Theory of Isothermal Currents and the Direct Determination of Trap Parameters in Semiconductors and Insulators Containing Arbitrary Trap Distributions

Equations are presented that permit the calculation of the isothermal current- (I) vs-time ($t$) characteristics for defect insulators and semiconductors in which the field is sufficiently high and the active region sufficiently thin so that recombination of free carriers is negligible. More important, however, it is shown that by plotting $\mathrm{It}$ vs ${log}_{10}t$ the resulting characteristic is either (a) in the case of distributed traps, a direct image of the trap distribution, or (b) in the case of discrete traps, exhibits a number of sharp maxima at various times, depending on the trap parameters. The technique permits the direct determination of the trap distribution without having to have an a priori knowledge of the trap parameters and without the necessity of laborious analyses.