Gunn instability in finite samples of GaAs: I. Stationary states, stability and boundary conditions

Abstract

The stationary states of a well-known phenomenological model of n-GaAs are characterized and constructed. Their dependence on realistic boundary conditions and their stability properties are analyzed. Two mathematical problems are studied corresponding to different biases. Under current bias, the total current is a known control parameter. Under voltage bias, the current is an unknown to be determined so as to keep the voltage constant. Under current bias, coexistence of multiple steady states is found for large enough samples. A theorem on stability under different bias conditions establishes, under appropriate conditions, a correspondence between critical values of the current and the voltage at which the basic stationary solution ceases to be stable. While under current bias, bifurcations from the stationary solution are branches of stationary solutions, under voltage bias bifurcating branches may be oscillatory. The consequences of this result for the bifurcation diagram of the Gunn instability are discussed.