A multi-objective optimization flow is developed to identify balanced compact optical proximity correction (OPC) models with ideal calibration accuracy, runtime performance and prediction accuracy. We demonstrate a model selection process based on Pareto front optimization to meet multiple modeling requirements in a single optimization step. A genetic search algorithm determines the final population that offers the best trade-off in set model properties. As a demonstration, we cooptimize calibration accuracy, verification accuracy and term count in a mode developed for hot spot prediction for a line and space memory layer. The optimization determines the minimum number of model terms to meet the off-nominal dose and focus patterning accuracy requirements in verification. Multi-objective optimization provides better verification process window condition (PWC) accuracy because of the multi-objective trade-off built into the genetic algorithm (GA). The optimizer also provides better calibration accuracy (Rms Weighted) than compact models with a fixed configuration because model composition is optimized during GA search. The resulting champion model is 30% more predictive and 5% faster in simulation using this approach. Results for a negative tone develop hole layer with a model complexity of up to 44 terms are also analyzed based on nominal only measurement data. We further show the models selected by multi-objective optimization have a lesser tendency to over-fit the calibration data. The methodology can be applied to streamline complex models for optimum performance and target error rate. In many cases, for smaller data sets, we show that simplified models provide improved verification accuracy within metrology error limits.
Tighter edge placement requirements for advanced nodes has driven model accuracy requirements, especially in the area of etch modeling. Etch model errors are becoming a larger part of the total model error and effects that could previously be ignored, now have to be addressed. To address systematic errors in etch modeling, new modeling techniques for etch modeling are presented, namely, Variable Edge Bias (VEB) model, the Reactive Ion Etch Variable Bias Model (RIE VEB), and finally, neural network assisted dual stage etch (N2E) model. The VEB RIE model enables the ability to represent trends relating to physical parameters, such as time and temperature into the model. To further improve model accuracy, a machine learning solution is introduced, which operates on the etch model’s residual error.
The fast rigorous model (FRM) is a first principles solver based on sequential simulations of photochemical reactions in photoresists. We report the evaluation of FRM relative to compact models (CM1) for NTD OPC model accuracy. We demonstrate equivalent or better accuracy to CM1 when FRM is combined with a CM1 model of the same composition. In the case of CTR to FRM comparison, FRM is 34% more accurate in calibration and prediction on average across 20 testcases. FRM is 5% more predictive than the most complex CM1 modelform tested with similar calibration accuracy. FRM supplemented with limited CM1 terms provides better verification accuracy for SRAF printing and hotspot detection. Further, the input data needed to train the FRM model in order to achieve high predictive accuracy is a fraction (1-5%) of that needed by more complex CM1 modelforms. Finally, we show through the Akaike Information Criteria method that FRM is more predictive than an equivalent CM1 model based on the degrees of freedom in the modelform and quantity of data available.
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