High temperature characterization of electrical barriers in ZnO varistors

Two main models have been proposed to describe the potential barriers in ZnO varistors: the surface oxidation and the surface states. It has been difficult to decide which of them better corresponds to the experimental observations. High temperature electrical characterization of these materials is an important tool to understand the formation of the electrical barriers. In 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 temperatures higher than similar to 700 degrees C it stays close to the ZnO band gap without crossing it. This behavior shows that the interface never presents a p-type character, a starting point to develop the surface states model. On the other hand, 700 degrees C is a temperature too low for the surface oxidation mechanism to be operative. It is then proposed that, during cooling down to similar to 700 degrees C, the interface Fermi level stays close to the middle of the band gap due to the adsorption and subsequent reaction 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 reduced electroneutrality condition, gave a donor density of similar to 3 x 10(17)cm(-3), which corresponds approximately to the density of carriers in the material for temperatures down to room temperature. This value is in a good agreement with those available in the literature. Knowing both the bulk and 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 from 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 room temperature and 400 degrees C, with no special significance, the decrease of the barrier height from 400 degrees-1153 degrees C induces an extra change of the conductivity from which a fictitious activation energy of 1.5 eV is obtained. Therefore, these two energies are not related to shallow and deep donors in ZnO grains.