Modeling of electron-electron scattering in Monte Carlo simulation of quantum cascade lasers

A theoretical model of electron-electron scattering in multisubband systems is proposed and used to set up a Monte Carlo simulator of quantum cascade lasers. Special features of the electron-electron scattering model are the following: (i) A fast and accurate computation of bare potential matrix elements by means of Fourier analysis is developed, (ii) A screening model is proposed that allows us to describe intersubband matrix elements, (iii) Nonequilibrium screening factors, denned through an effective subband temperature for each subband, are periodically reevaluated. (iv) The developed algorithm makes use of rejection procedures in order to determine the correct number of scattering events as well as the distribution of the final states. Other characteristics of the model are the following: the energy levels and the wave functions are determined in a self-consistent way, the Pauli exclusion principle is included, and the periodicity of the structure is accounted for. This model is applied to the study of a terahertz resonant phonon quantum cascade laser. A large influence of the screening model on the subband population is demonstrated. For the considered design, emission at a frequency as low as 1 THz is confirmed. We have found that the magnitude of population inversion phenomena may be strongly sensitive to electron-electron scattering, reducing the possible performance near 1 THz. © 2005 American Institute of Physics.