QUASI-PARTICLE CALCULATION OF THE DIELECTRIC RESPONSE OF SILICON AND GERMANIUM

We calculate the dielectric function epsilon-1(omega) of silicon and germanium for frequencies below the direct band gap at the experimental lattice constant as well as the pressure dependence of the static dielectric constant epsilon-1(P). Our theory is an extension of the local-density approximation (LDA). We include self-energy effects by adding an operator to the usual LDA Hamiltonian; i.e., H(k) = H(k)(LDA) + DELTA(k)P(ck). This form leads to a Ward-identity replacement p --> (epsilon-nk - H(k)(LDA))-1(epsilon-nk - H(k))p. Our theory is in agreement with experiment for epsilon-1(omega) at the level of a few percent. For epsilon-1(P), we are in agreement with experiments for silicon and some of the conflicting experiments for germanium. A prediction is made for the pressure dependence of the dielectric function of silicon beyond the linear regime.