First-principle calculation of the recombination cross-section assisted by acoustic phonons at shallow impurities in semiconductors

An original Monte Carlo study of the equilibrium microscopic and macroscopic recombination cross-sections at shallow impurity centres is presented. Both cross-sections are investigated in lightly doped p-Si as functions of the temperature and ionized acceptor concentration. In order to treat generation-recombination processes we extend the semi-classical Boltzmann equation through a simulation of the carrier motion in the energy-configuration space of an impurity centre. The analysis of the scattering rates as a function of the total carrier energy enables a microscopic interpretation of the capture process to be carried out. The role of excited levels is naturally included and found to be of main importance at increasing lattice temperatures. Numerical results are then compared with available experiments and existing analytical calculations.