Self-stabilization of high-frequency oscillations in semiconductor superlattices by time-delay autosynchronization

Abstract

We present a scheme to stabilize high-frequency domain oscillations in semiconductor superlattices by a time-delayed feedback loop. Applying concepts from chaos control theory we propose to control the spatiotemporal dynamics of fronts of accumulation and depletion layers which are generated at the emitter and may collide and annihilate during their transit, and thereby suppress chaos. The proposed method only requires the feedback of internal global electrical variables, viz., current and voltage, which makes the practical implementation very easy.

Noise-Induced Oscillations and Their Control in Semiconductor Superlattices

“…We also demonstrate that global feedback in the form of the difference between the current through the device at time t and the current at a delayed time t − τ can be used for the effective control of essential features of such noise-induced oscillations like time scales and coherence. This complements previous work on time-delayed feedback control of deterministic chaos in superlattices [Schlesner et al, 2003] and in other spatially extended semiconductor nanostructures modelled by reaction-diffusion systems [Baba et al, 2002;Beck et al, 2002;Franceschini et al, 1999;Schöll, 2004;Unkelbach et al, 2003].…”

Delay-Induced Multistability Near a Global Bifurcation

“…For instance, the transition from stationary to moving field domains in semiconductor superlattices has been shown to be associated with a saddle-node bifurcation on a limit cycle as described by Eq. (1) at K = 0 [Hizanidis et al, 2006], and time-delayed feedback control can also be realized in this system [Schlesner et al, 2003]. Already without delay, this system has been noted for its high multistability of stationary domain states [Kastrup et al, 1994[Kastrup et al, , 1996Prengel et al, 1994], and bistability or higher multistability has been found in many other semiconductor nanostructures, see e.g.…”

“…This method proved to be very powerful and has been successfully applied to various physical systems since then [Schöll & Schuster, 2007]. The scheme was improved by Socolar et al [1994], and other variants have been elaborated [Baba et al, 2002;Beck et al, 2002;Kittel et al, 1995;Schlesner et al, 2003;Unkelbach et al, 2003], and applied also to stochastic systems [Goldobin et al, 2003;Hauschildt et al, 2006;Janson et al, 2004]. Moreover, elegant analytical theories [Just et al, 1997] were developed supporting, thus, numerical findings.…”

Control of Complex Nonlinear Systems with Delay

“…For the detection goal, the resonance behavior in terms of a vanishing control force F yields the desired period. Note that the occurrence of this resonance can be very sensitive with respect to small changes of the time delay [SCH02r,SCH03a,SCH04a,KEH08]. One can also determine the period by optimization of a performance function which enables detection of unstable periodic orbits embedded in a strange attractor [HUN96,HUN96a,YAN00a].…”

“…In the latter case, the aim is to reduce the influence of unwanted high frequencies in the control force which eventually lead to the stabilization of the wrong timescales. If, for instance, these high frequencies are present in the system and yield generation of a feedback with the same fast timescale, a low-pass filter can help to overcome this limitation [SCH03a,SCH04a,SCH06]. To adjust the time-delayed feedback scheme to this obstacle, the control signal s in Eqs.…”