Bulk and grain boundary resistivities of donor-doped barium titanate ceramics

The electrical properties of both the bulk and the grain boundaries of positive temperature coefficient (PTC) resistors have been determined as a function of temperature ranging from 25 to 400 °C by application of impedance spectroscopy. The resistances of the bulk and the grain boundaries as well as the capacitance of the grain boundary regions of n-conducting BaTiO3 ceramics have been obtained by fitting an appropriate equivalent circuit to the impedance spectra. Samples of equal dimensions and composition but different grain sizes (2.8 and 6.6 μm) have been investigated. Whereas the bulk resistance remains almost constant throughout the whole temperature range, the grain boundary resistance shows a steep increase of several orders of magnitude (PTC effect) above the Curie temperature (around 90 °C). The grain boundary resistances of the disk-shaped samples (dimensions: 2.2 mm thickness, 8.0 mm diameter) vary typically between 35 Ω and 30 MΩ, and the bulk resistances are found to be approximately 4 Ω (bulk resistivity: 10 Ω cm). The variation of the grain boundary capacitance with temperature, depending remarkably on the grain size of the samples, follows the Curie–Weiss law. Both the steep increase of the grain boundary resistance and the Curie–Weiss behaviour of the grain boundary capacitance are described theoretically by application of an extended Heywang model. The defect chemistry in the grain boundary regions is modelled by assuming Schottky type space charge depletion layers. Optimized values for the temperature-dependent energy level and the density of the acceptor type grain boundary states are given.