Out-of-Equilibrium Step Meandering on a Vicinal Surface

A theory of step meandering on a vicinal surface is developed. At equilibrium, the meander $w\sim \left[\ln \right(L){]}^{1/2}$, where $L$ is the lateral extent. During step flow growth, the diffusive repulsion prevails over elasticity. It leads to new scaling laws for the meander $w$ as a function of the interstep distance $l$, etc. For a weak Schwoebel effect, we find $w\sim l^{1/4}$ (at equilibrium $w\sim l$). The diffusive repulsion behaves as $l\ln l$. Dynamics tend to “cure” meandering. At higher growth speed, deterministic roughening intervenes. In this regime we derive general nonlinear equations for interacting “lines.” Disordered structures seem to prevail.