GENERALIZED MONTE-CARLO APPROACH FOR THE STUDY OF THE COHERENT ULTRAFAST CARRIER DYNAMICS IN PHOTOEXCITED SEMICONDUCTORS

A generalized Monte Carlo method for the solution of the coupled set o f kinetic equations for the distribution functions and the interband p olarization is presented. The aim of this method is to combine the adv antages of the description within a fully quantum mechanical picture w ith the power of the Monte Carlo technique for the treatment of stocha stic processes. It is based on a decomposition of the kinetic equation s in a coherent and an incoherent part. The former is integrated direc tly while the latter is sampled by means of a Monte Carlo simulation. This allows us to treat on the same kinetic level carrier thermalizati on and relaxation as well as dephasing processes. In particular, the p roblem of photogeneration and its theoretical description is discussed . The equations of motion including the relevant scattering contributi ons are derived and presented in a way that emphasizes the symmetry be tween distribution functions and polarization. The scattering terms fo r the polarization are discussed in detail. We show that some of the a pproaches commonly used fail in describing correctly the effect of car rier-carrier interaction in the low-density limit. By including terms that have the structure of ''in-scattering'' terms for the interband p olarization, the experimentally observed features in the carrier dynam ics are well described in the whole density range.