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

TL;DR

This paper analyzes how nucleation causes the breakdown of metastable step-flow growth on vicinal surfaces, revealing a critical mound formation process with exponential destabilization times unaffected by thermal detachment or slope changes.

Contribution

It introduces a detailed mechanism for the destabilization of step-flow growth via mound formation and highlights limitations of continuum theories in evaluating critical activation energies.

Findings

Nucleation always destroys step-flow growth asymptotically.

Critical mound width scales as 1/sqrt(l_es).

Destabilization time grows exponentially with critical mound size.

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 l_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=1/sqrt(l_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->k+1) becomes larger than the probability for the mound to shrink (k->k-1). Thermal detachment induces correlations in the random walk, otherwise absent.