Dislocation and Grain Boundary Energies in Si and Ge from an Anharmonic Bond Charge Model

Abstract

The paper presents calculated line energy values for the reconstructed 60° and 90° glide-set partial dislocations in Si and Ge, formation and migration energy for the reconstructed kink on the reconstructed 90° partials, and energy data for the symmetric Σ = 9 and for two variants of the symmetric Σ = 11 tilt grain boundaries. Criteria are formulated to identify interatomic force field models which are able to provide reliable energy estimates. The anharmonic bond charge (a.bc) model is introduced as an example that approximately fulfills the basic criteria, i.e., describes well the second and third order elastic constants and the phonon dispersion curves. Deviations between energy estimates from the a.bc model and less reliable approaches are discussed. It is shown that in case of the = 11 tilt grain boundary the a.bc model gives different energetical ranking for the so-called Σ = 11A and the Σ = 11B variants in Si and Ge, in agreement with the experimental observations.