Synergetic effects of wafer rigidity and retaining-ring parameters on contact stress uniformity in chemical mechanical planarization

Here we use two-dimensional 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). In particular, the effective rigidity of the wafer (determined by the wafer carrier structure), the retaining-ring width and its back pressure are taken to be the design parameters. The purpose is to study the synergetic effects of such parameters on the contact stress uniformity, which directly affects the spatial uniformity of the material removal rate on the wafer surface. Our numerical results indicate that, for a given wafer rigidity, one may choose the retaining-ring width and back pressure to minimize the contact stress non-uniformity (NU). Also, the resulting minimum NU decreases with the effective wafer rigidity, suggesting that it is beneficial to use a soft (e.g., floating-type) wafer carrier. Moreover, for a soft wafer carrier, it is demonstrated that using a multi-zone wafer-back pressure profile is even more effective in reducing NU.