Modeling Convection-Driven Diffusion-Controlled Wet Chemical Etching Using a Total-Concentration Fixed-Grid Method

Abstract

A total-concentration fixed-grid method is presented to model the convection-driven wet chemical etching process. The proposed method is analogous to the enthalpy method used in the modeling of melting and solidification problems. A total concentration which is the sum of the unreacted etchant concentration and the reacted etchant concentration is defined. The governing equation based on the newly defined total concentration includes the interface condition. Hence the etchfront position can be found implicitly using the proposed method. The reacted etchant concentration is used to predict the etch front position while etching progresses. Since the grid size is fixed, there is no grid velocity, unlike the case with existing moving-grid approaches. Cartesian grids can be used to capture the complicated etch front evolved during etching. In this article, a two-dimensional, incompressible, Newtonian fluid with an infinitely fast reaction at the interface is considered. For demonstration purposes, a finite-volume method is used to solve the momentum equations, the continuity equation, and the convection-driven mass diffusion equation with prescribed initial and boundary conditions. The etch front evolution obtained using the proposed method is compared with the existing moving-grid method, and good agreement is found.