title: Kinetics of step bunching during growth: a minimal model.
abstract: 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.
authors.affiliation: Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic. slanina@fzu.cz
authors.forename: Frantisek
authors.initials: F
authors.lastname: Slanina
authors.forename: Joachim
authors.initials: J
authors.lastname: Krug
authors.forename: Miroslav
authors.initials: M
authors.lastname: Kotrla