Phenomenological description of polarization switching in ferroelectric semiconductors with charged defects

We have proposed the phenomenological description of polarization switching peculiarities in ferroelectric semiconductors with charged defects and prevailing extrinsic conductivity. More precisely, we have modified the Landau-Ginsburg approach and shown that the macroscopic state of the aforementioned inhomogeneous system can be described by three coupled equations for three order parameters. Both the experimentally observed coercive field values, well below the thermodynamic one, and the various hysteresis loop deformations (minor, constricted and double loops) have been obtained in the framework of our model. The obtained results qualitatively explain the ferroelectric switching in such bulk ferroelectric materials as SBN single crystals doped with Ce, lead zirconate titanate (PZT) films doped with Nd, and La-doped PZT ceramics.