Modeling pad wear and pad conditioning in chemical-mechanical polishing using population balance model.

摘要

Chemical mechanical planarization (CMP) has become the leading planarization technology in integrated circuit manufacturing. The CMP process is highly dependent on the surface condition of the pad. The height distribution of the pad asperities (PDF) together with the process conditions determines the chemical-mechanical removal rate and within wafer nonuniformity (WIWNU) as well as defects in the form of scratches. Understanding the asperity height distribution during polishing and conditioning is important in controlling many aspects of CMP and forms the basis of this dissertation.;This dissertation attacks the problem of predicting the pad asperity PDF by considering the effects of pad asperity wear due to contact with the wafer and the generation of asperities during pad conditioning. In CMP, the aggressiveness (pad cut-rate) of the conditioner should overcome the CMP pad wear-rate during the in situ conditioning in order to sustain a stable polish-rate. In this work, a population balance model (PBE) for pad asperities is used to model the pad wear and pad conditioning processes. Fluid mechanics is built into the pad wear model. Pad plastic deformation and variable diamond height for the conditioner are built into the conditioner model that have not been done in previous works. The results with variable diamond height show that the conditioned pad asperity PDF is Gaussian. The variance of the conditioned pad asperity PDF is decided by the variance of the cutting diamonds (active diamonds). The model results also show that a different interface gap between the conditioner and pad will give a different standard deviation of the resulting conditioned pad asperity PDF if the conditioner diamond height PDF is Gaussian. This is consistent with the experimental findings that with increasing load, the roughness of the conditioned pad asperity PDF increases. Model results in this work show that it is caused by the decreasing of the interface gap between the rough surface of the conditioner diamonds and the pad surface resulting in the change of the roughness of the active diamonds. Analytical solutions are also derived and found matching the Monte Carlo numerical results.