Stability of current filaments in a bistable semiconductor system with global coupling

Alekseev, Anton; Bose, Sanjay K.; Rodin, Pavel; Schöll, Eckehard

doi:10.1103/physreve.57.2640

Cited by 45 publications

(44 citation statements)

References 21 publications

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“…The filament has neutral stability with respect to the lateral shift when T is kept constant. 8 The current-voltage characteristic of the filament in a long structure is practically vertical, 2,5,8,41 and bends in the upper and lower parts when the filament becomes narrow ͑Fig. 1͒.…”

Section: Current Filament and Mechanism Of Its Motionmentioning

confidence: 99%

“…This bifurcation can be understood in terms of a stability analysis of the current filament performed in Ref. 8 for the standard two-component model ͑1͒,͑2͒: The spectrum of eigenmodes of a static filament includes a neutral mode ⌿ T with zero eigenvalue T ϭ0 which corresponds to translation. Existence of this neutral mode reflects the translation invariance of a static filament on a large spatial domain.…”

Section: Onset Of the Filament Motionmentioning

confidence: 99%

“…Therefore, apart from high-current filaments, there are patterns in form of low-current filaments: domains of low current density embedded into an on state. 5,8 Such filaments correspond to the upper part of the filamentary currentvoltage characteristic ͑Fig. 1͒, where the average current density is close to J on .…”

Section: E Motion Of Low-current Filamentsmentioning

confidence: 99%

“…This inhibition is crucial for the existence of current filaments which become unstable when the global coupling is eliminated by operating the device in the voltage-controlled regime. 2,8,10 The motion of the filament is induced by the effect of another slow diffusive inhibitor ͑temperature T). A similar nonlinear mechanism causes the motion of current filaments obtained by numerical simulations in Refs.…”

Section: F Reaction-diffusion Models For Traveling Spotsmentioning

confidence: 99%

“…[1][2][3][4][5][6] Current filamentation typically develops due to the spatial long wavelength instability -known as Ridley instability 1 -of the uniform state with a negative differential conductance when the device is operated via sufficiently large load resistance 7,8 ͑Fig. 1͒.…”

Section: Introductionmentioning

confidence: 99%

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Theory of traveling filaments in bistable semiconductor structures

Rodin

2004

Phys. Rev. B

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We present a generic nonlinear model for current filamentation in semiconductor structures with S-shaped current-voltage characteristics. The model accounts for Joule self-heating of a current density filament. It is shown that the self-heating leads to a bifurcation from static to traveling filament. Filaments start to travel when increase of the lattice temperature has negative impact on the cathode-anode transport. Since the impact ionization rate decreases with temperature, this occurs for a wide class of semiconductor systems whose bistability is due to the avalanche impact ionization. We develop an analytical theory of traveling filaments which reveals the mechanism of filament motion, find the condition for bifurcation to traveling filament, and determine the filament velocity.Comment: 13 pages, 5 figure

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Section: Current Filament and Mechanism Of Its Motionmentioning

confidence: 99%

Section: Onset Of the Filament Motionmentioning

confidence: 99%

Section: E Motion Of Low-current Filamentsmentioning

confidence: 99%

Section: F Reaction-diffusion Models For Traveling Spotsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Theory of traveling filaments in bistable semiconductor structures

Rodin

2004

Phys. Rev. B

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Fronten, Wellen und stationäre Muster in elektrochemischen Systemen

2001

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Oszillatorisches Verhalten ist bei nahezu allen elektrochemischen Reaktionen in einem bestimmten, wenn auch in manchen Fällen kleinen Bereich der externen Parameter beobachtet worden. Es ist jedoch erst während der letzten zehn Jahre gelungen, eine einheitliche Erklärung für das Auftreten dieser zeitlichen Selbstorganisationsphänomene bei den chemisch völlig unterschiedlichen elektrochemischen Reaktionen zu geben. Dieser Durchbruch gelang durch die Anwendung von Methoden und Konzepten, die in der nichtlinearen Dynamik entwickelt wurden, um die spontane Bildung von Ordnung in unterschiedlichen Disziplinen zu beschreiben. Dies ist wiederum nur möglich, weil auf einem gewissen Abstraktionsniveau diese Gesetzmäßigkeiten universell sind. Oszillationen sind nur eine mögliche Manifestation nichtlinearen Verhaltens. Beispiele anderer Erscheinungsformen, die häufig mit zeitlichen Instabilitäten eng verbunden sind, sind räumliche Strukturen und Wellen. Ausgelöst durch den theoretischen Fortschritt sowie die Entwicklung neuer experimenteller Methoden wurden während der letzten Jahre gezielte Untersuchungen zur räumlichen Musterbildung in elektrochemischen Systemen durchgeführt, die inzwischen in vielen Fällen eine Vorhersage erlauben, unter welchen Bedingungen eine räumliche oder zeitliche Strukturbildung zu erwarten ist. Dies eröffnet Perspektiven, nichtlineare Effekte zu nutzen, etwa zur Ausbeutesteigerung bei elektrokatalytischen Reaktionen. In diesem Aufsatz werden die physikalisch‐chemischen Mechanismen diskutiert, die zur Musterbildung in elektrochemischen Systemen führen, gleichzeitig werden die übergeordneten allgemeinen Prinzipien betont, die auch für Selbststrukturierungsprozesse in vielen chemischen und biologischen Systemen verantwortlich sind.

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Fronts, Waves, and Stationary Patterns in Electrochemical Systems

Krischer

Mazouz

Grauel

2001

Angew. Chem. Int. Ed.

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Oscillatory behavior has been observed for almost all electrochemical reactions in a certain, although sometimes small, range of external parameters. Only in the past ten years has it been possible, however, to find a common explanation for the occurrence of these temporal self‐organization phenomena of chemically completely different electrochemical reactions. The breakthrough was achieved because new methods and concepts, which had been developed in nonlinear dynamics to describe the spontaneous formation of order in various disciplines, could be applied. This development in turn was only possible because the underlying laws are universal at a certain abstract level. Oscillations are only one possible manifestation of nonlinear behavior. Examples of other features that are often closely associated with temporal instabilities are spatial structures and waves. Initiated by the theoretical progress and the development of new experimental techniques, spatial pattern formation in electrochemical systems has been targeted for investigations in the past few years. Based on these investigations, it can be predicted under which conditions temporal or spatial pattern formation can be expected. Furthermore, the possibility of predicting the occurrence of instabilities indicates that it might be feasible to exploit nonlinear effects to increase, for example, the yield of electrocatalytic reactions. Here we discuss physicochemical mechanisms that lead to pattern formation in electrochemical systems. At the same time, we stress the generic principles that are responsible for self‐structuring processes in many chemical and biological systems.

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Stability of current filaments in a bistable semiconductor system with global coupling

Cited by 45 publications

References 21 publications

Theory of traveling filaments in bistable semiconductor structures

Theory of traveling filaments in bistable semiconductor structures

Fronten, Wellen und stationäre Muster in elektrochemischen Systemen

Fronts, Waves, and Stationary Patterns in Electrochemical Systems

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