Etching Profiles at Resist Edges: I . Mathematical Models for Diffusion‐Controlled Cases

Abstract

Mathematical models are presented that describe diffusion‐controlled etching near resist edges. To understand the role of the various physical parameters, a simple maskless one‐dimensional model is studied first. The study of a purely diffusion‐controlled case suggests that mathematical models for etching problems may be solved by means of perturbation techniques that assume relatively small displacements of the etching surface. The perturbation procedure is then applied to a two‐dimensional problem that involves a mask. Assuming a stationary etchant and diffusion control, it is shown that etch rates are largest close to the resist edge. As a result, the etching profile reveals a bulging shape near the mask edge, confirming earlier observations reported in the literature. A case with convection is considered next. It is shown that the very same bulge that resulted from the analysis of the stationary case may also appear when convection plays a role. The perturbation procedure depends upon an important dimensionless parameter β. Tabulated values of this parameter for various etching systems are presented.