Defining a physically accurate laser bandwidth input for optical proximity correction (OPC) and modeling

Abstract

In this study, we discuss modeling finite laser bandwidth for application to optical proximity modeling and correction. We discuss the accuracy of commonly-used approximations to the laser spectrum shape, namely the modified Lorentzian and Gaussian forms compared to using measurement-derived laser fingerprints. In this work, we show that the use of the common analytic functions can induce edge placement errors of several nanometers compared to the measured data and therefore do not offer significant improvement compared to the monochromatic assumption. On the other hand, the highlyaccurate laser spectrum data can be reduced to a manageable number of samples and still result in sub 0.5nm error through pitch and focus compared to measured spectra. We have previously demonstrated that a 23-point approximation to the laser data can be generated from the spectrometry data, which results in less than 0.1nm RMS error even over varied illumination settings. We investigate the further reduction in number of spectral samples down to five points and consider the resulting accuracy and model-robustness tradeoffs. We also extend our analysis as a function of numerical aperture and illumination setting to quantify the model robustness of the physical approximations. Given that adding information about the laser spectrum would primarily impact the model-generation run-times and not the run-times for the OPC implementation, these techniques should be straightforward to integrate with current full-chip OPC flows. Finally, we compare the relative performance of a monochromatic model, a 5-point laser-spectral fingerprint, and two Modified Lorentzian fits in a commercial OPC simulator for a 32nm logic lithography process. The model performance is compared at nominal process settings as well as through dose, focus and mask bias. Our conclusions point to the direction for integration of this approach within the framework of existing EDA tools and flows for OPC model generation and process-variability verification.