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The extension of optical lithography to 7 nm node and beyond relies heavily on multiple litho-etch patterning technologies. The etch processes in multiple patterning often require progressively large bias differences between litho and etch as the target features become smaller. Moreover, since this litho-etch bias has strong pattern dependency, it must be taken into consideration during the Optical Proximity Correction (OPC) processes. Traditionally, two approaches are used to compensate etch biases: rule-based retargeting and model-based retargeting. The rule-based approach has a turn-around-time advantage but now has challenges meeting the increasingly tighter critical dimension (CD) requirements using a reasonable etch-bias table, especially for complex 2D patterns. Alternatively, model-based retargeting can meet these CD requirements by capturing the etch process physics with high accuracy, including the etch bias variability that arises from both patterning proximity effects and etch chamber non-uniformity. In the past, empirical terms have been used to approximate the etch bias due to pattern proximity effects but sometimes empirical models are known to have compromised model accuracy so a physical based approach is desired. This paper’s work will address the etch bias variability due to patterning proximity effects by using a physical approach based simplified chemical kinetics. It starts from a well calibrated After-Development-Inspection (ADI) model and the subsequent etch model is based on the ADI model contour. By assuming that plasma chemical species in the trenches are maintained in an equilibrium state, the plasma species act on the edges to induce etch bias. Methods are developed to evaluate plasma collision probability on trench edges for random layouts. Furthermore, the impact of resist materials on etch bias are treated with Arrhenius equation or as a second order reaction. Equations governing plasma collision probabilities on trench edges as a function of time are derived. An etch bias model can be calibrated based on those equations. Experimental results have shown that this physical approach to model etch bias is a promising direction to applications for full-chip etch proximity corrections.
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