Chaotic Current Oscillations Research Articles

Hyperchaos, Intermittency, Noise and Disorder in Modified Semiconductor Superlattices.

Weakly coupled semiconductor superlattices under DC voltage bias are nonlinear systems with many degrees of freedom whose nonlinearity is due to sequential tunneling of electrons. They may exhibit spontaneous chaos at room temperature and act as fast physical random number generator devices. Here we present a general sequential transport model with different voltage drops at quantum wells and barriers that includes noise and fluctuations due to the superlattice epitaxial growth. Excitability and oscillations of the current in superlattices with identical periods are due to nucleation and motion of charge dipole waves that form at the emitter contact when the current drops below a critical value. Insertion of wider wells increases superlattice excitability by allowing wave nucleation at the modified wells and more complex dynamics. Then hyperchaos and different types of intermittent chaos are possible on extended DC voltage ranges. Intrinsic shot and thermal noises and external noises produce minor effects on chaotic attractors. However, random disorder due to growth fluctuations may suppress any regular or chaotic current oscillations. Numerical simulations show that more than 70% of samples remain chaotic when the standard deviation of their fluctuations due to epitaxial growth is below 0.024 nm (10% of a single monolayer) whereas for 0.015 nm disorder suppresses chaos.

Synchronization of current oscillations in a dual-anode dissolution reaction in the presence of a common cathode electrode

The formation of synchronization patterns are explored as a result of coupling the dual anode oscillatory nickel electrodissolution and a single cathode hydrogen ion reduction reaction in an electrochemical cell. At the onset of current oscillations, with small surface area cathode in-phase synchronization patterns were recorded, which implies the presence of coupling between the anodic reactions. As the surface area of the cathode was increased, a transition from synchronized to desynchronized behavior was observed. Similarly, the extent of synchronization and thus the coupling can be diminished with increasing the individual resistances attached to the anodes. The effect of coupling induced by the cathode was interpreted with the ratio of charge transfer resistance of the cathode to the total external resistance in the cell. The coupling effects were further demonstrated with anti-phase synchronization of relaxation, and phase and identical synchronization of chaotic current oscillations. The experimental results about the coupling effect of the cathode were also explained with a kinetic model for the reactions. The results show that the nonlinear behavior of a complex cathode-anode cell can be greatly simplified when the majority of the overpotential is due to driving the anodic reactions to a far-from equilibrium state, while the relatively simple cathode (with small overpotential and fast kinetics) acts as a coupling element between the anodes. Such simplification can be a useful tool for interpreting the complex kinetic behaviors of galvanic and electrolytic cells that have time-scale separations between the cathodic and anodic processes.

Enhancing chaotic behavior at room temperature in GaAs/(Al,Ga)As superlattices

Previous theoretical and experimental work has put forward 50-period semiconductor superlattices as fast, true random number generators at room temperature. Their randomness stems from feedback between nonlinear electronic dynamics and stochastic processes that are intrinsic to quantum transitions. This work theoretically demonstrates that shorter superlattices with higher potential barriers contain fully chaotic dynamics over several intervals of the applied bias voltage compared to the 50-periods device which presented a much weaker chaotic behavior. The chaos arises from deterministic dynamics, hence it persists even in the absence of additional stochastic processes. Moreover, the frequency of the chaotic current oscillations is higher for shorter superlattices. These features should allow for faster and more robust generation of true random numbers.

Noise-enhanced chaos in a weakly coupled GaAs/(Al,Ga)As superlattice.

Noise-enhanced chaos in a doped, weakly coupled GaAs/Al_{0.45}Ga_{0.55}As superlattice has been observed at room temperature in experiments as well as in the results of the simulation of nonlinear transport based on a discrete tunneling model. When external noise is added, both the measured and simulated current-versus-time traces contain irregularly spaced spikes for particular applied voltages, which separate a regime of periodic current oscillations from a region of no current oscillations at all. In the voltage region without current oscillations, the electric-field profile consist of a low-field domain near the emitter contact separated by a domain wall consisting of a charge accumulation layer from a high-field regime closer to the collector contact. With increasing noise amplitude, spontaneous chaotic current oscillations appear over a wider bias voltage range. For these bias voltages, the domain boundary between the two electric-field domains becomes unstable and very small current or voltage fluctuations can trigger the domain boundary to move toward the collector and induce chaotic current spikes. The experimentally observed features are qualitatively very well reproduced by the simulations. Increased noise can consequently enhance chaotic current oscillations in semiconductor superlattices.

