Mathematical problems of holographic mask synthesis

摘要

SWHL Nanotech team have implemented effective algorithms and developed scalable software allowing to synthesize holographic masks for various lithography applications including MEMS, MOEMS and high-end IC production. Most of the technical problems of state-of-art projection photolithography such as 3D-imaging, quality optimization were stated and solved as a completely numerical problems in the case of holographic lithography approach. Nanotech SWHL team developed effective algorithms of the holographic mask synthesis based on FFT with the complexity of O(N ln N), which allowed to synthesize holographic masks for any IC layer. We developed the continuous phase-shifting optimization method based on WFS, DFS and gradient descent, in which a hologram is synthesized not for the original pattern, but for a pattern with altered amplitude and phase distribution. Like in other RET, the holographic mask synthesized for the properly altered pattern provides a much better-quality image of the original pattern. Thus, today it is possible to use modern computing clusters for the synthesis of holographic masks and to implement them in inexpensive and sustainable devices for holographic photolithography.