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When measuring the width of an isolated line or space on a wafer or photomask, only the feature's
image is measured, not the object itself. Often the largest contributors to measurement uncertainty are
the uncertainties in the parameters which affect the image. Measurement repeatability is often smaller
than the combined parametric uncertainty.
An isolated feature's edges are far enough away from nearest edges of other features that its image
does not change if this distance is increased (about 10 wavelengths in an optical microscope or
exposure tool, or several effective-beam-widths in a SEM). When the leading and trailing edges of the
same feature are not isolated from each other the metrology process becomes nonlinear. Isolated
features may not be amenable to measurement by grating methods (e.g., scatterometry), and there is no
hard lower limit to how small an isolated feature can be measured. There are several ways to infer the
size of an isolated feature from its image in a microscope (SEM, AFM, optical,...), and they all require
image modeling.
Image modeling accounts for the influence of all of the parameters which can affect the image, and
relates the apparent linewidth (in the image) to the true linewidth (on the object). The values of these
parameters, however, have uncertainties and these uncertainties propagate through the model and lead
to parametric uncertainty in the linewidth measurement, along with the scale factor uncertainty and the
measurement repeatability. The combined measurement uncertainty is required in order to decide if
the result is adequate for its intended purpose and to ascertain if it is consistent with other similar
results.
The parametric uncertainty for optical photomask measurements derived using an edge threshold
approach has been described previously [1]; this paper describes an image library approach to this
issue and shows results for optical photomask metrology over a linewidth and spacewidth range of 10
nm to 4 μm. The principles will be described, the 1-dimensional image library used and the method of
comparing images, along with a simple interpolation method, will be explained, and results presented.
This method is easily extended to any kind of imaging microscope and to p dimensions, where p is the
number of imaging parameters used. It is more general than the edge threshold method and leads to
markedly different results for features smaller than a wavelength.
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