Domain switching and spatial dependence of permittivity in ferroelectric thin films

A domain model consistent with the measured capacitance–voltage (CV) characteristics of lead zirconate titanate (PZT) capacitors is proposed. Two variants of this model are presented and compared with experimentally measured CV data. The basic model is developed adopting a macroscopic electric field that is spatially uniform through the depth of the film. Then, this model is generalized to allow a variation of the electric field with depth and to include a physically reasonable, position-dependent domain structure. Specifically, the spatial variation of the electric field is related to dopant–ion charges. As a result of the interaction between the domain properties and the electrical doping, a position dependent permittivity is induced, and the electrical properties of the capacitors are affected. Finally, computer simulations to fit the measured CV characteristics are performed to help understand the extent of the coupling between the domain properties and the electrical doping. It is found that there is a minimum doping level below which the doping does not affect the CV characteristic. A method for determining this minimum doping level from the CV curve is presented. The analysis of observed CV data demonstrates that niobium doping is responsible for partially compensating the p-type nature of PZT thin films. For the films measured here, the minimum noticeable doping level is about 1018 cm−3. It is also found that niobium doping slows the growth rate of polarization as the electric field increases, and has a tendency to increase the coercive field.