Stochastic model and simulation of GaN nanowires formation characterized by long incubation time followed by burst nucleation and growth

Abstract

A combined kinetic Monte Carlo algorithm and continuous thermodynamically based model for simulation of heterogeneous nucleation of GaN islands on a substrate under burst regime when a long incubation time is followed by a rapid nucleation of stable nuclei is developed. In this model the kinetics of GaN islands nucleation on a substrate during their aggregation and disaggregation is simulated directly by the Monte Carlo method while the size of stable nuclei is taken from the thermodynamic theory of nucleation with varying supersaturation under metastable conditions. Simulations are carried out in conditions close to the experimental data on the GaN nanowires growth. Both the height and radius distributions of nanowires are extracted from the simulations which start from the very beginning of the incident Ga and N atoms on a substrate and finish with a stable distribution of nanowires whose radii ri stopped to grow and the heights become 2–4 times larger than their radii. In contrast to standard Becker–Döring nucleation theory, where the following general behavior is known: the longer the incubation time the slower the nucleation rate, a combined hybrid Monte Carlo and metastable thermodynamic model suggested is able to predict a long incubation time followed by relatively rapid nucleation regime. A series of numerical simulations presented supports this conclusion.