This work includes two parts. First, we use 2D models of fluid film lubrication and contact mechanics to calculate the contact stress and fluid (i.e., slurry) pressure distributions on the wafer-pad interface in chemical mechanical planarization (CMP). Our numerical results indicate that, the resulting minimum contact stress non-uniformity (NU), which directly affects the spatial uniformity of the material removal rate on the wafer surface, decreases with the effective wafer rigidity (determined by the wafer carrier structure), suggesting that it is beneficial to use a soft (e.g.,...