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

The frequency- and wave-vector-dependent complex dielectric function ε(→q,ω) 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≤q≤(2πa) and 0≤ω≤24 eV. A comparison is made between the present results and the results of a calculation of ε(q,ω) for a free-electron gas in the random-phase approximation.