Bulk image formation over substrate topology using the finite element method

Abstract

A method for simulating exposure, post exposure bake and development process is described and applied for analyzing the problem of reflective stepped substrate. The method is based on the numerical solver of Helmholtz equation and the rigorous boundary condition which considers the entire system consisted of projection optics, photoresist and substrate. Therefore, it can be used to simulate bulk imaging effects due to the small depth of focus of the optical system and nonplanar substrate. Diffusion equation and the ray tracing model are used for simulating the post exposure bake and the development process, respectively. The developed photoresist pattern on the stepped reflective substrate topography are obtained, and it shows irregular resist profiles due to the reflection of light at the step edge.