Validity of a three-parameter dilogarithm dispersion function for the description of the energy dependence of the absorption coefficient of flash-evaporated V2O5 films

The X-ray diffraction patterns of vanadium pentoxide (V2O5) films, deposited by flash evaporation on glass slides upheld at 400 °C, reveal orthorhombic $$\alpha$$-V2O5with a prominent (001)-peak. The normal-incidence transmittance-wavelength $$(T_{\exp } (\lambda ) - \lambda )$$ spectra of the {air/flash-evaporated V2O5 film/glass slide/air} samples had been collected in the $$\lambda$$-range 400–1100 nm. There $$T_{\exp } (\lambda ) - \lambda$$ spectra exhibit a steep drop at, $$\lambda \approx 550\,{\text{nm}}$$ above which few broad, maxima/minima are displayed. The point-wise unconstrained minimization approach (PUMA) was implemented to fit the $${T}_{\text{exp}}\left(\lambda \right)-\lambda$$ data to a theoretical transmittance formula, $${T}_{\text{theor}}\left(\lambda ,{n}_{s}\left(\lambda \right);n\left(\lambda \right), \kappa \left(\lambda \right), d\right)$$. The analysis yielded a value for the thickness $$(d$$) of the $$\alpha$$-V2O5 films and for the spectral dispersion of its refractive index $$n(\lambda )$$ and extinction coefficient $$\kappa \left(\lambda \right)$$, with $${n}_{s}\left(\lambda \right)$$, the refractive index of glass slides was pre-calculated at each $$\lambda$$. The extracted $$n\left(\lambda \right)-\lambda$$ data fit well a two-constant Wemple-DiDomenico (WDD) equation in the film’s transparent and weak absorption regions. The $$\alpha \left(h\nu \right)$$, the absorption coefficient was calculated from $$\alpha \left(h\nu \right)\equiv 4\pi \kappa \left(\lambda \right)/\lambda$$ at each photon energy ($$h\nu$$). In this work, the $$\alpha \left(h\nu \right)$$-$$h\nu$$ data covering the band-tail and strong absorption regions, together with their overlapped region, were analyzed by a three-parameter Dilogarithm function $${\text{Li}}_{2} {\text{(h}}\nu {; }\alpha_{0} {,}\Gamma_{{\text{U}}} {\text{,E}}_{{\text{g}}} {)}$$ to determine simultaneously $$\alpha_{0} ,\Gamma_{U}$$ (Urbach-tail energy), and $${E}_{\text{g}}$$ (bandgap energy). For comparison, the $$\alpha \left(h\nu \right)-h\nu$$ data were fitted to the Tauc and Urbach $$\alpha \left(h\nu \right)$$-formulas in their limited spectral regions to find $${E}_{\text{g}}$$ and $${\Gamma }_{\text{U}}$$ separately, a procedure that involves complexity in picking properly the individual spectral range. Such problematic features are overcome in the three-parameter $$\alpha \left(h\nu \right)$$-Dilogarithm model.