Drift-dominated conduction within an Ohmic medium

Abstract

Drift‐dominated charge transport within an Ohmic medium is analyzed using the method of characteristics to convert the governing partial differential equations into a set of ordinary differential equations. As for earlier work within a lossless medium, the analysis is generalized to allow any initial and boundary conditions and any terminal constraint or excitation. For imposed currents the equations are exactly integrable, while for imposed voltages, the equations are easily integrated using the Runge‐Kutta method of numerical integration. Special cases examined are the charging transients for space‐charge‐limited conduction for step current and step voltage excitations from rest and the discharging transients for systems in the dc steady state for which the excitation is instantaneously open or short circuited.