1
|
Bonilla LL, Carretero M, Mompó E. Hyperchaos, Intermittency, Noise and Disorder in Modified Semiconductor Superlattices. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1702. [PMID: 36554107 PMCID: PMC9777605 DOI: 10.3390/e24121702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/31/2022] [Revised: 11/15/2022] [Accepted: 11/19/2022] [Indexed: 06/17/2023]
Abstract
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.
Collapse
Affiliation(s)
- Luis L. Bonilla
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
- Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - Manuel Carretero
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
- Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | - Emanuel Mompó
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
- Departamento de Matemática Aplicada, Universidad Pontificia Comillas, 28015 Madrid, Spain
| |
Collapse
|
2
|
Donvil B, Muratore-Ginanneschi P. Quantum trajectory framework for general time-local master equations. Nat Commun 2022; 13:4140. [PMID: 35842427 PMCID: PMC9288492 DOI: 10.1038/s41467-022-31533-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Accepted: 06/10/2022] [Indexed: 11/09/2022] Open
Abstract
Master equations are one of the main avenues to study open quantum systems. When the master equation is of the Lindblad-Gorini-Kossakowski-Sudarshan form, its solution can be "unraveled in quantum trajectories" i.e., represented as an average over the realizations of a Markov process in the Hilbert space of the system. Quantum trajectories of this type are both an element of quantum measurement theory as well as a numerical tool for systems in large Hilbert spaces. We prove that general time-local and trace-preserving master equations also admit an unraveling in terms of a Markov process in the Hilbert space of the system. The crucial ingredient is to weigh averages by a probability pseudo-measure which we call the "influence martingale". The influence martingale satisfies a 1d stochastic differential equation enslaved to the ones governing the quantum trajectories. We thus extend the existing theory without increasing the computational complexity.
Collapse
Affiliation(s)
- Brecht Donvil
- University of Helsinki, Department of Mathematics and Statistics, P.O. Box 68, FIN-00014, Helsinki, Finland.
- Institute for Complex Quantum Systems and IQST, Ulm University, Albert-Einstein-Allee 11, D-89069, Ulm, Germany.
| | - Paolo Muratore-Ginanneschi
- University of Helsinki, Department of Mathematics and Statistics, P.O. Box 68, FIN-00014, Helsinki, Finland.
| |
Collapse
|
3
|
Mompo E, Ruiz-Garcia M, Carretero M, Grahn HT, Zhang Y, Bonilla LL. Coherence Resonance and Stochastic Resonance in an Excitable Semiconductor Superlattice. PHYSICAL REVIEW LETTERS 2018; 121:086805. [PMID: 30192625 DOI: 10.1103/physrevlett.121.086805] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2017] [Indexed: 06/08/2023]
Abstract
Collective electron transport causes a weakly coupled semiconductor superlattice under dc voltage bias to be an excitable system with 2N+2 degrees of freedom: electron densities and fields at N superlattice periods plus the total current and the field at the injector. External noise of sufficient amplitude induces regular current self-oscillations (coherence resonance) in states that are stationary in the absence of noise. Numerical simulations show that these oscillations are due to the repeated nucleation and motion of charge dipole waves that form at the emitter when the current falls below a critical value. At the critical current, the well-to-well tunneling current intersects the contact load line. We have determined the device-dependent critical current for the coherence resonance from experiments and numerical simulations. We have also described through numerical simulations how a coherence resonance triggers a stochastic resonance when its oscillation mode becomes locked to a weak ac external voltage signal. Our results agree with the experimental observations.
Collapse
Affiliation(s)
- Emanuel Mompo
- 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
| | - Miguel Ruiz-Garcia
- 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
| | - Manuel Carretero
- 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
- Key Laboratory of Nanodevices and Applications, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou 215123, China
- College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China
| | - 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
| |
Collapse
|
4
|
Dhar RS, Razavipour SG, Dupont E, Xu C, Laframboise S, Wasilewski Z, Hu Q, Ban D. Direct nanoscale imaging of evolving electric field domains in quantum structures. Sci Rep 2014; 4:7183. [PMID: 25431158 PMCID: PMC4246203 DOI: 10.1038/srep07183] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2014] [Accepted: 11/07/2014] [Indexed: 11/22/2022] Open
Abstract
The external performance of quantum optoelectronic devices is governed by the spatial profiles of electrons and potentials within the active regions of these devices. For example, in quantum cascade lasers (QCLs), the electric field domain (EFD) hypothesis posits that the potential distribution might be simultaneously spatially nonuniform and temporally unstable. Unfortunately, there exists no prior means of probing the inner potential profile directly. Here we report the nanoscale measured electric potential distribution inside operating QCLs by using scanning voltage microscopy at a cryogenic temperature. We prove that, per the EFD hypothesis, the multi-quantum-well active region is indeed divided into multiple sections having distinctly different electric fields. The electric field across these serially-stacked quantum cascade modules does not continuously increase in proportion to gradual increases in the applied device bias, but rather hops between discrete values that are related to tunneling resonances. We also report the evolution of EFDs, finding that an incremental change in device bias leads to a hopping-style shift in the EFD boundary – the higher electric field domain expands at least one module each step at the expense of the lower field domain within the active region.
