CMP pad wear and polish-rate decay modeled by asperity population balance with fluid effect

An important task in chemical–mechanical polishing (CMP) is to determine when the pad should be changed or reconditioned. A model which can predict the pad asperity probability distribution function (PDF) during polishing and conditioning is valuable for this purpose. Previous work has been done without incorporating fluid mechanics into the model in L.J. Borucki, J. Eng. Math. 43 (2002) 105–114, but that will overestimate the pad wear because the fluid reduces the load applied on the individual asperities. This work models the wear of pad asperities and polish-rate decay in CMP by coupling the population balance model with fluid mechanics. Modeling results with and without fluid effect are compared. Polish-rate model results are compared with experimental data in D. Stein et al., J. Electron. Mater. 25 (10) (1996) 1623–1627, and the results agree with experimental results for both cases by using different wear rate coefficients to fit experimental data. A lesser wear rate coefficient must be used to fit Stein’s data for the fluid case compared to the case without fluid. The wear rate of the pad is calculated from the rate of change of the pad–wafer separation distance during polishing because only asperities above this distance will be in contact and worn down and that portion will be piled up at the pad–wafer separation distance on the PDF curve of the pad asperities. The PDF evolution model results with fluid show much less pad wear compared to the case without fluid. Also if fluid is neglected, pad–wafer separation distance will continue to drop until it is zero, while for the fluid case, it will eventually reach a dynamic steady-state with no pad wear indicating that the load is entirely supported by the fluid. Accurate predicting the interface gap (pad wear) is critical for controlling both mechanical and chemical removal rate and within wafer non-uniformity (WIWNU). These results show that fluid is an important factor which needs to be included into the model in predicting the interface gap and surface profile evolution of the pad during polishing and conditioning.