Empirical molecular-dynamics study of diffusion in liquid semiconductors

Abstract

We report the results of an extensive molecular-dynamics study of diffusion in liquid Si and Ge (l-Si and l-Ge) and of impurities in l-Ge, using empirical Stillinger-Weber (SW) potentials with several choices of parameters. We use a numerical algorithm in which the three-body part of the SW potential is decomposed into products of two-body potentials, thereby permitting the study of large systems. One choice of SW parameters agrees very well with the observed l-Ge structure factors. The diffusion coefficients D(T) at melting are found to be approximately 6.4\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ ${\mathrm{cm}}^{2}$/s for l-Si, in good agreement with previous calculations, and about 4.2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ and 4.6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}5}$ ${\mathrm{cm}}^{2}$/s for two models of l-Ge. In all cases, D(T) can be fitted to an activated temperature dependence, with activation energies ${\mathit{E}}_{\mathit{d}}$ of about 0.42 eV for l-Si, and 0.32 or 0.26 eV for two models of l-Ge, as calculated from either the Einstein relation or from a Green-Kubo-type integration of the velocity autocorrelation function. D(T) for Si impurities in l-Ge is found to be very similar to the self-diffusion coefficient of l-Ge. We briefly discuss possible reasons why the SW potentials give D(T)'s substantially lower than ab initio predictions. \textcopyright{} 1996 The American Physical Society.