Stability of crystals that grow or evaporate by step propagation

Abstract

We analyze the linear stability of a Stefan-like problem for moving steps in the context of W. K. Burton, N. Cabrera, and F. C. Frank’s theory of crystal growth [Philos. Trans. R. Soc. (London) A 243, 299 (1951)]. Asymmetry and departures from equilibrium at steps are included. The stability criterion depends on supersaturation and average step spacing, both experimentally accessible, and on dimensionless combinations of surface diffusivity, surface diffusion length, and adatom capture probabilities at steps, which can be estimated from bond models. This stability criterion is analyzed and presented graphically in terms of these physical parameters.