Effects of mobile donors on potential distribution in grain contacts of sintered ceramic semiconductors

Sintered ceramic semiconductors can be used to monitor the surrounding gas atmosphere. It is based on the conductivity response of the semiconductor to the surface reactions on the grains of porous material. Some nonstoichiometry defect donors, like oxygen vacancies in n-type semiconductors, may be mobile at relatively low temperatures, where semiconductor gas sensors operate. In such case, the donor concentration may considerably decrease in the space charge layer at the semiconductor surface, which may be reflected in the transport properties of electrons through the neck contacts between grains. We model here various neck contacts between spherical grains and compute the electrical potential at the conductive region from the Poisson–Boltzmann equation in cases of mobile single and double donors. The solutions are evaluated numerically with a finite difference method. According to the Schottky-defect model for oxygen vacancies, the surface concentration of donors is kept a fixed parameter in the calculations. The chosen material parameters are those of tin dioxide, which is the key material of semiconductor gas sensors. It is found that mobile donors may strongly modulate the distribution of electrical potential around the neck contacts, and thus, modify the transducing properties of the microstructure of ceramic semiconductor gas sensors.