An experimental and analytical investigation into the effects of process vibrations on material removal rates during polishing

摘要

Experimental testing, using both commercially available polishing machines and a specially built test platform, demonstrates that material removal rates (MRRs) observed during polishing of fused silica are strongly affected by nanometer-scale vibration amplitudes. Specifically, a nanometer level increase in system vibrations can produce MRRs approximately 150% higher than on an inherently smoother running machine. Moreover the higher spatial frequency surface roughness values are little-effected by the spectral content of the polishing machine. Polishing under controlled conditions, using the test platform, shows that for vibration amplitudes, face='roman'>A? face='roman'>~?1.6?μ face='roman'>m, and over a fairly wide range of vibration frequencies, MRR increases almost linearly with increasing input power. By contrast, for A? face='roman'>??10?μ face='roman'>m, MRR exhibits a rapid decay with increasing A. Order of magnitude analyses and physical arguments are presented in order to explain the qualitatively distinct MRR trends observed. In the small-amplitude limit, face='roman'>A? face='roman'>~?1.6?μ face='roman'>m, two arguments are presented which suggest that the total observed removal rate, face='roman'>MRR _{face='roman'>tot}, reflects the superposed action of chemical-mechanical removal, face='roman'>MRR _{face='roman'>cm}, and vibration-driven, flow-induced removal, face='roman'>MRR _{face='roman'>flow}, i.e., face='roman'>MRR _{face='roman' || '>tot}= face='roman'>MRR _{face='roman'>cm}+ face='roman'>MRR _{face='roman'>flow}. The analyses further indicate that face='roman'>MRR _{face='roman'>flow} primarily refl- cts cyclic viscous shears and pressure gradients extant within the thin, non-Newtonian slurry film that exists between the polishing tool and workpiece. Shears and pressure gradients, and corresponding flow-induced MRRs, are, in turn, found to scale as >>>> cellpadding='0' cellspacing='0'>> nowrap='nowrap' align='right'> style='font-size: 150%;'>√ style='border-top:solid 1px black;' nowrap='nowrap'>?A/d_o>ω, where A is the vibration amplitude, d_o? is the characteristic gap thickness between the tool and workpiece, and ω is the vibration frequency. In the large-amplitude limit, A? face='roman'>??5?μ face='roman'>m, experimental measurements and a simple scaling argument show that the polishing slurry film becomes thick enough that the workpiece and polishing tool lose direct contact. In this limit, observed MRRs thus reflect strictly vibration-driven, flow-induced removal. Comparisons of theoretical material removal rates, derived from the scale analyses presented, with experimentally measured removal rates, as observed in both the small- and large-amplitude limits, show that the models proposed provide reasonable predictions of observed removal rates.