# 2008 Research Summary

## Application of Machine Learning Techniques to Improve Convergence Properties of Model-Based OPC Algorithms

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Allan Xiao Yu Gu, Peiran Gao and Avideh Zakhor

An important step in today's integrated circuit (IC) manufacturing is optical proximity correction (OPC). In model-based OPC, masks are systematically modified to compensate for the non-ideal optical and process effects of the optical lithography system. The polygons in the layout are fragmented, and simulations are performed to determine the image intensity pattern on the wafer. If the simulated pattern on the wafer does not match the desired one, the mask is perturbed by moving the fragments. This iterative process continues until the pattern on the wafer matches the desired one. Although OPC increases the fidelity of pattern transfer to the wafer, it is quite CPU-intensive due to the simulations performed at each iteration; OPC for modern IC designs can take days to complete on computer clusters with thousands of CPUs.

In this work, linear regression techniques from statistical learning are used to predict the fragment movements, and the predictions are compared with the results obtained using model-based OPC. The goal is to reduce the number of iterations required in model-based OPC by using a fast, computationally efficient linear regression solution as the initial guess to model-based OPC. To determine the best linear regression model, we train and evaluate several linear regression models based on prediction error using 2μm by μm layout patterns extracted from a section of a 90 nm IC design, labeled design A. After selecting the best linear regression model, we train the model using patterns extracted from a different section of design A, and evaluate the prediction error on another section of design A as well as another 90 nm IC design labeled design B. Experimental results show that fragment movement predictions via linear regression models are close to those obtained via model based-OPCs. In addition, the predicted edge movements via linear regression models are shown to significantly decrease the number of iterations required in model-based OPC.