Abstract
Stochastic models are presented for the structure and conditioning of pads used in chemical-mechanical polishing of wafers. First the one-dimensional distribution function of surface depth in the case of a conditioned solid pad is described. Then, for characterizing the structure of a foamed pad, the theory of random closed sets is applied. An important distributional characteristic of a random closed set, the linear contact distribution function, yields the contribution to surface depth resulting from pores. As a special example the Boolean model is considered. This leads to a formula that describes the variability of the surface of a conditioned foamed pad after a certain time. Simulations and experimental data show a good agreement between theory and reality.
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Wiegand, S., Stoyan, D. Stochastic Models for Pad Structure and Pad Conditioning Used in Chemical-Mechanical Polishing. J Eng Math 54, 333–343 (2006). https://doi.org/10.1007/s10665-006-9036-3
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DOI: https://doi.org/10.1007/s10665-006-9036-3