The problem with submicrometer linewidth standards, and a proposed solution

摘要

Traceable linewidth measurements of tiny features on photomasks and wafers present interesting challenges. Usually technical solutions exist for the problems encountered, but traceability can be costly in time and labor. A measurement is useful only if its value exceeds its cost. One such problem is that an optical or electron microscope forms a scaled image of the linewidth object, which is measured instead of the object itself. Interpreting this image to identify the object's edges in it can be difficult, because the image depends on instrument and object parameters (such as topography and materials) not directly related to the linewidth. Use of a linewidth standard can provide a traceable measurement if the relevant object parameters are known to match those of the standard. In the majority of cases, however, the object being measured and the linewidth standard will differ in topography and/or materials. Then the instrument images of object and standard will also differ, leading to possible measurement errors. Traceability requires that these measurement errors be quantified -- a costly prospect. One can calculate the measurement error resulting from object/standard parameter differences. Then a measurement error tolerance can be chosen, and parameter tolerances can be found corresponding to a "parametric measurement uncertainty" that is consistent with it. These parameter tolerances define "islands of tolerance" in parameter space over which the parametric uncertainty will be tolerated. The larger the islands, the greater the measurement uncertainty, but the greater the number of different objects whose parameter differences fall on the island. While the calculations for the islands of tolerance may be complex, a single island can apply to a whole group of different objects, reducing the cost of measuring the parameters and calculating their effects. This is a way to obtain traceable linewidth measurements while balancing measurement cost and measurement uncertainty.