AlxSi1-xOn films exhibit a drastic change of proton conductivity across the film by reducing their thickness to less than 100 nm. The temperature and humidity dependence of conductivity of the sub-100 nm films is quite different from those of the thicker films. Furthermore, in the former thickness range, the value of conductivity markedly increases with reducing the film thickness, and its thickness dependence follows a power law with a fixed index of -2.1. This size-scaling effect can be explained by the percolation conductivity model that the probability for percolating of the conductive moiety in AlxSi1-xOn films increases with decreasing the thickness.
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