Nonequilibrium Phase Transitions in Semiconductors: Self-Organization Induced by Generation and Recombination Processes

ISBN-13: 9783642719295 / Angielski / Miękka / 2011 / 313 str.

Eckehard Sch LL

Opis

Semiconductors can exhibit electrical instabilities like current runaway, threshold switching, current filamentation, or oscillations, when they are driven far from thermodynamic equilibrium. This book presents a coherent theoretical des- cription of such cooperative phenomena induced by generation and recombination processes of charge carriers in semicon- ductors.

Spis treści

1. Introduction.- 1.1 Instabilities in Semiconductors.- 1.1.1 Negative Differential Conductivity.- 1.1.2 Mechanisms for NDC.- 1.1.3 Semiconductor Transport.- 1.2 Phase Transition Analogies.- 1.2.1 Equilibrium and Nonequilibrium Phase Transitions.- 1.2.2 Semiconductors as Nonequilibrium Systems.- 1.2.3 Bifurcation Phenomena.- 2. Bistability of Homogeneous Steady States.- 2.1 One-Carrier Models.- 2.1.1 Second-Order Phase Transitions.- 2.1.2 First-Order Phase Transitions.- 2.1.3 General M-Level Mechanisms.- 2.1.4 Critical Behavior.- 2.1.5 Cyclotron-Resonance Induced Phase Transitions.- 2.2 Two-Carrier Models.- 2.2.1 Models with Band-Band Impact Ionization.- 2.2.2 Models with Band-Trap Impact Ionization.- 2.2.3 Dynamics of Threshold Switching Transitions.- 2.2.4 Auger Recombination Induced Tristability.- 2.3 Excitonic Models.- 2.3.1 Stimulated Exciton Creation.- 2.3.2 Bound-Exciton Recombination and Optical Bistability.- 3. Small Fluctuations from the Homogeneous Steady State.- 3.1 Linear Modes of One-Carrier Models.- 3.1.1 Linearized Transport Equations.- 3.1.2 Stability and Differential Conductivity.- 3.2 Filamentary Instability.- 3.2.1 The Spectrum.- 3.2.2 Bifurcation of Layered or Filamentary Stationary Structures.- 3.3 Domain Instability.- 3.4 Electromagnetic Modes.- 3.4.1 Maxwell’s Equations in Media with NDC.- 3.4.2 Transverse Modes (k???).- 3.4.3 Longitudinal Modes (k???).- 3.4.4 Mixed Modes.- 3.5 Oscillatory Instability.- 3.5.1 Two-Level Models.- 3.5.2 Single-Level Models.- 4. Stationary Transverse Spatial Structures.- 4.1 Plane Current Layers.- 4.1.1 Phase Portraits.- 4.1.2 Equal-Areas Rule.- 4.1.3 Electron-Density Profiles.- 4.1.4 Current-Voltage Characteristics.- 4.2 Cylindrical Current Filaments.- 4.2.1 Electron-Density Profiles.- 4.2.2 Equal-Areas Rule.- 4.3 Influence of Boundaries.- 4.3.1 Lateral Boundary Conditions.- 4.3.2 Neumann Boundary Conditions.- 4.3.3 Dirichlet Boundary Conditions.- 4.4 Filamentation in Two-Carrier Models.- 4.4.1 Ambipolar Diffusion and Trapping.- 4.4.2 Equal-Areas Rules for Current Layers and Filaments.- 4.5 Multiple Filaments.- 5. Stability of Transverse Spatial Structures.- 5.1 Plane Current Layers.- 5.1.1 General Results.- 5.1.2 Unstable Modes of Depletion Layers.- 5.1.3 Stable Modes of the Kink Profile.- 5.2 Cylindrical Current Filaments.- 5.2.1 General Results.- 5.2.2 Unstable Mode.- 5.3 Finite Boundary Conditions.- 5.3.1 Neumann Boundary Conditions.- 5.3.2 Dirichlet Boundary Conditions.- 5.4 Fluctuation-Induced Phase Transitions.- 5.4.1 Nucleation of Current Filaments.- 5.4.2 Transverse Solitary Waves.- 6. Self-Sustained Oscillations and Chaos.- 6.1 Mechanisms for Oscillatory Behavior.- 6.1.1 Survey of Mechanisms.- 6.1.2 Transit-Time Oscillations.- 6.2 Limit-Cycle Oscillations.- 6.2.1 Circuit-Induced Oscillations.- 6.2.2 Impact-Ionization Induced Oscillations.- 6.2.3 Exciton-Induced Oscillations.- 6.3 Chaos.- 6.3.1 Routes to Chaos.- 6.3.2 Single-Carrier Effects.- 6.3.3 Impact-Ionization Assisted Driven Chaos.- 6.3.4 Impact-Ionization Induced Self-Generated Chaos.- 6.3.5 Two-Carrier Effects.- References.