A fixed-grid approach for diffusion- and reaction-controlled wet chemical etching

Abstract

A new mathematical model for wet chemical etching process is presented. The proposed method is a fixed-grid approach based on the total concentration of etchant. It is analogous to the enthalpy method used in the modeling of melting/solidification problems. The total concentration is the sum of the unreacted etchant concentration and the reacted etchant concentration. The reacted etchant concentration is used to capture the etchfront. The governing equation based on the total concentration is formulated. This governing equation is shown to be equivalent to the conventional governing equation. It also contains the interface condition. A procedure to update the reacted concentration is presented. Numerical results for one-dimensional diffusion-controlled and reaction-controlled etching are presented.