Advances in Inverse Lithography

As Moore's law has marched forward, progressively shrinking chip designs at a consistent pace, the manufacturing of those chips has raced to keep up. Through advances in lithography hardware and software, we now are in the realm of the single-digit-nanometer design nodes at leading chip foundries. This paper will review the method of Inverse Lithography Technology (ILT), which is the preferred computational method for photolithography. Indeed photolithographic masks were the first metasurfaces, and still the most important metasurface, economically, used in memory chips, storage, and microprocessors. Moreover, photolithographic mask designers were the early adopters of the mathematical optimization in optics, creating ILT, specifying intended wafer patterns and metrics, and using the mathematical machinery of level sets, functional derivatives, and adjoints to drive the mask design process.