Warnock presented the dependence of the polish rate on the wafer
shape, though it is completely a phenomenological model.1 Yu
et al. presented a physical CMP model that includes the effects of
polishing pad roughness and dynamic interaction between pad and
wafer. Two new feature-scale-polishing mechanisms based on asperity
theory are proposed and investigated experimentally. However, it
is not clear whether or how the asperity affects the global quality of
planarization.2 Warnock and Yu et al. both derive the reduction rate
of the step height assuming direct contact between pad and wafer
without considering the role of abrasive flow in between.