Polygon Fracture Method Considering Maximum Shot Size for Variable Shaped-beam Mask Writing

Abstract

Variable shaped-beam electron beam lithography systems are widely used for mask writing. The exposure data, which is an input for variable shaped-beam mask writing, must be a set of rectangles with considering maximum size limit. It is also crucial to fracture the layout into as few rectangles as possible for reducing the number of times the beam irradiated. Several methods have been proposed to find a solution that reduces the number of rectangles after fracturing. However, the larger the input size, the more difficult it becomes to obtain an optimal solution, and many methods give up on obtaining an optimal solution early. In this paper, we propose a new fracturing method for convex rectilinear polygons using dynamic programming, which cuts each polygon by slice-lines through concave vertices first. The proposed method can solve the problem in polynomial time. Computer experiments confirm the space and time complexity of the method and the proposed method can find the optimal solution as the existing method using ILP, but at an order of magnitude faster.