A Fixed Grid Numerical Methodology for Modeling Wet Chemical Etching

Abstract

A new mathematical model based on the total concentration approach is proposed for modeling wet chemical etching process. The proposed mathematical model is a fixed domain formulation of the etching problem. The governing equation based on the total concentration includes the interface condition too. The total concentration of etchant includes the reacted and the unreacted concentration of etchant. The unreacted etchant concentration is solved in both the etchant solution and the substrate (with zero unreacted etchant concentration). The reacted concentration of etchant is used to capture the etchfront during the progress of etching with time. Unlike the moving grid method, the etchfront is found implicitly with the total concentration method. Finite volume method is used to solve for the transient concentration distribution of etchant. The proposed method is applied from etching simple to complex geometries partially covered with mask. Results from the proposed approach are compared with the existing analytical and numerical solutions.