Roles of shape and size of component crystals in semiconductor gas Sensors: I. Response to oxygen

An attempt to derive a comprehensive theory on the roles of shape and size of component crystals in semiconductor gas sensors is described. Based on Poisson's equations, the depth profiles of the electric potential inside the component crystals under electron-depleted conditions are solved for each shape of plate, sphere, or column. By combining this electronic equilibrium with the gas adsorption equilibrium taking place outside, the reduced resistance (R/ R0) of each sensor device can be expressed as a function of reduced adsorptive strength (y) of the adsorbing gas for crystals that are different in shape and are of a reduced size (n). As an important phenomenon typically associated with small crystals, a new type of depletion (volume depletion) appears following the conventional one (regional depletion) on increasing y, and the transition to volume depletion takes place at smaller y as n decreases. In the stage of volume depletion, R/ R0 is linear to y, with a linearity constant inversely proportional to n.