A Fixed-Grid Method for Chemical Etching

Abstract

This paper presents a fixed-grid method for simulating chemical etching. This method is analogous to the enthalpy method used in the modeling of melting/solidification process. The total concentration of the etchant consists of two components: the unreacted etchant concentration and the reacted etchant concentration. The unreacted etchant concentration is solved in both the solution and the substrate (with zero unreacted etchant concentration). The reacted etchant concentration is used to capture the moving etch front of the solution-substrate interface. As the etch front is computed directly, there is no necessity to compute mesh velocity as for a moving grid approach, which changes a diffusion problem into a convective-diffusion problem. With the proposed approach, a diffusion problem remains a simple diffusion problem. In addition, by using a fixed grid, in contrast with a moving grid, Cartesian grid can be used to capture complicated etchfront in multi-dimensional problems. For illustration of the procedure, the proposed procedure is used to predict the etched front and etchant concentration in a one-dimensional diffusion-controlled etching problem