A Particle-Augmented Mixed Lubrication Modeling Approach to Predicting Chemical Mechanical Polishing

Abstract

Chemical mechanical polishing (CMP) is a manufacturing process that is commonly used to planarize integrated circuits and other small-scale devices during fabrication. Although a number of models have been formulated, which focus on specific aspects of the CMP process, these models typically do not integrate all of the predominant mechanical aspects of CMP into a single framework. Additionally, the use of empirical fitting parameters decreases the generality of existing predictive CMP models. Therefore, the focus of this study is to develop an integrated computational modeling approach that incorporates the key physics behind CMP without using empirical fitting parameters. CMP consists of the interplay of four key tribological phenomena—fluid mechanics, particle dynamics, contact mechanics, and resulting wear. When these physical phenomena are all actively engaged in a sliding contact, the authors call this particle-augmented mixed lubrication (PAML). By considering all of the PAML phenomena in modeling particle-induced wear (or material removal), this model was able to predict wear-in silico from a measured surface topography during CMP. The predicted material removal rate (MRR) was compared with experimental measurements of copper CMP. A series of parametric studies were also conducted in order to predict the effects of varying slurry properties such as solid fraction and abrasive particle size. The results from the model are promising and suggest that a tribological framework is in place for developing a generalized first-principle PAML modeling approach for predicting CMP.