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

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 lES, 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 Lc?1??lES, the length associated to the linear instability of a high-symmetry surface. The time required for the destabilization grows exponentially with Lc. Thermal detachment from steps or islands, or a steeper slope increase the instability time but do not modify the above picture, nor change Lc 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.