Method for semiconductor process optimization using functional representations of spatial variations and selectivity

A methodology for determining the optimal equipment settings for a processing step based on experimental designs and model-based optimization is presented. The method uses two-layered models. The first layer involves creating a spatial model-one for each film of interest-of the etch results. The second layer maps the coefficients of the spatial models to equipment settings. All this is done before any optimization scheme is employed. The process engineer may then optimize the etch process by maximizing coefficients which contribute to the desired maximum etch rate, while minimizing coefficients which contribute to nonuniformity. The engineer also may minimize coefficients which represent undesired etches, and thus obtain etch selectivity. This method may be used for other process optimization needs, such as thin-film depositions and patterned etches