Generalized Peierls–Nabarro model for studying misfit dislocation in a BN/AlN heterostructure

Abstract

Based on the solution of the balance problem for a semi-infinite lattice, we propose a generalization of the Peierls–Nabarro equation that is applicable to an interfacial misfit dislocation array. We obtain a relationship between the mass center displacement and the relative displacement. Under the assumption that the change in the interfacial layer spacing is sufficiently small that it can be ignored, this relationship allows us to reveal the core structure of the misfit dislocation and determine the interfacial atomic coordinates. As an example, a boron nitride/aluminum nitride heterostructure with a large lattice mismatch is studied using the equation. We find a good match between the theoretically predicted interfacial atomic configuration and that obtained from a first-principles calculation. Furthermore, the adhesion energy of the heterostructure is also evaluated, and the theoretical result coincides with that obtained from first-principles simulations.