(509c) Multiscale Modeling and Sequential Design of Experiments

Thin film deposition has found increasing use and is crucial in the production of many products such as solid oxide fuel cells, solar cells, ferroelectric actuators, and microelectronic devices. The performance of the thin film for these applications is dependent on the microstructure of the deposited film. It is also known that the microstructure of the thin film is affected by the processing conditions. However, mechanistic models that relate the processing conditions to the microstructure are not typically used in process design. Thin film deposition is also an inherently multiscale process when one includes the scale of the reactor (1cm-1m), grain sizes (100nm-10 microns), and grain boundary width and motion (1-10nm). In order to design the process accurately, a multiscale model is needed. A problem with developing models is deciding which existing model is best and what experiments can be done to improve the models. This problem has been tackled by many researchers such as Box et. al. [1], who outlined the general method and algorithm, and Fujiwara et. al. [2], who applied D-optimal experimental design, used their collected data to estimate parameters for their model, and decided whether the model was accurate enough. They used a Bayesian estimation to find parameter estimates for their crystallization model. In contrast, most operations for materials properties are optimized using design of experiments (DOE) and parameters are found via regression using response surface models [3].

This work combines the modeling of microstructure and a DOE approach and grounds the approach with direct experimental results. Using a specific case study which provides experimental results is critical to address the practical issues and constraints required for implementation of the model. The primary objective of this work is to determine the location of the optimum microstructure. Secondary objectives are to identify parameters in a mechanistic model which uses facet propagation and to identify experiments to improve understanding of the existing models. New techniques such as the cost of the experiment, effect of uncertainty of the parameter estimates, and robustness of design refine existing theory. To test our theory, we have an in-house chemical vapor deposition (CVD) system to grow films which will be used in constructing our model and performing the sequential experimental design that our method suggests. The system was designed to provide control of the many factors in CVD. We start with a two part design of experiments (DOE) approach. First, a screening experiment identifies important factors in the process and then a full DOE design, from which data is used to make an empirical and a mechanistic model. Improvements to each model can be made through additional experiments and each model is analyzed to see which one best fits the data, which model adequately describes the experimental data, and the extent to which the goals of optimum location and parameter identification are conflicting.

1. Stewart, W. E.; Shon, Y.; Box, G. E. P. “Discrimination and goodness of fit of multiresponse mechanistic models”; AIChE Journal; 1998, 44, 1404—1412

2. Fujiwara, M; Nagy, Z. K.; Chew, J. W.; Braatz, R. D. Journal Of Process Control; 2005, 15, 493—504

3. Topol, A. W. ; Tuenge, R. T.; King, C. N. Journal of Materials Research; 2004; 19, 697--706