A stochastic model of nanowire growth by molecular beam epitaxy

In this paper, a stochastic model of nanowire growth by molecular beam epitaxy based on probability mechanisms of surface diffusion, mutual shading, rescattering of adatoms, and survival probability is proposed. A direct simulation algorithm based on this model is constructed. A comprehensive study of kinetics of the growth of a family of nanowires initially distributed at a height from about tens of nanometers to about several thousand nanometers is carried out. The time range corresponds to an experimental growth of nanowires of up to 3–4 hours. The following statement is formulated and confirmed numerically: under certain conditions, which can be implemented in real experiments, the height distribution of nanowires narrows with time, that is, in the ensemble of nanowires their heights become aligned with time. For this, the initial radii distribution of the nanowires must be narrow and the density of the nanowires on the substrate must not be very high.