A theoretical evaluation of hydrodynamic and brush contact effects on particle removal during brush scrubbing

Wafer cleaning following chemical mechanical planarization, especially brush scrubbing, is a critical step in semiconductor device manufacturing that is not adequately understood. In this work, the effects of hydrodynamic forces, brush-particle adhesion, and brush-particle momentum transfer are quantified for spheroidal particles having aspect ratios ranging from 0.2 to 5. A critical particle Reynolds number approach was used to determine the effect of the hydrodynamic force and brush-particle adhesion on particle removal, while a moment balance approach was used to assess the effect of brush-particle momentum transfer on particle removal. Model systems of alumina particles adhering to and embedded in polished silicon dioxide and copper surfaces were considered. Results indicate that, in general, hydrodynamic forces can remove the majority of alumina particles adhering to silicon dioxide and copper, but if a particle becomes partially embedded in a surface, the addition of brush-particle adhesion and brush-particle momentum transfer may not be sufficient to cause particle removal.