Simulation of the charge transport across grain boundaries in p-type SrTiO3 ceramics under dc load: Debye relaxation and dc bias dependence of long-term conductivity

Abstract

A mathematical-physical model to describe the charge transport across grain boundaries in p-type SrTiO3 ceramics in the low-temperature regime for arbitrary dc voltage steps has been developed. The finite element model structure consists of a one-dimensional cross section through a ceramic scenario. Mathematical formulation comprises a coupled system of continuity equations (utilizing Maxwell-Boltzmann transport equations) and Poisson’s equation, with the appropriate boundary conditions for a potentiostatic simulation approach. The edges of the model are assumed to be blocking for ionic transport, and penetrable for electronic transport. The model was implemented exploiting routines from the numerical class library DIFFPACK™. After an initial electrostatic simulation a dc bias voltage step is applied. The evolution of the spatial profiles of electric potential, defect concentrations, space-charge density, and electric conductivity, and the current response are calculated. The results for the ceramic model structure confirm the experimentally observed Debye relaxation, and the characteristic dependence of long-term conductivity on the dc bias after space-charge polarization, before the onset of resistance degradation.