A Contact-Mechanics-Based Model for General Rough Pads in Chemical Mechanical Polishing Processes

Abstract

In this paper, a general rough-pad model is proposed for the chemical mechanical polishing (CMP) process. The proposed rough-pad model has several advantages over existing models. First, general height distribution functions and autocorrelation functions are used to describe the pad surface, which are easier to obtain than pad asperity height and curvature distributions in existing models. Second, the spectral representation technique and nonlinear transformation method used in the model allow rough-pad surfaces with general pad surface height distributions and autocorrelation functions. Thus, no assumption is made on the surface geometry and statistics of the pad. A conjugate-gradient iteration scheme combined with the fast Fourier transform technique is used to solve the resulting wafer–pad rough-contact problems to fully take into account the bulk deformation of the pad and the interactions among neighboring asperities. Model predictions are in good agreement with the experimental data in the existing literature. Based on the proposed model, the effects of CMP process parameters and underlying pattern geometries on dishing and erosion can be evaluated. The proposed model may also be used as a CMP pad design tool for improving dishing and erosion.