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

摘要

In this study, we discuss modeling finite laser bandwidth for application to optical proximitymodeling and correction. We discuss the accuracy of commonly-used approximations to the laser spectrumshape, namely the modified Lorentzian and Gaussian forms compared to using measurement-derived laserfingerprints. In this work, we show that the use of the common analytic functions can induce edgeplacement errors of several nanometers compared to the measured data and therefore do not offersignificant improvement compared to the monochromatic assumption. On the other hand, the highly-accurate laser spectrum data can be reduced to a manageable number of samples and still result in sub0.5nm error through pitch and focus compared to measured spectra. We have previously demonstrated thata 23-point approximation to the laser data can be generated from the spectrometry data, which results inless than 0.1nm RMS error even over varied illumination settings. We investigate the further reduction innumber of spectral samples down to five points and consider the resulting accuracy and model-robustnesstradeoffs. We also extend our analysis as a function of numerical aperture and illumination setting toquantify the model robustness of the physical approximations. Given that adding information about thelaser spectrum would primarily impact the model-generation run-times and not the run-times for the OPCimplementation, 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-spectralfingerprint, and two Modified Lorentzian fits in a commercial OPC simulator for a 32nm logic lithographyprocess. The model performance is compared at nominal process settings as well as through dose, focusand mask bias. Our conclusions point to the direction for integration of this approach within the frameworkof existing EDA tools and flows for OPC model generation and process-variability verification.