Simple model of polarization offset of graded ferroelectric structures

The abnormal polarization offset observed in case of graded ferroelectric structures is explained assuming the presence of a nonreversible part of polarization due to the imposed polarization gradient. It is shown that an upper limit for the offset should exist, fixed by the remnant polarization of the component materials considered as independent layers. This is valid for the structures in which polarization increases or decreases in steps from one layer to the other, but should also be valid for the structures with continuous gradient. However, large values of the charge offset could be achieved in the last case. The electric field dependence of the polarization offset is predicted, together with the possibility of obtaining large nonconventional pyroelectric coefficients. The simulation developed in the case of a bilayer ferroelectric structure and using data from the lead–lanthanum–zirconate–titanate system describes well the observed features of the graded ferroelectric structures.