Impedance and modulus spectroscopy of semiconducting BaTiO3 showing positive temperature coefficient of resistance

TLDR

Doped polycrystalline BaTiO₃ exhibiting a positive temperature coefficient of resistance is an electrically inhomogeneous material. Analysis of ac impedance data using the complex impedance plane representation yields the dc resistance of PTCR ceramics, while the complex electric modulus formalism probes their inhomogeneous nature. The impedance and modulus analysis reveals a two‑ or three‑element equivalent circuit, distinguishes grain‑boundary and bulk effects—grain‑boundary capacitances are temperature‑independent whereas bulk capacitance peaks at the Curie point and follows Curie–Weiss behavior above it—and shows that both contribute to the PTCR effect, exposing limitations in current theories.

Abstract

Polycrystalline barium titanate that has been doped to give a positive temperature coefficient of resistance (PTCR) effect is an inhomogeneous material electrically. Analysis of ac impedance data using the complex impedance plane representation gives the dc resistance of PTCR ceramics. By additional use of the complex electric modulus formalism to analyze the same data, the inhomogeneous nature of the ceramics may be probed. This reveals the presence of two, sometimes three elements in the equivalent circuit. Grain-boundary and bulk effects may be distinguished from capacitance data: grain-boundary effects have temperature-independent capacitances, whereas bulk effects show a capacitance maximum at the Curie point and Curie–Weiss behavior above the Curie point. Both grain-boundary and bulk effects appear to contribute to the PTCR effect. These results reveal limitations in current theories of the PTCR effect.