When the film thickness is considered as a parameter, a system composed of a transparent film on an absorbing substrate (in a transparent ambient) is characterized by a <i>range</i> of principal angle ø¯<sub>min</sub> ≤ ø¯ ≤ ø¯<sub>max</sub> over which the associated principal azimuth ψ¯ varies between 0° and 90° (i.e., 0° ≤ ψ¯ ≤ 90°) and the reflection phase difference Δ assumes either one of the two values: +π/2 or −π/2. We determine the principal angle ø¯(<i>d</i>) and principal azimuth ψ¯(<i>d</i>) as functions of film thickness <i>d</i> for the vacuum-SiO<sub>2</sub>-Si system at several wavelengths as a concrete example. When the film thickness exceeds a certain minimum value, more than one principal angle becomes possible, as can be predicted by a simple graphical construction. We apply the results to principal-angle ellipsometry. (PAE) of film-substrate systems; the relationship between ø¯ and ψ¯ during film growth is particularly interesting.
© 1977 Optical Society of America
R. M. A. Azzam and A.-R. M. Zaghloul, "Principal angle, principal azimuth, and principal-angle ellipsometry of film-substrate systems," J. Opt. Soc. Am. 67, 1058-1065 (1977)