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Mompó E, Carretero M, Bonilla LL. Designing Hyperchaos and Intermittency in Semiconductor Superlattices. Phys Rev Lett 2021; 127:096601. [PMID: 34506173 DOI: 10.1103/physrevlett.127.096601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2021] [Accepted: 07/30/2021] [Indexed: 06/13/2023]
Abstract
Weakly coupled semiconductor superlattices under dc voltage bias are excitable systems with many degrees of freedom that may exhibit spontaneous chaos at room temperature and act as fast physical random number generator devices. Superlattices with identical periods exhibit current self-oscillations due to the dynamics of charge dipole waves but chaotic oscillations exist on narrow voltage intervals. They disappear easily due to variation in structural growth parameters. Based on numerical simulations, we predict that inserting two identical sufficiently separated wider wells increases superlattice excitability by allowing wave nucleation at the modified wells and more complex dynamics. This system exhibits hyperchaos and varieties of intermittent chaos in extended dc voltage ranges. Unlike in ideal superlattices, our chaotic attractors are robust and resilient against noises and against controlled random disorder due to growth fluctuations.
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Affiliation(s)
- E Mompó
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, and Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - M Carretero
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, and Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - L L Bonilla
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, and Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
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Shao Z, Yin Z, Song H, Liu W, Li X, Zhu J, Biermann K, Bonilla LL, Grahn HT, Zhang Y. Fast Detection of a Weak Signal by a Stochastic Resonance Induced by a Coherence Resonance in an Excitable GaAs/Al_{0.45}Ga_{0.55}As Superlattice. Phys Rev Lett 2018; 121:086806. [PMID: 30192582 DOI: 10.1103/physrevlett.121.086806] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2017] [Indexed: 06/08/2023]
Abstract
The effect of a coherence resonance is observed experimentally in a GaAs/Al_{0.45}Ga_{0.55}As superlattice under dc bias at room temperature, which is driven by noise. For an applied voltage, for which no current self-oscillations are observed, regular current self-oscillations with a frequency of about 82 MHz are induced by exceeding a certain noise amplitude. In addition, a novel kind of a stochastic resonance is identified, which is triggered by the coherence resonance. This stochastic resonance appears when the device is driven by an external ac signal with a frequency, which is relatively close to that of the regular current self-oscillations at the coherence resonance. The intrinsic oscillation mode in the coherence resonance is found to be phase locked by an extremely weak ac signal. It is demonstrated that an excitable superlattice device can be used for the fast detection of weak signals submerged in noise. These results are very well reproduced by results using numerical simulations based on a sequential resonant tunneling model of nonlinear electron transport in semiconductor superlattices.
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Affiliation(s)
- Zhengzheng Shao
- College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China
| | - Zhizhen Yin
- Key Laboratory of Nanodevices and Applications, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou 215123, China
| | - Helun Song
- Key Laboratory of Nanodevices and Applications, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou 215123, China
| | - Wei Liu
- Key Laboratory of Nanodevices and Applications, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou 215123, China
| | - Xiujian Li
- College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China
| | - Jubo Zhu
- College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China
| | - Klaus Biermann
- Paul-Drude-Institut für Festkörperelektronik, Leibniz-Institut im Forschungsverbund Berlin e. V., Hausvogteiplatz 5-7, 10117 Berlin, Germany
| | - Luis L Bonilla
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, and Department of Materials Science and Engineering and Chemical Engineering, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - Holger T Grahn
- Paul-Drude-Institut für Festkörperelektronik, Leibniz-Institut im Forschungsverbund Berlin e. V., Hausvogteiplatz 5-7, 10117 Berlin, Germany
| | - Yaohui Zhang
- College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China
- Key Laboratory of Nanodevices and Applications, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou 215123, China
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Huang Y, Li W, Ma W, Qin H, Zhang Y. Experimental observation of spontaneous chaotic current oscillations in GaAs/Al0.45Ga0.55As superlattices at room temperature. ACTA ACUST UNITED AC 2012; 57:2070-2. [DOI: 10.1007/s11434-012-5198-8] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Hizanidis J, Schöll E. Control of coherence resonance in semiconductor superlattices. Phys Rev E Stat Nonlin Soft Matter Phys 2008; 78:066205. [PMID: 19256923 DOI: 10.1103/physreve.78.066205] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2008] [Revised: 10/13/2008] [Indexed: 05/27/2023]
Abstract
We study the effect of time-delayed feedback control and Gaussian white noise on the spatiotemporal charge dynamics in a semiconductor superlattice. The system is prepared in a regime where the deterministic dynamics is close to a global bifurcation, namely, a saddle-node bifurcation on a limit cycle. In the absence of control, noise can induce electron charge front motion through the entire device, and coherence resonance is observed. We show that with appropriate selection of the time-delayed feedback parameters the effect of coherence resonance can be either enhanced or destroyed, and the coherence of stochastic domain motion at low noise intensity is dramatically increased. Additionally, the purely delay-induced dynamics in the system is investigated, and a homoclinic bifurcation of a limit cycle is found.
