Modeling of anomalous hysteresis behavior of compositionally graded ferroelectric films at low fields

We study the hysteresis behavior of compositionally graded ferroelectric films by theoretical simulations. Anomalous vertical (polarization) shift behavior of hysteresis loops measured by a Sawyer-Tower circuit at low/medium applied fields is investigated. The anomalous ferroelectric response is discussed by the use of a multilayer model to account for the variation of properties across the film thickness. Electrical conductivities of the ferroelectric layers have been taken into account and time-dependent space-charge-limited conduction has been adopted. The effects of charge mobility and the amplitude of applied field on the D-E loop shift were examined. Theoretical calculations are discussed in relation to the experimental data from previous works.