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We measure pseudodielectric functions in the visible-deep ultraviolet spectral range of Pb(ZrxTi1−x)O3 (x=0.2,0.56,0.82) (PZT), Pb0.98Nb0.04(Zr0.2Ti0.8)0.96O3, Pb0.91La0.09(Zr0.65Ti0.35)0.98O3, and Pb0.85La0.15Ti0.96O3 films grown on platinized silicon substrates using a sol-gel method and on (0001) sapphire using a radio-frequency sputtering method. Using a parametric optical constant model, we estimate the dielectric functions (ϵ) of the perovskite oxide thin films. Taking the second derivative of the fitted layer dielectric functions and using the standard critical-point model, we determine the parameters of the critical points. In the second derivative spectra, the lowest band-gap energy peak near 4eV is fitted as a double peak for annealed PZTs due to the perovskite phase. As-grown PZTs have mainly pyrochlore phase and the lowest band-gap peak is fitted as a single peak. We also examine the effect of dopants La and Nb, which substitute at Pb and Zr (Ti) sites, respectively. We found three band gaps Ea(∼3.9eV), Eb(∼4.5eV), and Ec(∼6.5eV) in the order of increasing energy. The Ea and Eb band-gap energies were not sensitive to Zr composition. We discuss the change of critical-point parameters for PZTs in comparison to the band-structure calculations based on local-density approximation. The near constancy of the lowest band-gap energy independent of Zr composition is consistent with the band-structure calculations.
Lee et al. (Tue,) studied this question.