Modeling growth from the vapor and thermal annealing on micro- and nanopatterned substrates

We propose a -dimensional mesoscopic model to describe the most relevant physical processes that take place while depositing and/or annealing micro- and nanopatterned solid substrates. The model assumes that a collimated incident beam impinges over the growing substrate; scattering effects in the vapor and reemission processes are introduced in a phenomenological way as an isotropic flow. Surface diffusion is included as the main relaxation process at the micro- or nanoscale. The stochastic model is built following population dynamics considerations; both stochastic simulations and the deterministic limit are analyzed. Numerical aspects regarding its implementation are also discussed. We study the shape-preserving growth mode, the coupling between shadowing effects and random fluctuations, and the spatial structure of noises using numerical simulations. We report important deviations from linear theories of surface diffusion when the interfaces are not compatible with the small slope approximation, including spontaneous formation of overhangs and nonexponential decay of pattern amplitudes. We discuss the dependence of stationary states with respect to the boundary conditions imposed on the system.