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Computational Lithography by Xu Ma, Gonzalo R. Arce

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Chapter 11

Conclusions and New Directions of Computational Lithography

11.1 Conclusion

In this book, we described a variety of gradient-based inverse lithography algorithms for OPC and PSM optimizations, as well as simultaneous source and mask optimization. Different optical lithography systems, ranging from coherent to partially coherent imaging systems, were taken into account in these algorithms. We also presented a set of regularization frameworks to reduce the output pattern errors and complexity of the optimized mask and source patterns. Subsequently, these algorithms were extended to OPC and PSM optimizations under the thick-mask assumption, which accounted for the polarization and diffraction effects due to the 3D topography of the mask.

In Chapter 2, the fundamentals of the optical lithography systems were summarized. The Abbe's model and the Hopkins diffraction model were discussed, both of which are based on the spatial discretization of the source into a number of spatially incoherent point sources. In the Abbe's model, the coherent images generated by every source point are incoherently added together to produce the final partially coherent image. On the other hand, the Hopkins diffraction model is a simplified and approximate version of the Abbe's model, which carries out the integration over the source first, and the result directly provides the aerial image of the partially coherent image system. Subsequently, three types of approximation models were summarized ...

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