Complex Impedance Analysis of Nb-Doped (Ba0.6Sr0.4)TiO3 PTC (Positive Temperature Coefficient) Thermistors

Abstract

Frequency-dependent complex impedances were measured in Nb-doped (Ba_0.6Sr_0.4)TiO₃ PTC (positive temperature coefficient) ceramics. The complex impedance data were analyzed in Cole-Cole-type equivalent circuits by the computer fitting method in order to determine individual resistance and capacitance values of the bulk grain and grain boundary. The PTC effect was found to have originated from the temperature-sensitive behavior of the grain boundary resistance. The temperature dependences of dielectric constants of both the bulk grain and grain boundary calculated on the basis of the two-layer model agreed closely to those predicted by Heywang's model. The width and potential height of the grain boundary layer were estimated to be 0.26 µm and 0.1 eV, respectively, in the temperature range below -20°C. The estimated donor density of 6×10¹⁸ cm^-3 was much lower than calculated from the amount of Nb₂O₅ added.4