Double Injection in Insulators. II. Further Analytic Results with Negative Resistance

Abstract

The problem of double injection under varying lifetime conditions is analytically intractable when the physically important space charge is included in the analysis. The regional-approximation method is used to obtain approximate analytic solutions for two prototype insulator problems, both involving a single set of recombination centers and exhibiting a current-controlled negative resistance. In the first problem the centers are partially filled in thermal equilibrium; in the second problem they are completely filled. For both problems we assume that the capture cross section of a filled center for a free hole greatly exceeds that of an empty center for a free electron. This leads to a hole lifetime which increases with injection level, this being the source of the negative resistance. Earlier work based on the assumption of local neutrality is simplified in its domain of validity. Also, a previous analytic result for the first problem, yielding the threshold voltage at zero current, is derived in a simple manner which also yields the complete field and density distributions, previously unavailable.