Anomalous diffusion of ions in electrochromic tungsten oxide films

Amorphous tungsten oxide thin films were deposited by sputtering at different O₂/Ar ratios onto conducting substrates. Ion intercalation and diffusion in the films was studied by electrochemical impedance spectroscopy measurements in the frequency range 10 mHz–100 kHz and for potentials between 1.0 and 3.2 V vs. Li/Li⁺, using the film as working electrode in a Li⁺ containing electrolyte. The impedance data were in very good agreement with anomalous diffusion models. Different models were found to be applicable at potentials >1.8 V and <1.8 V. At high potentials ion intercalation was found to be reversible and an anomalous diffusion model describing ion hopping was favored. At low potentials ion intercalation was found to be irreversible and ion trapping takes place. In this latter range an anomalous diffusion model for the case of non-conserved number of charge carriers gave the best fit to experimental data. We obtained potential dependent diffusion coefficients in the range from 10⁻⁹ to 10⁻¹¹ cm²/s, and anomalous diffusion exponents in the range 0.1 to 0.4, with the films deposited at lower O₂/Ar ratios exhibiting the higher values.