On the contribution of electrostriction to charge-induced stresses in anodic oxide films

Electrostriction has been known for long as a major source of internal stress developing in oxide films during anodising. However, in many studies, the contribution of electrostriction is estimated using an oversimplified equation, leading to a systematic underestimation. In this work, a modified theory is first presented for linking the in-plane electrostriction stress to the applied electric field. The corrected equation explicitly takes into account the dielectric properties of the deformed material through the appropriate electrostriction parameters of the oxide film. A new experimental procedure is then described for measuring electrostriction stresses in situ during anodising, and applied to ultrathin (<100 nm) TiO2 films. Oxide films were first grown potentiodynamically on one side of cantilevered electrodes. The electric field in the oxide film was then systematically changed by repeatedly cycling up to the forming voltage. At the same time, the resulting in-plane electrostriction stress was determined from high-resolution in situ curvature measurements. For the TiO2 films considered, compressive in-plane electrostriction stresses up to −240 MPa were measured. This is an order of magnitude higher than previous predictions which neglected the contribution of the electrostriction parameters. Moreover, the measured stress values, their field-dependence and the derived electrostriction parameters are shown to be in agreement with the modified theory.