Preface; Contents; List of Contributors; Part I Introduction; 1 The COMSON Project; 1.1 Trends in Microelectronics; 1.2 Scope of the COMSON Project; 1.3 Methodology; 1.3.1 The Demonstrator Platform; 1.3.1.1 Objectives and Benefits; 1.3.1.2 State of the Art; 1.3.1.3 Basic Concepts; 1.3.2 E-Learning; 1.4 Modelling, Simulation and Optimisation; 1.4.1 Partial Differential Algebraic Equations; 1.4.2 Dynamic Iteration; 1.4.3 Model Order Reduction; 1.4.4 Optimisation; References; Part II Partial Differential Algebraic Equations; 2 PDAE Modeling and Discretization

2.1 Introduction on Modeling and PDAEs2.1.1 Mathematical Modeling in Nanoelectronics; 2.1.2 Classification of PDAE Models; 2.1.2.1 Refined Modeling; 2.1.2.2 Multiphysical Extensions; 2.2 Modeling, Analysis and Discretization of Coupled Problems; 2.2.1 Refined Modeling of Networks with Devices; 2.2.1.1 Modeling of Electric Networks; 2.2.1.2 Distributed Models for Devices; 2.2.1.3 Displacement Current and Device Capacitance Matrix; 2.2.1.4 The Drift-Diffusion Model; 2.2.1.5 Space Discretization of the Distributed Model: The Gummel Map

2.2.1.6 Space Discretization of the Distributed Model: The Box Integration Method2.2.1.7 Space Discretization of the Distributed Model: The Coupling Conditions; 2.2.2 Electro-Thermal Effects at the System Level; 2.2.2.1 Definition of the PDE-Based Thermal Element Model; 2.2.2.2 Analysis of the Thermal Element Model; 2.2.2.3 Evaluation of the Thermal Element Model; 2.2.2.4 Analysis of the Coupled System; 2.2.3 Multiphysics Modeling via Maxwell's Equations ; 2.2.3.1 Maxwell's Equations; 2.2.3.2 Conductor Models; 2.2.3.3 Discretization; 2.2.3.4 Discrete Vector Potential Formulation

2.2.3.5 Gauging of the Curl-Curl Equation2.2.3.6 Structure of the Coupled System; 2.2.4 Thermal and Quantum Effects in Semiconductors; 2.2.4.1 The Electron-Phonon System ; 2.2.4.2 The Maximum Entropy Principle ; 2.2.4.3 Closure Relations: Phonon Subsystem; 2.2.4.4 Closure Relations for Electrons; 2.2.4.5 Limiting Energy Transport and Lattice Heating Model; 2.2.4.6 Quantum Corrections; 2.2.4.7 Quantum Corrections in the High Field Approximation; 2.2.4.8 Quantum Corrected Energy-Transport and Crystal Heating Model; References

3 Simulation of Coupled PDAEs: Dynamic Iteration and Multirate Simulation3.1 Aim and Outline; 3.2 Theory of Dynamic Iteration Schemes for Coupled DAEs; 3.2.1 Description of Coupled Systems; 3.2.2 Iteration Schemes for Coupled DAE Systems; 3.2.3 Convergence and Stability; 3.2.3.1 Error Recursion; 3.2.3.2 Contraction and Local Error; 3.2.3.3 Stability and Convergence for Windowing Technique; 3.3 Applications in Electrical Engineering; 3.3.1 Refined Network Models; 3.3.2 Electro-Thermal Coupling