Statistical Measure for the Sharpness of the SEM Image

Published

July 1, 1997

Author(s)

Nien F. Zhang, Michael T. Postek, Robert D. Larrabee

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 a 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 (i.e., a dimensionless) 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.

Proceedings Title

Proceedings of SPIE,Metrology, Inspection, and Process Control for Microlithography XI, Susan K. Jones, Editor

Volume

3050

Conference Dates

March 10, 1997

Conference Location

Santa Clara, CA, USA

Conference Title

Scanning Probe Metrology III

Pub Type

Conferences

Keywords

Fourier transform, image analysis, kurtosis, metrology, scanning electron microscope, sharpness

Citation

Zhang, N. , Postek, M. and Larrabee, R. (1997), Statistical Measure for the Sharpness of the SEM Image, Proceedings of SPIE,Metrology, Inspection, and Process Control for Microlithography XI, Susan K. Jones, Editor, Santa Clara, CA, USA (Accessed October 16, 2025)