Effects of space charge on the currents

Note that the surface-charge field E(0) has the same sign as the surface-charge density r0. The field E(x) at position x in the oxide for the present case of a uniform space charge density follows readily from eqn. (41), viz. 

We restrict our consideration in the present example to a fixed voltage across the oxide film, so that V(L) is a constant. (This would be the case, for example, if a battery producing a fixed voltage, VB, was used to drive current through the sample). The critical point is then to notice in the above equation how the magnitude of the surface-charge field, E(0), 

we must ask what effects the respective variations in the surface-charge field will have on the particle currents originating near that interface in the two cases. This question does not have a straightforward answer in general because the various expressions for the particle current can be quite complicated, involving concentration gradients in addition to 

Let us now consider the particle current in the high-field limit for the cases depicted in Fig. 13. Equation (90) is applicable to each of these cases, so that it is possible to examine the predicted effects of the immobile (trapped) space charge on these particle currents. Utilizing our previous conclusion that space charge having the same sign as the surface-charge 

The present qualitative deductions can be supplemented by a more quantitative treatment which has been presented in the literature [ 21 ]. One can refer to that development for the predicted functional dependences of the current on space-charge density. 

---