Avalanche effects near nanojunctions.

In this article, we perform a computational investigation of a nanopore connected to external fluidic reservoirs of asymmetric geometries. The asymmetry between the reservoirs is achieved by changing the cross-sectional areas, and the reservoirs are designated as the micropore reservoir and macropore reservoir. When an electric field is applied, which is directed from the macropore towards the micropore reservoir, we observe local nonequilibrium chaotic current oscillations. The current oscillations originate at the micropore-nanopore interface owing to the local cascade of ions; we refer to this phenomenon as the "avalanche effects." We mathematically quantify chaos in terms of the maximum Lyapunov exponent. The maximum Lyapunov exponent exhibits a monotonic increase with the applied voltage and the macropore reservoir diameter. The temporal power spectra maps of the chaotic currents depict a low-frequency "1/f"-type dynamics for the voltage chaos and "1/f^{2}"-type dynamics for the macropore reservoir chaos. The results presented here offer avenues to manipulate ionic diodes and fluidic pumps.

Intermittency route to chaos and broadband high-frequency generation in semiconductor superlattice coupled to external resonator.

We investigate the onset of broadband microwave chaos in the miniband semiconductor superlattice coupled to an external resonator. Our analysis shows that the transition to chaos, which is confirmed by calculation of Lyapunov exponents, is associated with the intermittency scenario. The evolution of the laminar phases and the corresponding Poincare maps with variation of a supercriticality parameter suggest that the observed dynamics can be classified as type I intermittency. We study the spatiotemporal patterns of the charge concentration and discuss how the frequency band of the chaotic current oscillations in semiconductor superlattice depends on the voltage applied.

Subterahertz Chaos Generation by Coupling a Superlattice to a Linear Resonator

We investigate the effects of a linear resonator on the high-frequency dynamics of electrons in devices exhibiting negative differential conductance. We show that the resonator strongly affects both the dc and ac transport characteristics of the device, inducing quasiperiodic and high-frequency chaotic current oscillations. The theoretical findings are confirmed by experimental measurements of a GaAs/AlAs miniband semiconductor superlattice coupled to a linear microstrip resonator. Our results are applicable to other active solid state devices and provide a generic approach for developing modern chaos-based high-frequency technologies including broadband chaotic wireless communication and superfast random-number generation.

Fast Physical Random-Number Generation Based on Room-Temperature Chaotic Oscillations in Weakly Coupled Superlattices

An all-electronic physical random number generator at rates up to 80 Gbit/s is presented, based on weakly coupled GaAs/Ga0.55Al0.45As superlattices operated at room temperature. It is based on large-amplitude, chaotic current oscillations characterized by a bandwidth of several hundred MHz and do not require external feedback or conversion to an electronic signal prior to digitization. The method is robust and insensitive to external perturbations and its fully electronic implementation suggests scalability and minimal postprocessing in comparison to existing optical implementations.

Experimental observation of spontaneous chaotic current oscillations in GaAs/Al0.45Ga0.55As superlattices at room temperature

Spontaneous self-sustained chaotic current oscillations are observed experimentally in lightly-doped weakly-coupled GaAs/Al0.45Ga0.55As superlattices at room temperature for the first time. The mole fraction of Aluminum in the barrier is chosen to be 0.45 to suppress the thermal carrier leakage through the X-band valley. The effective nonlinearity induced by the sequential well-to-well resonant tunneling can still be strong enough to induce spontaneous chaotic current oscillations even at room temperature. The frequency spectrum of the chaotic current oscillations is ranged from DC to 4 GHz, which can be used as ultra-wide-band noise sources with a bandwidth of several Giga Hertz.

