A mixed elastohydrodynamic lubrication model with layered elastic theory for simulation of chemical mechanical polishing

Abstract

Mixed elastohydrodynamic lubrication (mixed EHL) model has been successfully used to study phenomena in chemical mechanical polishing (CMP) process. However, in various mixed EHL simulation frameworks, a polishing pad's deformation cannot correctly be described by adopted models for pad deformation such as elastic half-space model and Winkler elastic foundation model. Thus, a more accurate model for pad deformation is needed, since this is the prerequisite for an accurate prediction of contact pressure and material removal rate, which is critical for improvement of polishing quality. In this paper, a layered elastic theory, which is frequently used to calculate flexible pavement response to truck loading, is introduced into the mixed EHL model. It is found that this theory has a similar accuracy to the traditional 3D finite element method for calculating the pad deformation. However, its computational cost is much lower, which is especially important for accurate and efficient simulation of mechanical behavior and material removal rate (MRR) in CMP. In order to highlight benefits of the proposed theory, simulations are carried out based on three different pad deformation models with the mixed EHL model. The pad deformation behavior is found to have a significant influence on the final simulation results, especially the MRR prediction. By comparing the different simulation models, the proposed layer elastic theory is found to be an optimal model for describing the polishing pad deformation behavior in CMP and can provide accurate simulation results on contact pressure distribution and the material removal rate.