The problem of band bending in a metal oxide thin film/electrode layer was addressed, and equations were derived which related the voltage drop across the oxide to the O activity of the ambient in equilibrium with the oxide. Applied to the case of O vacancies, the results predicted situations where the vacancy charge was strongly localized adjacent to the metal interface. Comparing predictions to experimental results for the specific case of HfO2, it was found that the free energy of formation of the O vacancies was of the order of ~3eV; significantly smaller than the values theoretically predicted for bulk HfO2.

Band Bending and the Thermochemistry of Oxygen Vacancies in Ionic Metal Oxide Thin Films. S.Guha, P.Solomon: Applied Physics Letters, 2008, 92[1], 012909