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Affiliation(s)
- Johanne Hizanidis
- Instutut für Theoretische Physik, Technische Universität Berlin, Hardenbergstasse 36, D-10623 Berlin, Germany
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Hizanidis J, Balanov A, Amann A, Schöll E. Noise-induced front motion: signature of a global bifurcation. Phys Rev Lett 2006; 96:244104. [PMID: 16907247 DOI: 10.1103/physrevlett.96.244104] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2005] [Indexed: 05/11/2023]
Abstract
We show that front motion can be induced by noise in a spatially extended excitable system with a global constraint. Our model system is a semiconductor superlattice exhibiting complex dynamics of electron accumulation and depletion fronts. The presence of noise induces a global change in the dynamics of the system forcing stationary fronts to move through the entire device. We demonstrate the effect of coherence resonance in our model; i.e., there is an optimal level of noise at which the regularity of front motion is enhanced. Physical insight is provided by relating the space-time dynamics of the fronts with a phase-space analysis.
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Affiliation(s)
- J Hizanidis
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
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Schlesner J, Amann A, Janson NB, Just W, Schöll E. Self-stabilization of high-frequency oscillations in semiconductor superlattices by time-delay autosynchronization. Phys Rev E Stat Nonlin Soft Matter Phys 2003; 68:066208. [PMID: 14754298 DOI: 10.1103/physreve.68.066208] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2003] [Revised: 09/17/2003] [Indexed: 05/24/2023]
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.
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Affiliation(s)
- J Schlesner
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
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Amann A, Peters K, Parlitz U, Wacker A, Schöll E. Hybrid model for chaotic front dynamics: from semiconductors to water tanks. Phys Rev Lett 2003; 91:066601. [PMID: 12935095 DOI: 10.1103/physrevlett.91.066601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2003] [Indexed: 05/24/2023]
Abstract
We present a general method for studying front propagation in nonlinear systems with a global constraint in the language of hybrid tank models. The method is illustrated in the case of semiconductor superlattices, where the dynamics of the electron accumulation and depletion fronts shows complex spatiotemporal patterns, including chaos. We show that this behavior may be elegantly explained by a tank model, for which analytical results on the emergence of chaos are available. In particular, for the case of three tanks the bifurcation scenario is characterized by a modified version of the one-dimensional iterated tent map.
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Affiliation(s)
- A Amann
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
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Carpio A, Bonilla LL, Dell'Acqua G. Motion of wave fronts in semiconductor superlattices. Phys Rev E Stat Nonlin Soft Matter Phys 2001; 64:036204. [PMID: 11580419 DOI: 10.1103/physreve.64.036204] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2001] [Indexed: 05/23/2023]
Abstract
An analysis of wave front motion in weakly coupled doped semiconductor superlattices is presented. If a dimensionless doping is sufficiently large, the superlattice behaves as a discrete system presenting front propagation failure and the wave fronts can be described near the threshold currents J(i) (i=1,2) at which they depin and move. The wave front velocity scales with current as |J-J(i)|(1/2). If the dimensionless doping is low enough, the superlattice behaves as a continuum system and wave fronts are essentially shock waves whose velocity obeys an equal area rule.
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Affiliation(s)
- A Carpio
- Departamento de Matemática Aplicada, Universidad Complutense, Madrid 28040, Spain
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Amann A, Wacker A, Bonilla LL, Schöll E. Dynamic scenarios of multistable switching in semiconductor superlattices. Phys Rev E Stat Nonlin Soft Matter Phys 2001; 63:066207. [PMID: 11415206 DOI: 10.1103/physreve.63.066207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2000] [Indexed: 05/23/2023]
Abstract
We analyze the dynamics of charge distributions in weakly coupled, doped, dc voltage biased semiconductor superlattices subject to voltage steps of different sizes. Qualitatively different current responses to voltage switching processes have been observed experimentally. We explain them by invoking distinct scenarios for electric-field domain formation, validated by numerical simulations. Furthermore, we investigate the transient from an unstable to a stable point in the current-voltage characteristics after a steplike or ramplike increase of the external voltage.
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Affiliation(s)
- A Amann
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
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Carpio A, Bonilla LL, Wacker A, Scholl E. Wave fronts may move upstream in semiconductor superlattices. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 2000; 61:4866-76. [PMID: 11031528 DOI: 10.1103/physreve.61.4866] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/1999] [Indexed: 04/15/2023]
Abstract
In weakly coupled, current biased, doped semiconductor superlattices, domain walls may move upstream against the flow of electrons. For appropriate doping values, a domain wall separating two electric-field domains moves downstream below a first critical current, it remains stationary between this value and a second critical current, and then moves upstream above. These conclusions are reached by using a comparison principle to analyze a discrete drift-diffusion model, and validated by numerical simulations. Possible experimental realizations are suggested.
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Affiliation(s)
- A Carpio
- Departamento de Matematica Aplicada, Universidad Complutense, Madrid, Spain
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Zhang Y, Kastrup J, Klann R, Ploog KH, Grahn HT. Synchronization and Chaos Induced by Resonant Tunneling in GaAs/AlAs Superlattices. Phys Rev Lett 1996; 77:3001-3004. [PMID: 10062106 DOI: 10.1103/physrevlett.77.3001] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Mimura H, Hosoda M, Ohtani N, Tominaga K, Fujita K, Watanabe T, Grahn HT, Fujiwara K. Electric-field domain formation in type-II superlattices. Phys Rev B Condens Matter 1996; 54:R2323-R2326. [PMID: 9986168 DOI: 10.1103/physrevb.54.r2323] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Wacker A, Schwarz G, Prengel F, Schöll E, Kastrup J, Grahn HT. Probing growth-related disorder by high-field transport in semiconductor superlattices. Phys Rev B Condens Matter 1995; 52:13788-13791. [PMID: 9980590 DOI: 10.1103/physrevb.52.13788] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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