Determination of the bulk elastic properties of silicon via the Chadi method

Abstract

One of the simplest and yet most successful methods for determining the bulk elastic properties and surface geometries of the covalent solids has been the Chadi total energy minimization scheme. As a result of recent work, however, there are now strong grounds for questioning the validity of one of the basic assumptions which have been employed in implementing this particular approach. The assumption in question is the so-called 1 d 2 approximation whereby the tight-binding matrix elements appearing in the model Hamiltonian description of the host bandstructure are assumed to scale simply as the inverse square of the appropriate interatomic distance. We have therefore endeavoured to test this 1 d 2 model, and the possible alternative of using data derived from pressure dependent bandstructure calculations, by employing them both within the Chadi scheme in a determination of some of the lattice dynamical properties of silicon. In an earlier publication we have reported the results of such calculations on the two elastic constants C 11- C 12 and C 44, and some of the Γ and X point phonon mode distortions. In the present paper we extend these silicon calculations to incorporate the various L-point phonon modes. This enables us to draw quite general conclusions concerning the relative merit of these two spatial models, and the overall reliability of the Chadi total energy minimization scheme.