Transient injection currents in insulators with pre-existing trapped space charge

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Abstract
A theory of current pulse shape and transit time, in the presence of a uniform distribution of pre-existing trapped space charge, for arbitrary photoinjection density, with deep trapping, is developed. Solutions to the equations are displayed graphically. Limiting cases of the general equations provide, for the first time, new current and transit-time expressions, in the presence of trapped space charge, in the large-signal space-charge-limited mode, convenient for experiment, and yield those previously derived for the small-signal mode. Two kinds of transient space-charge-limited currents are considered, corresponding to cases where enough charge is injected into the insulator so that the field at the cathode is zero either initially or throughout the duration of the pulse. The currents and transit times are compared. All equations reduce to known results in the absence of a pre-existing trapped space charge. The results point the way to the eventual use of transient photocurrents as a probe of trapped-space-charge distributions.