Theory of the space-charge build-up and current transient in a weakly conducting layer with an induced conductivity gradient. Application to photoconduction and thermostimulated current analysis

The problem is considered of a weakly conducting layer in which the conductivity, initially uniform, becomes a function of depth when the layer is submitted to a temperature gradient, or irradiated by a partially absorbed exciting radiation. After discussing the steady state E(x, ∞) and ϱ(x, ∞) in the presence of the conductivity gradient, an integrodifferential equation is derived for the transient charge density ϱ(x, t). This equation is rewritten in terms of reduced, dimensionless coordinates, and solved by means of an iterative expansion technique involving an approximation which is justified a posteriori. Throughout the paper, extensive use is made of the depth x* where the value of the field is that of the applied field E0. Neglecting diffusion, the expression is obtained for x*(t) and for the current J(t) in the external circuit. J(t) is written in terms of ò (x*), ϱ(x*) and x*, all these quantities being explicit functions of time. Finally, the form of J(t) is discussed for various experimental parameters, and with respect to the relevance of this theory to photoconduction and thermostimulated current analysis.