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A model based on statistical method and elastic theory is presented to describe the wear mechanism of the silicon wafer surface during chemical-mechanical polishing. This model concerns the effects of applied pressure and relative velocity between the pad and the wafer on the removal rate during polishing and is capable of delineating the role of the mechanical properties of the slurry particles and the films to be polished. The removal rate is dependent on the elastic moduli of slurry particle and polished film. Comparisons with experimental data demonstrate the validity of the model for predicting relative removal rate for various dielectric films.

Abstract:The primary purpose of this study is to develop regional models of the lower part of flow duration curves (LPFDCs) to synthesize low-flow characteristics at ungauged sites in southern Taiwan. Because of the close relationship between low streamflow regimes and hydrogeological features, the model development first involved delimiting homogeneous hydrogeological regions by using two-step cluster analysis. Each homogeneous region was then discriminated by an equation developed on the basis of its hydrogeological features, which was then used to determine which of three sets of regional LPFDC models would be appropriate for a particular ungauged site. Each of the three sets of regional LPFDC models were developed using both conventional multivariate statistical regression and fuzzy regression. Thirty-four stream-gauged watersheds located in southern Taiwan provide the data set. The study results reveal that the regional LPFDC models developed in this study could be applied reasonably at ungauged sites.

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To better understand variations in the rate at which material is removed from a wafer during chemical-mechanical polishing (CMP), knowledge of the mechanical properties of the wafer surface is required. The nanoscale mechanical properties of undoped dielectric films were investigated using the nanoindentation technique. Crack resistance examined from the loading curve suggested that precursor cracks for SiH4-atmospheric pressure chemical deposition films with a tensile stress, as compared with other dielectric films with compressive stresses, appeared in the earlier stage of indentation. The hardness of dielectric films determined from the unloading curve could be considerably dependent on the film's preparation methods. Correlation between the Si-O bond densities and hardness were also studied. Experimental results showed that there was a linear relationship between the surface hardness and the removal rates of the undoped dielectric films under a well-controlled CMP process.