Dissipative electron-phonon system photoexcited far from equilibrium

We derive the steady-state electron distribution function for a semiconductor driven far from equilibrium by the inter-band photoexcitation assumed homogeneous over the nanoscale sample. Our analytical treatment is based on the generalization of a stochastic model known for a driven dissipative granular gas. The generalization is physically realizable in a semiconducting sample where electrons are injected into the conduction band by photoexcitation, and removed through the electron-hole recombination process at the bottom of the conduction band. Here the kinetics of the electron-electron and the electron-phonon (bath) scattering processes, as also the partitioning of the total energy in the inelastic collisions, are duly parametrized by certain rate constants. Our analytical results give the steady-state-energy distribution of the classical (non-degenerate) electron gas as function of the phonon (bath) temperature and the rates of injection (cw pump) and depletion (recombination). Interestingly, we obtain an accumulation of the electrons at the bottom of the conduction band in the form of a delta-function peak $-$ a non-equilibrium classical analogue of condensation. Our model is specially appropriate to a disordered, indirect band-gap, polar semiconducting sample where energy is the only state label, and the electron-phonon coupling is strong while the recombination rate is slow. A possible mechanism for the dissipative inelastic collisions between the electrons is also suggested.