Investigation of Resistivity and Permittivity for (Ba,Pb)TiO3 PTCR Ceramics

A scheme to examine quantitatively the interdependence between the measured resistance and permittivity data for semiconducting (Ba,Pb)TiO₃ samples having Curie points above 300°C was developed based on the Schottky-type potential barrier model. Specifically, the nonvanishing spontaneous polarization in the ferroelectric state was considered in terms of a useful parameter to explain the low resistivity below the Curie point. The resistivity derived from the measured permittivity shows a consistent temperature dependence with the dc measured one, i.e., the positive temperature coefficient of resistance (PTCR) characteristics. It is also observed that more satisfactory agreement can be achieved when the acceptor states are assumed to be distributed over a certain energy interval. The values of acceptor-state densities thus obtained are found to be in excellent agreement with those extracted from the slope in the Arrhenius plots of resistivity vs l/( T ε_m), where T is the absolute temperature and ε_m the dielectric constant. The validity of the present methodology is justified by obedience to the Curie–Weiss law for the calculated bulk dielectric constant.