Abstract
In the manufacturing of semiconductor wafers, the chemicals released into chambers might remain on the surfaces of the chambers after the manufacturing operation. The remaining chemicals can cause the appearance of contaminant particles on the surfaces of the subsequently processed wafers, and consequently reduce the yields. An important step in the manufacturing of wafers is to regularly clean the chamber to remove residual chemicals and maintain chamber cleanliness at a desired level. It is thus critical to establish an effective clean recipe for the chamber clean process. Zhang (2015) studied a gas purge experiment, which was conducted to study the effects of some clean factors and to find an optimal clean recipe. In Zhang (2015), a statistical model based on generalized linear model was proposed for the data of the experiment. In the model, the responses are assumed to be random variables with Poisson distributions, of which the parameters must follow some recursive formula. According to the possible forms of the recursive formula, the model was further classified into type I and type II models. Zhang (2015) discussed and gave methods of parameter estimation and testing for the type I models. In the thesis, we identify and discuss several issues about the model. We first develop the parameter estimation and testing procedures for the type II model, and use computer simulations to examine the accuracy of the procedures. Second, a classification method based on the principle of maximum likelihood is proposed to determine whether the data is generated from type I or type II models. We also verify the effectiveness of the classification method by computer simulation, and briefly discuss the impact of fitting a model of wrong type. Third, we generalize the model by introducing a dispersion parameter for data exhibiting overdispersion relative to a Poisson model. Under the new model, we adopt the quasi-likelihood approach to resolve the problems of estimating parameters and testing hypotheses. The new model and the analysis methods are demonstrated on a real data of purge experiment. Lastly, we discuss an issue of the design of the experiment, and obtain a criterion for determining the number of repeated measures of particle counts required to achieve a pre-specified level of testing power.