Influence of Stoichiometric Deviation and Temperature on Electron-Attempt-to-Escape Frequency in Non-Stoichiometric Titanium Dioxide Thin Films

The frequency formula for hopping electrons between randomly distributed oxygen vacancies within the variable-range-hopping model of Mott is derived, and the attempt-to-escape frequency is then extracted as a function of deviation from stoichiometry and temperature. These results are applied to nonstoichiometric titanium oxide thin films, with deviations from stoichiometry varying by 7 orders of magnitude relative to the stoichiometric counterpart and over a temperature range of 160–290 K. It is shown that the attempt-to-escape frequency decreases with increasing stoichiometry deviation and simultaneously weakly increases with increasing temperature. These results are qualitatively explained by using a microscopic view of an electron interacting with defective lattice vibrations.