Modeling and Numerical Simulation of Material Science, 2013, 3, 11-16
doi:10.4236/mnsms.2013.34B003 Published Online October 2013 (http://www.scirp.org/journal/mnsms)
Atomistic Simulation of Undissociated 60˚ Basal
Dislocation in Wurtzite GaN.
I. Belabbas1*, J. Chen2, Ph. Komninou3, G. Nouet4
1Groupe de Cristallographie et de Simulation des Matériaux, Laboratoire de Physico-Chimie des Matériaux et Catalyse.
Université Abderrahmane Mira, Bejaïa (06000), Algérie.
2CIMAP, UMR6252 CNRS-CEA-ENSICAEN-Université de Caen Basse-Normandie, 14032, France.
3Department of Physics, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece
4Centre de Recherche sur les Ions, les Matériaux et la Photonique, 6 Boulevard du Maréchal Juin, 14050 Caen cedex, France
Received May, 2013
ABSTRACT
We have carried out computer atomistic simulations, based on an efficient density functional based tight binding
method, to investigate the core configurations of the 60°basal dislocation in GaN wurtzite. Our energetic calculations,
on the undissociated dislocation, demonstrate that the glide configuration with N polarity is the most energetically fa-
vorable over both the glide and the shuffle sets.
Keywords: Gallium Nitride; 60°Basal Dislocation; Core Structure; Energy; Tight-binding; SCC-DFTB
1. Introduction
Wurtzite GaN layers were initially grown along the
[0001] direction, also called polar direction [1]. This led
to the fabrication of optoelectronic devices, based on
heterostructures, which are strongly affected by sponta-
neous and piezoelectric polarization effects [2]. These
effects are at the origin of the occurrence of a high inter-
nal electrostatic field which increases the separation be-
tween electrons and holes and thus reducing the overlap
of their wavefunctions [2]. The latter causes a strong
current dependence of the emission energy and a red shift
of optical transitions as well as reduces the emission effi-
ciency of optoelectronic devices [2]. The polarization-
related effects in wurtzite GaN heterostructures can be
completely avoided by adopting growth on alternative
orientations. Hence, various growth directions were ex-
plored. These were the non-polar directions: ,
and the semi-polar directions: , and
[3]. Then, GaN/AlGaN heterostructures grown
along non-polar or semi-polar directions were proven to
be free from polarization effects and thus demonstrate a
clear improvement of their optical properties with respect
to those elaborated along the polar direction.
The nature of threading dislocations contained in a
wurtzite GaN layer is directly related to the direction of
its growth. If the growth direction is [0001], i.e. the polar
direction, the threading dislocations are perfect prismatic
dislocations, which can be edge, screw or mixed [4].
However, if the growth direction is , i.e. the
non-polar direction, the threading dislocations can be
perfect or partial basal dislocations [4]. Perfect basal
dislocations are screw and 60°-mixed, while partial
basal dislocations are Shockley (edge, 30°-mixed), Frank
and Frank-Shockley partials [5].
During the last decade, threading prismatic disloca-
tions were extensively investigated in gallium nitride, at
both experimental and theoretical levels [4]. For these
dislocations, models for their core structures were pro-
posed and their impact on the electronic properties of
GaN was nearly elucidated [6-8]. The body of work
dedicated to basal dislocations in GaN still insufficient
compared to that to prismatic dislocations [4], while
among basal dislocations, partials [9] were more investi-
gated regarding the perfect ones [10,11]. The perfect
screw dislocation was investigated atomistically and the
energetic hierarchy of its core configurations was estab-
lished by Belabbas et al. [12]. The perfect 60°
dislocation was studied in cubic GaN by Blumenau et al.
[13] but unfortunately no theoretical report exists for the
wurtzite phase. At the experimental level, the perfect 60
°dislocation was observed by using electron micros-
copy. By combining conventional transmission electron
microscopy and cathodoluminescence measurements,
Albrecht et al. [14] investigated the 60°dislocation in
wurtzite GaN and analyzed its electronic and optical ac-
*Corresponding author.

