Cascade capture of charge carriers in highly doped semiconductors

We analyze the cascade capture of charge carriers due to the interaction with acoustic phonons in highly doped semiconductors using a model that describes the recombination of photo-ionized carriers as a continuous relaxation of carriers in the energy space at both positive and negative energies in the field of a set of impurity ions. Such description enables simultaneous calculation of non-equilibrium carrier distribution formed by interaction with acoustic phonons in the presence of impurity traps, and the time of recombination in a wide range of concentrations of capture centers and phonon temperatures. Additionally, we calculated the time of cascade recombination in the presence of fast scattering processes forming a Maxwellian distribution of free carriers. We show that experimentally observed concentration and temperature dependence of carrier life times in highly doped semiconductors can be described within the model of the cascade capture to uniformly spaced capture centers, and the main factor that determines the regime of cascade capture is the ratio of the thermal energy and the energy of the overlap of impurity potentials