Si dielectric function in a local basis representation: Optical properties, local field effects, excitons, and stopping power

Abstract

An atomiclike basis representation is used to analyze the dielectric function $\ensuremath{\epsilon}(\stackrel{P\vec}{q}+\stackrel{P\vec}{G},\stackrel{P\vec}{q}+{\stackrel{P\vec}{G}}^{\ensuremath{'}};\ensuremath{\omega})$ of Si. First, we show that a $s{p}^{3}{d}^{5}$ local basis set yields good results for the electronic band structure of this crystal and, then, we analyze the Si optical properties including local field and excitonic effects. In our formulation, we follow Hanke and Sham [W. Hanke and L. J. Sham, Phys. Rev. B 12, 4501 (1975); Phys. Rev. B 21, 4656 (1980)], and introduce excitonic effects using a many-body formulation that incorporates a static screened electron-hole interaction. Dynamical effects in this interaction are also analyzed and shown to introduce non-negligible corrections in the optical spectrum. Our results are found in reasonable agreement with the experimental evidence and with other theoretical results calculated with the computationally more demanding plane-wave representation. Finally, calculations for the stopping power of Si are also presented.