Simultaneous approach to model building and process design using experimental design: application to chemical vapor deposition
Wissmann, Paul J.
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In this thesis a tool to be used in experimental design for batch processes is presented. Specifically, this method is to aid in the development of a process model. Currently, experimental design methods are either empirical in nature which need very little understanding of the underlying phenomena and without the objective of more fundamental understanding of the process. Other methods are model based which assume the model is correct and attempt to better define the model parameters or discriminate between models. This new paradigm for experimental design allows for process optimization and process model development to occur simultaneously. The methodology specifically evaluates multiple models as a check to evaluate whether the models are capturing the trend in the experimental data. A new tool for experimental design developed here is called the grid algorithm which is designed to constrain the experimental region to potential optimal points of the user defined objective function for the process. It accomplishes this by using the confidence interval on the objective function value. The objective function value is calculated using the model prediction of the best performing model among a set of models at the predicted optimal point. This new experimental design methodology is tested first on simulated data. The first simulation fits a model to data generated by the modified Himmelblau function (MHF). The second simulation fits multiple models to data generated to simulate a film growth process. In both simulations the grid algorithm leads to improved prediction at the optimal point and better sampling of the region around the optimal point. This experimental design method was then applied to an actual chemical vapor deposition system. The films were analyzed using atomic force microscopy (AFM) to find the resulting film roughness. The methodology was then applied to design experiments using models to predict roughness. The resulting experiments were designed in a region constrained by the grid algorithm and were close to the predicted optimum of the process. We found that the roughness of a thin film depended on the substrate temperature but also showed a relationship to the nucleation density of the thin film.