I. BELABBAS ET AL.
12
tivities. They found it to be likely responsible for a para-
sitic luminescence around 2.9 eV. However, due the lim-
ited resolution of their used microscope, the previous
authors were not able to establish if this observed behav-
ior is that of a full or a dissociated dislocation. In a sub-
sequent study, Niermann et al. [15] have observed a dis-
sociated 60°dislocation by using high resolution trans-
mission electron microscopy. The separation between the
two resulting Shockley partials was found to be smaller
than 2 nm.
In the present contribution, we have carried out com-
puter atomistic simulations to investigate the core con-
figurations of the 60°basal dislocation in GaN wurtzite.
2. Models and Simulation Details
The 60°basal dislocation has a mixed character (edge and
screw). In the wurtzite crystal structure, this dislocation
is perfect and has its line along the direction and
its Burgers vector is which has a magnitude
equal to a (a = 3.18Ǻ stands for the basal lattice vector of
GaN). The 60°basal dislocation may have several core
configurations, which depends on the position of its
centre. If the latter is located between two narrowly
spaced {0001} planes, called the glide set, the dislocation
will have a glide configuration. However, if the centre of
the dislocation is situated between two widely spaced
{0001} planes, called the shuffle set, the dislocation will
have a shuffle configuration. As gallium nitride is a
compound semiconductor, a glide (or a shuffle) core
configuration may exists in two different polarities:
gallium or nitrogen. This depends on the nature of the
ending atom at the additional half plane, which is at the
origin of the edge component of the dislocation.
The 60°basal dislocation was modeled atomistically
by using the so-called supercell-cluster hybrid model
[6-8]. The atoms at the model’s lateral surface (Ga/N)
have to be saturated by fractionally charged (1.25e/0.75e)
pseudo-hydrogen atoms which allow getting rid of dan-
gling bonds and their associated unwanted gap states
[6-8]. The supercell-cluster hybrids were at least dou-
bled along direction in order to take into account
any possible reconstruction along the dislocation line.
The size of the models considered here is ranging from
750 to 1000 atoms and their lateral extension is typically
about 26Ǻ. Although the lateral extension of the model is
finite, periodic boundary conditions were applied later-
ally to the dislocation line while including a 50Ǻ of vac-
uum. The equilibrium atomic positions were obtained
through a minimization procedure based on the conjugate
gradient algorithm where energies and forces are evalu-
ated by using the SCC-DFTB method [16]. During this
step all the atoms, including those at the model’s lateral
surfaces, were allowed to relax freely. The equilibrium is
reached when the maximum force acting on each atom of
the system is well below 0.0001a.u.
3. Results and Discussion
For the 60°basal dislocation, we have considered four
core configurations: a shuffle configuration with nitro-
gen polarity (60°-SN), a shuffle configuration with gal-
lium polarity (60°-SGa), a glide configuration with a
gallium polarity (60°-GGa) and a glide configuration
with nitrogen polarity (60°-GN). These core configura-
tions are represented respectively in figures (1.a, 1.b, 1.c,
1.d). In the following we will present and discuss our
results concerning the atomic description of the previous
core configurations and their energetics.
3.1. Atomic Core Structure
The 60°-SN core configuration (Figure 1(a)) presents a
structure with an asymmetric 8-atoms ring. This is
different from the 8-atoms ring structure exhibited by the
prismatic edge dislocation which processes mirror plane
symmetry [17]. All the atoms forming the core are fully
coordinated except those of the column (1) which involves
dangling bonds (Figure 1(a)). The most compressed
bonds (-8.21%) are established between the atoms of
columns (1) and (8), while the most stretched bonds
(+13.33%) are established between the atoms of columns
(5) and (6). The chemical bonds involved in the core
present an angular dispersion ranging from 93°to 128
°.
The 60°-SGa core configuration (Figure 1(b)) has, as
in the previous one, a structure with an asymmetric 8-
atoms ring. However, while the 60°-SN configuration
exhibits a single period structure, a complex reconstruc-
tion takes place in the 60°-SGa configuration, leading to
doubling its period along the dislocation line. This re-
construction consists in establishing alternated Ga-Ga
bonds (2.81 Ǻ) between the atoms of columns (1) and (5),
while occurring in column (6) dangling bonds within a
2a period. In this core configuration, the most com-
pressed Ga-N bonds (-7.18%) are involved by the low
coordinated atoms of column (1) and those of column (8).
The most stretched Ga-N bonds (+17.44%) are estab-
lished between the atoms of columns (5) and (6). The
most extreme bond angles (79°and 154°) are recorded
for the atoms of column (5).
The 60°-GGa core configuration (Figure 1(c))
exhibits a structure with an asymmetric 5/7-atoms ring.
This core configuration includes only Ga-Ga bonds
separating the 5-atoms and 7-atoms rings, which make it
different from the symmetric core configuration of a
prismatic edge dislocation where both Ga-Ga and N-N
are separating the two atomic rings [17]. In the
configuration 60°-GGa, the Ga-Ga bonds (2.32 Ǻ) are
established between the atoms of columns (3) and (9). The

