Youzou Fukagawa

Lens System Adjustment in Semiconductor Lithography Equipment (Optimization for Lens Groups Rotation)

In this paper, we address the problem of lens abberation adjustment for lenses of semiconductor lithography equipment. The objective of abberation adjustment is to minimize the maximum value of abberation in any part of the images that are projected on the wafer. Formerly, an approximate solution method has been used, which is based on a brute force search for a subset of all cases. However, using that method, computational times are often long and a faster solution method is necessary. Nowadays, owing to significant progress in mathematical programming research, IP solvers can reach an optimal solution quite fast. That is why, in this paper, we propose an exact solution method based on 0-1 MIP (Mixed Integer Programming), which addresses the same “lens abberation” problem with the same objective of minimizing maximum absolute value of lens abberation. In real-world 9 instances, our solution method improves maximum abberation values by 18% to 56% over similar results from conventional solution methods.