A Contact-Mechanics Based Model for Dishing and Erosion in Chemical-Mechanical Polishing
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A CONTACT-MECHANICS BASED MODEL FOR DISHING AND EROSION IN CHEMICAL-MECHANICAL POLISHING
Joost J. Vlassak Division of Engineering and Applied Sciences, Harvard University 311 Pierce Hall, 29 Oxford Street, Cambridge MA 02138 ABSTRACT We present a new model for dishing and erosion during chemical-mechanical planarization. According to this model, dishing and erosion is controlled by the local pressure distribution between features on the wafer and the polishing pad. The model uses a contact mechanics analysis based on the work by Greenwood to evaluate the pressure distribution taking into account the compliance of the pad as well as its roughness. Using the model, the effects of pattern density, line width, applied down-force, selectivity, pad properties, etc. on both dishing and erosion can be readily evaluated. The model may be applied to CMP used for oxide planarization, metal damascene or shallow trench isolation. The model is implemented as an algorithm that quickly calculates the evolution of the profile of a set of features on the wafer during the polishing process. With proper calibration of the process parameters, it can be used as a tool in optimizing the CMP process and implementing CMP design rules. INTRODUCTION With the advent of shallow trench isolation (STI) and copper interconnects, chemicalmechanical polishing (CMP) has emerged as one of the most important operations in the fabrication of integrated circuits. Even so, the CMP process is still fairly poorly understood. This is so because, in spite of its apparent simplicity, CMP is a complicated process in which both mechanical and chemical factors play an important role. Chemical-mechanical polishing is very sensitive to pattern geometry effects and may results in dishing of metal lines and erosion of dielectrics. Since the surface topography of a wafer after a CMP process step has a significant impact on wafer yield, numerous attempts have been made to predict the evolution of the wafer surface during the polishing process. One of the first models that allowed quantitative predictions of wafer topography was a phenomenological model proposed by Warnock1. While useful in practice for predicting dishing and erosion, this type of model does not provide much insight in the actual CMP process. More recent models are mechanics based and can be classified in several groups. One group focuses on slurry hydrodynamics to determine the pressure distribution between the wafer and polishing pad. These models can be either wafer-scale2, 3 or feature-scale4 models. Another group of models is based on a contact-mechanics analysis of the CMP process. According to these models, elastic deformation of the polishing pad determines M4.6.1
the pressure distribution between wafer and pad and thus plays an important role in determining the wafer surface profile after polishing5, 6. Yet another model takes into account the roughness of the polishing pad and describes CMP in terms of asperity contacts between wafer and pad7. In this paper, we present a contact-mechanics b
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