Optical Modeling of Nanocrystalline TiO₂ Films

Abstract

The light transmittance, T, in nanocrystalline TiO2 films was studied as a function of the light wavelength, lambda, 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) = -0.5beta lambda(-4)a(3)d, with beta = 1.5 x 10(3) from visible to near-infrared wavelengths. The dependence and beta 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 microm because of nonnegligible internal multiple scattering. For the moderate thickness films, ln(T) proportional to lambda(gamma), where gamma 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.

The preparation and characterization of photocatalytically active TiO2 thin films and nanoparticles using Successive-Ionic-Layer-Adsorption-and-Reaction

“…Fig. 6 shows the optical transmission spectrum of TiO 2 thin films prepared by SILAR deposition on glass substrates as a function of the incident wavelength (nm) or hυ (eV) [23][24][25][26][27]. TiO 2 films were coated on both sides of glass substrates by appropriate dipping and rinsing cycles from 100 to 600 cycles.…”

“…The as-deposited films were subsequently annealed by hydrothermal dehydration at 200°C (100, 200, and 400 cy HT) and/or furnace annealing at 500°C for 3 h (100 cy HT + 500°C 3h, 200 cy HT + 500°C 3 h, and 400 cy HT + 500°C 3h). The 600 cycle films were obtained on firing in furnace at 500°C for 3 h. The absorption edges shifts to higher wavelengths with the increase of the particle sizes made by annealing at higher temperatures or the increase of film thickness on TiO 2 [13,23,25]. The dependence of the optical transmittance (T) on the wavelength (λ), particle size (a), and film thickness (d) is given by ln(T) ∝ βλ − 4 a 3 d, where β depends on the refractive indices of the particles and their fractional particles volume [25,[28][29][30].…”

Transparent Mesoporous Nanocomposite Films for Self‐Cleaning Applications

“…Light scattering in nanocrystalline TiO 2 films has been studied in detail by Usami and Ozaki. [28] It may be concluded from their work that the absorption rate from the TiO 2 particles may be deduced from the experimental extinction rate of the film by subtracting the contribution from the specular reflectance (as measured at near-IR wavelengths) and the contribution from light scattering. The latter was found to follow a simple Rayleigh scattering law that can be expressed as: a scat (k) = C k -4 a 3 d, where C is a constant depending on the index of refraction of the film, a is the particle diameter, and d is the film thickness.…”

Nanocrystalline Cu2O/p-Si solar light-responsive Schottky photodiode

“…The transmittance and reflectance spectra of the film are shown in Fig. 2 transmittance (T) is related to the effective scattering rate by the following relations [21],…”