Photometric methods for determining the optical constants and the thicknesses of thin absorbing films: selection of a combination of photometric quantities on the basis of error analysis

We select the best combinations of spectrophotometric quantities far the mo st accurate determination of the optical constants, n (refractive index), k (absorption coefficient), and the thicknesses of thin absorbing films. The basic comparative criteria used are the maximum absolute errors in the det ermination of n, k, and d that result from experimental errors in photometr ic measurements and in the optical constants of the substrates. We studied all possible combinations of photometric quantities T, T-s(theta), T-p(thet a), R, R-s(theta), R-p(theta), R-m, R-ms(theta), and R-mp(theta), at 0 degr ees < theta less than or equal to 70 degrees where T denotes transmission; R, reflection; the subscripts s and p, s- andp-polarized light; m, reflecti on from a thin film coated upon an opaque substrate; and superscript theta, the angle of incidence of light. The absence of the subscripts s and p imp lies nonpolarized light; that of the subscript m, a nonabsorbing substrate; and that of superscript theta, normally incident light. The error analysis that is made admits the following conclusions: (1) The best double combina tions are (TR), (TRm), (TRp70), and (TRmp70); (2) the best triple combinati ons are (TRRm), (TRRp70), (TRRmp70), (TRmRp70), and (TRmRmp70); (3) the met hods indicated above, suitably combined, are quite sufficient to provide th e maximum accuracy and reliability of n, h, and d for all practical situati ons; (4) TRR methods based on measurements with obliquely polarized light a re more suitable for thin films with n < 1, such as some metal films; (5) t he regions of n, k, and d/<lambda> with the highest and the lowest accuraci es do not overlap in either the TR or the TRR methods. Hence more combinati ons, preferably all, should be applied for the most accurate determination of n, h (and d), and the errors should be evaluated as a criterion for the best combination. (C) 2001 Optical Society of America.