ABSTRACT
Sampling the particle motion at various times throughout the simulation allows for the statistical estimation of physically interesting quantities, such as single particle distribution function, the average drift velocity in the presence of an applied electric field, the average energy of the particles. The particle-based picture, in which the particle motion is decomposed into free flights terminated by instantaneous collisions, is basically the same picture underlying the derivation of the semiclassical Boltzmann transport equation. In the Monte Carlo method, the dynamics of particle motion is assumed to consist of free flights terminated by instantaneous scattering events, which change the momentum and energy of the particle. The nonstationary one-particle distribution function and related quantities such as drift velocity, valley, or subband population, are then taken as averages over the ensemble at fixed time-steps throughout the simulation. Free carriers interact with the crystal and with each other through a variety of scattering processes that relax the energy and momentum of the particle.
