Geodesic
A stochastic model of the nanowires growth by molecular beam epitaxy
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 2, pp. 181-199

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In this paper a stochastic model of the nanowire growth by molecular beam epitaxy based on probability mechanisms of surface diffusion, mutual shading, adatoms rescattering and survival probability is proposed. A direct simulation algorithm based on this model is implemented, and a comprehensive study of the growth kinetics of a family of nanowires initially distributed at a height of about tens of nanometers to heights of about several thousands of nanometers is carried out. The time range corresponds to growing nanowires experimentally for up to 3–4 hours. In this paper we formulate a statement, which is numerically confirmed: under certain conditions, which can be implemented in real experiments, the nanowires height distribution becomes narrower with time, i.e. in the nanowires ensemble their heights are aligned in the course of time. For this to happen, it is necessary that the initial radius distribution of nanowires be narrow and the density of the nanowires on a substrate be not very high. 
@article{SJVM_2017_20_2_a5,
     author = {K. K. Sabelfeld and E. G. Kablukova},
     title = {A stochastic model of the nanowires growth by molecular beam epitaxy},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {181--199},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2017_20_2_a5/}
}
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K. K. Sabelfeld; E. G. Kablukova. A stochastic model of the nanowires growth by molecular beam epitaxy. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 2, pp. 181-199. http://geodesic.mathdoc.fr/item/SJVM_2017_20_2_a5/