Wafer Defect Inspection Optimization: Models, Analysis and Algorithms

37 Pages Posted: 13 May 2019

See all articles by Zhongshun Shi

Zhongshun Shi

University of Tennessee, Knoxville - Department of Industrial and Systems Engineering

Ming Qin

affiliation not provided to SSRN

Weiwei Chen

Rutgers, The State University of New Jersey - Supply Chain Management Department

Siyang Gao

affiliation not provided to SSRN

Leyuan Shi

affiliation not provided to SSRN

Date Written: April 6, 2019

Abstract

The prevalence of electronic devices has propelled the tremendous growth of the semiconductor industry in the past half century. The manufacturing of semiconductor wafers is a long and delicate process, where defect points may occur and cause the failure of the entire circuit. As more advanced devices introduce tiny and harder-to-detect defects, improvements in wafer defect inspection technologies are highly desired by the industry. One promising direction is to optimize the positioning of inspection regions for the e-beam inspection tool, so as to cover all suspect defect points on a target area of a wafer while maximizing the throughput of the scan. To this end, we formulate this defect inspection optimization problem (DIOP) as a mixed integer linear programming (MILP) model, and enhance the formulation using variable reduction. To address the computational challenge of solving large-scale DIOP instances, we further propose three approximation methods with theoretical bounds, namely, a constant-factor approximation algorithm that provides heuristic solutions quickly, a polynomial-time approximation scheme (PTAS) that has a strong performance guarantee, and an MILP-based hybrid method that combines the PTAS framework and MILP formulation and is suitable for parallel computing by design. Numerical experiments on synthetic and industry instances show the efficiency and effectiveness of the proposed methods. Particularly, for large-scale instances, the hybrid algorithm is capable of generating near-optimal solutions with theoretical guarantees within practically acceptable computational time.

Keywords: wafer defect inspection, e-beam inspection, discrete optimization, approximation algorithm

JEL Classification: C6

Suggested Citation

Shi, Zhongshun and Qin, Ming and Chen, Weiwei and Gao, Siyang and Shi, Leyuan, Wafer Defect Inspection Optimization: Models, Analysis and Algorithms (April 6, 2019). Available at SSRN: https://ssrn.com/abstract=3371939 or http://dx.doi.org/10.2139/ssrn.3371939

Zhongshun Shi

University of Tennessee, Knoxville - Department of Industrial and Systems Engineering ( email )

Knoxville, TN 37996
United States

Ming Qin

affiliation not provided to SSRN

Weiwei Chen (Contact Author)

Rutgers, The State University of New Jersey - Supply Chain Management Department ( email )

Piscataway, NJ
United States

Siyang Gao

affiliation not provided to SSRN

Leyuan Shi

affiliation not provided to SSRN

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