Optical Modeling of Nanocrystalline TiO2 Films

The light transmittance, T, in nanocrystalline TiO2 films was studied as a function of the light wavelength, λ, the nanocrystal radius, a, and the film thickness, d. Two types of TiO2 nanoparticles were employed: a commercial powder (P25) and synthesized particles from titanium isopropoxide (SP). The X-ray diffraction measurements revealed that both P25 and SP are mainly anatase and the average crystal sizes, 2a, of P25 and SP are 50.3 and 23.7 nm, respectively. Despite the visual difference between micron-order thin films of P25 and SP, the light hemispherical transmittance corrected with the surface specular reflectance has a clear dependence of ln(T) = −0.5βλ-4a3d, with β = 1.5 × 103 from visible to near-infrared wavelengths. The dependence and β value were successfully explained by the simplest model on the basis of the Rayleigh scattering theory. This indicates that the nanocrystalline TiO2 thin films are a typical medium where the simplest scattering model is a good approximation. However, the model was inapplicable to light scattering in relatively thick P25 films of 1.5−3.0 μm because of nonnegligible internal multiple scattering. For the moderate thickness films, ln(T) ∝ λγ, where γ increases from −4 in proportion to the film thickness is an alternative approximation. With these light scattering models, the light absorption rate of the TiO2 crystal was successfully evaluated from experimental extinction rates.