Nonlinear dynamics and chaos in semiconductors /
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| Author / Creator: | Aoki, Kazunori. |
|---|---|
| Imprint: | Bristol ; Philadelphia : Institute of Physics Pub., c2001. |
| Description: | xii, 580 p. : ill. ; 25 cm. |
| Language: | English |
| Series: | Series in condensed matter physics |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/6251294 |
Table of Contents:
- Preface
- 1. Introduction
- 1.1. What is chaos?
- 1.1.1. Logistic map
- 1.1.2. Ergodic theorem
- 1.1.3. Chaos includes many unstable periodic states
- 1.1.4. Entropy positive
- 1.2. Universality and individuality
- 1.2.1. From universality
- 1.2.2. Towards individuality
- 1.3. Motivations
- 1.3.1. From the viewpoint of semiconductor chaos
- References
- 2. Nonlinear carrier transport in semiconductors
- 2.1. Carrier transport theory
- 2.1.1. Statistics of carriers
- 2.1.2. The Boltzmann equation
- 2.2. Nonequilibrium phase transitions
- 2.2.1. High-field regime: the Gunn effect
- 2.2.2. High-field instability and chaos
- 2.2.3. Low-field regime: the SNDC
- 2.3. Two-level impact-ionization model
- References
- 3. S-shaped negative differential conductivity and the nonequilibrium phase transition
- 3.1. Scattering processes
- 3.1.1. Ionized-impurity scattering: Brooks-Herring formula
- 3.1.2. Ionized impurity scattering in compensated semiconductors
- 3.1.3. Neutral impurity scattering
- 3.1.4. Excitations of neutral impurity
- 3.1.5. Impact ionization
- 3.2. Impact-ionization model
- 3.2.1. Approximated one-level impact-ionization model (model A)
- 3.2.2. One-level impact-ionization model (model B)
- 3.3. Thermodynamical consideration of the SNDC
- 3.4. Equal area rule and pattern formation
- 3.5. Measurement of a localized filamentary current
- References
- 4. Nonlinear dynamics, stability and instability in carrier transport
- 4.1. Catastrophe theory
- 4.1.1. One-parameter family (m = 1)
- 4.1.2. Two-parameter family (m = 2)
- 4.1.3. Four-parameter family (m = 4)
- 4.2. Breakdown of perfect delay
- 4.3. Linear stability analysis
- 4.4. Mathematical version of the instability model: an analog for the impact-ionization avalanche
- 4.5. A physical model of the impact-ionization avalanche
- 4.6. Periodically driven chaos
- 4.7. Period doubling bifurcation to chaos
- 4.7.1. Sensitive dependence on initial conditions
- 4.8. Fundamentals of period doubling bifurcation
- 4.9. Intermittent behavior
- 4.10. Growth of chaos
- 4.11. Semiconductor chaos, U-sequence and Sarkovskii's theorem
- 4.12. Semiconductor chaos and the dissipative structure
- References
- 5. Observation of chaos and experimental methods
- 5.1. Encounter with chaos
- 5.2. Firing wave instability
- 5.3. Electron-beam-induced instability
- 5.4. Periodically driven chaos
- 5.5. Route to crisis-induced intermittency
- 5.6. Mechanism of crisis-induced intermittency
- References
- 6. Characterizing chaos
- 6.1. Fractal dimensions and fractal sets
- 6.1.1. Hausdorff-Besicovitch dimension
- 6.1.2. Embedding method
- 6.1.3. Capacity dimension
- 6.1.4. Information dimension
- 6.1.5. Lyapunov dimension
- 6.1.6. Correlation dimension
- 6.1.7. Relation among the dimensions
- 6.2. Lyapunov spectrum
- 6.3. f([alpha]) spectrum
- 6.4. Circle-map behavior
- 6.5. Fractal basin boundary
- References
- 7. Novel phenomena in semiconductors
- 7.1. Dissipation energy and its fluctuation
- 7.2. Deterministic noise amplification
- 7.3. Hall-field instability
- 7.3.1. Simulations with positive differential conductivity
- 7.3.2. Simulations with negative differential conductivity
- 7.4. Cross-over current instability
- 7.5. Cross-talk coupling
- References
- 8. Towards a second new paradigm of semiconductor chaos
- 8.1. Towards an understanding of fully developed electronic turbulence
- 8.1.1. Numerical aspects of pattern dynamics in bulk semiconductors
- 8.1.2. Dynamical Hall-field instability in crossed electric and magnetic fields
- 8.1.3. Nucleation process of a current filament
- 8.1.4. Spatiotemporal behaviors of localized current filaments in silicon p-n-p-n diodes
- 8.1.5. Experimental aspects of pattern dynamics in bulk semiconductors--part I
- 8.1.6. Experimental aspects of pattern dynamics in bulk semiconductors--part II
- 8.2. Towards a second new paradigm
- 8.3. Chaos in device structures and superlattices
- 8.3.1. Chaos in electronic devices and circuits
- 8.3.2. Chaos in device structures
- References
- Index
