Abstract
Semiconductor superlattices are a very interesting example of a nonlinear dynamical system with a large number of degrees of freedom. They show a strongly nonlinear behavior and they are well suited for the observation of current instabilities. In the present work, the dynamical behavior of undoped photoexcited superlattices has been analyzed by numerical continuation methods and bifurcation theory within the framework of a simple drift-diffusion model. The control parameters are the applied dc voltage and the carrier density, which are related to the laser power. We compile our results in a phase diagram and locate the lines where the system undergoes qualitative changes of behavior. The oscillatory regions are related to the appearance and disappearance of Hopf tongue crossings, for which oscillations appear as sub- or supercritical bifurcations. This implies the existence of voltage windows of current oscillations and hysteresis in appropriate parameter ranges, which agrees with recent experimental observations.
