MODELING, OPTIMIZATION AND CONTROL OF SPATIAL UNIFORMITY IN MANUFACTURING PROCESSES

Spatial uniformity, or the uniformity of product output characteristics at different locations in a batch of product is modeled, optimized, and controlled using a methodology called ''Multiple Response Surfaces'' which may be used to characterize the results of an experimental design. Multiple, low-order polynomial models are used to model the output characteristics at each of several sites within a batch of product. The uniformity model is then obtained by manipulating these multiple models. The Multiple Response Surfaces approach is compared to the traditional method of fitting a single high-order polynomial to the calculated uniformity. Experimental results on several processes, confirm the expectation that similar or improved modeling accuracy is obtained with fewer data points using the new methodology due to the ability to use low-order models. Characteristics of the Multiple Response Surfaces approach including noise immunity and restrictions to classes of model forms are examined both analytically and in application to plasma etching, silicon epitaxy, tungsten CVD and the simulation of polysilicon LPCVD.