Model for the potential barrier depth along the grain boundaries of an ultrathin tin dioxide gas sensor

A potential barrier model along the grain boundaries in ultrathin tin dioxide (SnO₂) gas sensors is presented. It is assumed that the negatively charged oxygens are adsorbed only on the grain boundaries. The potential barrier depth is expressed as functions of grain size, donor concentration and surface coverage of adsorbed oxygen ions at the boundaries. A direct consequence is that the conduction electrons are effectively confined in a grain when the film thickness becomes smaller than a critical value. This indicates a drastic increase in resistivity with decreasing film thickness in air, and thus an occurrence of an extremely high gas sensitivity.