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3.2.6 A Statistical Measure of Image Sharpness for Scanning Electron Microscopes
Nien Fan Zhang In industry applications, such as automated on-line semiconductor production, users of scanning electron microscope (SEM) metrology instruments would like to have these instruments function without human intervention for long periods of time. At the present time, no self-testing is incorporated into these instruments to verify that the instrument is performing at a satisfactory performance level. Therefore, there is a growing realization of the need for the development of a procedure for periodic performance testing. One approach to this issue is the sharpness technique. It is known that the low-frequency changes in the video signal contain information about the large features and that the high-frequency changes carry information on finer details. When a SEM image has fine details at a given magnification, namely, when there are more high- frequency changes in it, we say it is sharper. Since an SEM image is composed of a two- dimensional (2-D) array of data, the 2-D Fourier transform generates a 2-D spatial frequency spectrum. We observe that when an SEM image is visually sharper than a second image, the high spatial frequency components of the first image are larger than those of the second. The following is an illustrative example. Part a of the attached figure shows the performance of a cold FESEM on a heavy gold-coated oxide test sample at low accelerating voltage. This micrograph was taken following a tip change. This image appears to be far less sharp and lacking in resolution when it compared with a similar micrograph (Part c of the figure) taken when the same instrument was operating more optimally. Parts b and d show the 2-D spatial Fourier frequency magnitude distributions for the images in the Parts a and c, respectively. From these figures it is clear that for the sharper image in Part d of the figure, its cone, which represents the magnitude distribution of the Fourier transform of the image, is wider than that of the image in Part b of the figure. For a given univariate random variable, the kurtosis is defined as a ratio of the fourth and squared second central moments. A distribution with smaller kurtosis is more flat-topped or has a larger shoulder than that with larger kurtosis. Multivariate kurtosis has been proposed by Mardia (1970). Treating the normalized spatial spectrum as a probability density function, a sharper SEM image corresponds to a spectrum which has a large shoulder or has a flatter shape. Thus, it can be concluded that the corresponding kurtosis of the sharper image is smaller. Therefore, an increase in kurtosis portends that the sharpness of an SEM image has been degraded relatively. This work has been facilitated by the use of a relatively simple, easy to fabricate test target which may become a NIST reference material (SRM 2091), thus making it readily available for any user. The present method has been demonstrated to be useful for monitoring the performance of manual, semi-automated, and automated SEM instrumentation. This paper is published in Scanning (1999) 21, 246-252.
Figure 9: Scanning electron micrographs and their two-dimensional Fourier frequency magnitude distributions. (a) Scanning electron micrograph of heavily coated oxide taken following a tip change. (b) Two-dimensional Fourier frequency magnitude distributions of image (a). (c) Scanning electron micrograph of the same sample as above, but taken when the instrument is functioning at a high level of performance. (d) Two-dimensional Fourier frequency magnitude distributions of image (c). Note that there are more high frequency elements present in the Fourier frequency magnitude distribution from Figure 1c.
Date created: 7/20/2001 |