Lens System Adjustment in Semiconductor Lithography Equipment

Abstract

In this paper, we address the problem of lens aberration adjustment for lenses of semiconductor lithography equipment. The objective of aberration adjustment is to minimize the maximum value of aberration 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, MIP (Mixed Integer Programming) 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, which addresses the same “lens aberration” problem with the same objective of minimizing maximum absolute value of lens aberration. In real-world 9 instances, our solution method improves maximum aberration values by 18% to 56% over similar results from conventional solution methods.

Keywords

• semiconductor lithography
• stepper
• aberration
• integer programming
• optimum design
• systems engineering
• optical instrument
• precision instrument