A mathematical model for chemical–mechanical polishing based on formation and removal of weakly bonded molecular species

This paper presents a mathematical model that describes the chemical–mechanical synergy and mechanism of material removal in chemical–mechanical polishing (CMP). The physical basis of the model is that chemical reactions convert strongly bonded surface atoms/molecules to weakly bonded molecular species while the mechanical action delivers the energy that is needed to break the weak molecular bonds, thereby removing the surface materials at the molecular scale. Three key variables are defined to describe the chemical–mechanical synergetic effects. Close-form equations are derived relating these variables to the process parameters, making use of the concepts of chemical–mechanical equilibrium, chemical kinetics, contact mechanics, molecular binding energy and random-process probability. The model is applied to the process of silicon-wafer CMP. The governing equation of the material removal reveals some insights into the process. It also offers some sensible explanations to the effects of the operating and material parameters on the rate of material removal and process quality.