Flux Methods for the Analysis of Transport Problems in Semiconductors in the Presence of Electric Fields

A calculational technique based upon the detailed study of flux interactions between various parts of a diffusion-recombination system, whose foundations have been discussed elsewhere in the literature, is extended to include cases where electric fields may be acting upon the particles of the system. The analysis is worked out in detail for systems obeying Boltzmann statistics in which the field satisfies the condition $\mu E_0\ll \overline{c}$, where $\overline{c}$ is the mean thermal velocity. Analytic solutions for the reflection and transmission coefficients of a sheet of material of arbitrary thickness for incident carriers are worked out for constant electric fields; approximate or numerical methods are applicable for nonconstant fields. The effect of the details of scattering and recombination processes upon the solutions is considered. A simple example is worked out to exhibit areas of agreement between this method and the more conventional calculational techniques and to demonstrate certain advantages in generality and conceptual simplicity associated with the flux method.