Macroscopic and microscopic modelling in chemical-mechanical polishing (CMP) process

This dissertation investigates various modelling issues in Chemical Mechanical Polishing (CMP) process, with focus on abrasive particle dynamics, macroscopic modelling of the process, microscopic modelling of material removal and nonuniformity issues in CMP.; Abrasive particle dynamics is first examined. The goal is to understand how abrasive particles behave in the material removal process. It was found that only a very small fraction of submicron particles in the slurry are able to settle down on the pad away from the slurry delivery point during CMP, whereas settling will occur for particles on the order of tens of microns and larger. It was also shown that the location of the slurry delivery point has a significant effect on material removal, and away from this point the deposition of particles can be ignored. A preliminary study on abrasive particle collision in the slurry showed that significant particle collision is possible during CMP.; Macroscopic analysis of the process is presented next. Two CMP operating regimes, hydrodynamic lubrication regime and contact regime, are identified. It was found that low applied pressure, high relative velocity, and high pad porosity lead to small gap size between the wafer and the pad, thus favor hydrodynamic lubrication. The nonlinear effect of pad compressibility is shown as well. It was demonstrated that for pads with low compressibility, increasing pad compressibility increases the slurry film thickness, therefore favors hydrodynamic lubrication; for pads with high compressibility however, the opposite is true---increasing pad compressibility narrows the gap, therefore contacts between the wafer and the pad are more likely. It was also shown that if the gap between the wafer and the pad is small, the effect of slurry flow on the contact between the wafer and the pad is very small, thus can be ignored without loss of accuracy. Analysis of contact regime mechanics showed that the pad properties, including pad asperity height distribution, pad asperity size distribution and pad stiffness, determine how the contacts between the pad and wafer occur.; A microscopic analysis is conducted following the macroscopic study. A general material removal model in the contact regime was developed. It was found that only some portion of the abrasive particles in contact with the wafer and the pad contributes to the material removal process. A criteria was given to identify those particles. The model shows why characterization of the wafer surface properties after chemical reaction is critical in understanding the material removal mechanisms in CMP. It was shown that Luo's formula is a specific case of the general model.; Based on the macroscopic and microscopic analysis, non-uniformity issues in CMP are discussed. The macroscopic non-uniformity was first analyzed using beam on an elastic foundation model, and the results showed that softer pad produces better within-wafer-nonuniformity. This model is appropriate if the pad has very fine pad asperities, which are smaller than the feature size on the wafer surface. Otherwise, the edge of the wafer will be removed much faster than bulk of the wafer, which is explained using a punch indentation model. On the feature level, it was found that the relative size of the pad asperity and the feature size on the wafer plays a very important role. If the pad asperity size is much larger than the feature size on the wafer, a hard pad will produce better uniformity across features, i.e. local uniformity. On the other hand, if the pad asperity is much smaller than the feature size on the wafer surface, a soft pad will generally produce better uniformity across the wafer.