A valence force field for the silicon crystal

A Lifson-Warshel force field (1968), which goes beyond the harmonic approximation and is well adapted for calculations in defect structures, has been developed for the silicon crystal. The parameters of this field have been determined by least-squares fitting of the phonon dispersion curves, which are reproduced with an accuracy comparable with that of harmonic valence force fields. Several of these parameters were kept constant during this fitting at values derived from silicon molecular data. The stacking fault energy, which vanishes for harmonic valence force fields, is calculated in reasonable agreement with experiment.