Instabilities of steps induced by the drift of adatoms and effect of the step permeability

We theoretically study step wandering and step bunching induced by the drift of adatoms with attention to the permeability of steps. The critical drift velocity to induce the instability is calculated, and Monte Carlo simulation is performed to test the linear analysis. In sublimation, when the step distance is small in comparison with the surface diffusion length, the wandering and bunching of steps can occur simultaneously with the step-down drift if steps are impermeable. The instabilities do not occur simultaneously if steps are permeable: the bunching occurs with the step-up drift, and the wandering with the step-down drift. In growth, when the step distance is small, the bunching occurs with the step-down drift and the step wandering occurs with the step-up drift irrespective of the permeability, in agreement with Metois and Stoyanov [Surf. Sci. 440, 407 (1999)]. The change of the permeability with increasing temperature can explain the instabilities observed in Si(111) vicinal face [M. Degawa et al., Jpn. J. Appl. Phys 38, L308 (1999)].