Modeling the effect of SiO2 additions and cooling rate on the electrical behavior of donor-acceptor codoped positive temperature coefficient thermistors

Abstract

The resistivity-temperature [ρ(T)] characteristics of two series of (Ba,Ca)TiO3 based positive temperature coefficient (PTC) of resistance thermistors, prepared with different levels of SiO2 addition and cooling rates, have been analyzed in the context of the double Schottky barrier model. A significant improvement in fit, compared to earlier studies, was achieved between the modeled and experimental ρ(T) behavior over the full temperature range of the PTC transition through the incorporation of experimentally obtained permittivity data, coupled with an optimized acceptor energy spread (0.40±0.05eV). The permittivity below the Curie temperature (TC) increased slowly when either the SiO2 content or cooling rate was increased, but above TC the permittivities were almost unaffected. The bulk resistivity and average grain size were affected only slightly by increases in SiO2 addition or cooling rate, but the gradient of the ρ(T) curve and peak resistivity gradually decreased due to a reduction in surface state density from 1.1×1014to5.9×1013cm−2 at an acceptor energy depth of 1.57–1.60eV. A reduction in room temperature resistivity with increasing SiO2 content and cooling rate was consistent with a concomitant reduction in the ratio of residual surface charge unit density to permittivity.