Band bending and the thermochemistry of oxygen vacancies in ionic metal oxide thin films

We address the problem of band bending in a metal oxide thin film/electrode layer and derive equations relating the voltage drop across the oxide to the oxygen activity of the ambient in equilibrium with the oxide. Applied to the case of oxygen vacancies, the results predict situations where the vacancy charge is strongly localized adjacent to the metal interface. Comparing predictions to experimental results for the specific case of Hf O2, we find that the free energy of formation of the oxygen vacancies are of the order of ∼3 eV, significantly smaller than the numbers theoretically predicted for bulk Hf O2. © 2008 American Institute of Physics.