Static Space Charge and Capacitance for a Single Blocking Electrode

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Abstract
Static space‐charge distributions in materials having one charge blocking and one ohmic electrode are considered with special emphasis on the situation where charge carriers of only one sign are mobile but which may recombine bimolecularly with fixed charges of opposite sign. The dependence of potential, charge, and electric field on distance from the blocking electrode cannot be obtained exactly in closed form but various simple approximate relations are obtained and are compared with accurate digital computer solutions of the exact relation between potential and distance. Comparison is most significant when the distance scale is normalized by the effective Debye length, a quantity which is shown to depend on recombination ratio when charges of only one sign are mobile. The dependence of total space‐charge and differential and static space‐charge capacitance on applied potential and recombination is obtained in closed form, and it is shown that recombination can lead to peaks in the curves of static and differential capacitance versus applied potential. Observation of these peaks should afford a simple method of determining recombination ratio and other pertinent parameters of the material. Finally, the addition of a charge‐free layer in series with the space‐charge region is considered, and the effect of such addition on differential capacitance investigated. The combination of a charge‐free layer and space‐charge region represents a combination of Mott's and Schottky's theories of rectification insofar as capacitance effects are concerned and is therefore pertinent to measurements on barrier‐layer rectifiers as well as to material with a completely blocking electrode.