Breakdown of metastable step-flow growth on vicinal surfaces induced by nucleation

Abstract

We consider the growth of a vicinal crystal surface in the presence of a step-edge barrier. For any value of the barrier strength, measured by the length ${\ensuremath{\ell}}_{\mathrm{ES}}$, nucleation of islands on terraces is always able to destroy asymptotically step-flow growth. The breakdown of the metastable step-flow occurs through the formation of a mound of critical width proportional to ${L}_{c}\ensuremath{\sim}1∕\sqrt{{\ensuremath{\ell}}_{\mathrm{ES}}}$, the length associated to the linear instability of a high-symmetry surface. The time required for the destabilization grows exponentially with ${L}_{c}$. Thermal detachment from steps or islands, or a steeper slope increase the instability time but do not modify the above picture, nor change ${L}_{c}$ significantly. Standard continuum theories cannot be used to evaluate the activation energy of the critical mound and the instability time. The dynamics of a mound can be described as a one dimensional random walk for its height $k$; attaining the critical height (i.e., the critical size) means that the probability to grow $(k\ensuremath{\rightarrow}k+1)$ becomes larger than the probability for the mound to shrink $(k\ensuremath{\rightarrow}k\ensuremath{-}1)$. Thermal detachment induces correlations in the random walk, otherwise absent.