Continuum nonlinear surface evolution equation for conserved step-bunching dynamics

A continuum version of surface evolution due to step bunching is derived from the basic Burton-Cabrera-Frank model in the limit when the desorption length is large. We obtain a new equation that, in contrast to Benney equation which is valid in the opposite limit, reveals coarsening. This study solves the dilemma of coarsening, and offers a consistent picture with experimental observations on Si(111) where desorption length is large. We find that the typical length scale increases with time like ${t}^{1/2}$ as observed experimentally. The evolution equation obtained here is generic in the sense that any other system enjoying the same symmetries and obeying the same conservation law should fall in the same class.