Tunneling through surface barrier and modified mass action law in nanostructured metal oxide semiconductors

The surface barrier of metal oxide semiconductors was studied, under spherical symmetry, for grains smaller than the depletion width, w the condition which makes the material properly nanostructured. Thus, it was possible to explain the lower observed surface barrier due to the unpinning of Fermi level with respect to coarser grained materials. The model allowed us to explain the different behavior of conductance in gas of two sets of sensors with grains having two well distinct characteristic radii (R< w and R>w). In the first case (R<w), the overlapping of barriers can take place in the presence of a gas, an effect which strongly affects the tunneling contribution to conductivity with respect to the thermionic one, at the same temperature. The behavior of conductance in the presence of gases and the effect of temperature have been explained through the mechanism of barrier modulation through gas chemisorption assuming that the density of vacancies can only be modified by interstitial oxygen diffusion in and out of the nanograins. The apparent contradiction of the density of vacancies dependence on the field is finally solved.