Current Self-Oscillations and Chaos in Semiconductor Superlattices

Abstract

Weakly coupled semiconductor superlattices represent a non-linear system, which exhibits tunable current self-oscillations and chaos. The non-linearity originates from resonant tunneling between two-dimensional subbands in adjacent wells. The current oscillations are due to a recycling motion of a charged monopole over several superlattice periods. The charged monopole appears, because the nonlinearity of the system in connection with a large carrier density results in the formation of electric-field domains in these systems. The monopole separates the different field regions. Current self-oscillations have been observed in doped and undoped, photoexcited superlattices up to frequencies of several GHz. A single period of the current oscillations contains additional spikes with a frequency more than one order of magnitude above the fundamental oscillation frequency. These spikes are a signature of the well-to-well hopping of the monopole. The fundamental oscillation frequency can be varied over more than two orders of magnitude by changing the applied voltage within a single sample. For different samples, a variation of the barrier width by a factor of three has resulted in a change of the fundamental oscillation frequency by more than three orders of magnitude. The frequency scales with the resonant coupling of the subbands in adjacent wells. In several samples, current self-oscillations have been observed up to room temperature. Recently, undoped superlattices have been used to investigate the carrier density dependence of the boundary between static and dynamic domain formation by varying the photoexcitation intensity. With increasing carrier density, the current oscillations disappear via a supercritical Hopf bifurcation, a subcritical Hopf bifurcation, and a homoclinic connection. The chaotic behavior of such a system, which was predicted through calculations within a simple drift-diffusion model, has also been investigated. The bifurcation diagram of the power spectra under application of an external ac voltage shows the well-known route to chaos via alternating windows of frequency locking and quasi-periodicity. Real-time current traces have been used to construct Poincaré sections, which support this interpretation. However, for other dc voltages, the route to chaos can become much more complex. Recently, the multi-fractal dimension of the chaotic attractors has been determined as a function of the dc voltage using the experimentally derived Poincaré sections.