Instability of vicinal crystal surfaces with transparent steps: Transient kinetics and non-local electromigration

The steps at the crystal surfaces could be partially transparent in the sense that the migrating adatoms can cross the steps without visiting a kink position. In the case of significant transparency the velocity of a given step in a given moment is affected by atomic processes which took place at rather distant terraces in rather earlier moments. The reason is that an adatom needs time to cross many terraces before attaching to a kink position. That is why the theory of crystallization with non-local kinetics should account for the time dependence of the adatom concentrations on the terraces. Such a transient growth model (going beyond the quasi-static approximation of the BCF theory of crystal growth) is developed here for the limit of slow kinetics at the steps and fast surface diffusion. This model predicts instability of the vicinal surface (in agreement with the earlier studies) but rather different expression for the wavelength of the most unstable mode, which depends only on the ratio between the step transparency and the step kinetic coefficients.