Numerical analysis of electrical response: Statics and dynamics of space-charge regions at blocking electrodes

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Abstract
The steady-state and transient electrical properties of a material containing one or two species of mobile charge carrier in contact with blocking electrodes are examined. The systems treated are 2, 20, and 40 Debye lengths in extent and exemplify the transition from thin-film or membranelike behavior to the more usual case in which well-defined space-charge layers form at each electrode. The static capacitance of the electrode/material/electrode system is examined and the response of the system to a step-function applied potential difference is obtained by numerical simulation. The simulation results show clearly the role of the system length and charge carrier mobilities in determining the system response. The decay of total current following the potential step is numerically fitted to a sum of exponential decays. The nonlinear character of system response becomes apparent when the transient current associated with the formation of space-charge layers in response to a potential step is compared with that which accompanies the decay of the space-charge layers following the sudden restoration of zero potential difference between the electrodes. The redistribution of charge carriers and the electrostatic potential both in the steady state and at representative times during the transient response are presented and discussed.