This research involves the extension of regression methods in statistics to deterministic but very complicated responses. The motivating application is from semiconductor process and device design. In this application there are computer programs that simulate the physics of the fabrication and the operation of semiconductor devices. The result is that electrical properties of semiconductors can be computed as a function of the process specifications in their fabrication. A combination of long running times for the programs and a large number of variables that describe the process make it necessary to use statistical techniques to find optimal settings of the input variables. One can run the simulators at a set of points and fit the model to the computed values, for interpolation and extrapolation to other possible settings of those values. By choosing the points in a structured manner that incorporates some randomness, one can estimate the uncertainty in the model. This project is in the area of statistics and probability and offers a number of statistical applications to the semiconductor industry. The research is to explore an approach that reflects some standard settings in computer experiments: many dimensions, comparatively few data points, and a need to fit a complex function.
