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Numerical algorithms for system level electro-thermal simulation / author: Massimiliano Culpo. 2009
Inhalt
Preface
Contents
List of abbreviations
Motivation
Modeling
State of the art in electro-thermal simulation
Challenges in electro-thermal engineering of ICs
State of the art in electro-thermal simulation
Overview and setting of the proposed method
Electro-thermal models at the system level
Conservation laws
Standard device models and MNA
Extended electrical models
Thermal element model
Coupled electro-thermal system
Analysis
Analysis of a coupled electro-thermal system
Assumptions on the heat diffusion operator
Well posedness of the thermal element model
Well posedness of the coupled system
Numerical Discretization
Patched mesh method
Patched space definition and interpolation estimates
Approximation of diffusion-reaction equations
Numerical solution of the coupled system
Discretization of the electro-thermal model
Solution of non-linear algebraic equation systems
Evaluation of the thermal element
Numerical validation
CMOS inverter
Description of the circuit
Simulation results
Power nMOS-FET
Description of the device
Simulation results
Appendix
Graph theory
Basic definitions
Kirchhoff's laws
DAE theory
Linear DAEs with constant coefficients: Kronecker index
Extension of index concepts to non-linear DAEs
PDE theory
Function spaces
Variational formulation of elliptic problems
Resolution of diffusion-reaction equation layers
Model problem exhibiting internal layers
Solution decomposition
Discretization of the model problem
Summary and Bibliography
Summary
Bibliography
List of Figures
List of Tables
Index