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 of kinetic equations for the distribution functions and the interband polarization is presented. The aim of this method is to combine the advantages of the description within a fully quantum mechanical picture with the power of the Monte Carlo technique for the treatment of stochastic processes. It is based on a decomposition of the kinetic equations in a coherent and an incoherent part. The former is integrated directly while the latter is sampled by means of a Monte Carlo simulation. This allows us to treat on the same kinetic level carrier thermalization and relaxation as well as dephasing processes. In particular, the problem of photogeneration and its theoretical description is discussed. The equations of motion including the relevant scattering contributions are derived and presented in a way that emphasizes the symmetry between distribution functions and polarization. The scattering terms for the polarization are discussed in detail. We show that some of the approaches commonly used fail in describing correctly the effect of carrier-carrier interaction in the low-density limit. By including terms that have the structure of ‘‘in-scattering’’ terms for the interband polarization, the experimentally observed features in the carrier dynamics are well described in the whole density range.