Theoretical analysis of <0001> tilt grain boundaries in GaN at the atomic scale
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Theoretical analysis of tilt grain boundaries in GaN at the atomic scale Jun Chen1, Pierre Ruterana and Gérard Nouet Laboratoire d’Etude et de Recherche sur les Matériaux, FRE 2149 CNRS, Institut des Sciences de la Matière et du Rayonnement, 6 Boulevard du Maréchal Juin, 14050 Caen Cedex, France. 1 Laboratoire Universitaire de Recherche Scientifique d’Alençon, Institut Universitaire de Technologie, 61250 Damigny, France.
ABSTRACT Epitaxial layers of GaN contain a very high density of threading dislocations. In the first stage of growth they may form low and high angle grain boundaries. Energetic calculations of tilt grain boundaries have been performed with the Stillinger-Weber potential modified to take into account the wrong bonds Ga-Ga and N-N. The variation of the energy has been calculated as a function of the rotation angle. Two minima exist with special atomic structures based on a limited number of structural units. They are used to describe the other misorientations in terms of dislocation cores. INTRODUCTION
The III-V nitride semiconductors have known a very fast evolution for the last decade with the fabrication of LED’s and LDs [1]. These semiconductors, GaN, AlN and InN are characterised by direct band gaps ranging from less than 1.0 eV for InN, to 6.2 eV for AlN. They are highly promising in devices active from infrared to the ultraviolet range. They are grown by heteroepitaxy due to the lack of suitable bulk crystals for substrates. The layers contain large densities of threading dislocations which can reach 1010 cm-2. Other crystallographic defects such as prismatic stacking faults, inversion domain boundaries, nanopipes are also present. The origin of this very high density of threading dislocations is connected to the growth process resulting in a mosaic structure of slightly misoriented grains [2]. Thus, low-angle and high-angle grain boundaries may form and their atomic structures have been analysed by high resolution transmission electron microscopy (HREM) [3]. Energetic calculations have been performed on special grain boundaries described in terms of the coincidence site lattice concept [4]. In the case of wurtzite structure, high resolution electron microscopy analysis of special grain boundaries was performed in zinc oxide [5] and gallium nitride [3]. It was shown that the atomic structure of tilt grain boundaries in gallium nitride is based on periodic structure involving different cores of the 1/3< 1120 > edge dislocations. Atomistic simulation of these dislocation cores [6,7] and of some coincidence grain boundaries was undertaken to determine their relative stability [8,9]. The aim of this study is the systematic calculation of the energy of tilt grain boundaries in the 0°-60° range.
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INTERATOMIC POTENTIAL The energetic calculations in nitride semiconductors dealt with the core structure of edge and screw threading dislocations by using ab initio local- density functional cluster method or a density functional based on tight binding method [10,11] and density-functio
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