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Advances in Condensed Matter Physics
Volume 2018, Article ID 3038795, 8 pages
Research Article

Threading Dislocations Piercing the Free Surface of an Anisotropic Hexagonal Crystal: Review of Theoretical Approaches

1Laboratoire de Physique de la Matière Condensée et Nanosciences LR 11 ES 40, Faculté des Sciences, Université de Monastir, rue de l’Environnement, 5019 Monastir, Tunisia
2Université Grenoble Alpes, CNRS, SIMaP, 38000 Grenoble, France

Correspondence should be addressed to Roland Bonnet; rf.rfs@tennoblar

Received 20 February 2018; Accepted 29 March 2018; Published 10 May 2018

Academic Editor: Sergei Sergeenkov

Copyright © 2018 Salem Neily et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Inclined threading dislocations (TDs) piercing the oriented free surface of a crystal are currently observed after growth of oriented thin films on substrates. Up to date the unique way to treat their anisotropic elastic properties nearby the free surface region is to use the integral formalism, which assumes no dislocation core size and needs numerical double integrations. In a first stage of the work, a new and alternative approach to the integral formalism is developed using double Fourier series and the concept of a finite core size, which is often observed in high-resolution transmission electron microscopy. In a second stage, the integral formalism and the Fourier series approaches are applied to the important case of a TD piercing the basal free surface of a hexagonal crystal. For this particular geometry, easy-to-use expressions are derived and compared to a third approach previously known for a plate-like crystal. Finally, the numerical interest and the convergence of these approaches are tested using the basal free surface of the GaN compound, in particular for TDs with Burgers vectors c and (a + c).