Theory of Conductivity of Semiconductors

Abstract

The author's older theory of conduction in polarizable media is generalized in such a way as to include rectification. An electronic component (positive holes or electrons) and an ionic component (negative or positive ions) are taken into account. The former are subjected to the boundary conditions of the MottSchottky theory, the latter to the boundary conditions of the author's theory of polarization. Significant deviations from the Mott-Schottky theory are caused by the ionic component.In Sec. I the fundamental equations are established in a general way and the boundary conditions are discussed. In the remainder of the present paper only the limiting case is treated where all impurity centers are either completely associated or completely dissociated. In Sec. II(a) the general procedure for treating the time-dependent equations is sketched, and subsequently the special case of simple ac is treated in detail. An expression for the current is obtained without the omission of any terms [Eq. (21)]; however, its evaluation requires the introduction of a simplified "zero solution." Then the complete expression for the frequency dependence of the equivalent susceptance and conductance is established (Sec. II(b)). Finally, in Sec. III, the theory is compared with the results of ac measurements performed in this laboratory on locally manufactured selenium disks. The theory explains the frequency dependence of capacitance and conductance over the range from about 2000 to 200,000 cps, if the presence of two species of ions of different mobilities is assumed. From this agreement ionic data, i.e. the concentrations of the carriers, their mobilities, diffusivities, and the thickness of the depletion layer, are derived and discussed.