A physical model for dishing during metal CMP

A physically based model for dishing during metal chemical mechanical polishing (CMP) is presented. The control of dishing is important for advanced damascene metal interconnect technologies. However, the modeling of dishing is still in an initial phase. Material removal mainly takes place at the contact areas between the rough polish pad and the substrate. Therefore, a numerical model of the contact area of the pad and wafer, and the number of contacts and the size distribution of the contact areas as function of polish parameters and pad properties, was developed. The number of contacts appeared directly proportional to the applied pressure. In addition, the contact size distribution was strongly dependent on pad morphology. It was weakly dependent on the applied pressure and the Young's modulus of the pad. Thereafter the dishing phenomenon was modeled using these results. For an arbitrary linewidth, the metal was removed by two groups of pad asperities, one group with contact size smaller than the linewidth (group S) and one with contact size larger than the metal linewidth (group B). By considering the material removal rate of these two groups of asperities separately and using a modified form of Preston's law, a model was developed that describes the dishing during (over)polishing for an arbitrary metal line. The model contains one free parameter. The model was compared with experimental results obtained from state-of-the-art copper CMP. Excellent agreement was observed between data and the model.