A Theory of Friction for Chemical-Mechanical Planarization

Removal rates in chemical-mechanical planarization depend on the pad/wafer coefficient of friction (COF). COF data are in turn functions of speed V and pressure p collectively called Stribeck curves. Here we develop a new Stribeck curve theory starting with the physics of partially lubricated contact. Motivated by contact data, solid contact areas are assumed to have nano-scale roughness that captures slurry and restricts flow during wafer encounters, creating a thin, incompressible layer. This produces credible Stribeck curves, which are generated and studied in dimensionless form. We characterize the abscissa and slope where the COF is at half maximum and find that their product depends only on the ratio of the mean solid contact area fluid thickness to the asperity summit elastic deformation. This leads to a method for parameterizing Stribeck curve models from COF data that successfully models tungsten data, in which the COF depends only on V, and copper data in which it appears to depend on V/p and suggests that the difference is due to the mechanics of the pad surface. Further characterization also yields a very simple and powerful Stribeck curve compact model. Model predictions are verified using pad topography and contact data.