An Alternating Direction Method of Multipliers for Inverse Lithography Problem

TL;DR

This paper introduces an ADMM-based optimization approach for inverse lithography, effectively handling complex subproblems and demonstrating convergence and practical efficiency through numerical examples.

Contribution

It develops a novel ADMM framework with direct threshold truncation solution for inverse lithography, improving computational efficiency and convergence analysis.

Findings

The method effectively solves the inverse lithography optimization problem.

Numerical examples demonstrate the approach's efficiency and accuracy.

The convergence of the proposed ADMM method is rigorously analyzed.

Abstract

We propose an alternating direction method of multipliers (ADMM) to solve an optimization problem stemming from inverse lithography. The objective functional of the optimization problem includes three terms: the misfit between the imaging on wafer and the target pattern, the penalty term which ensures the mask is binary and the total variation regularization term. By variable splitting, we introduce an augmented Lagrangian for the original objective functional. In the framework of ADMM method, the optimization problem is divided into several subproblems. Each of the subproblems can be solved efficiently. We give the convergence analysis of the proposed method. Specially, instead of solving the subproblem concerning sigmoid, we solve directly the threshold truncation imaging function which can be solved analytically. We also provide many numerical examples to illustrate the effectiveness of the method.