• 1. Modeling and Simulation
  • 1.1 Introduction
  • 1.2 Engineering Design
  • 1.3 Circuit, Device and Process Models
  • 1.4 Simulation
  • 1.5 Preview and Organization
  • 1.6 Summary
• 2. The Circuit Equations
  • 2.1 Introduction
  • 2.2 Ohm's and Kirchoff's Laws
  • 2.3 A Simple Resistive Circuit
  • 2.4 Charge in a Linear Capacitor
  • 2.5 Current in the Linear Capacitor
  • 2.6 The Linear Inductor
  • 2.7 Summary
  • 2.8 Exercises
• 3. Transistors and Semiconductor Circuits
  • 3.1 Introduction
  • 3.2 Band Theory for Semiconductors
  • 3.3 Drift and Diffusion
  • 3.4 The pn-junction
  • 3.5 The Ideal Diode
  • 3.6 Nonlinear Capacitance in a Diode
  • 3.7 Modeling the MOS Transistor
  • 3.8 Overview of a Circuit Simulator
  • 3.9 Summary
  • 3.10 Exercises
• 4. Numerical Integration of Circuit ODEs
  • 4.1 Introduction
  • 4.2 An Analytic Circuit Model
  • 4.3 Dynamical Systems
  • 4.4 Existence and Uniqueness
  • 4.5 Numerical Solution of the Circuit Equations
  • 4.6 The Forward Euler Method
  • 4.7 Stability and the Backward Euler Method
  • 4.8 A Differential-Algebraic System
  • 4.9 The Trapezoidal Integration Method
  • 4.10 Remarks on Nonuniqueness
  • 4.11 Summary
  • 4.12 Exercises
• 5. Solving Nonlinear Circuit Equations
  • 5.1 Introduction
  • 5.2 A Simple Nonlinear Circuit
  • 5.3 Newton's Method
  • 5.4 Further Examples of Nonlinear Circuits
  • 5.5 Ramping and Damping
  • 5.6 Summary
  • 5.7 Exercises
• 6. Circuit Models and Parameter Extraction
  • 6.1 Introduction
  • 6.2 Device Models for Circuit Simulation
  • 6.3 Parameter Extraction
  • 6.4 Statistical Variations of Model Parameters
  • 6.5 Summary
  • 6.6 Exercises
• 7. Semiconductor Device Modeling
  • 7.1 Introduction
  • 7.2 Transport Equation
  • 7.3 Drift-Diffusion Equations
  • 7.4 Approximate Formulation
  • 7.5 Grid Refinement
  • 7.6 Numerical Modeling Results
  • 7.7 Augmented Drift-Diffusion Models
  • 7.8 Multigrid and Multilevel Schemes
  • 7.9 p-methods and Multilevel Schemes
  • 7.10 Summary
  • 7.11 Exercises
• 8. Hydrodynamic Device Equations
  • 8.1 Introduction
  • 8.2 Hot Carriers
  • 8.3 1D Steady-state Problem
  • 8.4 1D Time-dependent Problem
  • 8.5 Lax-Wendroff and Taylor-Galerkin Schemes
  • 8.6 Quantum Hydrodynamics
  • 8.7 Some Extensions
  • 8.8 Summary
  • 8.9 Exercises
• 9. Grid Generation and Refinement
  • 9.1 Introduction
  • 9.2 Point Insertion Strategies
  • 9.3 Quadtree and Octree Data Structures
  • 9.4 Error Indicators
  • 9.5 Iterative Solution with Refinement
  • 9.6 Redistribution
  • 9.7 Moving Grids
  • 9.8 Summary
  • 9.9 Exercises
• 10. Ion Implantation
  • 10.1 Introduction
  • 10.2 Analytic Distribution Functions
  • 10.3 Energy Loss and Scattering
  • 10.4 Ion Trajectories in Amorphous Targets
  • 10.5 Ion Trajectories in Crystalline Targets
  • 10.6 Summary
  • 10.7 Exercises
• 11. Single Species Diffusion
  • 11.1 Introduction
  • 11.2 Diffusion as a Random Walk
  • 11.3 Diffusion in a Continuum
  • 11.4 Intrinsic (Low Concentration) Diffusion
  • 11.5 Extrinsic (High Concentration) Diffusion
  • 11.6 Transport and Segregation Coefficients
  • 11.7 Impurity Clustering
  • 11.8 Field-aided Diffusion
  • 11.9 Lateral Diffusion and Emitter-Push
  • 11.10 The Boltzmann--Matano Technique
  • 11.11 Numerical Solution
  • 11.12 Summary
  • 11.13 Exercises
• 12. Multiple Species Diffusion
  • 12.1 Introduction
  • 12.2 Equilibrium Models
  • 12.3 Nonequilibrium Models
  • 12.4 Boundary and Initial Conditions
  • 12.5 Diffusivities and Reaction Rate Constants
  • 12.6 Simulations
  • 12.7 Hierarchy of Models
  • 12.8 Theoretical Analysis
  • 12.9 Summary
  • 12.10 Exercises
• 13. Integrating Reaction-Diffusion Systems
  • 13.1 Introduction
  • 13.2 The Method of Lines
  • 13.3 Multistep Methods
  • 13.4 Backward Differentiation Formula Methods
  • 13.5 Solving Nonlinear Algebraic Systems
  • 13.6 Solving Linear Systems
  • 13.7 Direct and Iterative Methods
  • 13.8 Preconditioners
  • 13.9 Conjugate Gradient and Least-squares
  • 13.10 Krylov Projection Methods
  • 13.11 Numerical Experiments in 3D
  • 13.12 Summary
  • 13.13 Exercises
• 14. Specialized Diffusion Topics
  • 14.1 Introduction
  • 14.2 Rapid Thermal Processing
  • 14.3 Diffusion in Polysilicon
  • 14.4 Impurity Diffusion During Oxidation
  • 14.5 Diffusion During Epitaxy
  • 14.6 Gallium-Arsenide Diffusion Models
  • 14.7 Rapid Prototyping of Diffusion Models
  • 14.8 Summary
  • 14.9 Exercises
• 15. Silicon Oxidation
  • 15.1 Introduction
  • 15.2 Diffusion of Oxidant
  • 15.3 Mathematical Analysis of Diffusion
  • 15.4 Approximate Models
  • 15.5 Viscous Oxide Flow
  • 15.6 Free Surface Conditions
  • 15.7 Silicon Oxidation Results
  • 15.8 Planar and Cylindrical Oxidation
  • 15.9 Summary
  • 15.10 Exercises
• 16. Crystal Growth
  • 16.1 Introduction
  • 16.2 Coupled Flow and Heat Transfer
  • 16.3 Transient Analysis
  • 16.4 Phase Change
  • 16.5 Summary
  • 16.6 Exercises
• 17. Technology Computer Aided Design
  • 17.1 Introduction
  • 17.2 Process Simulation
  • 17.3 Device Simulation
  • 17.4 Circuit Simulation
  • 17.5 Practical Considerations
  • 17.6 Summary
  • 17.7 Exercises