The chemical reaction of a sample with atmospheric gases causes a significant error in the determinantion of the complex refractive index n = 1 − δ + <i>i</i>β in the extreme-ultraviolet region. The protection of samples removes this effect but hampers the interpretation of measurements. To overcome this difficulty, we derive the exact dependences on film thickness of the reflectivity and transmissivity of a protected film. These dependences greatly simplify the determination of δ and β when the spectra of several films with different thickness and identical protection are measured. They also allow the verification of the δ(ω) obtained from the Kramers–Kronig relation and even make the Kramers–Kronig method unnecessary in many cases. As a practical application, the optical constants of Sc and Ti are determined at ħω = 18–70 eV and 18–99 eV, respectively. The essential feature of our experimental technique is deposition of a film sample directly on a silicon photodiode that allows easy operation with both thin (~10-nm) and thick (~100-nm) films. The comparison of calculated reflectivities of Si–Sc multilayers with the measured values shows the high accuracy of the determined δ(ω) and β(ω).
© 2004 Optical Society of America
(160.3900) Materials : Metals
(260.7200) Physical optics : Ultraviolet, extreme
(300.6560) Spectroscopy : Spectroscopy, x-ray
(340.6720) X-ray optics : Synchrotron radiation
(340.7480) X-ray optics : X-rays, soft x-rays, extreme ultraviolet (EUV)
Yu. A. Uspenskii, John F. Seely, N. L. Popov, A. V. Vinogradov, Yu. P. Pershin, and V. V. Kondratenko, "Efficient method for the determination of extreme-ultraviolet optical constants in reactive materials: application to scandium and titanium," J. Opt. Soc. Am. A 21, 298-305 (2004)