Statistical measure for the sharpness of SEM images

Nien-Fan Zhang; Michael T. Postek Jr.; Robert D. Larrabee; Andras E. Vladar; William J. Keery; Samuel N. Jones

doi:10.1117/12.275935

7 July 1997 Statistical measure for the sharpness of SEM images

Nien-Fan Zhang, Michael T. Postek Jr., Robert D. Larrabee, Andras E. Vladar, William J. Keery, Samuel N. Jones

Proceedings Volume 3050, Metrology, Inspection, and Process Control for Microlithography XI; (1997) https://doi.org/10.1117/12.275935
Event: Microlithography '97, 1997, Santa Clara, CA, United States

Abstract

Fully automated or semi-automated scanning electron microscopes (SEM) are now commonly used in semiconductor production and other forms of manufacturing. Testing and proving that the instrument is performing at a satisfactory level of sharpness is an important aspect of quality control. The application of Fourier analysis techniques to the analysis of SEM images is useful methodology for sharpness measurement. In this paper, a statistical measure known as the multivariate kurtosis, is proposed as a useful measure of the sharpness of SEM images. Kurtosis is designed to be a measure of the degree of departure of a probability distribution from the Gaussian distribution. It is a function of both the fourth and the second moments of a probability distribution. For selected SEM images, the two- dimensional spatial Fourier transforms were computed. Then the bivariate kurtosis of this Fourier transform was calculated as though it were a probability distribution, and that kurtosis evaluated as a characterization tool. Kurtosis has the distinct advantage that it is a parametric measure and is sensitive to the presence of the high spatial frequencies necessary for acceptable levels of sharpness. The applications of this method to SEM metrology will be discussed.

Citation Download Citation

Nien-Fan Zhang, Michael T. Postek Jr., Robert D. Larrabee, Andras E. Vladar, William J. Keery, and Samuel N. Jones "Statistical measure for the sharpness of SEM images", Proc. SPIE 3050, Metrology, Inspection, and Process Control for Microlithography XI, (7 July 1997); https://doi.org/10.1117/12.275935

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