A stochastic model for the effects of pad surface topography evolution on material removal rate decay in chemical-mechanical planarization

The role of stochastic variations in pad surface topography evolution during a chemical-mechanical planarization or polishing (CMP) process is investigated. The roughness of the pad surface is considered, while the blanket film wafer is smooth and flat. The material removal rate (MRR) for CMP is modeled utilizing elastic as well as inelastic contact between the wafer and pad. Evolution of the pad surface topography is observed to have a significant influence on the MRR variations. A distinguishing feature of this paper is the MRR evolution equation for a single asperity. It is observed that an elastic contact model significantly underestimates the experimental trend. The selection of the initial probability density function (pdf) used in an MRR time-evolution model is shown to be a key issue. It is observed that reasonably small changes in numerical estimates of pdf parameters can have a significant effect on the accuracy of material removal model predictions. By extending the model to the case of inelastic contact between the wafer and pad asperities, it is found that model performance can be notably improved. Finally, it should be mentioned that the emphasis here on statistical elements, combined with the approach of developing mean MRR models based on models for individual asperities, allows one to easily incorporate more realistic model assumptions, an example being that pad asperities have tip curvatures and spacing that are random.