Inferences of slurry bow wave width from mean coefficient of friction and directivity in chemical mechanical planarization

Retaining rings with different slot designs (i.e. sharp and rounded) were exposed to identical polishing conditions, and at 2 different slurry flow rates, to study their tribological attributes and to see whether trends existed between frictional forces and previously reported bow wave width values. Two separate parameters, namely, coefficient of friction (COF) and directivity (Δ) were extracted and analyzed. Average COF values indicated that both rings operated in “boundary lubrication” regardless of slurry flow rate. A slight trend was observed between bow wave width and average COF such that higher bow wave widths (resulting from higher flow rates) were shown to cause a drop in COF. However, COF values in all cases were not far from the precision of our instruments. In contrast, the shape of the shear force and normal force data clusters were found to be markedly different for both ring designs and slurry flow rates, pointing to the utility of the directivity parameter (which captured the ratio of the variance of shear force to that of normal force) to provide information on bow wave characteristics. Here, wider bow waves caused a significant drop in directivity for both ring designs indicating significant differences in the stick-slip events for each case and paving the way for deducing bow wave characteristics through tribological studies alone.