Data assimilation for accurate simulation of oxygen precipitate distributions in Si wafers during the cascade process.

In this study, a multi-objective data-assimilation framework was applied to a physics-based simulator to improve predictions of bulk micro-defects (BMDs) in silicon wafers during a three-step cascade thermal process. A simulation capable of reproducing the formation, growth, and dissolution behavior of BMDs in silicon wafers during heat-treatment processes was employed. The depth-resolved BMD density and size distributions were formulated as a multi-objective optimization problem that simultaneously minimizes the squared errors between the experimentally measured bulk radii and the radii calculated by the simulation. The fitting parameters were optimized using a genetic algorithm (GA). Data assimilation reduced BMD growth-rate errors by 57 % for the first-to-second step and by 69 % for the second-to-third step. The assimilated model successfully reproduced the nonlinear BMD size evolution during intermediate processes. These results demonstrate that integrating data assimilation into the simulation enables more accurate prediction of BMD distributions throughout the cascade process and provides a foundation for defect-aware wafer–device co-design and digital-twin development in semiconductor manufacturing.