Laplacian growth models for porous silicon formation-stability analysis

We develop a Laplacian model of interface growth which includes basic features of the anodization of silicon in hydrofluoric acid. Our aim is to find mechanisms for the characteristic properties of porous silicon formation, such as the transition from electropolishing to pore formation and the typical pore distance. The local etching rate of the interface between the semiconductor and the electrolyte is determined by the local current density. We model the diffusive transport of charge carriers in the semiconductor and of reactants in the electrolyte including the basic features of the electrochemical reaction at the interface. A linear stability analysis of a flat and planar interface is performed in order to study the initial state of pore formation.