High temperature characterization of electrical barriers in ZnO varistors

Two main models have been proposed to describe the potential barriers in Zn O varistors: the surface oxidation and the surface states. It has been diff icult to decide which of them better corresponds to the experimental observ ations. High temperature electrical characterization of these materials is an important tool to understand the formation of the electrical barriers. I n this work, using literature data describing ZnO varistor characteristics at high temperature, up to 1153 degrees C, we calculate the energy position of the equilibrium Fermi level at the grain boundary interface, and found that this parameter decreases with the increase of temperature, and for tem peratures higher than similar to 700 degrees C it stays close to the ZnO ba nd gap without crossing it. This behavior shows that the interface never pr esents a p-type character, a starting point to develop the surface states m odel. On the other hand, 700 degrees C is a temperature too low for the sur face oxidation mechanism to be operative. It is then proposed that, during cooling down to similar to 700 degrees C, the interface Fermi level stays c lose to the middle of the band gap due to the adsorption and subsequent rea ction of oxygen with ZnO surfaces/grain boundaries. For lower temperatures, when the interface Fermi level separates from the middle of the band gap, it is proposed that it follows the variation of the bulk Fermi level, which in turn is caused by shallow donors in ZnO. A calculation assuming a reduc ed electroneutrality condition, gave a donor density of similar to 3 x 10(1 7)cm(-3), which corresponds approximately to the density of carriers in the material for temperatures down to room temperature. This value is in a goo d agreement with those available in the literature. Knowing both the bulk a nd the interface Fermi levels, it is then possible to calculate the barrier height at any temperature, and it is observed that it is almost constant f rom room temperature up to similar to 400 degrees C, with a value of 0.8 eV , and than decreases monotonously up to 1153 degrees C. Taking these values , it is possible to calculate the variation of the low voltage conductivity with temperature, and it is found that, apart from the variation between r oom temperature and 400 degrees C, with no special significance, the decrea se of the barrier height from 400 degrees-1153 degrees C induces an extra c hange of the conductivity from which a fictitious activation energy of 1.5 eV is obtained. Therefore, these two energies are not related to shallow an d deep donors in ZnO grains.