Relative performances of effective medium formulations in interpreting specific composite thin films optical properties

Several powerful effective medium formulations/approximation (EMA) and associated theories with different origins and concepts have been discussed and utilized here in order to model the experimental refractive index evolutions of ZrO2–SiO2 and Gd2O3–SiO2 composite films with respect to their compositional mixings. Amongst these formulations, the Bo¨ttcher’s generalized theory has been noticed to have more versatility and can simulate varieties of experimental observations incorporating a form factor parameter to account for the grain structure and morphology to a great extent. The refractive index modeling results of most of the available theories were compared with respect to their functional evolutions and limitations. It was noticed that at higher silica fractions (>20%) in our composite films, the effective experimental refractive index parameters have remained close to the most modeling results and Bo¨ttcher’s expression has shown to fit the observable parameters very accurately. However, under low silica compositions (<20%) the refractive index values of the composite films depicted different functional evolutions. Such deviations have been attributed to the various morphological, grain structure and band gap supremacies observed in these specific composite films which are not accounted by the effective medium formulations and approximations. These observations are well supported by the atomic force microscopy results.