The optical dielectric function: Excitonic effects at E0 critical point

In this work we propose an analytical expression for the complex dielectric function which includes both discrete and continuum exciton effects. The proposed analytical model takes into account accurately the excitonic effects, while it satisfies the requirements that the imaginary part of the dielectric function is an odd function of energy, and the real part of the dielectric function is an even function. We show that accurate introduction of broadening leads to equations for the dielectric function containing only elementary functions, with terms dependent on the exciton order m describing discrete exciton states. The proposed model describes well the experimental data for the absorption edge of GaN.