Abstract

Semiempirical potentials for silicon, germanium, and their alloys are derived with use of the modified-embedded-atom-method formalism. Following Baskes [Phys. Rev. Lett. 59, 2666 (1987)], it is found that the host electron density which is a linear superposition of atomic densities in the embedded-atom method (EAM) must have an angular modification in order to properly describe the bond-bending forces in the diamond-cubic structure. The angular dependence of this host electron density was found to be in qualitative agreement with the density of a first-principles calculation. As in the EAM, the potential functions are determined by using the measured lattice constants, sublimation energies, elastic constants, and alloying energies of silicon and germanium. In addition, first-principles calculations of structural energies are used. The potentials are used to calculate the energetics and geometrics of point defects, surfaces, metastable structures, and small clusters. In all cases, the calculations have been compared to first-principles calculations and experiment when available. The calculations predict that the vacancy mechanism is the dominant diffusion mechanism in both silicon and germanium. Surface energies and relaxations of the low-index faces of Si and Ge are compared with first-principles calculations.