A Morphological Approach to Constructing Interatomic Potentials: An Application to Silicon
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A MORPHOLOGICAL APPROACH TO CONSTRUCTING INTERATOMIC POTENTIALS: AN APPLICATION TO SILICON. P. DALLOT and P. D. BRISTOWE
Department ofMaterials Science and Engineering MIT, Cambridge, MA 02139 ABSTRACT A framework for constructing interatomic potentials is proposed and applied to the case of silicon. The construction relies on a geometrical approach in which we try to reproduce the
morphology of the Born-Oppenheimer surface. In particular, we develop a new technique for constructing four body terms. It consists of building invariant coordinate systems on the
configuration space of four atoms, thus allowing the choice of the four body term morphology. The potential that we develop has a two and a four body part. It is adjusted to match the only geometrical information known from the Born-Oppenheimer surface which is the position of its minimum of energy and its curvature at that point, as given by the dynamical matrix. The potential is then tested on point defects and surface structures in silicon. INTRODUCTION Within the framework of the Born-Oppenheimer approximation, the total energy of an isolated system of N interacting atoms is seen as a function of the atomic positions, usually referred to as the Born-Oppenheimer surface (B-O). The objective of this paper is to find an approximation to this surface, specifically for silicon. The point of view that we adopt in order to describe this surface is to focus on its topological form. What we would like to describe is the morphology of this surface, that is, the list and local description of its critical points in the configuration space of the N interacting atoms. Such a task is known to be impractical as soon as N is large (N=5 would be challenging, except for the simplest potentials). The difficulty in reaching the above goal lies in the fact that there is no analytic theory to construct global forms. All we can do is add functions together, the shapes of which are well understood. These functions will represent local interactions and their sum will be the N-body potential that is meant to approximate the B-O surface. We then hope that choosing the shape of the local functions will allow us to control the resulting morphology of the potential. The only way to validate the resulting potential, however, is to test how well it compares to experimental observation and ab-initio calculations. It is a geometrical approach similar to this that Stillinger and Weber [I ] used in constructing their potential. In this paper, we develop the total energy as a sum of two and four body terms. The two body term is responsible for most of the binding energy (-4.5 eV/atom). The four body term is responsible for reproducing the force constants. The lattice constant is a result of the competition between these two terms. In the next section we present a method that we have developed for choosing the shape of a four body term. We then present the actual two and four body potentials that we have obtained and the first results of their application to defects in silicon. CHOOSING A FOU
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