IMF2017

Positive temperature coefficient of resistivity (PTCR) materials are widely used in the electronics industry for applications including temperature sensors, overheat protection, time delay circuits and current limiters for overvoltage or overcurrent protection, current stabilisers etc. In this respect, doped barium-titanate ceramics has attracted a considerable attention for small size processing and designing. AC conductivity studies of various BaTiO3 or similar ceramics produced equivalent circuits used for the impedance spectra fitting within the framework of RCPE elements serial connection (CPE- constant phase element), as a generalization of the Cole element. They corresponds to details of the ceramics grains structure and its dynamics: grain interior boundary, grain boundary, free electrons concentration, etc. which is typical behavior of diffuse ferroelectric or relaxor materials. One of models that explains PTC effect is the Heywang model, in terms of grain boundaries potential barriers of the Shottky type. In order to consider quantum transport under the influence of an electron-electron interaction in a mesoscopic conductor, the Boltzmann-Poisson model is investigated jointly. In this presentation it will be considered an improved version of the existing model that corresponds to correct quadratic relation for varistor effect in the case of Heywang potential, in the approximation of one relaxation time for the Cole element. Validity conditions of this new model will be discussed.