Stochastic models for material removal rate (MRR) in chemical mechanical planarization (CMP) process

Most of the previous work related to the prediction of the material removal rate (MRR) in CMP process to date has been concerned with the ideal case, wherein there is no randomness associated with either the pad or the slurry. In the work of this dissertation, we investigated the material removal rate (MRR) by taking some of the randomness into account, including randomly varying pad asperity heights and/or randomly varying slurry particle sizes.; The MRR decay phenomenon as well as the MRR variation on the slurry particle size distribution has gained more and more attention in CMP industry. However, very few efforts have been done on the mechanism of the MRR decay up to date. In this work on the MRR decay, the role of stochastic variations in pad surface topography evolution during a CMP process is investigated. The MRR for CMP is modeled utilizing elastic as well as inelastic contact between flat wafer and rough pad. Evolution of pad surface topography is observed to have a significant influence on the MRR variations. A distinguishing feature of this work is the MRR based on material removal for each single asperity. It is observed that an elastic contact model significantly underestimates the experimental trend. The selection of the initial PDF (Probability Density Function) of pad asperity height distribution used in an MRR decay model is shown to be a key issue. It is observed that reasonably small changes in numerical estimates of PDF parameters can have a significant effect on the accuracy of MRR model predictions. By extending the model to the case of inelastic contact between the wafer and pad asperities, it is found that model performance can be notably improved.; The work in the MRR decay model considers material removal in relation to direct contact between the pad and the wafer. The influence of the slurry particles is not considered. However, because the pad is soft compared to both the wafer and the slurry particle, it is, in fact, the slurry particle-wafer contact that relates most directly to material removal. Furthermore, the chemical reaction between the slurry and the wafer surface material creates a softer layer on the surface of the wafer and changes the mechanical properties of wafer surface material. The slurry abrasive particles entrapped in the wafer-pad contact region are indented into the wafer surface and plough materials off from the wafer surface as the particles slide across the wafer surface. Several investigators have explored the mechanisms of material removal due to the pad-slurry particle-wafer contact. The methods of estimating the number of slurry particles actively participating in the material removal are different among these investigators. In this dissertation, we first compare the MRR predictions accompanying two different assumptions on the active particles participating in the material removal. Elements of these two models are then combined with time varying MRR models to a third (dynamic) MRR model. The dynamic MRR model is able to explain the experimentally observed MRR decay phenomenon due to pad surface topography evolution and considers the MRR variation with respect to particle size distribution in addition to the mean value of particle sizes.