Ab initio study of the high-pressure phase transition from the cubic-diamond to the β-tin structure of Si

We have studied the high-pressure phase transition from the cubic-diamond (cd) to the β-tin structure of silicon. This work has been performed using the plane-wave pseudopotential approach to density-functional theory (DFT) and density-functional perturbation theory (DFPT) within the local-density approximation (LDA). We present results on the pressure dependence of ground-state properties, such as lattice-parameters, and electronic band structure. Furthermore, the pressure dependence of the phonon-dispersion curves is shown. The calculated transition pressure and volumes are in good agreement with experimental values. In particular, our results show no softening of phonon modes near transition. Finally, our calculation of pressure-dependent phonon-dispersion curves allows the calculation of the pressure vs. temperature phase diagram within the quasi-harmonic approximation.