A model for chemical-mechanical polishing of a material surface based on contact mechanics

A new contact-mechanics-based model for chemical-mechanical polishing is presented. According to this model, the local polish rate is controlled by the pressure distribution between features on the wafer and the polishing pad. The model uses an analysis based on the work by Greenwood to evaluate this pressure distribution taking into account pad compliance and roughness. Using the model, the effects of pattern density, applied down-force, selectivity, pad properties, etc. on the evolution of the wafer surface can be readily evaluated. The interaction between individual pad asperities and the wafer pattern is investigated in detail. It is shown that the pressure distribution between an asperity and the wafer surface is discontinuous at edges of features that have different nominal polish rates and that this pressure discontinuity dominates the polish rate and dishing of narrow features.The model is implemented as an algorithm that calculates the evolution of the profile of a set of features on the wafer during the polishing process. The model can be applied to chemical-mechanical polishing used for oxide planarization, metal damascene or shallow trench isolation.