Line shapes for electron-hole plasmas in semiconductors. I. The heavy-hole to spin-orbit split-band transitions in electron-hole droplets in Ge

Abstract

We report details of a new theory for the luminescence and absorption line shapes of electron-hole plasmas in semiconductors. The theory includes the physical processes which lead to the creation of single-plasmon or particle-hole pairs. It is the extension to line-shape problems of the random-phase approximation which has been successful for the thermodynamic properties of electron-hole liquids. Extensive calculations are presented and compared to experiments on the cross section for absorption due to heavy-hole to spin-orbit split-band transitions in electron-hole droplets in Ge. Good agreement with the observed broad line shape is obtained when details of the valence-band structure of Ge are included. In an appendix, we present an analysis of the dielectric function in the spherical model for the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$ valence-band Hamiltonian of diamond and zinc-blende semiconductors for finite spin-orbit splitting.