Theory of Transient Space-Charge-Limited Currents in Solids in the Presence of Trapping

The problem of transient space-charge-limited currents in insulating and conducting crystals is treated mathematically. With a number of simplifying assumptions, solutions are derived for the time-dependent current and space-charge distribution following the onset of injection, the latter taking place via an ohmic contact under an applied voltage-pulse. Exact analytical solutions are given for the two limiting cases of no trapping and fast trapping. For flow in an insulator under slow trapping, approximate expressions are derived which are valid or trapping-times larger than twice the transit time. For shorter trapping times the equations of flow are solved numerically and the solutions presented in graphical form.