Monte Carlo simulation and analysis of two-dimensional carrier motion in an external field

The motion of carriers in an external field is modelled by Monte Carlo simulation in two-dimensional continuous space. The mean square displacement R2 of carriers as functions of the relative field strength λ and time t is carried out by theoretical calculation and numerical simulation. It is shown that the motion of carriers is a combination of diffusion and drift in a determinate proportion. As time t increases, there exists a crossover from dominant diffusion to dominant drift. The crossover time tc, diffusion coefficient D and drift velocity v as a function of the relative field strength λ are obtained by analysis and simulation. The drift velocity can be quantitatively compared with experimental data. The motion of electrons in semiconductors and magnetron sputter ion deposition plasma provides perfect experimental support to this model.