A new nonlinear-micro-contact model for single particle in the chemical–mechanical polishing with soft pad

A new mathematical micro-contact model based on the Sneddonʹs equation is developed for chemical–mechanical polishing (CMP) with soft pad. The main feature of the model is incorporation of the large elastic pad deformation for particle/pad contact. The model strongly shows that the large deformation of the soft pad can significantly affect the micro-contact force between the single sandwiched particle and the soft pad. Besides, the new model also predicts a nonlinear dependence of indentation depth of a slurry particle into the wafer surface on the parameters of the soft pad and the wafer. The predicted results based on the current model are shown to be consistent with the published experimental date. The results are also compared with those calculated by the ZC model, and show that the present model is more complete in describing the micro-contact of wafer/particle/pad for CMP process. The results and analysis reveal some insights into the micro-contact on the performance of the CMP with soft pad.