Understanding the hillock-and-valley pattern formation after etching in steady state

We derived a simple mean field model that accounts for the formation of hillock-and-valley patterns after etching in steady state. The mechanisms and their interrelations that lead to these patterns experimentally observed are described. Hillocks and valleys present characteristic size distributions that are governed by the relative etching rates of particles in different sites. In particular, we focus on how etching processes determine the surface morphology and the resulting hillock size distribution. The dependence of these mechanisms on the model parameters is specifically addressed. Monte Carlo simulations were carried out in one dimension using a restricted-solid-on-solid model with nearest neighbor interactions. The outcomes of the mean field model and Monte Carlo simulations are compared.