Chemiresistive metal oxides are widely used in the fabrication of gas sensors. The theory of gas sensitivity of metal oxide sensors has been developed based on the gas-solid interactions on the metal oxide surface. These interactions led to a charge transfer that is well described by the Poisson-Boltzmann equation. The receptor function of metal oxides can be modelled based on this differential equation. Here, precise results of numerical solution of Poisson-Boltzmann equation and the more general Poisson-Fermi-Driac equation show the limitations of approximated solutions and found even where the accumulation layer created near the surface of metal oxide grains, the Poisson-Boltzmann approximation is not valid anymore and the Poisson-Fermi-Dirac equation must be used. Here, the combination of Poisson-Boltzmann relation, surface reactions and gas diffusion has been solved numerically to derive an exact solution for temporal variation of the sensor conductivity. The established model can be used for both thin and thick oxide layers. The model has been simulated with different combinations of effective parameters. Among the results, the significant effect of decreasing the grain size and the thickness of the sensitive layer on increasing the sensitivity of the sensor can be noted. Also, using the presented equations, the ultimate electrical potential limit for each grain was estimated. For example, for spherical grains with a diameter of 50 nm the surface potential will not exceed 0.3 volts when the doping level is 2.5 × 10 17 cm -3 . To experimentally investigate the model, a thin film sensor was fabricated by RF sputtering of ZnO on quartz substrate. The transient response of the sensor to an oxygen pulse was recorded. The results showed that the proposed model for the transient response of the metal oxide gas sensor is in good agreement with the experimental response Key Words : Gas sensor, metal oxide, transient response, electrical potential, Poisson-Fermi-Dirac, sensor modeling.
