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As mentioned above, besides high conductivity (~106 S), effective TCO thin films should have a very low absorption coefficient in the near UV-VIS-NIR region. The transmission in the near UV is limited by Eg, as photons with energy larger than Eg are absorbed. A second transmission edge exists at the NIR region, mainly due to reflection at the plasma frequency. Ideally, a wide band gap TCO should not absorb photons in the transmission ¡°window¡± in the UV-VIS-NIR region. However, there are no ¡°ideal¡± TCOs thin films, and even if such films could be deposited, reflection and interference would also affect the transmission. Hence, 100% transparency over a wide region cannot be obtained. The optical properties of TCOs transmission T, reflection R, and absorption A, are determined by its refraction index n, extinction coefficient k, band gap Eg, and geometry. Geometry includes film thickness, thickness uniformity, and film surface roughness. T, R and, A are intrinsic, depending on the chemical composition and solid structure of the material, whereas the geometry is extrinsic. There is a negative correlation between the carrier density and the position of the IR absorption edge, but positive correlation between the carrier density and the UV absorption edge, as Eg increases at larger carrier density (Moss-Burstein effect). As a result, the TCO transmission boundaries and conductivity are interconnected. The width of the VIS transmission window of a TCO film with thickness deposited on a transparent substrate is affected not only by the optical parameters of the TCO film but also by the optical properties of the substrate. The refractive index nsub of the most common substrates are ~1.45 for fused silica and ~1.6 for various glasses. The extinction coefficient of the substrate (ksub) is generally < 10-7, hence any light absorption would take place in the film, where generally kfilm> ksub. For films thicker than 100 nm, several interference bands could be formed, producing maximal and minimal values of T when either the wavelength or thickness is varied. When kfilm 0, the peak transmission (Tmax) is equal to the transmission of the substrate. Hence, assuming that the sample is in air, Tmax = 90% and 93% for films deposited on glass and fused silica, respectively. The minimum sample transmission (Tmin) in air is expressed by: As most TCO films have values of n in the VIS in the range 1.8 ¨C 2.8, Tmin will be in the range 0.8 ¨C 0.52. Tmin is closely approximated by the relation: Tmin = 0.051n2-0.545n+1.654. As n in the VIS decreases with wavelength, Tmin increases with wavelength, but will not exceed ~0.8. When the film extinction coefficient is not negligible and affects the transmission, Tmax < Tsub, and Tmin also decreases. By decreasing the TCO film thickness, T is increased but the sheet resistance decreases. Combining together the optical and electrical properties of the film, the fraction of the flux absorbed in a film (A) is given by the expression: Fig. 1 presents plots of the fraction of the absorbed power at wavelength of 400 nm and k ~0.02 as a function of the conductivity for three representative values of RS. For a given low values of RS necessitate using thick films, and lower conductivity requires the use of even thicker films, resulting in an increase in the loss of radiative power. The dependence of film thickness on the conductivity for three values of Rs is presented in Fig. 2. Using the same film conductivity, applications requiring the lowest RS will be thicker and, and the absorbed fraction will be higher. At present, only high quality ITO is compatible at present with the condition that the absorbed power fraction be lower than 10% and RS = 10 At lower extinction coefficient (k) films with lower conductivities can be used, e.g., when k = 0.002 instead of 0.02, the absorbed power A is lower by a factor of ~8, and allows the use of thicker films. The combination of film thickness, conductivity, and extinction coefficient determine the absorption of the radiation flux. However, when the total transmission T is considered, reflection and interference must be considered, which depend on the refractive indices of the substrate and the film, and the film thickness. A general formula for T and R was given by Cisneros. |
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3Â¥2011-03-16 17:27:12













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