Physical Model for the Small-Scale Residual Topography in Chemical Mechanical Polishing

In previous work, the small-scale topography evolution of the wafer surface was investigated for a typical interlevel dielectric chemical mechanical planarization process by means of a Fourier analysis of surface profiler scans. It was found that the amplitudes of the individual frequency components decay exponentially at a rate that depends on the respective spatial frequency. In this paper, a physical model of these findings is proposed, based on a linearized approximation of the Greenwood-Williamson approach to describe the contact between the pad and the wafer surface. The frequency dependency of the decay rates is attributed to the visco-elastic properties of the pad material (polyurethane). This connection is consistent with dielectric susceptibility measurements that show that the observed frequency dependency stems from a visco-elastic beta-transition in polyurethane. The resulting model not only describes the experimental data for a previous test pattern but also shows good agreement to measurements of a typical dynamic random access memory topography after chemical mechanical polishing. In addition, the current model reduces the systematic errors of the predicted topography as compared to the previous empirical model.