Numerical simulation of porous silicon morphology using a monotone iterative method

In this work, a convergent monotone iterative system based on finite difference approximations is proposed to solve numerically a novel porous silicon formation model. This model includes chemical, physical and electrical processes involved in the porous growth and is formulated as a weakly coupled parabolic partial differential system. Important properties like nonnegativity, boundedness, stability and convergence of the numerical solution are demonstrated by means of the upper and lower solutions technique. The computational porous silicon formation model is validated by experimental evidence. Numerical simulations of the porous silicon morphology in two dimensions are shown along with the effects of parameters variation.