employed during last years for large
systems. The static approach is the first one. The geom-
etry of defect is defined first, then strain and stress field
are calculated using theory of elasticity combined to fi-
nite element method [3,4]. Another method is to use an
atomic approach with an appropriate physical model like
the valence force field, or ab-inition calculations [5]. The
main problems of these calculations still remain a detailed
description of the elementary mechanism involved in the
creation of heterostructures or defects during the epitaxial
growth.
A completely different and useful method for the study
of atomic details in epitaxial growth is the kinetic Monte
Carlo (KMC) method. The idea of this method is to find
a significant set of events in order to describe correctly
the general behavior of the layer growth, and to define a
realistic activation energy for each of the possible events
on the surface. Using a sophisticated model, strain and
stress are introduced in the activation barriers [7–9]. As a
consequence, relaxation of crystal becomes necessary at
each step needed to perform the growth. This type of
method carry out an important computational time lead-
ing to simplify the energetic model and/or to work in a
two-dimensional [7] or quasi-two-dimensional space [10].
In all above models, the point and extended defects
are inherently absent. This is due to the basic principle of
the solid on solid (SOS) method which excludes vacancies
from the beginning. Our model goes beyond this approx-
imation.
Our simulation procedure allows for the defect obser-
vation by taking the local strain and stress into account,
using an atomic approach with a semi-empirical potential
energy term. Our choice is the valence force field (VFF)
which is governed by its simplicity and ability to describe
semiconductor properties [11].
The dynamical study of elementary atomic process in-
voked during growth is the second way to investigate the
a
e-mail: sahlaoui@fstbm.ac.ma

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The European Physical Journal Applied Physics
The purpose of this paper is to show by Monte Carlo
simulation and Valence Force Field (VFF) approximation
of strain energy that grooves with (111) facets are formed
as a result of the stress in the deposited layer associated
with the lattice mismatch. The filling of these grooves is ef-
fected by deposition of atoms on (111) facets. The growth
on an imperfect substrate is investigated. In Section 2 we
describe the model and the simulation procedure. Results
of the simulation are presented in Section 3.
2 Model description
The general simulation based on SOS model has previ-
ously been described in detail [12]. Our new description
of the model goes beyond the SOS approximation.
A Monte Carlo (MC) process is combined with a va-
lence force field (VFF) energetic model, in order to de-
scribe strain effects, due to different nature of material
deposited on the substrate. The KMC method is based on
a set of elementary atomic mechanisms. Their determina-
tion is certainly one of the key points of KMC simulation,
as a significant set of events is necessary to describe the
correct behavior of film growth. When an event is real-
ized, local strain and stress fields are modified, so that
the surface structure is relaxed by minimizing its strain
energy, which is expressed by the VFF potential. Acti-
vation energy and a hopping rate are then calculated for
each possible event on the surface. As a result, the more
strained regions correspond to the lower activation ener-
gies for events. A MC time can be determined including
a random part, and the event associated with the lowest
time is executed. A new cycle can then begin.
Fig. 1. Schematic representation of an interlayer migration,
(1) is the initial position, (2) is a perfect crystal site where an
atom cannot be fixed as the site labeled (V) is vacant, (3) is an
intermediate interstitial position and (4) is the final position
two layers below (1).
step edge. From site (1) the atom makes a classical migra-
tion to position (2) where it can not be fixed as the site
labeled (V) is a vacant site. Consequently, the position (3)
is reached as interstitial unstable position because of its
bending VFF term becoming large, and thus a rapid mi-
gration leading to position (4) is executed. These motions
are, of course, completely reversible. This event could be
considered as a single motion, but if one decomposes it, the
interstitial position stands out as a very simple and logical
stage. But the outstanding point of this interlayer migra-
tion is its generalization to more than two layer crossing
steps by keeping the same initial (1)-(3) and final (3)-(4)
motions by introducing several intermediate interstitial-
interstitial (3)-(3) motions.
(iii) Reactions between interstitial atoms are a recent
improvement in our model. The reactions allow collective
incorporation of atoms in interstitial positions. The re-
sult is the introduction of atoms in hanging positions (or
suspended configurations) with only one bond directed to-
ward the substrate and a second one with an atom in an
upper layer as shown in Figure 2. This atomic position is
of first importance for the observation of defects like va-
cancies or dislocations. This configuration is beyond the
SOS model for semiconductors where atoms are bonded
two times with the underneath layers. The SOS model
excludes vacancies and overhangs from the beginning.
