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Nonlinear Wave Methods for Charge Transport

ISBN: 978-3-527-40695-1
287 pages
March 2010
Nonlinear Wave Methods for Charge Transport (3527406956) cover image
The present book introduces and develops mathematical techniques for the treatment of nonlinear waves and singular perturbation methods at a level that is suitable for graduate students, researchers and faculty throughout the natural sciences and engineering. The practice of implementing these techniques and their value are largely realized by showing their application to problems of nonlinear wave phenomena in electronic transport in solid state materials, especially bulk semiconductors and semiconductor superlattices. The authors are recognized leaders in this field, with more than 30 combined years of contributions.
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Preface.

Acknowledgments.

1. Introduction.

1.1 Overview of Nonlinear Wave Phenomena.

1.2 Nonlinear Waves and Electronic Transport in Materials.

1.3 Structural Outline of the Book.

2. Dynamical Systems, Bifurcations, and the Chapman-Enskog Method.

2.1 Introduction.

2.2 Review of Dynamical Systems Concepts.

2.3 Analysis of the Hopf Biofurcation: An Introduction to the Chaman-Enskog Methods.

3. Excitable Media I: Continuum Systems.

3.1 Introduction.

3.2 Basic Excitability – the FitzHugh-Nagumo System.

3.3 Matched Asymptotics: Excitability and Oscillations.

3.4 The Scalar Bistable Equation: Wave Pulses as Heteroclinic Connections.

3.5 Traveling Waves of the FitzHugh-Nagumo System.

4. Excitable Media II: Discrete Systems.

4.1 Introduction.

4.2 The Spatially Discrete Nagumo Equation.

4.3 Asymptotic Construction of Pulses.

4.4 Numerically Calculated Pulses.

4.5 Propagation Failure.

4.6 Pulse Generation at a Boundary.

4.7 Concluding Remarks.

5. Electronic Transport in Condensed Matter: From Quantum Kinetics to Drift-diffusion Models.

5.1 Introduction.

5.2 Superlattices.

5.3 Concluding Remarks.

6. Electric Field Domains in Bulk Semiconductors I: the Gunn Effect.

6.1 Introduction.

6.2 N-shaped Current-Field Characteristics and Kroemer’s Model.

6.3 Stationary Solutions and Their Linear Stability in the Limit L >> 1.

6.4 Onset of the Gunn Effect.

6.5 Asymptotics of the Gunn Effect for Long Samples ad N-shaped Electron Velocity.

6.6 Asymptotics of the Gunn Effect for Long Samples and Saturating Electron Velocity.

6.7 References on the 1D Gunn Effect and Closing Remarks.

7. Electric Field Domains in Bulk Semiconductors II: Trap-mediated Instabilities.

7.1 Introduction.

7.2 Drift-Diffusion Transport Model for Trap-Mediated System.

7.3 Nondimensional  Form and the Reduced Model.

7.4 Steady States, J-E Curves, and Steady Wave Solutions on the Infinite Line under Current Bias.

7.5 Nonlinear Wave Solutions in Finite Samples under Voltage Bias.

7.6 Multiple Shedding of Wavefronts in Extrinsic Material.

8. Nonlinear Dynamics in Semiconductor Superlattices.

8.1 Introduction.

8.2 Spatially Discrete Model for the Doped Weakly Coupled SL.

8.3 Nondimensionalization of the Discrete Drift-Diffusion Model.

8.4 Wave Fronts and Stationary States under Current Bias.

8.5 Static Field Domains in Voltage-Biased SLs.

8.6 Relocation of EFDs.

8.7 Self-Sustained Oscillations of the Current.

8.8 Spin Transport in Dilute magnetic Semiconductor Superlattices.

9. Nonlinear Wave Methods for Related Systems in the Physical World.

9.1 Introduction.

9.2 Superlattice Transport Model with Both Vertical and Lateral Dynamics.

9.3 Semi-Insulating GaAs.

9.4 Multidimensional Gunn Efect.

9.5 Fluctuations in Gunn Diodes.

9.6 Dynamics of Dislocations in Mechanical Systems: Nanoarrays.

Index.

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Luis L. Bonilla received his Ph.D. in physics from the Universidad Nacional de Educacion a Distancia (UNED), Madrid, in 1981. After conducting postdoctoral research for three years at the Mathematics Department at Stanford University, he took positions as associate professor at the Universities of Sevilla and Barcelona, both Spain. In 1992, he accepted his current post of Professor of Applied Mathematics at the University Carlos III in Madrid. Professor Bonilla's research interests lie in the modeling and asymptotic analysis of nonlinear problems in condensed matter physics, including electronic and mechanical properties. He is the author and co-author of more than 180 research papers and book chapters.

Stephen W. Teitsworth received his Ph.D. in Physics in 1986 from Harvard University, where he also carried out postdoctoral research. For the past several years, he has been a faculty member of the Physics department at Duke University. His current research interests center on experimental and theoretical studies of nonlinear electronic transport and optoelectronic properties of semiconductor-based materials, with a focus on spatially periodic systems such as superlattices.
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"This monograph may be a useful reference for graduate students or researchers from different fields: for condensed matter physicists, applied mathematicians,
engineers working in most fields as well as those interested in applications of nonlinear dynamics ideas to describe and analyse scientific problems." (Contemporary Physics, 8 November 2011)

 

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