Simultaneous determination of refractive index, extinction coefficient, and void distribution of titanium dioxide thin film by optical methods

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Abstract
The refractive index n(λ) and the extinction coefficient k(λ) of a TiO2 film prepared by electron-beam evaporation are determined in the spectral region 1.5–5.5 eV. The transmission spectrum of the TiO2 film on a vitreous silica specimen is inverted to get the k(λ) of TiO2 in its interband transition region. Above 3.5 eV, k(λ) is used to get the coefficients of the quantum mechanically derived dispersion relation of an amorphous TiO2. These coefficients and n ∞ are used to determine n(λ). The modeling procedure is applied to spectroscopic ellipsometry data of a TiO2 film on a c-Si specimen, and the void distribution of the film is revealed. With spectroscopic ellipsometry data above the fundamental band gap, valuable information about surface roughness is obtained. The effective thickness of this rough surface layer is confirmed by an atomic force microscopy measurement.