Porosity model for flows in CMP

Abstract

In an effort to explore the contribution of the pad, which is usually full of pores, to the performance of CMP (chemical mechanical polishing), a three-dimensional flow model of CMP is presented by assuming that the fluids in the porous layer comply with Darcy’s law, which states that the flow velocity is proportional to the pressure gradient and inverse proportional to the viscosity. The flow equation is deduced accordingly and, by taking advantage of the multi-level technique and line relaxation technique, numerical simulations are carried out to reveal the relationships between the load capacities and operational parameters (including pivot height, roll angle and pitch angle), under conditions with different porous parameters and different thicknesses of the porous layer. The little porous parameter will lead to a prominent increase of load capability (for instance, the load and the moment predicted), which is still augmented by the thicker layer parameter. This will result in a higher material removal ratio of CMP. A pad full of large pores will be used to deduce load capability, facilitating the free flow of the fluids through the pores. The research will add some insights on the mechanism of the CMP technique.