Dynamics of exciton formation for near band-gap excitations

We present a microscopic density matrix description of the formation of excitons after optical excitation of a semiconductor. Three types of dynamical processes taking place after the optical excitation are analyzed: (a) decoherence, (b) incoherent redistributions of occupations among excitonic states or among unbound electron-hole pairs, and (c) formation of excitons. The competition of different scattering mechanisms under varying excitation energies in the vicinity of the band gap is studied for a two band GaAs quantum-wire model. The respective influences of piezoelectric and deformation potential coupling to acoustic phonons, Fröhlich coupling to optical phonons, interface roughness, and radiative decay are compared. A comprehensive picture of the formation process is obtained by following the time evolution of the $1s$ exciton population in dependence of the center of mass momentum. For the times studied here (up to 50 ps) we find no significant impact of radiative decay. All other scattering mechanisms have noticeable influences on the dynamics. Piezoelectric coupling is particularly important for the decoherence above the band gap, while emission of longitudinal optical phonons turns out to be the most efficient process for exciton formation as soon as it is energetically allowed. Exciting at the threshold for the emission of longitudinal optical phonons we find an exciton formation time of $\approx 4\hspace{0.5em}\mathrm{ps}$ at a temperture of 80 K, which increases dramatically when the excitation energy is lowered towards the band edge. The relative importance of the competing mechanisms varies significantly for the different aspects of the dynamics (decoherence, redistribution, formation) and it also depends crucially on the excitation energy. The effects of the different scattering mechanisms are in general not additive.