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: ͑i͒ A fast and accurate computation of bare potential matrix elements by means of Fourier analysis is developed. ͑ii͒ A screening model is proposed that allows us to describe intersubband matrix elements. ͑iii͒ Nonequilibrium screening factors, defined through an effective subband temperature for each subband, are periodically reevaluated. ͑iv͒ 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.

Based on a three-level rate equations model, we analyze through numerical simulations the population and photon number dynamics present within the cavity of a midinfrared quantum cascade laser. We find in particular that the injection current influences significantly the electron number dynamics trajectory. In addition, the equations that allow for the determination of the turn-on delay ͑t th ͒ and buildup ͑⌬t͒ times are derived within the premises of our model in the most general case. The effects of the spontaneous emission factor ␤ on ⌬t are also explored.

Electron mobility and diffusion coefficients in monolayer silicene are calculated by Monte Carlo simulations using simplified band structure with linear energy bands. Results demonstrate reasonable agreement with the full-band Monte Carlo method in low applied electric field conditions. Negative differential resistivity is observed and an explanation of the origin of this effect is proposed. Electron mobility and diffusion coefficients are studied in low applied electric field conditions. We demonstrate that a comparison of these parameter values can provide a good check that the calculation is correct. Low-field mobility in silicene exhibits -T 3 temperature dependence for nondegenerate electron gas conditions and -T 1 for higher electron concentrations, when degenerate conditions are imposed. It is demonstrated that to explain the relation between mobility and temperature in nondegenerate electron gas the linearity of the band structure has to be taken into account. It is also found that electron-electron scattering only slightly modifies low-field electron mobility in degenerate electron gas conditions.