Modeling the resistance-temperature characteristic of a positive temperature coefficient thermistor, using experimentally determined permittivity data

Abstract

The resistivity-temperature [ρ(T)] and current-voltage [j(V)] characteristics of a (Ba,Ca)TiO3 based donor/acceptor codoped positive temperature coefficient of resistivity thermistor have been analyzed in the context of the double Schottky barrier (DSB) model, using experimentally measured permittivity data. The best fit between the modeled and experimental ρ(T) behavior occurred for a broad acceptor energy fluctuation width (Δ=0.35eV). Modeling the ρ(T) behavior below the Curie temperature required a nonvanishing surface charge, consistent with a residual potential barrier. j(V) characteristics showed satisfactory agreement with the DSB model at low applied voltages per grain boundary (Vgb⩽0.13–0.22eV).

Synthesis of Lead-Free Air-Sintered BaTiO3–(Bi1/2Na1/2)TiO3-Based Positive-Temperature-Coefficient of Resistance Ceramics by Ca Addition and the Defect Chemistry of Semiconductivity

“…Achieving a low RT or RT semiconductivity is considered as a major criterion in attaining the PTC effect in air-sintered BT-or BBNTx-based electroceramics. According to the double Schottky barrier (DSB) model [1][2][3][4]20) for BT-based PTC ceramics, it is generally accepted that the PTC resistivity is exponentially related to the grain boundary Schottky barrier height [' 0 ðT Þ] both below and above T C , where ' 0 ðT Þ is inversely proportional to the effective bulk donor density represented by the bulk electron hopping center (Ti 3þ ) concentration. Thus, any increase in Ti 3þ concentration is expected to be associated with a reduction in both RT and max and vice versa.…”

The Positive Temperature Coefficient of Resistivity in BiFeO3 Films

“…No PTCR was observed even when the voltage increased to 40 V, that is, 10 times that in the Au/BFO1/YBCO capacitor. In most publications about PTCR, the authors suggest that the PTCR results from the grain boundaries of the bulk materials [ 27 , 28 ]. Nevertheless, Figure 3 illustrates that there are more grain boundaries in the BFO2 thin film than in the BFO1 film.…”

PTCR effect in donor doped barium titanate: review of compositions, microstructures, processing and properties

“…33 Furthermore, according to the Heywang-Jonker's model, the electrical resistivity profile r(T) above the ferroelectric Curie point of donor doped barium titanate ceramics can be modelled and was verified successfully using experimentally determined permittivity data reported by Brzozowski and Castro 8 and Zubair and Leach. 34…”