Effect of annealing treatments on positive temperature coefficient of resistance properties of barium titanate ceramics and a new model for the positive temperature coefficient of resistance effect

Alternating current impedance has shown the presence of three electrical components in a semiconducting barium titanate ceramic that has been processed to give a positive temperature coefficient of resistance (PTCR) effect. Two of the component resistances, $R1$ and $R2,$ each present a PTCR effect and, from the temperature dependence of their capacitances, they are attributed to different regions, nonferroelectric and ferroelectric, respectively, at the surfaces of individual grains or in the region of inter-grain contacts. The influence of isothermal annealing in air at 1000, 1100, and 1200 °C on these PTCR effects was investigated. At the resistance maxima, $Rmax$ and $Tmax,$ two types of dependence were found for both $R1$ and $R2.$ At short times, $Rmax$ decreased and $Tmax$ shifted to higher temperatures; at long times, the reverse occurred and $Rmax$ increased while $Tmax$ shifted to lower temperature. Capacitance values for both regions were constant at short times but decreased at long times, indicating a thickening of the regions responsible for $R1$ and $R2$ at long times. The room temperature resistance $R25$ was constant at short times but increased dramatically at long times, leading to a decrease in the magnitude of the PTCR effect. A model to account for the observed changes is proposed. Freshly fired ceramics are oxygen deficient and semiconducting; grain surfaces are Ti rich. Oxidative annealing creates an oxidized surface layer and an electron depletion layer just inside the grain surfaces. Counter diffusion through these layers of $Ba2+$ and $O2−$ ions then occurs so as to partially restore electroneutrality; consequently, the concentration of surface acceptor states, $Ns,$ decreases initially. On prolonged annealing, further oxidation occurs: oxide ions diffuse into the grain cores, with counter diffusion of electrons to the grain surfaces where they are trapped by additional absorbed oxygens leading to an increase in $Ns.$ An explanation is given as to how both ferroelectric and nonferroelectric regions of the ceramics exhibit a PTCR effect. The key parameter that controls the activation barrier to conduction appears to be the polarization of the lattice associated with dipolar fluctuations and ferroelectric domains rather than with the polarizability of the different regions.