On the other hand, when an event is produced the
structure will be relaxed. We use the VFF semi-empirical
potential in order to describe the elastic part of the total
energy. In our energetic model, the strain energy is ex-
pressed quadratically in terms of bond length and bond
angle variations as [11,15]:
Different events are involved in this simulation. We
have classified them in three main categories.
(i) The classical standard events are the basic events used
in most MC simulation. They are deposition, evaporation
and surface migrations.
(ii) Interlayer migrations via interstitials are also classical
events. These events permit atomic migrations from an
initial position in a layer number N to a final position in
a layer N + 2 or N − 2, two atomic layers above or be-
low [13,14]. The origin of such migrations is related to the
local configuration. In some circumstances a stressed atom
cannot move in the layer in which is situated. Normally,
the moving atom would occupy a vacant site in the layer
N + 1 or N − 1. However, in the zincblende lattice, this
position is an interstitial site and therefore unstable. The
atom will thus move rapidly to the nearest substitutional
site in layers N+2 or N−2. To allow the motion, the inter-
mediary layer N +1 or N −1 should be fully complete, at
least locally. It should be noticed that interstitial atoms
are not bulk atoms, but atoms at the surface, therefore
very mobile, and which correspond to interstitial configu-
rations in the crystal. A high strain energy is associated
with these configurations because of the important bond
bending, thus the associated motion is several orders of
magnitude faster than other types of movements.
X
X
Estress
=
kr(∆r/r)2 +
kθ(∆θ)2.
(1)
bonds
bond angles
The force parameters kr and kθ are calculated from the
To describe this motion, let us consider the step cross- elastic constant [11] of the materials so that no adjustable
ing (Fig. 1) of an atom initially in position (1) close to parameter is used in our simulation. In virtue of the fact

M. Sahlaoui et al.: Simulation of surface morphology and defects in heteroepitaxied thin films
173
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Fig. 2. Schematic representation of a reaction between interstitials giving rise to an atom in “suspended” configuration, also
called “hanging” position.
that in usual semiconductors, the value of kr is 20 to 50 the case of CdTe/GaAs, were used. Typical square sub-
times larger than kθ, we have performed the relaxation in strate sizes were (20 × 20) or (30 × 30) atoms. The depo-
two steps, relaxing successively bond lengths and bond an- sition rate was fixed to 2 monolayers (ML) per second at
gles. We have made a further approximation in writing the the growth temperature of 700 K. Values of force param-
energy as a quadratic expression of the atomic displace- eter (kθ) are set to 1.1 eV for GaAs and 0.4 eV for CdTe
ments. The analytical expression obtained is more compli- obtained from their elastic constants [11]. The chemical
cated, owing to the introduction of cross-terms, but speeds bond energy are set to 1.8 eV for GaAs and 1.0 eV for
up the computation, since the atomic displacements are CdTe. The chemical bond energy between the substrate
obtained directly, using a non-iterative Newton-Raphson atom and a deposited atom is taken as 1.4 eV, the aver-
method.
It should be pointed out that the energy minimization
age of the bond energies of bulk GaAs and CdTe.
We have presented in a previous work [12] the con-
sequences of interlayer migrations for CdTe/GaAs ma-
terials and their role on the layer roughening has been
demonstrated. They are at the origin of the creation of
valleys with (111) oriented facets along [110] and [1,-1,0]
directions, in agreement with experimental observations.
The deposited films are not flat, but present grooves with
identical facets, in agreement with experimental observa-
tions [16–19]. When the interactions between atoms in in-
terstitial sites are taken into account, growth is affected. A
non flat surface is developed which is the sign that inter-
layer migrations have begun to reduce the elastic energy
of the deposited film. Roughening is then introduced by
(111) oriented facets (Fig. 3). The facetting is known to be
due to the anisotropy of migration rate on crystallographic
faces. This phenomenon allows a lateral stress relaxation
of the film, the valleys bottoms are stress concentration ar-
eas where the dislocation energy barrier was calculated to
be very small [26]. Atoms arriving in these valleys reach
highly strained unstable positions. The energy distribu-
is performed to adjust atomic positions around their lat-
tice position. The atomic configurations and their bonding
state are not allowed to change during this minimization.
Therefore the minimization procedure leads to a local sec-
ondary minima, in agreement with the irreversible nature
of the growth and the fact that the growing film should
stay in a metastable state.
