- L. J. Borucki, Thomas P. Witelski, C. P. Please, P. Kramer, D. Schwendeman, A theory of pad conditioning for chemical-mechanical polishing,
Journal of Engineering Mathematics, vol. 50 no. 1
pp. 1-24 [issues.aspx] .
(last updated on 2004/09/23)
Statistical models are presented to describe the evolution of the surface roughness of polishing pads during the pad conditioning process in chemical-mechanical polishing. The models describe the time-dependent development of the surface-height probability density function of solid pads during fixed height or fixed cut-rate conditioning. An integral equation is derived for the effect of conditioning on a foamed pad in terms of a model for a solid pad. Models that combine wear and conditioning are then discussed for both solid and foamed pads. Models include the dependence of the surface roughness on the shape and density of the diamonds used in the conditioner and on tool operating parameters. Good agreement is found with Monte Carlo simulations and with experimental data.