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3.1.10 Estimating The Measurement of Pitch in Metrology Instruments

Nien Fan Zhang

Statistical Engineering Division, ITL

Michael T. Postek

Robert D. Larrabee

Precision Engineering Division, MEL

NIST is in a process of developing a new low-accelerating-voltage scanning electron microscope (SEM) magnification calibration reference standard 2090. This standard will be useful for all applications in which the SEM is currently being used, but it has been specially tailored for many of the particular needs of the semiconductor industry. In order for the NIST certification process to be complete, an estimate of the pitch measurement and its uncertainty must be evaluated. As the precision and accuracy of metrology instruments are pushed to the nanometer level, the evaluation of the performance of the pitch measurement algorithm becomes increasingly important. Figure 1 shows the diagram of the NIST SRM 2090a prototype SEM magnification standard. The left hand-side is a lowest magnification drawing showing the 3 mm and 1 mm pitch patterns, while the right hand-side of Figure 1 is at high magnification showing the two 4 micrometer ($\mu$m) and eight 0.2 $\mu$m pitch structures as well as the focusing and astigmatism-correction crosses.

The prototype SRM 2090a data was obtained by using the NIST SEM-based metrology system. A pitch distance between two pitch structures is defined as the distance between the left (or right) edge of one pitch structure and the left (or right) edge of another pitch structure. Mathematically, when the SEM signals at the edges are parallel straight lines the pitch distance is uniquely defined. However, in reality, when measurements are done by an SEM system as described above, the edges formed by discrete data points are not necessarily parallel.

Traditionally, a least squares regression line is fitted to the data points corresponding to each of the left (or right) edges of a pitch structure. Then, the distance between the two fitted lines (corresponding to two left or two right edges) at a certain height on the vertical axis is assigned as the pitch distance between the pitch structures. A disadvantage for this approach is that the pitch distance varies with the height at the vertical axis because in general these two fitted regression lines are not parallel. Another disadvantage for the traditional algorithm is that it is difficult to estimate the uncertainty of the pitch distance. We developed a statistical model based algorithm to eliminate this kind of uncertainty. The estimator of pitch distance and its uncertainty have been derived. Evaluations based on simulations show that the uncertainty of measurement of the pitch distance by the new method is smaller than that by the traditional one. This work has been presented by Nien Fan Zhang at the SPIE's (The International Society for Optical Engineering ) 1996 International Symposium on Microlithography.


Figure 10: This figure shows the diagram of the SRM 2090a prototype SEM magnification standard.

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Date created: 7/20/2001
Last updated: 7/20/2001
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