A lattice Monte Carlo model for nanostructure formation analysis

A kinetic lattice Monte Carlo model of semiconductor nanostructures formation with a diamond-like crystal lattice structure is proposed. Elementary events of the model are diffusion hops, adsorption, desorption, and chemical reactions. An event-scheduling algorithm to perform computations in real time for a wide temperature range is described. A modified event selection algorithm correctly takes into account rare events in simulation. Simulation results of high temperature annealing of GaAs(111)A substrates under Langmuir conditions are discussed. A good agreement between calculated and experimental values of congruent temperature and activation energies of gallium and arsenic evaporation confirms the model validity and the algorithm efficiency. The proposed model can be used to analyze the growth of filamentary silicon and gallium arsenide nanocrystals of diameter $3$–$50$ nm and the formation of silicon clusters of size $1$–$20$ nm in silicon dioxide.