DOMAIN SWITCHING AND SPATIAL DEPENDENCE OF PERMITTIVITY IN FERROELECTRIC THIN-FILMS

A domain model consistent with the measured capacitance-voltage (CV) c haracteristics of lead zirconate titanate (PZT) capacitors is proposed . Two variants of this model are presented and compared with experimen tally measured CV data. The basic model is developed adopting a macros copic electric field that is spatially uniform through the depth of th e film. Then, this model is generalized to allow a variation of the el ectric field with depth and to include a physically reasonable, positi on-dependent domain structure. Specifically, the spatial variation of the electric field is related to dopant-ion charges. As a result of th e interaction between the domain properties and the electrical doping, a position dependent permittivity is induced, and the electrical prop erties of the capacitors are affected. Finally, computer simulations t o fit the measured CV characteristics are performed to help understand the extent of the coupling between the domain properties and the elec trical doping. It is found that there is a minimum doping level below which the doping does not affect the CV characteristic. A method for d etermining this minimum doping level from the CV curve is presented. T he analysis of observed CV data demonstrates that niobium doping is re sponsible for partially compensating the p-type nature of PZT thin fil ms. For the films measured here, the minimum noticeable doping level i s about 10(18) 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. (C) 1997 American Institute of Physics.