Lattice dynamics of Si calculated with a semiempirical approach.

Abstract

Phonon dispersion curves, spectral densities, thermodynamic functions, and displacement correlation functions are calculated for bulk Si within a simple and efficient semiempirical scheme that is based on Chadi's total-energy ansatz for covalent semiconductors. With an empirical tight-binding electronic band structure, and the lattice constant ${a}_{0}$ and the bulk modulus B as the only input, atomic force constants of arbitrary range can be calculated by use of tight-binding Green functions so that the dynamical matrix of the system can be set up. The agreement with previous calculations and with experiment is surprisingly good in view of the simplicity of the approach. The simple formal structure of the theory allows us to analyze the physical origin and nature of the various contributions entering the dynamical matrix very clearly. In particular, the importance of fifth-nearest-neighbor force constants for the flattening of the TA modes, e.g., at the X point, typical for covalent semiconductors, can be demonstrated. The influence of different electronic band structures on the phonon properties is also discussed.