Effects of step changes in excitation from a steady state on the transient electric field and space charge behavior for unipolar ion conduction: II. Step changes in voltage

Abstract

The previous analysis of the transient electric field and space charge behavior for drift-dominated unipolar ion conduction is continued and extended by considering steady-state systems for which the terminal voltage is instantaneously increased or decreased including short-circuit conditions. Representative boundary conditions considered are a field-threshold condition whereby charge injection occurs whenever the emitter electric field reaches a critical value and the case where the injected charge density is proportional to the emitter electric field. For a step change in voltage, the electric field also changes everywhere by a constant so that its average value remains proportional to the voltage, although the spatial derivative which is proportional to the charge density is continuous. With a field-threshold condition for charge injection, a step increase in voltage results in spontaneous charge injection to keep the emitter electric field constant, while step decreases in voltage result in no charge injection until the emitter field reaches the critical value. For small voltages the critical field is never reached, resulting in no further charge injection, so the analysis reduces to a pure initial-value problem as the system approaches the uniform electric field of an ideal capacitor. For step-down voltages, the emitter electric field could become negative reversing the direction of motion of the charges. Detailed plots of the electric field and space charge distributions for representative voltage steps and charge injection boundary conditions are presented.