Effects of Diffusion and Thermal Generation on Double Injection in Semiconductors

Abstract

The theoretical treatment of the double-injection semiconductor regime has been extended to include first diffusion and then both diffusion and thermal generation. When only diffusion is included, the results parallel earlier results for the insulator regime. Large deviations from the simple Lampert theory are found even when the sample length L is as great as 50 times the ambipolar diffusion length La. The electric field distribution is characterized by exponentially increasing regions from the boundaries in which ε∝ exp |x/La|, merging into a central region which approximates the Lampert distribution ε∝(x—x0)1/2. The current—voltage characteristic approximately follows a I∝V2+s law, where s is a monotonically increasing function of La/L, the magnitude of the current being larger than predicted by Lampert. The inclusion of thermal generation leads to a very large transition region between the Ohmic and high-level regimes. For values of the ratio τl/τ≳10 between low-level and high-level lifetimes, this region extends over currents from 10-2-106 times the transition current between the Ohmic and high-level regimes. A portion of this transition region (for τl/τ≳1) has an almost exact I∝V2 current—voltage characteristic over about two orders of magnitude of current, which may be easily mistaken for high-level behavior. In this region the effective-length approximation has its greatest validity, current being the Lampert expression times (L/Leff)3, where Leff=L—Q(2La), and Q is independent of I and is only a slowly varying function of L/La. Parallel results were found for the inclusion of both diffusion and thermal generation into the insulator regime.