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Critical Dimensions and the Feature Model With fear of stating the obvious, the measurement of a lithographic feature size, or critical dimension (CD), is, well, critical. The issues of measurement precision and accuracy, especially in an environment without established standards, present a complex picture to the metrology tool user. To help bring clarity to one small piece of the bigger CD measurement puzzle, I’d like to discuss an important issue that rarely receives attention: the feature model. Our discussion will center around the measurement of long line- or space-type patterns in lithography, but the concepts apply broadly to any CD measurement. A cross-section of a photoresist profile has, in general, a very complicated two-dimensional shape (see Figure 1, for example). Measurement of such a feature to determine its width has many complications. Let’s suppose, however, that we have been able to measure the shape of this profile exactly so that we have a complete mathematical description of its shape. How wide is it? It takes only a little thought to realize that the answer depends on how you define the width. The original shape of the photoresist profile is simply too complex to be unambiguously characterized by a single width number. The definition of the width of a complex shape requires the definition of a feature model1. A feature model is a mathematical function described by a conveniently small number of parameters. For our application, one of these parameters should be related to the basic concept of the width of the resist profile. The most common feature model used for this application is a trapezoid (Figure 1). Thus, three numbers can be used to describe the profile: the width of the base of the trapezoid (linewidth, w), its height (profile thickness, D), and the angle that the
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side makes with the base (sidewall angle, q). To be perfectly general, the position of the feature (defined, for example, by the centroid Chris A. Mack, of the feature model) can be KLA-tencor specified and the shape can be made asymmetrical by allowing a different sidewall angle for each side. Obviously, to describe such a complicated shape as a resist profile with just three numbers is a great simplification. One of the keys to success is to pick a method of fitting this feature model to the profile that preserves the important properties of the profile (and its subsequent use in the device). Thus, we can see that, even given an exact knowledge of the actual photoresist profile, there are two potential sources of error in determining the critical dimension: the choice of the feature model and the method of fitting the feature model to the resist profile. Consider Figure 2, which shows resist profiles through focus exhibiting different curvatures of their sides. Using a trapezoidal feature model will obviously result in a less than perfect fit, which means that the criterion for best fit will influence the answer. What is the best feature model and best method of fitting the feature model to measured data for a given application? I’ll discuss this issue in the next edition of this column. References: 1 . SEMI Standard SEMI P35-0200E, Te rminology for M i c rolithography Metro l o g y.
F i g u re 1. Ty pical phot ores ist pr ofile and its correspon din g “best
F i g u r e 2. Resist profiles at the extremes of focus show h ow the
fi t” tra pezoi dal feature model.
c u rv a t u re of a pattern cross-s ecti on can cha nge.
Fall 2001
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