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Until now, metrologists had no statistics-based method to determine the sampling needed for an experiment before the start that accuracy experiment. We show a solution to this problem called inverse total measurement uncertainty (TMU) analysis, by presenting statistically based equations that allow the user to estimate the needed sampling after providing appropriate inputs, allowing him to make important “risk versus reward” sampling, cost, and equipment decisions. Application examples using experimental data from scatterometry and critical dimension scanning electron microscope tools are used first to demonstrate how the inverse TMU analysis methodology can be used to make intelligent sampling decisions and then to reveal why low sampling can lead to unstable and misleading results. One model is developed that can help experimenters minimize sampling costs. A second cost model reveals the inadequacy of some current sampling practices—and the enormous costs associated with sampling that provides reasonable levels of certainty in the result. We introduce the strategies on how to manage and mitigate these costs and begin the discussion on how fabs are able to manufacture devices using minimal reference sampling when qualifying metrology steps. Finally, the relationship between inverse TMU analysis and hybrid metrology is explored.

We have developed a new local overlay measurement technique on actual device patterns using a critical dimension scanning electron microscope (CD-SEM), which can be applied to two-dimensional (2D) device structures such as a static random access memory contact hole array. CD-SEM overlay measurement can provide additional local overlay information at the site of device patterns, complementary to the optical overlay. The methodology includes the use of pattern symmetry to cancel out many process effects and reduce measurement uncertainty. CD-SEM overlay metrology was compared with conventional optical overlay metrology in terms of measurement uncertainty and overlay model analysis, and very good correlation was confirmed. The developed methodology was applied to local overlay measurement of double patterning contact hole layers of leading edge devices. The local overlay distribution was obtained across the device area, and spatial correlation of the overlay error vectors was examined over a large range of distances. The applications of CD-SEM overlay metrology were explored, and methodologies were introduced to examine both the overlay of double patterning contacts at the edge of an array and lithographic process-induced overlay shift of contacts. Finally, a hybrid optical CD-SEM overlay metrology was introduced in order to capture a high order, device weighted overlay response.