Metastability of Step Flow Growth in 1+1 Dimensions

(Received 3 April 1995, received in final form 10 April 1995, accepted 19 April 1995)

Abstract
We introduce a "minimal" model of crystal growth in 1+1 dimensions, which includes random deposition, surface diffusion of singly bonded adatoms, and perfect step edge barriers to completely suppress interlayer transport. We show that the stable step flow regime predicted by Burton-Cabrera-Frank theories is destabilized by island formation. The transition to an asymptotic Poisson-like growth mode, in which the surface width grows indefinitely as the square root of the number of layers, occurs after a transition time , where is the step spacing of the vicinal surface, D is the surface diffusion constant and F is the deposition rate. The Poisson regime is preceded by an intermediate scaling regime in which the surface width grows linearly with the number of layers, as has been reported in recent experiments. The relation to the Cahn-Hilliard theory for thermodynamically metastable states is outlined. Stable step flow is possible in the limit . This case is solved exactly, and the terrace lengths are shown to have a Poisson distribution.