The stability of rapidly growing or evaporating crystals

Abstract

Solutions for the growth rate of perturbations in the locations of moving steps on a growing or evaporating crystal are presented. They are obtained by solving an equation derived by R. Ghez, H. G. Cohen, and J. B. Keller [J. Appl. Phys. 73, 3685 (1993)] based upon the Burton–Cabrera–Frank theory of crystal growth. They agree with the results derived via the adiabatic approximation when the dimensionless growth rate is small, which shows that those results are correct. However, when the growth rate is large the present exact results differ from those of the adiabatic approximation, as might be expected.