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.