Measuring Optical Constants from the UV to X-ray Wavelengths; how it was (and is) done

摘要

Optical constants of solids, n the index of refraction, and k the extinction coefficient, are essential for designing components for use in optical instruments, i.e., reflectors, transmitters, etc. In the UV region (4000 - 2000 A) there are many transmitting glasses and crystals from which ellipsometers can be constructed, consequently extensive use of ellipsometry over the long wavelength part of this region can provide index of refraction values of non-absorbing media accurate to five significant figures. As the wavelength decreases, however, the ellipsometric technique becomes difficult because the components of the measuring apparatus become absorbing. In the extreme ultraviolet (XUV) from 2.000 to 2 A less precise techniques are used. Over most of this region the reflectance vs. angle of incidence (R vs. φ) method is the mainstay. Such n,k measurements can be accurate to three significant figures, seldom more. Furthermore, the method is n,k dependent, i.e., in certain regions of the n,k plane the precision for n or k becomes less than three significant figures while the other value may be more precise; an n,k uncertainty principle. Some ellipsometric instrumentation has been developed for the XUV but the spectral range is limited. Other techniques are available for limited spectral ranges; for example, measuring n from R vs. φ curves and measuring k from transmission through thin films, measuring R at near normal incidence over extended wavelength ranges and using the Kramers-Kronig (KK) relations to obtain n,k. Non-optical techniques, such as bombardment of unbacked films with electrons to determine the location and shape of their plasmon oscillation, are useful for limited wavelength ranges.