Kinetics of step bunching during growth: a minimal model.

We study a minimal stochastic model of step bunching during growth on a one-dimensional vicinal surface. The formation of bunches is controlled by the preferential attachment of atoms to descending steps (inverse Ehrlich-Schwoebel effect) and the ratio d of the attachment rate to the terrace diffusion coefficient. For generic parameters (d>0) the model exhibits a very slow crossover to a nontrivial asymptotic coarsening exponent beta approximately 0.38 . In the limit of infinitely fast terrace diffusion (d=0) linear coarsening (beta=1) is observed instead. The different coarsening behaviors are related to the fact that bunches attain a finite speed in the limit of large size when d=0 , whereas the speed vanishes with increasing size when d>0 . For d=0 an analytic description of the speed and profile of stationary bunches is developed, and a connection to the problem of front propagation into an unstable state is pointed out.