Analysis of an Inverse Problem Arising in Photolithography

TL;DR

This paper formulates and analyzes a well-posed inverse problem in photolithography, aiming to determine optical masks for desired circuit patterns, with a focus on mathematical modeling and convergence of approximations.

Contribution

It introduces a variational formulation for the inverse shape design problem in photolithography and establishes convergence properties of the approximation methods.

Findings

A well-posed variational formulation for the inverse problem.

Convergence properties of the proposed approximation.

Foundation for numerical solution development.

Abstract

We consider the inverse problem of determining an optical mask that produces a desired circuit pattern in photolithography. We set the problem as a shape design problem in which the unknown is a two-dimensional domain. The relationship between the target shape and the unknown is modeled through diffractive optics. We develop a variational formulation that is well-posed and propose an approximation that can be shown to have convergence properties. The approximate problem can serve as a foundation to numerical methods.