For many years, lithographic resolution has been the main obstacle in keeping the pace of transistor densification to meet
Moore's Law. For the 32 nm node and beyond, new lithography techniques will be used, including immersion ArF
(iArF) lithography and extreme ultraviolet lithography (EUVL). As in the past, these techniques will use new types of
photoresists with the capability to print smaller feature widths and pitches. Also, such smaller feature sizes will require
thinner layers of photoresists, such as under 100 nm.
In previous papers, we focused on ArF and iArF photoresist shrinkage. We evaluated the magnitude of shrinkage
for both R&D and mature resists as a function of chemical formulation, lithographic sensitivity, scanning electron
microscope (SEM) beam condition, and feature size. Shrinkage results were determined by the well accepted
methodology described in ISMI's CD-SEM Unified Specification. A model for resist shrinkage, while derived elsewhere, was presented, that can be used to curve-fit to the shrinkage data resulting from multiple repeated
measurements of resist features. Parameters in the curve-fit allow for metrics quantifying total shrinkage, shrinkage rate,
and initial critical dimension (CD) before e-beam exposure. With these parameters and exhaustive measurements, a
fundamental understanding of the phenomenology of the shrinkage trends was achieved, including how the shrinkage
behaves differently for different sized features. This work was extended in yet another paper in which we presented
a 1-D model for resist shrinkage that can be used to curve-fit to shrinkage curves. Calibration of parameters to describe
the photoresist material and the electron beam were all that were required to fit the model to real shrinkage data, as long
as the photoresist was thick enough that the beam could not penetrate the entire layer of resist.
In this paper, we extend this work yet again to a 2-D model of a trapezoidal photoresist profile. This model thus allows
CD shrinkage in thin photoresist to be solved, which is now of great interest for upcoming realistic lithographic
processing. It also allows us to predict the change in resist profile with electron dose and the influence of initial resist
profile on shrinkage characteristics. In this work, the results from the previous paper will be shown to be consistent with
numerically simulated results, thus lending credibility to these papers' postulations. Also, results from this 2-D
profile model can also give clues as to how we might, in the future, model the shrinkage of contour edges of 3-D shapes.
With these findings, we can conclude with observations about the readiness of SEM metrology for the challenges of
future photoresist measurement, as well as estimate the errors involved in calculating the original CD from the shrinkage