The Nearest Uniformity Producing Profile (NUPP) optimization criterion for thin-film processing applications

Abstract

A criterion for spatial uniformity control in thin-film deposition processes (e.g., chemical vapor deposition for semiconductor manufacturing) is presented, applicable to any measurable film quality (thickness, composition, microstructure, and electrical properties, among others) for all deposition systems where the substrate is rotated to improve uniformity. The approach is based on identifying the subspace of all deposition profiles on the stationary substrate that produce uniform films under rotation and then projecting a deposition profile to be controlled onto a sequence of uniformity producing basis functions spanning that subspace to determine the “Nearest Uniformity Producing Profile” (NUPP). This criterion depends only on the geometrical characteristics of the deposition system, and control and optimization methods can be developed to reduce the deviation from the NUPP giving a widely applicable film control methodology. An important contribution of the NUPP concept and underlying theory is that the latter reveals new structure in the uniformity and nonuniformity producing subspaces, providing insight into thin-film process design and control principles and an opportunity to unify these principles across a range of reactor designs. The implementation of this uniformity criterion is demonstrated using a numerical toolbox developed using the object-oriented features of MATLAB.