A Stochastic Model for the Effects of Pad Surface Topography Evolution on Material Removal Rate Decay in Chemical Mechanical Polishing (CMP)

摘要

The role of stochastic variations in pad surface topography evolution during a Chemical Mechanical Planarization or Polishing (CMP) process is investigated. The roughness of the pad surface is considered. The wafer surface is considered smooth, however only blanket film on the wafer surface is considered. The material removal rate (MRR) for oxide CMP is modeled utilizing elastic as well as inelastic contact between wafer and pad. Evolution of pad surface topography is observed to have a significant influence on the wafer-to-wafer MRR variations. Contrary to the discussion in Borucki, the initial Pearson type PDF of pad asperity height distribution is discussed and an alternative and rigorous derivation of the PDF evolution equation which is different from Borucki is presented. The Regularity conditions for the pad asperity height PDF evolution are discussed through the theorem of Diffusion Markov Process. A derivation corresponding to the simple assumption for the mean MRR formula of Borucki is presented. Model results are compared with experimental results and it shows that a combination of inelastic contact analysis with the new pad asperity height PDF evolution equation most reliably capture the observed experimental trend.