I. BELABBAS ET AL.
13
latter contains under- coordinated Ga atoms. The most
compressed Ga-N bonds (-5.64%) are involved between
the (3) and (9) atomic columns, while the most stretched
bonds (+10.77%) are established between the atoms of
columns (5) and (6) and those of columns (6) and (7).
The most extreme bond angles (90°and 138°) are
recorded for the atoms of column (3).
The 60°-GN core configuration (Figure 1(d)) has a
structure with an asymmetric 5/7-atoms ring, which con-
tains some N-N bonds. The considerable difference in
bond lengths between the N-N bonds (1.58 Ǻ), involved
in this configuration, and the Ga-Ga bonds, involved in
the previous configuration, makes the 60°-GN core con-
figuration less spatially extended than the 60°-GGa core
configuration. In the configuration 60°-GN, the column (9)
does contain under-coordinated N atoms. The most com-
pressed Ga-N bonds (-6.67%) are established between
the atoms of columns (8) and (9). The most stretched
bonds (+7.18%) are involved by, in one hand, the atoms
of columns (2) and (3) and, in the other hand, by the at-
oms of columns (5) and (6). The bond angles present a
dispersion ranging from 92° to 134°.
3.2. Energetics
The energetic hierarchy of the four core configurations of
the 60°basal dislocation was accessed through a com-
bination of continuum elasticity theory and atomistic
calculations based on the SCC-DFTB method. The total
strain energy (total ) associated with a dislocation can be
represented as a sum of elastic () and core ()
contributions:
E
elastic
Ecore E
totalelastic core
EE E

 (1)
within linear elasticity, the elastic strain energy per unit
length stored in a cylinder of radius R around the disloca-
tion is given by the relation [18]:
(d)
1 2
3
4
5
6
7
8
9
10
(a)
1 2
3
4
5
6
7
8
(b)
1 2
3
4
5
6
7
8
(c)
1 2
3
4
5
6
7
8
9
1
Figure 1. Ball and stick models for relaxed core configurations of the mixed 60° basal dislocation, projected along the [1120]
direction. Black balls represent gallium atoms and the white ones nitrogen atoms. (a): View of the 60°-SN core configuration.
(b): View of the 60°-SGa core configuration. (c): View of the 60°-GGa core configuration. (d): View of the 60°-GN core configu-
ration.

I. BELABBAS ET AL.
14
(/) for
elastic cc
EAlnRR RR
2
(2)
where Rc is the dislocation core radius. For a mixed type
dislocation, the pre-logarithmic factor is related to both
the edge and screw components of the Burgers vector of
the dislocation (be and bs respectively) and it is given,
within anisotropic elasticity, by the relation [18]:
2
(1 /4) ()
eess
A
KbK b

 (3)
In the case of a mixed basal dislocation, the energy
factors e
K
and
s
K
, associated respectively with the
edge and the screw components, are given by the rela-
tions [18]:
1/2
4411 3313
11 3313
3311 331344
()
()
(2
e
CCCC
KCCC
CCCC C


 



)




(4a)
and
44 66s
K
CC (4b)
where are the elastic constants of the material.
ij
Within the SCC-DFTB method, one can define the ex-
cess energy of a single atom as its difference in energy in
the system with presence of the defect and that in bulk
material. Hence, the total strain energy (total ) contained
in a cylinder of radius R around the dislocation is evalu-
ated by summing the excess of energy related to individ-
ual atoms belonging to this area. In order to determine
the core parameters of the dislocation, i.e. core energy
and core radius, we plotted the total strain energy (total )
versus ln(R), for the four considered core configurations
(Figure 2). These curves exhibit three distinct domains: a
central linear region bordered by two non-linear ones.
The linear region represents the so-called elastic region
while the non-linear region close to the centre of the dis-
location represents the so-called core region. The ap-
pearance of a quick enhancement of the strain energy, in
the second non-linear region, is attributed to surface ef-
fects.
C
E
E
Fitting the linear parts of the strain energy curves with
equation (2) allowed us to determine the values of the
pre-logarithmic factor (Afit) which represents the slope of
these curves. The obtained values are ranging from
-1.3% to -10.4% (Table 1) with respect to theoretical
value of A = 0.77eV/Ǻ, evaluated by using equation (3)
and the experimental values of the elastic constants.
The core radius of a particular core configuration is
defined as the value of the radius from which the strain
energy curve cesses of being linear, when going to the
centre of the dislocation. The core energy is defined as
the value of the energy corresponding to the core radius
[7]. The obtained core energies and radii of the four core
configurations of the 60°basal dislocation are summa-
rized in Table 1. Then, the comparison of the core ener-
gies, evaluated at a common radius of 6Å, shows that
within the glide set, the configuration with a nitrogen
core (60°-GN) is energetically favorable over the con-
figuration with a gallium core (60°-GGa). However, the
opposite is observed in the shuffle set, where the con-
figuration with a gallium core (60°-SGa) has lower core
energy than the configuration with a nitrogen core (60°
-SN). The core configuration 60°-GN was found to be
the most energetically favorable over both the glide and
the shuffle sets. Otherwise, our calculations show that the
core energy difference of the glide configurations (0.53
eV/Å) is higher than that of the shuffle ones (0.11eV/Å).
Core region Elastic region
Surface
Figure 2. The total strain energy per unit length stored in a cylinder of radius R as a function of ln(R) for different core con-
figurations of the 60° basal dislocation: 60°-SN, 60-SGa, 60°-GN and 60°-GGa.

