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.
Minority carrier diffusion length measurements in 6H-SiC J. Appl. Phys. 97, 053703 (2005); 10.1063/1.1853501Influence of crystal quality on the electronic properties of n-type 3C-SiC grown by low temperature low pressure chemical vapor deposition
A computer simulation of dye-sensitized nanocrystalline solar cells is presented. Specifically, formulation and a numerical simulation method are described in detail. The theoretical model consists of the following differential equations: an equation for charge conservation, current equations for electrons in semiconductor matrixes and ion species in electrolytes, and an equation for charge separations in the sensitized electrodes. The differential equations are solved with the Newton-Raphson method after discretization of the equations. A simulation of current-voltage characteristics of the dye-sensitized solar cells is presented. Limitations of the model are also described.
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