Circuit, Device and Process Simulation: Mathematical and Numerical Aspects

Overview

This book presents for the first time a unified treatment of the physical processes, mathematical models and numerical techniques for circuit, device and process simulation. At the macroscopic level linear and nonlinear circuit elements are introduced to yield a mathematical model of an integrated circuit. Numerical techniques used to solve this coupled system of ODEs are described. Microscopically, current flow within a transistor is modeled using the drift-diffusion and hydrodynamic PDE systems. Finite ...
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Overview

This book presents for the first time a unified treatment of the physical processes, mathematical models and numerical techniques for circuit, device and process simulation. At the macroscopic level linear and nonlinear circuit elements are introduced to yield a mathematical model of an integrated circuit. Numerical techniques used to solve this coupled system of ODEs are described. Microscopically, current flow within a transistor is modeled using the drift-diffusion and hydrodynamic PDE systems. Finite difference and finite element methods for spatial discretizations are treated, as are grid generation and refinement, upwinding, and multilevel schemes. At the fabrication level, physical processes such as diffusion, oxidation, and crystal growth are modeled using reaction-diffusion-convection equations. These models require multistep integration techniques and Krylov projection methods for successful implementation. Exercises, programming assignments, and an extensive bibliography are included to reinforce and extend the treatment.
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Editorial Reviews

Booknews
Presents a unified treatment of the physical processes, mathematical models, and numerical techniques for circuit, device, and process simulation. Offers a model of an integrated circuit based on linear and nonlinear circuit elements, a model of current flow within a transistor using the drift-diffusion and hydrodynamic PDE systems, and models for physical processes such as diffusion, oxidation, and crystal growth, as well as finite difference and finite element methods for spatial discretizations. Contains chapter summaries, exercises, and programming assignments. For a graduate electrical engineering course in simulation, and for researchers in the semiconductor industry. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780471960195
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 6/19/1996
  • Edition number: 1
  • Pages: 440
  • Product dimensions: 6.79 (w) x 9.72 (h) x 1.23 (d)

Table of Contents

Preface
1 Modeling and Simulation 1
2 The Circuit Equations 14
3 Transistors and Semiconductor Circuits 30
4 Numerical Integration of Circuit ODEs 52
5 Solving Nonlinear Circuit Equations 70
6 Circuit Models and Parameter Extraction 85
7 Semiconductor Device Modeling 105
8 Hydrodynamic Device Equations 147
9 Grid Generation and Refinement 171
10 Ion Implantation 190
11 Single Species Diffusion 213
12 Multiple Species Diffusion 238
13 Integrating Reaction-Diffusion Systems 261
14 Specialized Diffusion Topics 295
15 Silicon Oxidation 312
16 Crystal Growth 354
17 Technology Computer Aided Design 370
Bibliography 390
Index 422
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