Wafer Defect Inspection Optimization With Partial Coverage—A Numerical Approach

Electron beam inspection (EBI) with high resolution is a promising technique to improve the defect inspection on the surface of patterned wafer. However, high resolution usually means long inspection time, which results in the low throughput and limitation of EBI applied in practice. This study aims to optimize the inspection time of EBI by reducing the total number of inspection regions without loss of the accuracy. We first refine this defect inspection optimization problem as a partial congruent square cover problem. Then, we propose two novel mixed-integer linear programming models for this problem. To deal with the large-scale problems, an approximation algorithm is developed to obtain the high-quality solutions. This approximation algorithm efficiently utilizes the linear programming (LP) rounding technique and greedy strategy based on the proposed model. Compared with the existing algorithms in the literature, numerical results show the superiority of the proposed model and algorithm.