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Stochastic Model for Nucleation on Crystalline Semiconductor Surfaces in Gas-Phase Epitaxy

We have derived an analytical expression for the rate of nucleation on the growing surface of crystalline semiconductors. The calculation is simplified by counting monomers adsorbed on a small block during a window period. The rate is the product of the probability that more than two monomers are adsorbed on the block, and the probability that these adatoms encounter on the surface. The nucleation rate is found to be strongly dependent on the flux of monomers, and even more strongly on the residence time, which is generally in agreement with experimental results.