Curvilinear Mask Optimization for Inverse Lithography Based on B-splines and Constrained Delaunay Triangulation

Abstract

In this paper, we propose a gradient-based method to optimize curvilinear masks in optical lithography. The mask pattern is represented by periodic B-spline curves. We apply constrained Delaunay triangulation to discretize the domains circled by the spline curves. Subsequently, we establish an explicit relationship between the integral points and the control points of the boundary spline curve. Based on the relationship, we derive explicit formulas of the gradient of the optimization objective function with respect to the coordinates of the control points. Then we propose an inverse lithography algorithm to optimize the curvilinear mask pattern. Finally, the results of the numerical experiments demonstrate the feasibility and extensive adaptability of our method.