Predictive modeling of mixed abrasive slurry for enhanced performance in tungsten chemical mechanical polishing: A particle number concentration approach

As semiconductor devices continue to scale down and incorporate increasingly complex multilayer structures, chemical mechanical polishing (CMP) faces critical challenges in simultaneously achieving high removal rates (RR) and excellent within-wafer non-uniformity (WIWNU). Conventional single abrasive slurries and mass concentration–based mixed abrasive slurry (MAS) models have reached their performance limits, primarily because they disregard the actual number distribution of particles and the effects of polydispersity. In addition, traditional light-scattering analysis for particle size measurement cannot accurately determine the mixing ratios of different sized abrasives in polydisperse conditions. To overcome these limitations, this study used a scanning mobility particle sizer (SMPS) to precisely quantify particle number concentrations in mixed slurries and incorporated these data into a predictive MAS model. The contact area analysis, further supported by packing density calculations, indicated that the maximum contact area occurs at an optimal composition of 55 % large particles (113 nm) and 45 % small particles (55 nm). Tungsten CMP experiments verified these predictions, achieving up to a 6.45-fold increase in removal rate and a 54.1 % reduction in WIWNU compared with single abrasive slurries under same total particle counts. Moreover, the removal rate exhibited a strong linear correlation with the calculated total contact area (R² = 0.90), while the number-based model substantially reduced prediction errors relative to conventional mass-based models (RMSE: 129.84 vs. 223.38; MAPE: 17.55 % vs. 24.12 %). These results demonstrate that particle number concentration-based modeling provides a quantitative basis for slurry optimization, enabling the simultaneous enhancement of efficiency and uniformity in advanced tungsten CMP.