Predictive model of the optical response of amorphous $WO3$ to ion intercalation

The optical response of an amorphous tungsten oxide half cell upon varying degrees of protenation is examined. First, the indium tin oxide transparent conductor’s dielectric function is determined from a parameterized version of the ionized impurity scattering model of Hamberg and Granqvist [I. Hamberg and C. G. Granqvist, Appl. Phys. Lett. 44, 721 (1984)]. Then the tungsten oxide data are interpreted using two theoretical optical dispersion formulas. The first is the polaron conductivity theory of Reik and Reese [H. G. Reik and D. Reese, J. Phys. Chem. Solids 28, 581 (1967)] and the second is the parametric semiconductor model of Johs et al. [B. Johs et al., Thin Solid Films 313–314, 137 (1998)]. It is found that the parametric semiconductor model is able to reproduce the measured optical spectra extremely well. The resulting set of dielectric functions is interpreted in terms of the intercalated charge. An empirical model is constructed to explain the observed behavior of the imaginary part of the dielectric function, which should be appropriate for device modeling. The real part of the dielectric function is then readily determined by application of the Kramers–Krönig relations, which are inherent to the parametric semiconductor model.