Dynamics of electronic transport in a semiconductor superlattice with a shunting side layer

We study a model describing electronic transport in a weakly coupled semiconductor superlattice with a shunting side layer. Key parameters include the lateral size of the superlattice, the connectivity between the quantum wells of the superlattice and the shunt layer, and the conduction properties of the shunt layer. For a superlattice with small lateral extent and high quality shunt, static electric field domains are suppressed and a spatially uniform field configuration is predicted to be stable, results that may be useful for proposed devices such as a superlattice-based terahertz oscillators. As the lateral size of the superlattice increases, the uniform field configuration loses its stability to either static or dynamic field domains regardless of shunt properties. A lower quality shunt generally leads to regular and chaotic current oscillations and complex spatiotemporal dynamics in the field profile. Bifurcations separating static and dynamic behaviors are characterized and found to be dependent on the shunt properties.

Modeling chaotic current oscillations in semi-insulating GaAs with rate-equations of impact ionization and field-enhanced trapping

We investigated the effect of adding the field-dependent recombination process, namely field-enhanced trapping, to the generation-recombination processes of charge carriers that model current oscillations in semiconductors. The main new features arising from this modification are identified in bifurcation diagrams with the electric field as the control parameter. The characteristic of the bifurcation diagrams is a function of impurity energy. Thus, we generated a set of bifurcation diagrams for a range of the impurity energy and applied bias. The energy dependence of the bifurcation diagrams is discussed considering the context of the competition between the generation-recombination mechanisms impact ionization and field-enhanced trapping.

Self-stabilization of chaotic domain oscillations in superlattices by time-delayed feedback control

Semiconductor superlattices driven into the regime of negative differential conductivity often exhibit complex or even chaotic self-sustained current oscillations due to travelling field domains. For a reliable operation of a superlattice as an electronic oscillator, such unpredictable and irregular conditions should be avoided. In this work we present a theoretical analysis, proposing a novel scheme to stabilize high-frequency domain oscillations in semiconductor superlattices by a time-delayed feedback loop.

Chaotic, mixed-mode and periodic oscillations during the electro-oxidation of copper in trichloroacetic acid

The current oscillations of a copper electrode in trichloroacetic acid solutions were studied in this paper. The Cu/CCl3COOH system is a new electrochemical oscillator, showing rich dynamic behaviour on two controllable parameters: the trichloroacetic acid concentration (CCCl3COOH) and the imposed potential (E). Phase trajectories were reconstructed from time series using time delaymethods in order that the complex oscillations could be analyzed. Five kinds of oscillations, periodic and quasiperiodic mixed-mode, aperiodic, small amplitude and chaotic current oscillations, were observed. The EDS (energy dispersive spectroscopy) technique was used to analyze the elemental composition of the film formed on the surface of the copper electrode after the current oscillations.

Nonlinear dynamics time series analysis of chaotic current oscillations in a semi-insulating GaAs sample

We have carried out our experiments on a semi-insulating GaAs sample grown by low temperature Molecular Beam Epitaxy. Three parameters were used to fine tune the experiments, namely, temperature, illumination, and applied bias. We have used powerful tools of time series analysis in order to assess the embedding dimension through near false nearest neighbors. We have also measured the maximum Lyapunov exponent and the correlation dimension [1]. The main contribution was in presenting new experimental data and its analysis which presents self-generated chaos.

Conditions for the onset of current oscillations at the limiting current of the iron electrodissolution in sulfuric acid solutions

The experimental conditions and parameters that control the transition from a steady to an nonsteady limiting current and vice versa in the anodic Fe dissolution are studied in sulfuric acid solutions by using a downward-facing Fe electrode. Periodic and chaotic current oscillations are observed at the beginning of the limiting current region within a fixed potential region by decreasing the sulfuric acid concentration, by increasing the Fe-disk rotation rate and by increasing a series external resistance. It is found that current oscillations emerge when theIR drop exceeds a critical value (IR)crit. The latter depends on the hydrodynamic conditions pertaining to the system. This is realized by the differences appeared in the value of (IR)crit on using a stationary or a rotating Fe electrode. The effect of hydrodynamic conditions is shown by additional experimental results obtained by using an upward-facing Fe electrode, by increasing the density and viscosity of the solution on addition of glycerol, and by altering the solution properties near the Fe surface on addition of halide ions.

