Journal of Engineering Mathematics

, Volume 50, Issue 1, pp 1–24 | Cite as

A theory of pad conditioning for chemical-mechanical polishing

  • Leonard J. Borucki
  • Thomas Witelski
  • Colin Please
  • Peter R. Kramer
  • Donald Schwendeman
Article

Abstract

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 evolution 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. The 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 cutting tips used in the conditioner and on other operating parameters. Good agreement is found between the model, Monte Carlo simulations and with experimental data.

abrasive wear chemical-mechanical polishing surface roughness 

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Leonard J. Borucki
    • 1
  • Thomas Witelski
    • 2
  • Colin Please
    • 1
  • Peter R. Kramer
    • 2
  • Donald Schwendeman
    • 2
  1. 1.Formerly Motorola IncArizonaU.S.A. E-mail
  2. 2.Department of MathematicsDuke UniversityDurham, North Carolina 27708-0320U.S.A

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