Random forest-based robust classification for lithographic hotspot detection

Abstract. With continuous downscaling of feature sizes, potentially problematic patterns (hotspots) have become a major issue in generation of optimized mask design for better printability. The lithography process sensitive patterns in a design lead to degradation of both electrical performance and manufacturing yield of the integrated circuit. Due to sequential flow of very large-scale integration (VLSI) design and manufacturing, missing any hotspot has an adverse impact on product turnaround time and cost. The lithographic samples are generally defined using a combination of continuous variables (to represent aerial image and pattern density) and categorical variables (to represent allowed layout design rules). The conventional hotspot classification techniques suffer from suboptimum performance due to their inability to efficiently represent and use the above-mentioned feature metrics. In general, the number of hotspots in the lithographic data is much less compared to the total number of patterns in a full-chip design. It makes the input data imbalanced and adds additional difficulties in the decision making processes. We present a robust technique to detect the process sensitive patterns using random forest-based machine learning technique. The emphasis is put on the layout features extraction techniques to improve the performance of the proposed approach. The simulation results show that the patterns susceptible to variations under different dose and focus conditions undergo a drastic change in their aerial image characteristics even when the geometry is varied by a very small margin. We observed from our analysis that the minimum number of false negatives can be achieved with reasonable increase in the number false positives. Moreover, compared to conventional hotspot classification techniques, we are able to achieve a very low percentage of false negatives with a binary classifier trained on an imbalanced dataset. Another key observation from our analysis is that the random forest method can obtain the most representative heuristics required to define categories from the lithographic datasets with continuous and categorical variables. In addition, our proposed approach can easily be integrated with commercially available electronic design automation tools and in-house design simulators to make the process flow viable in terms of a business perspective.