A Comparison of Active Particle Models for Chemical Mechanical Polishing

Abstract

A multitude of models exist to predict the material removal rate (MRR) during CMP. Common among many of these models is the prediction of the MRR based on the product of the material removal rate per particle (MRRPP) and the number of active particles, Nact, actively contributing to the material removal. Discrepancies between CMP models and experiments are sometimes compensated for by empirical wear coefficients that are used as fitting parameters placed on the overall CMP model. However, such empirical correlations can obscure deficiencies in the prediction of the material removed per particle and the number of active particles. A decoupled understanding of both MRRPP and Nact is essential for accurate modeling of CMP. This work investigates the predictions of several active particle models, decoupled from the prediction of the MRR, to assess their agreement. In addition to the number of active particles, the models are used to predict the number of particles in the interface and the number of particles eligible to become active. It is found that although the models differ greatly in their assumptions to predict these quantities, there is some similarity in their prediction of the number of active particles.