Grain boundary electrical barriers in positive temperature coefficient thermistors

Both current-voltage (I-V) and capacitance-voltage (C-V) characteristics were studied in Nb-doped BaTiO₃ bicrystals to verify the potential barrier model. The potential barrier of n-i-n structure can reasonably describe the observed data in comparison with that of double Schottky barrier (DSB) model. The difference in the I-V characteristics between the two models is characterized by the appearance of the sub-ohmic behavior with α<1. In the DSB model, the barrier height is kept almost the same because the acceptor states are strongly pinned by the Fermi level. When the acceptor states are completely occupied, the potential barrier will collapse and then the current will increase steeply.