Collapse
Affiliation(s)
- Rudra Sankar Dhar
- Department of Electrical and Computer Engineering, Waterloo Institute for Nanotechnology, University of Waterloo, 200 University Ave. West, Waterloo, N2L3G1, Ontario, Canada
| | - Seyed Ghasem Razavipour
- Department of Electrical and Computer Engineering, Waterloo Institute for Nanotechnology, University of Waterloo, 200 University Ave. West, Waterloo, N2L3G1, Ontario, Canada
| | - Emmanuel Dupont
- National Research Council, Bldg. M-50, 1200 Montreal Rd, Ottawa, Ontario K1A0R6, Canada
| | - Chao Xu
- Department of Electrical and Computer Engineering, Waterloo Institute for Nanotechnology, University of Waterloo, 200 University Ave. West, Waterloo, N2L3G1, Ontario, Canada
| | - Sylvain Laframboise
- National Research Council, Bldg. M-50, 1200 Montreal Rd, Ottawa, Ontario K1A0R6, Canada
| | - Zbig Wasilewski
- Department of Electrical and Computer Engineering, Waterloo Institute for Nanotechnology, University of Waterloo, 200 University Ave. West, Waterloo, N2L3G1, Ontario, Canada
| | - Qing Hu
- Department of Electrical Engineering and Computer Science, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139, USA
| | - Dayan Ban
- Department of Electrical and Computer Engineering, Waterloo Institute for Nanotechnology, University of Waterloo, 200 University Ave. West, Waterloo, N2L3G1, Ontario, Canada
| |
Collapse
|
5
|
Wang C, Cao JC. Current oscillation and chaotic dynamics in superlattices driven by crossed electric and magnetic fields. CHAOS (WOODBURY, N.Y.) 2005; 15:13111. [PMID: 15836265 DOI: 10.1063/1.1856431] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We have theoretically studied current oscillation and chaotic dynamics in doped GaAsAlAs superlattices driven by crossed electric and magnetic fields. When the superlattice system is driven by a dc voltage, a stationary or dynamic electric-field domain can be obtained. We carefully studied the electric-field-domain dynamics and current self-oscillation which both display different modes with the change of magnetic field. When an ac electric field is also applied to the superlattice, a typical nonlinear dynamic system is constructed with the ac amplitude, ac frequency, and magnetic field as the control parameters. Different nonlinear behaviors show up when we tune the control parameters.
Collapse
Affiliation(s)
- C Wang
- State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050, P. R. China
| | | |
Collapse
|
6
|
Carpio A, Bonilla LL, Luzón A. Effects of disorder on the wave front depinning transition in spatially discrete systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:035207. [PMID: 11909150 DOI: 10.1103/physreve.65.035207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2001] [Indexed: 05/23/2023]
Abstract
Pinning and depinning of wave fronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators with nearest-neighbor coupling and subject to random external forces. The presence of weak randomness shrinks the pinning interval and it changes the critical exponent of the wave front depinning transition from 1/2 to 3/2. This effect is derived by means of a recent asymptotic theory of the depinning transition, extended to discrete drift-diffusion models of transport in semiconductor superlattices and is confirmed by numerical calculations.
Collapse
Affiliation(s)
- A Carpio
- Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | | | | |
Collapse
|
7
|
Carpio A, Bonilla LL, Dell'Acqua G. Motion of wave fronts in semiconductor superlattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 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] [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.
Collapse
Affiliation(s)
- A Carpio
- Departamento de Matemática Aplicada, Universidad Complutense, Madrid 28040, Spain
| | | | | |
Collapse
|
8
|
Bonilla LL, Escobedo R. Two-dimensional oscillatory patterns in semiconductors with point contacts. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:036203. [PMID: 11580418 DOI: 10.1103/physreve.64.036203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2001] [Indexed: 05/23/2023]
Abstract
Planar samples of n-GaAs with attached point contacts at different dc voltages may display a variety of spatiotemporal patterns arising from the dynamics of curved charge dipole waves. Patterns rank from oscillations due to recycling and motion of simple quasiplanar or cylindrical wave fronts to more complex patterns that include merging and splitting of different fronts. Results of numerical simulations are interpreted by means of simple one-dimensional asymptotic theories.
