Modern statistical modeling techniques for characterizing the spatial response of a single-wafer process are presented. These techniques overcome the limitations of the commonly used ordinary least squares estimation procedure and provide models for the expected value and variance of the response. In addition, a procedure for generating a model of the covariance structure which relates the various points on the wafer is presented. These methods are applied to the characterization of the rapid thermal chemical vapor deposition of polysilicon on top of a layer of silicon dioxide. The results of this study indicate that the simultaneous estimation of mean and variance models results in a significantly better representation of the data than the standard constant-variance estimation of a mean model.