Nonlinear Semiconductor Resistors

A phenomenological theory for the nonlinear voltage-current characteristic curve displayed by a granular aggregate of silicon carbide is presented. The theory, which should apply to granular semiconductors other than silicon carbide, is based on a very simple model of the aggregate and on the assumption that the essential resistance is located at the grain-grain contacts, the impedance of the bulk material being considered negligibly small. The current i is related to the voltage V by the equation i=kAPn/mdn−2Vn/tn,where A is the cross-sectional area of the aggregate, t the thickness, P the applied pressure, and d the average particle diameter. The constants k, n, and m are structure-sensitive, that is, they depend on the physical-chemical nature of the particles forming the aggregate. Factors influencing the values of these constants include impurity concentration in the semiconductor, elastic constants, and particle shape. The validity of this equation is supported by careful measurements made on granular aggregates of silicon carbide.