Average flow model with elastic deformation for CMP

We present a three-dimensional (3D) average flow model considering elastic deformation of pad asperities for chemical mechanical planarization. To consider the contact deformation of pad asperities in the calculation of the flow factor, 3D contact analysis of a semi-infinite solid based on the use of influence functions is conducted for computer-generated rough surfaces. The average Reynolds equation and boundary conditions of both force and momentum balance are used to investigate the effects of pad roughness and external pressure conditions on a film thickness and wafer position angles. It is found that the position angles decrease with the increasing of the applied pressure and the roughest pad has the highest position angles at any given load. Comparing elastic and rigid pads, the minimum film thickness formed between the elastic pad and the wafer is thinner than that between the rigid pad and the wafer.