Effects of polarization and permittivity gradients and other parameters on the anomalous vertical shift behavior of graded ferroelectric thin films

We studied theoretically the dependence of the "polarization offset" on various parameters in compositionally graded ferroelectric thin films. Our model adopts the Landau-Khalatnikov equation to describe hysteresis behavior and takes the time-dependent space-charge-limited conductivity into account to investigate the effects of polarization and permittivity gradients, charge mobilities, and thickness in graded ferroelectric thin films. We found that both polarization and permittivity gradients are requisite for the occurrence of offset phenomena. It is also found that larger gradients of remanent polarization and permittivity, a smaller thickness, and a larger charge mobility can generally enhance the effect of vertical offsets. The qualitative agreement between simulation and experiment further supports our previous notion that the asymmetric conduction current arising as a result of the composition gradient is an important factor leading to the polarization offset phenomenon.