A multiscale model for chemical mechanical planarization

We present a multiscale contact mechanics and hydrodynamics simulation model for CMP. The model is based on satisfying the force and moment balance equations appropriate for a rotational CMP tool. A hyper-elastic material model is used for our asperity scale model to account for large deformations of soft polymer asperities. Contact force is determined as a function of compression for a single asperity. The results of the single asperity model are used in an extended Greenwood-Williamson (GW) model to compute the wafer scale contact stress caused by the compression of multiple asperities, A finite element formulation of a wafer scale model is solved by the commercial finite element program ANSYS to determine the contact stress of the bulk pad of a Finite thickness for a specified deformation, as a function of position. The local fluid film heights are computed from the asperity compression relative to that of the bulk pad, and are used to compute hydrodynamic fluid pressures. We iteratively solve the 'soft' elastohydrodynamic contact problem, i,e., solid-solid contact problem coupled with fluid pressure until the global force and moment balances are satisfied for given operating conditions. Finally, we compute the relative material removal rates across a wafer based on asperity contact stress.