Influence of strain on space-charge distribution at ferroelectric thin-film free surfaces

Ferroelectric perovskites are wide-bandgap semiconductors and therefore are often modeled as perfect dielectrics. However, space charges can play an important role in regions with large electric fields, such as at domain walls, free surfaces, near electrodes, etc. In this paper, we apply a mesoscale model to examine the space-charge distribution at free-surface closure domain patterns in a ferroelectric thin film. The model uses a conventional electromechanical phase-field approach for ferroelectric domain patterns in combination with drift–diffusion based equations to model space-charge distribution. We additionally apply a boundary element method to compute the stray electric fields outside the ferroelectric free surface. We probe the influence of mechanical strain, such as would be applied through a substrate, on the distribution of space charge. We find an indirect, but strong, coupling between mechanics and space-charge distribution. The physical mechanism of this coupling is as follows: the mechanical strain induces changes in the domain patterns and polarization distribution; this in turn changes the local electric fields sufficiently that space charges are redistributed on the free surface rather than moving towards the bottom electrode. We note two interesting features of this coupling: first, the coupling mechanism is operative only at free surfaces due to the complex domain patterns in these regions, and would not occur in the bulk; second, although domain patterns are visually only marginally changed by the presence of space charges, the changes in electric field due to these seemingly small changes is significant and this provides the coupling with space charge. 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.