I. BELABBAS ET AL. 15
Table 1. The calculated core radii (Rc), core energies (Ec) of the different configurations of the 60° dislocation. To facilitate
comparison between dislocations with different core radii, the core energy (E’c) corresponding to a radius of 6Ǻ is introduced.
Also indicated, the calculated pre-logarithmic factors: (Afit) (SCC-DFTB), (A) (anisotropic elasticity theory) of the different
core configurations of the 60° dislocation.
60°-SN 60°-SGa 60°-GN 60°-GGa
Afit (eV/Ǻ)
A (eV/Ǻ)
Rc (Ǻ)
Ec (eV/Ǻ)
E’c (@ R=6Ǻ) (eV/Ǻ)
0.720
0.770
3.720
1.530
1.874
0.690
0.770
3.760
1.440
1.762
0.760
0.770
4.260
1.200
1.460
0.740
0.770
3.820
1.660
1.994
One can consider that the core energy of a given dis-
location has two contributions: i)- a contribution due to
heavily strained bonds (non-linear strain) and ii)- a sec-
ond contribution which is due to dangling bonds. Based
on the latter consideration, one can attempt to understand
the obtained energetic hierarchy of the core configura-
tions of the 60°dislocation.
As the two glide core configurations (60°-GN, 60°
-GGa) exhibit comparable bond distortions, one may ar-
gue that the contribution which makes the difference in
the establishment of their energetic hierarchy is that of
dangling bonds. This implies that N-dangling bonds are
less energetic than the Ga-dangling bonds. As this has to
be also valid for the shuffle configurations, one may ex-
pect that the 60°-SN configuration is more energetically
favorable than the 60°-SGa configuration. However, the
inversion of the energetic hierarchy revealed by our pre-
sent calculations is directly related to the reconstruction
that occurs at the 60°-SGa core. Indeed, by a rearrange-
ment of core atoms, the reconstruction allows getting rid
of Ga-dangling bonds and then leads to a particular bond-
ing state which is less energetic than N-dangling bonds.
4. Summary and Conclusions
By performing atomistic computer simulations, we have
investigated the structure of the 60°basal dislocation
core configurations as well as their energetics in
hexagonal gallium nitride. Our calculations were carried
out by using an efficient self-consistent based density
functional theory tight binding method (SCC-DFTB).
For the undissociated 60°dislocation, we have
considered four core configurations; two belong to the
glide set (60°-GN, 60°-GGa ) and the two others belong
to the shuffle set (60°-S N, 60°-SGa). Each of these core
configurations was found to contain a row of under-
coordinated atoms. These atomic columns are those
defining the polarity (Ga/N) of the core as they are
located at the end of the additional half plane which is at
the origin of the edge component of the dislocation.
Otherwise, all the core configurations exhibit single
period structures but the 60°-SGa one, where recon-
structions occurring along the dislocation line lead to a
structure with a double period.
Our energetic calculations demonstrate that within the
glide set, the configuration with a nitrogen core (60°
-GN) is more energetically favorable than the configura-
tion with a gallium core (60°-GGa). However, the oppo-
site occurs in the shuffle set, where the configuration
with a gallium core (60°-SGa) has lower core energy
than the configuration with a nitrogen core (60°-SN).
The core configuration 60°-GN was found to be the
most energetically favorable over both the glide and the
shuffle sets.
5. Acknowledgements
I. B. acknowledges the financial support from Abderah-
mane Mira university of Bejaia. The computations were
performed at “CRIHAN”, Centre de Ressources Infor-
matiques de HAute Normandie, (http://www.crihan.fr).
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