Statistical Process Control for Monitoring the Particles With Excess Zero Counts in Semiconductor Manufacturing

Abstract

In modern semiconductor manufacturing, one type of measured particle count data contains excess zeros, and the ratio of zeros in the measurements is usually larger than 50%. This type of particle count sample data cannot be well modeled by popular defect models such as Poisson, zero-inflated Poisson, generalized zero-inflated Poisson, and Neyman and Gamma-Poisson models. In this paper, a threshold-Poisson model was proposed to describe the particles with excess zero counts, and the method for parameter estimation was developed. Via comparison with those popular models by using 15 measured samples, it showed that the measurements are better modeled by the threshold-Poisson model. A control chart called threshold-c control chart was proposed and the control limits were derived. A reasonable minimum sample size for constructing control chart was also discussed based on simulations.