Dielectric-matrix calculation of the volume-plasmon dispersion relation for silicon.

Abstract

Plasmon-band splitting in silicon has been the subject of theoretical interest recently, since reports of its experimental observation using coherent inelastic x-ray scattering. The theoretical plasmon-dispersion relation can be obtained from dielectric-response theory and knowledge of the electronic structure of the solid. In this work the frequency- and wave-vector-dependent dielectric matrix (DM) has been calculated in the random-phase approximation, with a nonlocal empirical pseudopotential (EPM) electronic band structure. We present results for the volume-plasmon dispersion relation along high-symmetry directions in the first Brillouin zone. Contrary to previous local EPM-based DM calculations, this nonlocal EPM band structure results in excellent agreement with the experimental plasmon-dispersion anisotropy. In addition, these dispersion results are in better agreement with experiment than previous local-density-approximation calculations. Evidence for a weak \ensuremath{\approxeq}2-eV band gap is found at the L point. Unlike previous calculations, the presence of two plasmon resonances is directly observable from the calculated loss function in the \ensuremath{\Lambda} direction. \textcopyright{} 1996 The American Physical Society.