A Topological Theory of Domain Velocity in Semiconductors

A theory is given for the velocity of a free, steadily travelling domain of high electric field in a semiconductor exhibiting a negative differential conductivity. Explicit results are derived for the cases for which the domain behavior is dominated either by the (electric-field dependent) diffusion of electrons, or by the rate of transfer of electrons between states having different mobilities. It is shown that the solution for the electric-field distribution has the required properties only if the system of differential equations involved possesses singular points with special topological properties; this requirement serves to fix the domain velocity. The velocity depends only on the properties of the semiconductor at that high electric field where the effective drift velocity of electrons is equal to that outside the domain.