Comparative Anatomy of Models for Double Injection of Electrons and Holes into Solids

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Abstract
The several models for double injection of electrons and holes into solids are shown to fall into three groups: field‐dominated, diffusion‐dominated, and hybrid models. The current‐voltage relation for the field‐dominated models can be written out of hand, within a factor of two, using the criterion: ambipolar drift transit time of free pairs=lifetime of free pairs. Current‐voltage dependencies J ∝ Vn, with n ranging from 1.5 to 3, depend on whether the material is insulating or semiconducting and the recombination monomolecular or bimolecular. In the diffusion‐dominated models the current increases indefinitely while the voltage across the body of the sample remains constant at a value 2kT/e exp (L/2LD), where L and LD are the sample length and diffusion length, respectively. In the hybrid models, a field‐dominated current in one part of the sample is matched to a diffusion‐dominated current in the remainder of the sample. For all of the models reviewed, solutions for the current‐voltage relations are obtained within a factor of two by relatively simple physical arguments.