Uniformly Propagating Solutions of Transport and Poisson Equations for Periodic Field Domains

Time-dependent solutions of the Poisson and transport equations containing drift and diffusion for the case of field domains propagating undeformed and with constant velocity through a crystal are discussed in terms of an analysis of their projections in the $n-E$ plane, where $n$ is the carrier concentration and $E$ the magnitude of the electric field. Two principal models are discussed: one for a trap-controlled crystal (CdS type), and the other for a trap-free crystal (GaAs type, Gunn effect) for field-dependent recombination or field-dependent mobility. It is found that, in addition to the "triangular" domains, periodic propagating solutions can exist. Conditions on the values of the domain velocity and the current are derived.