Calculation of the electric potential and surface oxygen ion density for planar and spherical metal oxide grains by numerical solution of the Poisson equation coupled with Boltzmann and Fermi-Dirac statistics

Abstract

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 modeled based on this differential equation. Here, the precise results of numerical solution of the Poisson equation coupled with Fermi-Dirac statistics and its approximated version that is the Poisson-Boltzmann equation is calculated to find the exact spatial variation of the electrical potential inside the metal oxide grain. The results are utilized to derive characteristic curves that relate surface oxygen ion density to the surface electrical potential and near surface electron density. The effects of grain size, grain shape and doping level on the results are also studied. It is shown that approximated solutions are only valid in limited range of conditions and the numerical solution should be used when a valid receptor function is sought.