Modelling tool for chemical-mechanical polishing design and evaluation

Wafer-scale phenomenological modeling, combined with an automatic model validation algorithm, has been implemented in a chemical-mechanical polishing (CMP) modeling software environment called Plane-View. The wafer-scale material removal model is an enhanced Preston equation that admits a nonuniform pressure distribution. Automatic model validation is performed using the Levenberg-Marquart minimization scheme and film thickness data. A three-step model validation procedure is established where sets of material removal profiles are automatically read by Plane-View, which then adjusts the model parameters to optimize the model's fit, creates formulae that capture the behavior of those parameters as a function of process conditions, and stores formulae in a library for easy access by users. This article describes the software architecture, the wafer-scale model, the theoretical aspects of model validation, and a demonstration of the model and validation results using a set of five test wafers.