Frequency- and Wave-Vector-Dependent Dielectric Function for Silicon

Abstract

The frequency- and wave-vector-dependent complex dielectric function $\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}},\ensuremath{\omega})$ is calculated for silicon. The energy eigenvalues and eigenvectors which are used have been obtained from energy-band calculations based on the empirical pseudopotential method. Explicit results are given in the [100] direction in the range $0\ensuremath{\le}q\ensuremath{\le}(\frac{2\ensuremath{\pi}}{a})$ and $0\ensuremath{\le}\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\le}24$ eV. A comparison is made between the present results and the results of a calculation of $\ensuremath{\epsilon}(q,\ensuremath{\omega})$ for a free-electron gas in the random-phase approximation.