TABLE OF CONTENTS Eberhard Spiller
Lawrence Livermore National Laboratories
Livermore, California
| =1- ?+ik | refractive index |
| ? i | grazing angle of propagation in layer i |
| | propagation angle measured from normal in layer i |
| q, q s | momentum transfer perpendicular to and along surface |
| d | layer thickness |
| ? | multilayer period, ?= d 1+ d 2 |
| f, ? s | spatial frequency and period on a surface or boundary |
| r nm , t nm | amplitude reflection and transmission coefficients |
| PSD | two-dimensional power spectral density |
| a(f) | roughness replication factor |
The reflectivity of all mirror materials is small beyond the critical grazing angle, and multilayer coatings are used to enhance this small reflectivity by adding the amplitudes reflected from many boundaries coherently. The multilayers for the extreme ultraviolet (EUV) and X-ray region can be seen as an extension of optical coatings toward shorter wavelengths or as artificial one-dimensional Bragg crystals with larger lattice spacings than natural crystals. In contrast to the visible region, no absorption-free materials are available for wavelengths ? < 110 nm. In addition, the refractive indices of all materials are very close to one, resulting in a small reflectance at each boundary and requiring a large number of boundaries to obtain substantial reflectivity. For absorption-free materials, a reflectivity close to 100 percent can always be obtained, independent of the reflectivity of an individual boundary, r 12, by making the number of boundaries, N, sufficiently large, Nr 12 >>1. Absorption limits the number of periods...
