The kinetics of fast steps on crystal surfaces and its application to the molecular beam epitaxy of silicon

Crystal growth by molecular beam epitaxy (MBE) occurs under conditions of high supersaturation. The classic growth theory of Burton, Cabrera, and Frank (BCF) is based on the assumption that surface steps move slowly. Consequently, it requires modifications to be applicable to MBE because the velocities of surface steps may be large. In addition, because such steps are asymmetric structures, as observed experimentally by field ion microscopy, capture probabilities from above and from below a step must differ markedly. Hence the adatom concentration distribution cannot be at equilibrium at steps; there, it also suffers a discontinuity. We propose a model that treats surface step motion as a Stefan problem and that also respects its physical asymmetry. Calculations are presented which extend and complete recently published results that had imposed the restrictive condition of local equilibrium at steps. Step velocity is estimated as a function of supersaturation, degree of asymmetry, and step density. Concentration profiles are then computed; they are found to be generally skewed. In all cases, we show that the behavior of the growing crystal is convective rather than diffusive when the supersaturation is large. Consequently, we can understand the extraordinary insensitivity of the MBE of Si to changes in growth temperature and orientation.