Space-Charge Effects on Emission-Limited Current Flow in Insulators

The effect of electron traps on the current-voltage (J-V) relationship and the charge distribution in insulators, under conditions of space-charge-limited current flow, is well understood. This paper extends the consideration of trapping effects into the region of emission-limited current flow. Trapped space charge distorts the field in the insulator so that the usual J-V relationship for emission-limited current in a vacuum, J ∝ exp (constant) V½, which is often applied to insulators, will not be observed initially. It is shown that at sufficiently high voltages, however, the trapped space charge becomes negligible and the above J-V relationship is obtained. A calculation is done to obtain the J-V characteristic in an insulator throughout the emission-limited region, for typical values of trapping depth, trapping density, and barrier height. The resulting curves show that the transition from space-charge-limited to emission-limited current occurs at reasonable voltages, and that at these voltages, space-charge effects are large enough to be readily observed in practice. It is shown that the absence of space-charge effects at higher voltages is a consequence of field lowering of the barriers around trapping sites. In addition, several general results are obtained concerning field and charge distributions in insulators containing traps.