Collapse
Affiliation(s)
- L L Bonilla
- Escuela Politécnica Superior, Universidad Carlos III de Madrid, 28911 Leganés, Spain
| | | |
Collapse
|
9
|
Carpio A, Bonilla LL. Wave front depinning transition in discrete one-dimensional reaction-diffusion systems. PHYSICAL REVIEW LETTERS 2001; 86:6034-6037. [PMID: 11415422 DOI: 10.1103/physrevlett.86.6034] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2001] [Indexed: 05/23/2023]
Abstract
Pinning and depinning of wave fronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators with nearest-neighbor coupling and controlled by constant external forces. A theory of the depinning transition for these systems, including scaling laws and asymptotics of wave fronts, is presented and confirmed by numerical calculations.
Collapse
Affiliation(s)
- A Carpio
- Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain
| | | |
Collapse
|
10
|
Amann A, Wacker A, Bonilla LL, Schöll E. Dynamic scenarios of multistable switching in semiconductor superlattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:066207. [PMID: 11415206 DOI: 10.1103/physreve.63.066207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [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.
Collapse
Affiliation(s)
- A Amann
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany
| | | | | | | |
Collapse
|
11
|
Carpio A, Bonilla LL, Wacker A, Scholl E. Wave fronts may move upstream in semiconductor superlattices. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY 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] [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.
Collapse
Affiliation(s)
- A Carpio
- Departamento de Matematica Aplicada, Universidad Complutense, Madrid, Spain
| | | | | | | |
Collapse
|
12
|
Gravé I, An S. Switching and control of electric field configurations along multi-quantum well structures. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0963-9659/7/2/030] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
13
|
Gaa M, Schöll E. Traveling carrier-density waves in n-type GaAs at low-temperature impurity breakdown. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:16733-16741. [PMID: 9985803 DOI: 10.1103/physrevb.54.16733] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
14
|
Mimura H, Hosoda M, Ohtani N, Tominaga K, Fujita K, Watanabe T, Grahn HT, Fujiwara K. Electric-field domain formation in type-II superlattices. PHYSICAL REVIEW. B, CONDENSED 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] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
15
|
Bulashenko OM, García MJ, Bonilla LL. Chaotic dynamics of electric-field domains in periodically driven superlattices. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:10008-10018. [PMID: 9982566 DOI: 10.1103/physrevb.53.10008] [Citation(s) in RCA: 24] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
16
|
Kastrup J, Prengel F, Grahn HT, Ploog K, Schöll E. Formation times of electric-field domains in doped GaAs-AlAs superlattices. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:1502-1506. [PMID: 9983612 DOI: 10.1103/physrevb.53.1502] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
17
|
Bergmann MJ, Teitsworth SW, Bonilla LL, Cantalapiedra IR. Solitary-wave conduction in p-type Ge under time-dependent voltage bias. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:1327-1335. [PMID: 9983592 DOI: 10.1103/physrevb.53.1327] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
18
|
Keay BJ, Allen SJ, Galán J, Kaminski JP, Campman KL, Gossard AC, Bhattacharya U, Rodwell MJ. Photon-assisted electric field domains and multiphoton-assisted tunneling in semiconductor superlattices. PHYSICAL REVIEW LETTERS 1995; 75:4098-4101. [PMID: 10059814 DOI: 10.1103/physrevlett.75.4098] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
19
|
Wacker A, Schwarz G, Prengel F, Schöll E, Kastrup J, Grahn HT. Probing growth-related disorder by high-field transport in semiconductor superlattices. PHYSICAL REVIEW. B, CONDENSED 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] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
20
|
Kastrup J, Klann R, Grahn HT, Ploog K, Bonilla LL, Galán J, Kindelan M, Moscoso M, Merlin R. Self-oscillations of domains in doped GaAs-AlAs superlattices. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:13761-13764. [PMID: 9980583 DOI: 10.1103/physrevb.52.13761] [Citation(s) in RCA: 47] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
21
|
Bulashenko OM, Bonilla LL. Chaos in resonant-tunneling superlattices. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:7849-7852. [PMID: 9979770 DOI: 10.1103/physrevb.52.7849] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
22
|
Klann R, Kwok SH, Grahn HT, Hey R. Time-resolved photoluminescence investigations of electric-field domain formation in GaAs-AlAs superlattices. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:R8680-R8683. [PMID: 9979925 DOI: 10.1103/physrevb.52.r8680] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
23
|
Kwok SH, Norris TB, Bonilla LL, Galán J, Cuesta JA, Martínez FC, Molera JM, Grahn HT, Ploog K, Merlin R. Domain-wall kinetics and tunneling-induced instabilities in superlattices. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:10171-10174. [PMID: 9977696 DOI: 10.1103/physrevb.51.10171] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
24
|
Kwok SH, Grahn HT, Ramsteiner M, Ploog K, Prengel F, Wacker A, Schöll E, Murugkar S, Merlin R. Nonresonant carrier transport through high-field domains in semiconductor superlattices. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:9943-9951. [PMID: 9977669 DOI: 10.1103/physrevb.51.9943] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
|
25
|
|