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Using the Feature Model to Define CD In the last edition of this column I described the feature model, a simple mathematical shape with a small number of parameters that is used to approximate a much more complicated real feature crosssection. Figure 1 shows the most common feature model used for extracting critical dimensions (CDs), the trapezoidal feature model. As I mentioned last time, the necessary use of an overly-simplified feature model to extract a single CD value from a complex resist profile has two fundamental error sources (independent of any measurement error): error in the use of a simplified feature model and errors associated with the method of finding the “best fit� of the model to the actual feature. Since the choice of the feature model is based both on relevance and convenience, and since the trapezoid is so commonly used for CD metrology, the impact of the feature model choice will not be discussed here. When fitting the feature model to the data, there are many possible methods. For example, one could find a best fit straight line through the sidewall of the profile, possibly excluding data near the top and bottom of the profile. Alternately, one could force the trapezoid to always match the actual profile at some point of interest, for example at the bottom. Whenever the shape of the actual profile deviates significantly from the idealized feature model, the method of fitting can have a large impact on the results.
For example, as a lithography process goes out of focus, the resist profile and the resulting feature size will change. But because the shape of the resist Chris A. Mack, KLA-Tencor profile is deviating from a trapezoid quite substantially at the extremes of focus, CD can be a strong function of how the data was fit. Figure 2 compares the measured CD through focus (as simulated with PROLITH) for two different feature model fitting schemes: a best fit line through the sidewall and fitting the trapezoid to match the actual profile at a set threshold (height above the substrate). Near best focus the two methods give essentially the same value since the resist profile is very close to a trapezoid. However, out of focus there can be a significant difference in the CD values (>5%) based only on the fitting method used. In real metrology systems the actual resist profile is never known. Instead, some signal (secondary electrons versus position, scattered light intensity versus wavelength) is measured that can be related to the shape of the resist profile. This signal is then fit to some model, which ultimately relates to the feature size being measured. Although a bit more complicated, the same principles still apply. Both the feature model and how that model is fit to the data will affect the accuracy of the results.
Figure 2. Using resist profiles at the extremes of focus as an
30
Figure 1. Typical photoresist cross-section profile and its corre-
example, the resulting measured feature size is a function of how
sponding "best fit" trapezoidal feature model.
the feature model is fit to the profile.
Winter 2002
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