In the vacuum ultraviolet and extreme ultraviolet (EUV), the indices of refraction of all materials become complex: N = n + ik, or N = 1- d + ik. Here, n is the standard index of refraction, which makes light travel more slowly in a material than in vacuum, and also leads to the bending of light at interfaces. The quantity k is known as the extinction coefficient, and it leads to decay in the amplitude of the light wave propagating in the medium. This is simply absorption: light causes excitations in the material, thus losing energy.
The intensity within the absorbing medium decays exponentially: I = I0 exp(-at), where a=4pk/λ is known as the absorption coefficient, t is the thickness within the medium, and λ is the wavelength. It is often useful to know the full index of refraction. No lenses can be used in the EUV, but knowing the index is essential in designing mirror-based optical system. Mirrors are often made from synthetic multilayers, and the properties of these systems depend very much on the indices of the constituent materials. And the advent of extreme ultraviolet lithography (EUVL) is leading to interest in increasing the absorption of photoresists, the photosensitive materials with which the components of microchips are printed.
Measurements of EUV optical constants are often made by measuring the absorption or near-normal-incidence reflectivity, then performing transforms to obtain both the real and imaginary parts of the index. These sorts of measurements have considerable uncertainty because they require knowledge of parameters over all wavelengths from the infrared to x-ray, and some assumptions must be made in order to constrain the result.
We use angle-dependent reflectivity, which can uniquely determine both the real and imaginary parts of the index. Reflection and refraction in absorbing media obey all the same laws as in transparent media in the visible, except that the index of refraction is complex, so amplitudes and angles are also complex. (A good discussion can be found in J. D. Jackson, Classical Electrodynamics, second edition, Wiley, 1975, chapter 7.)
We have generally made measurements on thin films deposited onto substrates. Such measurements have the advantage that the interference between the top and the film-substrate interface makes the measurement much more sensitive to absorption in the film. The interference leads to fringes. The spacing of the fringes is related to the film thickness, and the depth to the absorbance. This is shown in Fig. 1, which shows the reflectance of two materials, one with high absorption and one with low absorption.
Absorption is important in EUV lithography. An EUV photon has about 14 times as much as a deep UV photon, therefore many fewer photons are involved in exciting the photoresist, the imaging medium for integrated circuit production. This leads to some roughness or blurring of the lines. Increasing the absorption reduces the excited volume, thereby reducing the statistical noise. We have provided measurements to several EUVL materials developers in order to optimize absorption in imaging materials and performance of EUV mirrors.