This VFF presents several advantages: (i) it is well
adapted to non compact semiconductor structures, (ii)
this model is simple enough to execute the multi-million
minimizations needed to simulate the growth, (iii) activa-
tion energy is depending on the local strain can be simply
defined.
3 Results and discussion
3.1 Perfect surface
Simulations of heteroepitaxial growth of thin films on an tion, calculated in our model in the case of Figure 3, in-
(100)-oriented substrate have been carried out and the in- dicates a lower energy of atoms on the surface from 0 to
terface structure investigated. The substrate surface was 0.05 eV. This results from the easy relaxation of surface
assumed to be perfect and unreconstructed. A lattice mis- atoms while bulk atoms, with three or four bound are less
match of 14.6% and physical parameters corresponding to easily relaxed and present higher strain energy from 0.05

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The European Physical Journal Applied Physics
atoms are stressed at these vacant positions, they climb
in the other positions to form a stable vacancy. Long term
stabilization occurs when triply bonded atoms surround
the vacant site.
In the first interpretation, these vacant sites are as-
similated to isolated vacancies. In reality, the observation
of different cross-section on successive (110) planes shows
that vacancies are not isolated but grouped in lines or
planes. These vacancies have a tendency to extend with
growth time. They allow relaxation of the local stress and
serve as a germ for interface dislocations always in very
small numbers, and small sizes in the simulations.
The relaxation of the deposited layers by the forma-
tion of isolated vacancies is not an efficient process; the
majority of point defects created are grouped as the defect
extends. Only a few isolated point defects can be observed
within the material. The extension of defects also remains
limited owing to simulation conditions. Indeed, atoms in
interstitial positions are very mobile and migrate between
valleys formed by (111) facets. These movements are in-
dispensable for the creation of defects, but considerably
increase the computation time. To obtain a reasonable cal-
culation time, we have been forced to slow more or less, the
totality of movements on the surface. Thus, conditions of
simulation are far from the thermodynamic equilibrium as
the experimental conditions. Consequently germs of dislo-
cations that form in different positions of the layer have
not enough time, when growing, to be aligned on a long
range. As a result of this slowing movements, some atoms
in the bottom of valleys are covered by incoming atoms,
before having time to relax. In these cases, the relaxation
of strain occurs a few atomic distances away, causing a
segmented dislocation line.
¯
Fig. 3. Projection on a (011) plane of a growing film on a
perfect surface showing V-shaped defects with (111) facets.
to 0.25 eV. But these bulk atoms are blocked by atoms in
upper layers and can not move without producing cracks
in the deposited film. Nevertheless the nucleation of dislo-
cation is the combination of the atomic strain relaxation
and a set of particular event that we are going to describe
in what follows. As a result, an atom coming in the bottom
of the valley is quasi-immediately evacuated on the (111)
facets to an intermediate interstitial position with a global
reduction of the elastic energy in this region. As clearly
shown in Figure 3, the growth continues on (111) facets
to fill the groove. In fact the mobility of atoms in intersti-
tial sites caused by the local stress and the impossibility
for these atoms to be fixed in more stable substitutional
sites induce the movements of interstitial sites and lead to
the growth on (111) facets. This begins with the appari-
tion of atoms in “suspended configuration” that present
a dangling bond toward the substrate and never occupy
the vacancies in lower levels because of the large strain en-
ergy associated with them, but they are localized on (111)
planes. The growth continues normally on the upper lay-
ers. The result is the filling of cavities by the deposition of
(111) successive planes on the (111) facets, leaving vacant
sites in the bottom of the grooves. This morphology can
be explained in the following map. During migration and
because of a significant number of atoms in interstitial po-
sitions, an atom can approach others atoms in the same
situation with relative case. The atoms can interact with
So, in order to study morphological structure and dy-
namic growth of strained CdTe film in a more quantita-
tive way, the simulations of reflection high energy elec-
tron diffraction (RHEED) have been carried out. We have
calculated RHEED intensity using kinematic theory for
out-of-phase condition defined by q d = π, where q is
⊥
⊥
the momentum transfer normal to the surface, and d is
the step height corresponding to adjacent (100) atomic
plane. Under such condition, the specular beam intensity
of RHEED is inversely related to the degree of surface
roughness which has calculated as the fluctuation in the
height to which the film has grown in a given local region
of substrate [23].
