Operational interfaces require knowledge of the interface response to applied bias. The electronic structure near the electrode will be determined by a combination of the above phenomena. For example, bias can induce the formation of filaments of oxygen vacancies or the migration of the latter towards electrodes as in resistive switching, whereas in tunnel regime capacitors atomic distortions can change under bias via the inverse piezoelectric effect.
Phenomenological and first-principles-based theoretical approaches have been deployed to understand the electronic structure at the interface under polarization. Classical semiconductor theory of the metal/insulator interface applied to FE capacitors, including the effect of polarization on band line-up and transport, describes charge injection in terms of the interface whereas the leakage current may be bulk limited. Theory has also shown that the local chemistry at the electrode/FE interface can enhance ferroelectricity. Dissimilar electrodes can induce a built-in electric field in the FE film. Extensive work on FE tunnel junctions has demonstrated the crucial role of the interface chemistry on tunneling probabilities. First principle calculations even predict an ohmic barrier but this may be due to the underestimation of the band gap. Knowledge of the microscopic layer polarization is vital because the interface induced changes of the electronic structure are expected to take place over a 1-2 nanometers.