Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors

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Cambridge University Press, Feb 22, 2001 - Mathematics - 406 pages
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Nonlinear transport phenomena are an increasingly important aspect of modern semiconductor research. This volume deals with complex nonlinear dynamics, pattern formation, and chaotic behavior in such systems. It bridges the gap between two well-established fields: the theory of dynamic systems and nonlinear charge transport in semiconductors. This unified approach helps reveal important electronic transport instabilities. The initial chapters lay a general framework for the theoretical description of nonlinear self-organized spatio-temporal patterns, such as current filaments, field domains, fronts, and analysis of their stability. Later chapters consider important model systems in detail: impact ionization induced impurity breakdown, Hall instabilities, superlattices, and low-dimensional structures. State-of-the-art results include chaos control, spatio-temporal chaos, multistability, pattern selection, activator-inhibitor kinetics, and global coupling, linking fundamental issues to electronic device applications. This book will be of great value to semiconductor physicists and nonlinear scientists alike.

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Chapter 1 Semiconductors as continuous nonlinear dynamic systems
Chapter 2 Concepts of nonlinear charge transport in semiconductors
Chapter 3 Pattern formation and oscillatory instabilities in semiconductors
Chapter 4 Impactionizationinduced impurity breakdown
Chapter 5 Nonlinear carrier dynamics in crossed electric and magnetic fields
Chapter 6 Stationary and oscillating domains in superlattices
Chapter 7 Spatiotemporal chaos

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About the author (2001)

Eckehard Schöll was born on February 6, 1951 in Stuttgart, Germany. He received his Diplom degree in physics (MSc) from the University of Tuebingen, Germany, in 1976, his PhD degree in applied mathematics from the University of Southampton in 1978, and his Dr. rer. nat. degree and the veni legendi from Aachen University of Technology (RWTH Aachen), Germany, in 1981 and 1976 respectively. During 1983-4 he was a Visiting Assistant Professor in the Department of Electrical and Computer Engineering, Wayne State University Detroit, Michigan. Since 1989 he has been a Professor Theoretical Physics at the Technical University of Berlin. His research interests include the theory of nonlinear charge transport and current instabilities in semiconductors, in particular, low-dimensional structures: nonlinear spatio-temporal dynamics, chaos, and pattern formation; and electro-optical nonlinearities. Dr Schöll is the author of the book Nonequilibrium Phase Transitions in Semiconductors (1987), translated into Russian in 1991, and the coauthor of The Physics of Instabilities in Solid State Electron Devices (1992), and has edited Theory of Transport Properties of Semiconductor Nanostructures (1998). He has published almost 200 articles in international journals such as Physical Review Letters, Physical Review, Europhysics Letters, Semiconductor Science and Technology, Applied Physics Letters, the Journal of Applied Physics, and many others. In 1997 he was awarded a prize as Champion of Teaching by the Technical University of Berlin.