Principles of a phenomenological theory of Gunn-effect domain dynamics

Abstract

Starting from a few basic assumptions, namely the continuity equation for the carrier current, the Poisson equation, and a static drift-velocity field-strength characteristic, systems of ordinary differential equations are derived, describing the dynamic behaviour in the Gunn-effect. Solutions are obtained and discussed in the following cases: (1) steady-state domains, allowing generalization to space-dependent doping density in some cases; (2) linear approximation, yielding a condition for sample stability; (3) time-dependent processes like domain formation and extinction. The last point especially provides some new understanding of dynamic phenomena because many results can be gained, without any numerical calculation, by geometric consideration using the characteristic, e.g. the relation between triangular and trapezoidal domains sometimes discussed, and the triggered operation are investigated in this way. Hence, a reciprocity theorem between high field and low field domains is derived, and a direct verification of the principle of minimum entropy production is obtained in some cases.