Analysis of Local Planarization with Polishing Time, Film Thickness, Chemical Non-Uniformity, Line Density, Line Width,
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Analysis of Local Planarization with Polishing Time, Film Thickness, Chemical Non-Uniformity, Line Density, Line Width, and Pad Relaxation Property Jinru Bian and John Quanci Rodel Inc. Abstract Theoretical chemical mechanical polishing local planarization models as a function of polishing time and film removal are reviewed, and re-derived in a systematic and correlative way. The derived models employ pad viscoelastic and relaxation properties to explain the experimental phenomena that step height local planarization is an exponential function of line width at the same line density, and also account for the affect of pattern density and polishing of two different materials at the same time on step height planarization. Introduction It is well known that step height or final dishing results are strongly dependent on feature line width, even though the line density is the same. In addition, planarization is further affected by line density and polishing rate variations due to polishing different materials at the same time, such as in barrier polishing. Several chemical mechanical polishing (CMP) models have been proposed to describe planarization as a function of these processing parameters and polish time [1-6]. None of these models explore planarization as a function of line width at a constant line density and have not systematically discussed planarization as a function of the film removed. In the literature, a model of pad bending with a simple support and uniform load is often used to model the step-height reduction as a function of pad properties. The maximum bending, Ym, at the center will be, Ym = C PL4/EI3, where C is a constant, P, loading, L, the length between two supports, I, pad thickness, and E, Young modulus. This free bending model does not provide information on local down force. Furthermore, if there is contact at the trench bottom surface with a down force, the two-support model is no longer selfconsistent, since the bending is not “free bending”. If the bending model is used to explain an increase of step height (or final dishing) with line width, the model predicts that dishing increases with the 4th order of line width. In reality, step heights are often found experimentally to level off at high line widths. Thus correct mathematical functions must be sought to interpret the trend of step height with line width. The correct step-height function should at minimum show first, an increase of step height or dishing with line width, and second, the first derivative must be a decreasing function of line width and becomes zero at a line width high enough, to be consistent with experiment results. The above bending model, with a 4th order of line width, obviously is improper for the requirement. In addition, the models need the capability to be extended to account for the impact of pattern density, lower dishing with lower line density, and material polishing rate differences, such as seen in barrier polishing. In this communication, the local planarization equations are first re-derived as a f
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