Influence of polarization spatial distribution on screening in polycrystalline ferroelectrics-semiconductors

Using the Landau-Devonshir thermodynamic potential the spatial distribution of polarization in polycrystalline ferroelectrics-semiconductors is calculated for the case of BaTiO3. It is shown that this distribution plays an important role in the screening of electric fields of charged grain boundaries. When polarization reorientation in the space region takes place the screening is most effective, the potential barrier height and, hence, resistivity values in the ferroelectric phase being the lowest resulting in large positive temperature coefficient of resistivity (PTCR) effect. The value of the PTCR effect as well as the dimensions of the grain boundary space charge region depend on the tnutial orientation of grain boundary electric field and the spontaneous polarization in the bulk of the grain.