NIST logo

Publication Citation: Statistical Measure for the Sharpness of the SEM Image

NIST Authors in Bold

Author(s): Nien F. Zhang; Michael T. Postek; Robert D. Larrabee;
Title: Statistical Measure for the Sharpness of the SEM Image
Published: July 01, 1997
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.
Conference: Scanning Probe Metrology III
Proceedings: Proceedings of SPIE,Metrology, Inspection, and Process Control for Microlithography XI, Susan K. Jones, Editor
Volume: 3050
Pages: pp. 375 - 387
Location: Santa Clara, CA
Dates: March 10, 1997
Keywords: Fourier transform,image analysis,kurtosis,metrology,scanning electron microscope,sharpness
Research Areas: Metrology, Manufacturing