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Summary
Summary
Mathematical Analysis of Evolution, Information, and Complexity deals with the analysis of evolution, information and complexity. The time evolution of systems or processes is a central question in science, this text covers a broad range of problems including diffusion processes, neuronal networks, quantum theory and cosmology. Bringing together a wide collection of research in mathematics, information theory, physics and other scientific and technical areas, this new title offers elementary and thus easily accessible introductions to the various fields of research addressed in the book.
Author Notes
Wolfgang Arendt is head of the Institute of Applied Analysis at the University of Ulm, Germany. Having obtained his degrees from the University of Nice, France, and Tuebingen, Germany, he worked for eight years as a professor at the University of Besançon in France before accepting a chair at the University of Ulm in Germany. He held visiting positions at the University of California at Berkeley, and the universities of Nancy, Oxford, Zuerich, Canberra, Sydney and Lecce. Professor Arendt's fields of research are partial differential equations and functional analysis with special emphasis on evolution equations.
Wolfgang P. Schleich is head of the Institute of Quantum Physics at the University of Ulm, Germany, and Distinguished Adjunct Professor at the University of North Texas in Denton, USA. He has published more than 250 papers on problems of quantum optics, foundations of quantum mechanics and general relativity and is the author of the highly acclaimed textbook Quantum Optics in Phase Space, published with Wiley-VCH. For his work he has received numerous awards and honours.
Table of Contents
| Preface |
| Color Tables |
| 1 General Properties of Nitrides. Introduction |
| 1.1 Crystal Structure of Nitrides. |
| 1.2 Gallium Nitride. |
| 1.3 Aluminum Nitride. |
| 1.4 Indium Nitride. |
| 1.5 Ternary and Quaternary Alloys. References. |
| 2 Electronic Band Structure and Polarization Effects. Introduction. |
| 2.1 Band Structure Calculations. |
| 2.2 General Strain Considerations. |
| 2.3 Effect of Strain on the Band Structure of GaN. |
| 2.4 kp Theory and the Quasi-Cubic Model. |
| 2.5 Quasi-Cubic Approximation. |
| 2.6 Temperature Dependence of Wurtzite GaN Bandgap. |
| 2.7 Sphalerite (Zinc blende) GaN. |
| 2.8 AlN. |
| 2.9 InN. |
| 2.10 Band Parameters for Dilute Nitrides. |
| 2.11 Confined States. |
| 2.12 Polarization Effects. References. |
| 3 Growth and Growth Methods for Nitride Semiconductors. Introduction |
| 3.1 Substrates for Nitride Epitaxy |
| 3.2 A Primer on Conventional Substrates and their Preparation for Growth. |
| 3.3 GaN Epitaxial Relationship to Substrates. |
| 3.4 Nitride Growth Techniques. |
| 3.5 The Art and Technology of Growth of Nitrides. |
| 3.6 Concluding Remarks. References |
| 4 Extended and Point Defects, Doping, and Magnetism. Introduction |
| 4.1 A Primer on Extended Defects |
| 4.2 TEM Analysis of High Nitrogen Pressure (HNP) Solution Growth (HNPSG) and HVPE-Grown GaN. |
| 4.3 Point Defects and Autodoping. |
| 4.4 Defect Analysis by Deep-Level Transient Spectroscopy. |
| 4.5 Minority Carrier Lifetime. |
| 4.6 Positron Annihilation. |
| 4.7 Fourier Transform Infrared (FTIR), Electron Paramagnetic Resonance, and Optical Detection of Magnetic Resonance. |
| 4.8 Role of Hydrogen. |
| 4.9 Intentional Doping. |
| 4.10 Ion Implantation and Diffusion for Doping. |
| 4.11 Summary |
| References. |
| Index. |
| Appendix. |
