Modelling Convection Driven Wet Chemical Etching Using a Total Concentration 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 concentration is used to predict the etchfront 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 are used to capture the complicated etchfront evolved during etching. The etching process is assumed two-dimensional. The model assumes an infinitely fast reaction at the interface and the flow is assumed incompressible of Newtonian fluid. For demonstration purposes, a finite-volume method is used to solve the resulting set of governing momentum equations, the continuity equation and the convection driven mass diffusion equation with prescribed initial and boundary conditions. The effect of flow parameters- the Reynolds number and the Peclet number on the etch profile growth is studied.