Relaxation of the step profile for different microscopic mechanisms

Abstract

Theoretical and experimental studies of the rate of decay of metastable structures are compared quantitatively. The effect of decay mechanism, size, and periodicity of the structure on the rate of decay is evaluated within both a coarse-grained step-based model and a continuum model. For high-amplitude structures, the decay scales with size (N) and time as (t/Nα)−β. The exponents α and β depend on the mass transport mechanism. The size scaling is α=4 for locally conserved diffusive flux and α=2 for locally nonconserved flux. The time scaling exponent is β=1/5 for diffusive limited mass transport and β=1/4 for step attachment limited mass transport. Experiments were performed on metastable structures of controlled sizes 3–5 nm in height, prepared by direct current heating on Si(111). Quantitative agreement with theoretical predictions of both scaling (α=4.3±0.5, β=0.2−0.3) and absolute rate of decay were obtained.