The growth of semiconductor crystals by molecular beam epitaxy often involves the motion of distinct steps, which are the boundaries of incomplete atomic layers. We review some of the crystal growth mechanisms based on step generation and motion. Ising models have been widely used to study equilibrium faceting and crystal growth. We discuss more general models of steps which are based on molecular dynamics calculations of atomic motion and empirical interatomic potentials. These models include the possibility of surface and step reconstructions, and here we discuss their influence on the step energy and motion. We find that certain types of steps have a structure with drastically reduced energy compared to unreconstructed steps. We have also examined the effect of stress resulting from misfit in epitaxial systems. We find that 1% misfit can completely change the nature of a step, since its excess energy may change sign from negative to positive, or vice versa. Simulations of molecular beam epitaxy give direct information on the conditions under which step growth mechanisms play a role.
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