A Total Concentration Fixed-Grid Method for Two-Dimensional Diffusion-Controlled Wet Chemical Etching

Abstract

This article presents a total concentration method for two-dimensional wet chemical etching. The proposed procedure is a fixed-grid approach. It is analogous to the enthalpy method used for modeling melting/solidification problems. The governing equation is formulated using the total concentration of the etchant. It includes the reacted and the unreacted concentrations of the etchant. The proposed governing equation includes the interface condition. The reacted concentration is used to capture the etchant-substrate interface implicitly. Since the grids are fixed, a diffusion problem remains a diffusion problem unlike the moving grid approach where the diffusion problem becomes the convection-diffusion problem due to the mesh velocity. For demonstration purposes, the finite volume method is used to solve for the transient concentration distribution of etchant. In this article, two-dimensional diffusion-controlled wet chemical etching processes are modeled. The results obtained from the proposed total concentration method are compared with available “analytic” solutions and solutions from moving-grid approach.