A semitheoretical formalism based on classical electromagnetic wave theory has been developed for application to the quantitative treatment of reflection spectra from multilayered anisotropic films on both metallic and nonmetallic substrates. Both internal and external reflection experiments as well as transmission can be handled. The theory is valid for all wavelengths and is appropriate, therefore, for such experiments as x-ray reflectivity, uv-visible spectroscopic ellipsometry, and infrared reflection spectroscopy. Further, the theory is applicable to multilayered film structures of variable number of layers, each with any degree of anisotropy up to and including full biaxial symmetry. The reflectivities (and transmissivities) are obtained at each frequency by solving the wave propagation equations using a rigorous 4 x 4 transfer matrix method developed by Yeh in which the optical functions of each medium are described in the form of second rank (3 x 3) tensors. In order to obtain optical tensors for materials not readily available in single crystal form, a method has been developed to evaluate tensor elements from the complex scalar optical functions (n) obtained from the isotropic material with the limitations that the molecular excitations are well characterized and obey photon-dipole selection rules. This method is intended primarily for infrared vibrational spectroscopy and involves quantitative decomposition of the isotropic imaginary optical function (k) spectrum into a sum of contributions from fundamental modes, the assignment of a direction in molecular coordinates to the transition dipole matrix elements for each mode, the appropriate scaling of each k vector component in surface coordinates according to a selected surface orientation of the molecule to give a diagonal im (n) tensor, and the calculation of the real (n) spectrum tensor elements by the Kramers-Kronig transformation. Tensors for other surface orientations are generated by an appropriate rotation matrix operation. To test the viability of this approach, three sets of experimentally derived infrared spectra of oriented monolayer assemblies on quite distinctively different substrates were chosen for simulation: (1) n-alkanethiols self- assembled onto gold, (2) n-alkanoic acid salt Langmuir-Blodgett (LB) monolayers on carbon, and (3) n-alkanoic acid salt LB monolayers on silica glass. The formalism developed was used to simulate the spectral response and to derive structural features of the monolayers. Good agreement was found where comparisons with independent studies could be made and, in general, the method appears quite useful for structural studies of highly organized thin films.
