A molecular-scale analytic model to evaluate material removal rate in chemical mechanical planarization considering the abrasive shape

Abstract

This paper presents a theoretical model of material removal rate (MRR) in the process of chemical mechanical planarization (CMP), in which the morphology effect of abrasive particles is taken into account using a shape factor. In contrast to previous models based on the continuum material removal mechanism, the physical basis of the current model is that the wafer material is primarily removed by de-bonding the chemistry-weakened surface molecules. It is shown that a non-linear relationship between the shape factor and the MRR is given rise to by two opposite effects. On one hand, the increase in the shape factor results in the decrease in the number of the effective particles participating in the material removal, and subsequently contributing to the decrease in the MRR. On the other hand, the particle/wafer contact diameter is enhanced with the increase in shape factor, leading to the increase in the MRR. The simulation results match well with the published experimental data in the range of low polishing pressure conditions. With further increase in the pressure, the effect of the shape factor on the MRR becomes significantly pronounced, which might be ascribed to the influence of the abrasive shape on the micro-contact state of the pad/abrasive/wafer. In addition to the shape factor, most variables involved in the CMP process, such as processing conditions (velocity, pressure), pad properties (modulus, hardness and asperity size) abrasive characteristics (size, concentration and distribution) and wafer hardness, were also addressed in the present model.