Non-Linear Process Model for CMP-APC

For Si dioxide-film CMP process in semiconductor manufacturing, which requires high precision, run-to-run control has been developed. The run-to-run control is a kind of repetitive control to adjust polishing time at every start of work in a work sequence. This control is based on a process model, which expresses the relation between polishing time and polished thickness. The model is non-linear for Si dioxide-film CMP with Ceria slurry and it contains many parameters. However the parameters must be determined by product type. Therefore, a modeling method of nonlinear process models is developed for multi-product high-volume manufacturing. In this method, model is determined by selecting the optimum combination of arbitrary terms, whose parameter values satisfy constraints of non-linear polishing process. The result shows that the model can be selected using more than 10 samples. Calculated polishing time achieves high precision in film-thickness after CMP. The standard deviation of film-thickness after CMP is less than 1% of target film-thickness.