COMPETITION BETWEEN NOISE AND DETERMINISM IN STEP FLOW GROWTH

The continuum equations of Burton, Cabrera, and Frank are extended to include thermal fluctuations and used to derive a nonlinear stochastic equation describing the meandering of an isolated step on a crystal f ace grown from a vapor. Meandering is found to result from a unique co mpetition between thermal noise, which dominates close to equilibrium, and deterministic noise (spatiotemporal . chaos), which becomes incre asingly dominant beyond the morphological instability point. Numerical and analytical results characterizing the step roughness as a functio n of the supersaturation and the noise strength, k(B)T/gammax(s), are presented.