A Feature-Scale Greenwood-Williamson Model for Metal Chemical Mechanical Planarization

In this work, a new feature-scale model is proposed for investigating the interaction between the wafer pattern and individual pad asperities in the process of chemical mechanical planarization (CMP). Based on the contact mechanics equation and the modified Greenwood-Williamson (GW) model which captures the evolution of feature curvature and the modification of the pad asperity height distribution, the discrete convolution and fast Fourier transform (DC-FFT) technique is adopted and combined with the Picard iteration method to calculate the direct contact pressure distribution between the wafer surface and the polishing pad. The computed pressure is then used to determine the local removal rate of the underlying patterns and predict the evolution of the wafer surface profile. Furthermore, the method is extended to capture the metal dishing as the feature size changes. It is shown that the present model can avoid the false simulated results produced by directly applying the original GW model for CMP when the feature size approaches zero. Otherwise, the calculated surface profile and dishing values of pattern geometries are in good agreement with the experimental data. Therefore, this model can not only be used to simulate the evolution of the wafer surface for global planarization at lower technology nodes, but can also be applied to provide some basic design rules for improving the process parameters and reducing the time and cost for developing new architectures.