Experiments on Synchronization and Control of Chaos on Coupled Electrochemical Oscillators

Experiments were carried out on synchronization and control of complex chaotic dynamics observed during the dissolution of two and four coupled nickel electrodes in sulfuric acid under potentiostatic conditions. In a given potential range the individually measured currents exhibit asynchronous chaotic oscillations. The complexity (as measured by the correlation dimension) of the chaotic oscillations depends on the extent of coupling among the electrodes. Thus, the effectiveness of a combined synchronization-delayed-feedback procedure can be tested on systems with increasing complexity. We show that the asynchronous chaotic oscillations can be converted to synchronized and simple, periodic current oscillations by a two-step procedure. The chaotic current oscillations of coupled electrodes are first synchronized by perturbations of external resistors that are connected individually to each electrode. Then, the desired periodic orbit is stabilized by perturbations of the potential. We also observed that certain nonvanishing perturbations could lead to only partially synchronized, so-called “clustered” chaotic states.

Complex periodic and chaotic current oscillations related to different states of the localized corrosion of iron in chloride-containing sulfuric acid solutions

Current oscillations generated during pitting of Fe in chloride-containing 0.75 M H 2 SO 4 solutions were monitored and analyzed under potentiostatic conditions in a wide range of chloride ion concentrations. The increase of chloride ion concentration leads to: (i) deviation of the oscillation type from monoperiodicity observed in the chloride-free system and (ii) increase of the current in the passive region up to a limiting value and simultaneously to the disappearance of the passive-to-active transition region in the I – E curve. The current oscillations for relatively low chloride ion concentrations (≤20 mM) are complex periodic or aperiodic depending on the potential. For relatively high chloride ion concentrations (>20 mM) the current oscillations become aperiodic (chaotic). Two limiting cases of the pitting growth process are distinguished on the basis of the type of oscillation observed for low and high chloride ion concentrations. First, the unstable pit growth related to complex periodic oscillations; the oxide passive film is formed but it is destabilized by Cl − ions. Then repeated breakdown and formation of the passive film occurs and the current oscillates between a maximum and a minimum value which represent the active and passive states, respectively, of the specific Fe ∣ 0.75 M H 2 SO 4 + x M Cl − system. The second case of aperiodic (chaotic) oscillations is related to a continued pit growth; the formation of the oxide passive film is prevented and a salt layer is formed resulting in a limiting current region with oscillations. The potential and the Cl − ion concentration in the vicinity of the Fe electrode control the pitting corrosion and the oscillatory phenomena associated with it. Polishing state pitting was found to proceed at more positive potentials and high Cl − ion concentrations.

Spontaneous current oscillations in n-GaAs in high magnetic fields

Spontaneous regular and chaotic current oscillations have been observed in n-GaAs at 4.2 K. The dependencies of the frequency of these regular oscillations on the temperature and high magnetic field were investigated. A non-monotonic dependency of the frequency on magnetic field was found for the first time. The Arrhenius plot of the temperature dependence of the frequency of the regular oscillations gives an activation energy of about 0.31 meV, which is much less than the values of the ionization energies of the ground and the first excited states of the corresponding shallow impurity level in n-GaAs. This value appears to be consistent with the activation energy for hopping conduction of electrons in the impurity band.

Controlling Electrochemical Chaos in the Copper−Phosphoric Acid System

Model calculations indicate that chaotic current oscillations during anodic electrodissolution of copper into phosphoric acid may be controlled by applying a simple map-based algorithm. In the experiments, the unstable period-one and period-two orbits embedded in the chaotic attractor have been stabilized by small perturbations of the anodic potential. We present the results of an experimental test for a power law relating the average chaotic transient time to the size of maximum perturbation allowed during control. The reported experimental results are in good agreement with the theoretical predictions by Ott, Grebogi, and Yorke.

Transition between synchronization and chaos in doped GaAs/AlAs superlattices

The transition between chaotic and periodic regimes in spontaneous current oscillations of weakly coupled, doped GaAs/AlAs superlattices has been observed by varying the external d.c. bias. The chaotic current oscillations are observed for voltage ranges, which exhibit a large negative differential conductance in the time-averaged I–V characteristic. Since this system can be described by a spatially distributed, non-linear system with many degrees of freedom, the coupling between the degrees of freedom in the chaotic windows is repulsive, while in the periodic windows it is attractive.