Crystal symmetry, step-edge diffusion, and unstable growth

We study the effect of crystal symmetry and step-edge diffusion on the surface current governing the evolution of a growing crystal surface. We find there are two possible contributions to anisotropic currents, which both lead to the destabilization of the flat surface: terrace current jt, which is parallel to the slope m=∇z(x, t), and step current js, which has components parallel (j‖s) and perpendicular (j⊥s) to the slope. On a high-symmetry surface, terrace and step currents are generically singular at zero slope, and this does not allow one to perform the standard linear stability analysis. As far as a one-dimensional profile is considered, j⊥s is irrelevant and j‖s suggests that mound sides align along [110] and [11̄0] axes. On a vicinal surface, js destabilizes against step bunching; its effect against step meandering depends on the step orientation, in agreement with the recent findings by Pierre-Louis et al. [Phys. Rev. Lett. 82 (1999) 3661].