Inverse analysis of material removal data using a multiscale CMP model

This paper describes a mechanical model for a representative dual axis rotational chemical mechanical planarization (CMP) tool. The model is three-dimensional, multiscale and includes sub-models for bulk pad deformation, asperity deformation, lubrication based slurry flow, carrier film deformation, wafer compliance and material removal by abrasive particles in the slurry. With the model, material removal rate (MRR) can be determined as a function of stress applied to the wafer, relative sliding speed, and material and geometric parameters of the pad and slurry. Experimental material removal rate profiles obtained from Cu polishing experiments performed on a wafer without rotation are analyzed as an inverse problem. We use MRR data to predict local CMP conditions such as fluid film thickness, fluid pressure and contact pressure. The results are consistent with available experimental and analytical information. This inverse technique offers promise as an improved method of CMP model verification.