Narrowing of terrace-width distributions during growth on vicinal surfaces

We present analytic and numerical results for the steady-state, non-equilibrium terrace-width distribution (TWD) of steps during growth on vicinal surfaces. Kinetic Monte Carlo shows that the TWD narrows progressively with increasing flux until the model breaks down. The narrowing corresponds to kinetic repulsion between moving steps, due to the intrinsic asymmetry of the adatom diffusion current on a growing surface. With a 1-dimensional (1D) model, from a Burton-Cabrera-Frank approach, we make contact with previous work, in which the attachment asymmetry can also be due to electromigration or to asymmetry in attachment rates; we deduce an expression for the narrowing via a Fokker-Planck analysis. We illustrate how Ehrlich-Schwoebel barriers (although inducing an instability in 2D) also lead to such asymmetry and narrowing.