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Wepropose an integratedcontact mechanics and density-step-heightmodel of pattern dependencies for the chemical-mechanical polishing (CMP) of multi-level copper interconnects, and show preliminary comparisons with experimental data for the overburden copper removal stage. The model uses contact mechanics to correctly apportion polishing pressure on all sections of an envelop function that reflects the long-range thickness differences on the chip, or region of interest. With the pressure over the entire envelop known, the density-step-height part of the model is then used to compute the amount of material removed in the local “up-areas” and “down-areas”. ThismodelshowspromiseinaccuratelyandefficientlypredictingpostCMPcopperanddielectric thicknesses across an entire chip.

this paper, we introduce a mathematical model for chemical mechanical polishing #CMP# of reverse tone etchback shallow trench isolation #STI# structures. We present a detailed formulation of the model and describe CMP experiments using a newly designed STI CMP characterization mask to validate the model. A methodology for extracting the model parameters is also proposed. An improved modeling methodology that incorporates density averaging effects fits the experimental data more accurately. Finally, we use the model to predict the effects of pre-CMP step height, pattern density, polish time, pad hardness, and slurry selectivity on dishing and nitride erosion. 2001 The Electrochemical Society. #DOI: 10.1149/1.1348266# All rights reserved. Manuscript submitted June 1, 2000; revised manuscript received November 21, 2000. Shallow trench isolation #STI#<F1

In previous work, we have formalized the notions of "planarization length" and "planarization response function" as key parameters that characterize a given CMP consumable set and process. Once extracted through experiments using carefully designed characterization mask sets, these parameters can be used to predict polish performance in CMP for arbitrary product layouts. The methodology has proven effective at predicting oxide interlevel dielectric planarization results.In this work, we discuss extensions of layout pattern dependent CMP modeling. These improvements include integrated up and down area polish modeling; this is needed to account for both density dependent effects, and step height limits or step height perturbations on the density model. Second, we discuss applications of the model to process optimization, process control (e.g. feedback compensation of equipment drifts), and shallow trench isolation (STI) polish. Third, we propose a framework for the modeling of pattern dependent effects in copper CMP. The framework includes "removal rate diagrams" which concisely capture dishing height and step height dependencies in dual material polish processes. I. MOTIVATION: PATTERN DEPENDENT CMP CONCERNSThe motivation for this work is the presence of substantial pattern dependencies in CMP. As illustrated in Fig. 1, these concerns arise in a variety of key CMP process applications. In oxide or interlevel dielectric (ILD) CMP, the global planarity or oxide thickness differences in different regions across the chip is a key concern. In addition, the remaining local step height (or height differences in the oxide over patterned features and between patterned features) may also be of concern, although such local step heights are typically small compared to the global nonplanarity across the chip resulting from pattern density dependent planarization. In shallow trench isolation (STI), one is typically concerned about dishing within oxide features resulting from over-polish, as well as the erosion of supporting nitride and in some cases the details of the corner rounding near active areas. In metal polishing (such as in copper damascene), one is concerned also with dishing into metal lines, as well as the erosion of supporting oxide or dielectric spaces in arrays between lines.In this paper, we begin by reviewing previous work on characterization and modeling of oxide CMP pattern dependencies. In Section II, we review the density-dependent oxide CMP model, as well as the important determination of "effective density" based upon a planarization length or planarization response function determination. In Section III, we also review a recent advance in oxide modeling, through which a step height dependent model (proposed elsewhere) has been integrated with the effective density model to produce an integrated time-evolution model for improved accuracy in step height and down area polish prediction. In Section IV we present example applications of the oxide characterization and modeling methodology. These inclu...

Our group has proposed several chip-scale CMP models, with key assumptions including the notion of planarization length in the pattern density model [1], and step height dependent polishing rate in the density step height model [2]. In the effective density model, planarization length is the characteristic length of an elliptic weighting function based on the long-range pad deformation and pressure distribution during CMP. This semi-physical model is often adequate and usually gives a fitting error of a few hundred angstroms. As ever-shrinking device size pushes for tighter control of post CMP uniformity, however, we need a chip-scale CMP model with better accuracy.In this work, we re-examine the physical basis for averaging weighting functions and step height dependence, particularly in the context of contact mechanics based model formulations. The comparison of the two models confirms that the analytical density and step height models can be viewed as approximations to the contact wear model. The study also suggests a new dependence of contact height on line space and pattern density.