Fundamental limitations of LIGA x-ray lithography : sidewall offset, slope and minimum feature size.

Analytical and numerical methods are used to examine photoelectron doses and their effect on the dimensions of features produced by deep x-ray lithography. New analytical models describing electron doses are presented and used to compute dose distributions for several feature geometries. The history of development and final feature dimensions are also computed, taking into account the dose field, dissolution kinetics based on measured development rates, and the transport of PMMA fragments away from the dissolution front. We find that sidewall offsets, sidewall slope and producible feature sizes all exhibit at least practical minima and that these minima represent fundamental limitations of the LIGA process. The minimum values under optimum conditions are insensitive to the synchrotron spectrum, but depend strongly on resist thickness. This dependence on thickness is well approximated by simple analytical expressions describing the minimum offset, minimum sidewall slope, minimum producible size of positive and negative features, maximum aspect ratio and minimum radius of inside and outside corners