Size effect of nanoparticles in chemical mechanical polishing - a transient model

When a workpiece to be polished is placed on the carrier of a polishing machine, it is pressed down to the polishing pad. Large abrasives make contact between the pad and the workpiece before the smaller ones. The larger abrasives are pressed into the pad and indented into the workpiece. These particles are the active abrasives and participate in material removal. The abrasives with a size less than the gap between the pad and the workpiece move freely in the valleys/voids of the pad and are inactive. As the gap decreases during the polishing process, smaller abrasives trapped between the pad and the workpiece become active in polishing. Thus, the process of chemical-mechanical polishing is dynamic, while all previous modeling is static. This paper establishes a dynamic model for the abrasives. The modeling considers the transient motion of the workpiece/particle/pad in the vertical direction and the change of the roughness of the workpiece. A study of the transient motion shows an increasing number of active particles and a changing polishing rate in the first 2 min. It also demonstrates that the viscoelastic properties of the pad and the workpiece surface roughness are important factors in determining the polishing rate. This paper also shows that when the average particle size is smaller than an optimum size, the polishing rate increases with increasing particle size for the same particle density or same wt% abrasives. Yet, if the average particle size is larger than the optimum size, the polishing rate decreases with increasing particle size.