Microscopic Removal Function and the Relationship Between Slurry Particle Size Distribution and Workpiece Roughness During Pad Polishing

Various ceria and colloidal silica polishing slurries were used to polish fused silica glass workpieces on a polyurethane pad. Characterization of the slurries' particle size distribution ( PSD ) (using both ensemble light scattering and single particle counting techniques) and of the polished workpiece surface (using atomic force microscopy) was performed. The results show the final workpiece surface roughness is quantitatively correlated with the logarithmic slope of the distribution function for the largest particles at the exponential tail end of the PSD . Using the measured PSD , fraction of pad area making contact, and mechanical properties of the workpiece, slurry, and pad as input parameters, an Ensemble Hertzian Gap ( EHG ) polishing model was formulated to estimate each particle's penetration, load, and contact zone. The model is based on multiple Hertzian contact of slurry particles at the workpiece–pad interface in which the effective interface gap is determined through an elastic load balance. Separately, ceria particle static contact and single pass sliding experiments were performed showing ~1‐nm depth removal per pass (i.e., a plastic type removal). Also, nanoindentation measurements on fused silica were made to estimate the critical load at which plastic type removal starts to occur ( P crit ~5 × 10 −5 N). Next the EHG model was extended to create simulated polished surfaces using the Monte Carlo method where each particle (with the calculated characteristics described above) slides and removes material from the silica surface in random directions. The polishing simulation utilized a constant depth removal mechanism (i.e., not scaling with particle size) of the elastic deformation zone cross section between the particle and silica surface, which was either 0.04 nm (for chemical removal) at low loads (< P crit ) or 1.0 nm (for plastic removal) at intermediate loads (> P crit ). The simulated surfaces quantitatively compare well with the measured rms roughness, power spectra, surface texture, absolute thickness material removal rate, and load dependence of removal rate.