The extreme ultraviolet (EUV) region, covering the wavelength of about 4 nm to 40 nm, is unique because EUV is strongly absorbed by all matter. The resulting short penetration depth into solids means that no refractive elements exist for this spectral region and that normal-incidence reflectivity is very low. Historically, EUV beams could only be deflected or focused by mirrors operating at near-grazing-incidence angles, where reflectance remains high. Such optics have limited image formation capabilities, which limited applications. Also, since gases absorb, any EUV optical device must operate in vacuum.
In 1974 Eberhard Spiller demonstrated theoretically that one could obtain high normal-incidence EUV reflectivity by coating a very smooth substrate with a multilayer stack of alternating high- and low-index thin films. EUV multilayers work by adding weak reflections from many surfaces in phase. They can be thought of as long-period crystals obeying the Bragg condition, 2dsinθ = mλ, or as short-period half-wave stacks. In either case, the period is roughly half an effective optical path.
The way a material refracts, reflects, and transmits light is characterized by the optical constants unique to that material, which are the index of refraction n and the absorption index k. These are the components of the complex index of refraction, N = n+ik. Understanding and predicting EUV multilayer performance requires precise knowledge of the appropriate optical constants of the material. Such measurements are difficult to make because the presence of even a nanometer-thick layer of oxide or another impurity on the films can lead to large uncertainties in the results. Until recently, accurate information on EUV optical constants was scarce.
The National Institute of Standards and Technology (NIST) now has a special facility to determine EUV optical constants. In it, we deposit thin films using magnetron sputtering. We then transfer test pieces under vacuum (10-8 torr) into our measurement chamber, without ever exposing the films to atmosphere. This setup allows us to take measurements before any noticeable contamination occurs.
Basically, all techniques to measure the optical constants depend on the Fresnel equations, which relate the reflectivity or transmittance to the values of n and k. The measurement chamber is a reflectometer that allows us to make measurements of reflectance as a function of angle, beginning at near-grazing incidence and going well beyond the critical angle. These results are then fit to the Fresnel equations. We compensate for surface roughness using the Nevot-Croce model.
We can treat the reflection from an optically thick film as though it reflected from bulk material, since radiation does not penetrate to the bottom of the film. When possible, however, we also deposit optically thin films in which radiation does penetrate to the bottom surface, giving rise to interference (Kiessig) fringes. The amplitude and spacing of these fringes are extremely sensitive measures of the absorption and optical path length through the film. The data from both sets of measurements are then fit to the Fresnel equations (see figure).
Amplitude and spacing of Kiessig fringes for optically thin film of silicon generate sensitive measures of the absorption and optical path length through the film.
In addition to the optical constants of the constituents, the reflectivity of a multilayer mirror depends on how well it is fabricated, i.e., on the smoothness of the substrate and the interfaces and on the accuracy of the periods. Once a mirror is fabricated, it must be characterized. Here again we use our reflectometer to provide a point-by-point map of reflectivity over the whole surface of the mirror.
The NIST effort in EUV optics supports two very important applications: the development of mirrors for EUV lithography now spear-headed by the EUV Limited Liability Corp. (Livermore, CA) and EUV astronomy being pursued by NASA and its academic collaborators. oe
Charles Tarrio, Thomas Lucatorta
The authors are with the Photon Physics Group, National Institute of Standards and Technology.