Use of hybrid phenomenological and statistical effective-medium theories of dielectric functions to model the infrared reflectance of porous SiC films

The reflectance of porous silicon carbide (PSC) thin films on SiC substrates is measured in the infrared reststrahlen region by Fourier transform infrared reflectance spectroscopy and is compared to simulated spectra based on phenomenological and Bergman statistical effective-medium dielectric functions. The phenomenological models evaluated include the Bruggeman, cavity- and sphere-Maxwell-Garnett (C-MG and S-MG), Landau-Lifshitz/Looyenga (LLL), and Monecke models. In addition, modifications to the Bruggeman and C-MG models with variable particle shapes and surface layers are examined. Hybrid versions of the C-MG and LLL models are also considered, alternatively by using a phenomenological mixing approach, which gives a direct physical interpretation of the topology, and by directly mixing the statistical spectral density functions of the C-MG and LLL effective dielectric functions. This latter statistical hybrid model gives the best (and quite good) agreement with experiments. The differences in the hybrid models are understood by comparing their spectral density functions. The dip (or splitting) in the PSC film reststrahlen band is attributed to surface optical phonon modes.