Numerical simulations in the theory of crystal growth

The methodology of computer simulations of crystal growth is described. Two main methods, kinetic Monte Carlo and molecular dynamics, are discussed. The principle of kinetic Monte Carlo simulations is explained in detail, including recent developments of algorithms. Particular attention is paid to approximations which are made in the construction of discrete growth models. Applications of the Monte Carlo method for three different kind of problems: kinetic roughening, near equilibrium growth, and far-from-equilibrium molecular beam epitaxy growth are presented together with examples of representative results. Possibilities of employing molecular dynamics simulations are discussed as well, and examples of results are also given. The range of applicability of different methods on present-day computers is evaluated.

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