Figure 4a shows the calculated RHEED of the dynamic
each other through a common bond. These atoms which heteroepitaxial growth (CdTe/GaAs) and homoepitaxial
are doubly bonded are in “suspended configurations”, i.e. growth (GaAs/GaAs) used for comparison. The figure
with one dangling bond towards lower layers.
gives informations on the growth mode. The oscillations
Figure 3 also shows a local growth on the (111) facets. are interpreted as a layer by layer growth for the homoepi-
We can also observe the formation of vacancies that repre- taxy case, one period of the RHEED intensity oscilla-
sent point defects within the material [20]. In fact, atoms tions corresponding to the completion of two monolayers.
in suspended configurations fill the cavities delimited by On the contrary, in heteroepitaxial growth, we can note
(111) facets and valleys in (110) directions with dangling clear oscillations during first stage of growth, after that
bond toward vacant sites of the lower layers. A vacant site a decrease of the RHEED intensity is observed, in agree-
becomes a vacancy if it is stabilized. In fact, vacant posi- ment with experimental observation [24] (case of CdTe
tions may be occupied by atoms from the gaseous phase on ZnTe). This situation corresponds to the Stranski-
or by migrations of atoms in the deposited layers. But if Krastanov mode for CdTe/GaAs. In fact, during first

M. Sahlaoui et al.: Simulation of surface morphology and defects in heteroepitaxied thin films
175
Fig. 5. Cross section of the growing film in the case of the
stepped surface.
step on the substrate formed by 30×30 atoms. The planes
are numbered from 1 to 30 in [110] or [1,-1,0] direction.
In the second case, we study the effects of the presence
of floating atoms from the substrate on the growth. We
first start by the 1ML step case. Figure 5 shows the cross
section of the growing film by a (110) plane, taken out
of our simulations. Dark circles represent the step atoms.
We noted firstly that the morphology in the successive
(100) planes shows large variations of the statistical layer
height fluctuations from one to another plane. For a better
clarity we have chosen the plane number 28 represented
in Figure 5. We can observe the atomic arrangement at
the step edge. We can see a typical structure of the dislo-
cation with the valley appearing at the first stage of the
growth localized near the step edges. The dislocation for-
mation mechanism is the same as described previously.
The difference is that the valleys are well expanded in
height and strongly localized near the step edge. This dif-
ference results from the strain and stress fields generated
by the step. Consequently, a missing half plane is going
to be formed at the bottom of the valley near the step
edge. The global morphology of the growing films shows
the presence of depressions characteristic of dislocation at
the step edges [20].
In the literature, the steps have been expected to have
a singular influence in the defects generation. In our simu-
lation, we have noticed that step edges neighborhood are
favorable for localization of dislocation in agreement with
experimental observations [21,22].
In the second case the deposition started with some
atoms from the substrate adsorbed on a (100) flat sur-
face. These atoms are distributed randomly and cover the
substrate with approximately 33% in the example repre-
sented in Figure 6. Dark circles represent these adsorbed
atoms. Figure 6 shows a cross section of the deposited film.
We can observe clearly that grooves are well expanded
Fig. 4. (a) Rheed oscillations versus coverage (or time:
growth rate is 2ML/s) in two cases: homoepitaxial growth
(GaAs/GaAs) and heteroepitaxial growth (CdTe/GaAs). (b)
The roughness of deposited layers.
stage of growth, the high-bond energy between deposited
layer and substrate leads to the interlayer migrations to-
ward a lower layer where atoms are stabilized and then
allow initial layer by layer growth. This is generally the
case of homoepitaxial growth where the interactions be-
tween second nearest neighbours are important [25]. We
ascribe the change in the RHEED intensity to the relax-
ation of deposited layers and the formation of the three
dimensional clusters with (111) facets as described below.
The growth continues on the upper layers inducing a rough
front of growth as seen in Figure 4b.
3.2 Imperfect surface
The influence of defects on the surface is an interesting in height in comparison to the case of a perfect surface.
problem that we have started to investigate. In this section This behavior is due to the strain and stress generated
we report preliminary results on two examples of an im- by the presence of atoms from the substrate in the first
perfect surface. The first case correspond to 1 ML height layer. In fact these atoms permit the stabilization of the

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The European Physical Journal Applied Physics
qualitatively identified to localize defects because of the
important strain and stress in these regions.
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4 Conclusion
In this article, we have described an atomic defect
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