Elastic constants of silicon using Monte Carlo simulations

Abstract

Elastic constants of a bulk silicon crystal are calculated using the Monte Carlo (MC) technique in conjunction with an isoenthalpic-isotension-isobaric ensemble (HtN ensemble) and the Stillinger-Weber (SW) potential or one of the Tersoff potentials. This MC method is the counterpart of the Parrinello-Rahman HtN molecular dynamics. We present HtN MC calculations of the adiabatic elastic constants of a crystalline silicon at three different temperatures, using an HtN ensemble fluctuation formula, and compare with the corresponding results from EhN ensemble molecular dynamics (MD) simulation. Calculation of the elastic constants of SW silicon using HtN MC simulation is a superior technique when compared to a corresponding HtN MD simulation that failed to produce accurate results. The calculation of the elastic constants using the HtN ensemble is, in general, slower in convergence than the corresponding calculation using the EhN ensemble. It is still a useful technique for the calculation of elastic constants, because it does not require any knowledge of the derivatives of the potential, which could be nontrivial for potentials with terms beyond two body. In order to investigate the convergence of another potential, elastic constants of the latest silicon Tersoff potential were calculated at a nonzero temperature. The zero-temperature elastic constants of Si SW and Si Tersoff potentials were also calculated using a direct method and extrapolation of HtN MC results to zero temperature.