Recent development in the study of statistical mechanics of steps and related crystal growth theories are reviewed. Topics include morphology and fluctuations of steps in equilibrium and in growth, instabilities in surface diffusion fields, and relation between growth mechanisms and growth laws.
By a random walk method with imaginary weight, step tension and equilibrium crystal shape (ECS) are calculated for stoichiometrically binary systems with hexagonal ZnS-type crystal structure. A pencil-like three-dimensional ECS is obtained. The habit change of the ECS with temperature and partial vapor pressure is studied.
The relaxation process of the crystal shape near the facet is studied by means of a time-dependent Ginzburg-Landau equation. During the relaxation process, the surface gradient p behaves as p〜(⊿x)^<l/2> (⊿x: distance from the facet edge) off the facet edge and p〜⊿x quite near the facet edge. This result gives a possible explanation for the discrepancy between theory and experiment on the facet edge critical behavior.
The growth kinetics by molecular-beam epitaxy (MBE) is studied on the stepped surface by means of a kinetic equation describing the deposition and diffusion of atoms on the basis of the SOS (solid-on-solid) model. The kinetic equation is derived by using site-dependent point approximation of the path probability method. It is shown that the growth mode changes from the layer-by-layer mode on the terraces to the step propagation mode as the temperature is increased. The results agree qualitatively well with reflection high-energy electron diffraction (RHEED) measurements on GaAs (001) with miscut angle.