Modeling effects of abrasive particle size and concentration on material removal at molecular scale in chemical mechanical polishing

A novel material removal model as a function of abrasive particle size and concentration was established in chemical mechanical polishing (CMP) based on molecular scale mechanism, micro-contact mechanics and probability statistics. A close-form equation was firstly developed to calculate the number of effective particles. It found nonlinear dependences of removal rate on the particle size and concentration, being qualitatively agreement with the published experimental data. The nonlinear relation results from the couple relationship among abrasive number, slurry concentration and surface atoms' binding energy with the particle size. Finally, the system parameters such as the operational conditions and materials properties were incorporated into the model as well.