Abstract
AbstractA mathematical model for the crystal growth over nonplanar substrates by metalorganic molecular beam epitaxy (MOMBE) is proposed. The substrate consists of crystal facets of various orientation, and of masks where no growth takes place. Surface diffusion, adsorption and desorption of atoms are taken into account. The surface diffusion processes between simultaneously growing facets are a function of the step density, which is preset by the substrate orientation. A nonlinear partial differential equation of first order in time and of fourth order in space is derived to describe the evolution of the crystal surface. Numerical simulations are presented which are in good agreement with measurements of InP crystals grown by MOMBE. In particular, experimentally observed small surface corrugations near facet edges can be explained by our model.
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