A new method for associating discrete surface growth models with stochastic evolution equations

MARCOS F. CASTEZ; ROBERTO C. SALVAREZZA; HERNÁN G. SOLARI

La Pedrera, Rocha, Uruguay

Otro; International School on Crystal Growth, Characterization and Applications; 2003

International Union of Crystallography

The increased technological requirements of hight quality solid films (atomically smooth), in particular in rapidly developing field of nanotechnology, has stimulated the interest in the understanding of the physical processes that determine interface dynamics and surface morphology. This has renewed the interest in earlier models of surface growth, and has motivated the developing of new ones for more complex situations (substrate nanotrenches, nanocavities). While kinetic (atomistic) models and continuum theories are two different approaches for surface growth study, but to find a connection between both remains an open problem. In this work we propose a new general method to connect discrete growth models with discrete stochastic evolution equations, for means of a regularization procedure. Contrary to earlier attempts in this sense, our treatment no requires a formulation in terms of a Master equation followed for a Kramers-Moyal expansion, since the nonlinear Langevin equation is obtained directly from the microscopic rules defining the model. The method is applied to the well known Family model, for which the corresponding evolution equation is obtained and their continuous limit is analyzed.