Modeling of chemical-mechanical polishing with soft pads

A new model is developed for chemical-mechanical polishing with soft pads. Contrary to prevalent views based on the existing polishing rate equation (i.e., the Preston's equation), the new model predicts a nonlinear pressure dependence of the polishing rate. It is shown that the fundamental mechanism of the pressure dependence for CMP with a soft pad is completely different from that with a hard pad. This new model, which is shown to be consistent with experimental evidence, resolves an apparent inconsistency between the Preston's equation and experimental observations concerning the pressure dependence of the polishing rate. The new model provides an important starting point for elucidating the other aspects of the CMP process including the pattern-density dependence of the planarization rate.