Optical Constants of Metals in the Extreme Ultraviolet I A Modified Critical-Angle Technique for Measuring the Index of Refraction of Metals in the Extreme Ultraviolet*

Abstract

A simple method for measuring the index of refraction, n, of substances that have an index less than unity and a very small extinction coefficient has been developed. It is similar to the usual critical-angle method which measures the index by direct location of the critical angle. The presence of a small amount of absorption makes direct location of the critical angle impossible since it erases the discontinuity in the slope of the reflectance vs angle of incidence curve, on which the critical angle method depends. The angle at which the slope of the curve is a maximum very nearly equals the critical angle, however, so that instead of determining n from the position of a discontinuity in the slope of the reflectance vs angle of incidence curve, it may be obtained from the angle of maximum slope. Four sources of error, which cause the position of maximum slope to shift away from the critical angle, are: large values of k; the presence of an absorbing layer, such as an oxide; interference effects that may be present if the sample to be studied is in the form of a layer on a substrate; and polarization of the incident radiation. The magnitude of the errors arising from these effects are discussed and the method is compared with an interference method for measuring n.