Transient electric field and space-charge behavior for unipolar ion conduction

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Abstract
New analysis is presented using a unipolar ion‐mobility conduction model in planar geometry which solves for the transient behavior of the bulk electric field and space‐charge distributions as a function of time and space, as well as the resulting time dependence of the terminal quantities of voltage and current. The charge‐conservation quasilinear partial differential equation is solved using Lagrange's method with the method of characteristics. The analysis is generalized to handle any physically allowed initial and boundary conditions for any type of applied excitation. Special cases are examined of the turn‐on transient with the application of a step voltage or current, contrasting the behavior between space‐charge‐limited conditions where the emitter electric field is zero to those where the emitter field is nonzero. Much of the analysis yields closed‐form expressions.