A Closed-form Analytic Model for Ild Thickness Variation in Cmp Processes

CMP planarization of oxide results in excellent long-range uniformity compared to other planarization techniques but remains hampered by systematic pattern sensiti vities. In the recent literature, se veral semi-empirical or physically-based models have been proposed to explain ILD thickness pattern sensitivities in CMP, but all of these models either fail to predict key empirical results, are not described fully, or do not present tractable closed form models. In this paper , we develop and derive a closed form model for ILD thickness variation and verify this model on datasets obtained o ver different polishing tools, consumable sets, and process conditions, and as a function of polishing time.