A wafer-scale material removal rate profile model for copper chemical mechanical planarization

Abstract

Chemical mechanical polishing (CMP) models based on the Preston equation, which states that the material removal rate (MRR) is proportional to the product of the pressure and relative velocity, have focused on representing the average MRR as a function of the pressure and relative velocity. In this study, we tried to establish a semi-empirical CMP model, which can provide the MRR profile. The model is based on a modified form of the Preston equation and involves the use of a spatial parameter ( Ω). The relative velocity distribution, normal contact stress distribution, and chemical reaction rate distribution are considered for obtaining the MRR profile in the copper CMP process. The results of the modeling and experimental analysis performed in this study facilitate process optimization and provide information that can contribute to the development of a wafer-scale CMP simulator.