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

The frequency- and wave-vector-dependent complex dielectric function $\epsilon (\overrightarrow{\mathrm{q}},\omega )$ 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 $0\le q\le \left(\frac{2\pi }{a}\right)$ and $0\le \hslash \omega \le 24$ eV. A comparison is made between the present results and the results of a calculation of $\epsilon (q,\omega )$ for a free-electron gas in the random-phase approximation.