Experiment and Theory for the Thickness Effect of Nano Metal Oxide Gas Sensing Thin Film Optimum Size of Crystal Grains and Theory of Mesoscopic Effect

For pt. I see ibid., p.Z001463-8, (2006). The existence of the optimum film thickness and optimum grain size of nano metal oxide gas sensing thin films is given by experiment results. The existence of the optimum grain size is examined theoretically to be a new mesoscopic effect, resulting from the failure of Fermi statistic law of the adsorbed negative oxygen ion concentration when the grain size reduces to a certain range. According to Kubo´s theory that as the grain size reduces to a characteristic length r_m the grain would be neutrality, Fermi statistics is modified, and therefore, the theoretical result of the optimum grain size r₀*=2r_m is yielded. With the Kubo´s formula of electron work function, the values of r_m and r₀* can be estimated, which consist with the experimental results