Contents

• I. Preamble
  • 1. Zusammenfassung
  • 2. Abstract
  • 3. Acknowledgment
  • 4. List of Acronyms
  • 5. List of Symbols
  
  
• II. Optimization and Inverse Modeling for Technology Computer Aided Design
  • 6. Introduction
    • 6.1 Historical Overview
    • 6.2 Technology Computer Aided Design
    • 6.3 Outline of the First Part
  • 7. Optimization and Approximation
    • 7.1 Introduction
    • 7.2 The Response Surface Methodology and Its Problems
    • 7.3 Univariate Bernstein Polynomials
    • 7.4 Multivariate Bernstein Polynomials
    • 7.5 Total Variation and the Variation Diminishing Property
    • 7.6 Examples
    • 7.7 Solving Design for Manufacturability Problems
  • 8. Optimization by Evolutionary Computation
    • 8.1 Introduction
    • 8.2 Representation of the Variables
    • 8.3 Operators for Continuous Variables
      • 8.3.1 Selection
      • 8.3.2 Crossover
      • 8.3.3 Mutation
    • 8.4 How Genetic Algorithms Work
      • 8.4.1 Evolutionary Computation
      • 8.4.2 The Classic Genetic Algorithm
      • 8.4.3 A State of the Art Algorithm
    • 8.5 Schemata and the Schema Theorem
    • 8.6 Comparison of Local Optimizers and Evolutionary Computation
      • 8.6.1 Advantages and Disadvantages of Local Optimizers
      • 8.6.2 Advantages and Disadvantages of Evolutionary Algorithm Optimizers
    • 8.7 Examples
  • 9. Design and Implementation of Siesta
    • 9.1 Introduction and Overview
    • 9.2 Seal (Siesta Extension and Application Language)
      • 9.2.1 Parallelization
      • 9.2.2 Persistent Object Storage
      • 9.2.3 Setting Up Experiments
      • 9.2.4 Calling Simulation Tools
      • 9.2.5 Inverse Modeling
      • 9.2.6 License Management
      • 9.2.7 Input Deck Handling
    • 9.3 Available Optimizers
      • 9.3.1 Ego
      • 9.3.2 Genopt
      • 9.3.3 Siman
      • 9.3.4 Direct
      • 9.3.5 Donopt
      • 9.3.6 Lmmin
    • 9.4 Specification of the Siesta Optimizer Protocol
      • 9.4.1 Requests Sent from the Optimizer to the Framework
      • 9.4.2 Results Sent from the Framework to the Optimizer
      • 9.4.3 Examples
  
  
• III. Applications
  • 10. Introduction
    • 10.1 Manufacturing Steps
      • 10.1.1 Wafers and Crystal Preparation
      • 10.1.2 Masks
      • 10.1.3 Photolithographic Process
      • 10.1.4 Deposition
      • 10.1.5 Etching
      • 10.1.6 Doping
      • 10.1.7 Conductors and Resistors
      • 10.1.8 Oxides
      • 10.1.9 Epitaxy
    • 10.2 Topography Simulation and Motivation
    • 10.3 Outline of the Second Part
  • 11. Smoothing Monte Carlo Simulation Results
    • 11.1 Introduction
    • 11.2 The Algorithm
    • 11.3 A Three-Dimensional Example
    • 11.4 Summary
  • 12. Simulation of Surface Evolution
    • 12.1 Introduction
    • 12.2 Overview of Topography Simulation
    • 12.3 The Transport of Particles above the Wafer
    • 12.4 A Radiosity Formulation for Luminescent Reflection
    • 12.5 The Mechanism of Deposition of Silicon Dioxide from TEOS
      • 12.5.1 The Heterogeneous Deposition Model
      • 12.5.2 The Homogeneous Intermediate-Mediated Deposition Model
      • 12.5.3 The Heterogeneous Deposition with Byproduct Inhibition Model
      • 12.5.4 Deposition Rate
    • 12.6 The Mechanism of Deposition of Silicon Nitride
    • 12.7 Simulation of Silicon Dioxide from TEOS for Power MOSFETs
    • 12.8 Simulation of Void Formation during Backend Processes
    • 12.9 Simulation of Deposition after Transport in the Diffusion Regime
    • 12.10 Summary
  • 13. The Level Set Method
    • 13.1 Methods for Describing Moving Boundaries
      • 13.1.1 String Based Methods
      • 13.1.2 The Cellular Approach
      • 13.1.3 The Level Set Method
    • 13.2 The Basics of the Level Set Method
    • 13.3 Variations of the Level Set Method and Advanced Algorithms
      • 13.3.1 The Boundary Value and the Initial Value Formulation
      • 13.3.2 Methods for Speeding Up the Solution of the Level Set Equation
      • 13.3.3 Extending the Speed Function
    • 13.4 Surface Extraction and Void Detection
    • 13.5 Finite Difference Schemes
      • 13.5.1 First Order Space Convex
      • 13.5.2 Second Order Space Convex
      • 13.5.3 Stability
    • 13.6 A Fast and Precise Level Set Algorithm
    • 13.7 Coalescing Surface Elements
    • 13.8 The ELSA Simulator
    • 13.9 Summary
  • 14. Inverse Modeling of Silicon Self-Interstitial Cluster Formation
    • 14.1 Introduction
    • 14.2 Modeling Silicon Self-Interstitial Cluster Formation and Dissolution
    • 14.3 Inverse Modeling and Results
    • 14.4 Summary
  • 15. Inverse Modeling of Arsenic Diffusion after Pre-deposition
    • 15.1 Introduction and Measurements
    • 15.2 Inverse Modeling and Results
    • 15.3 Summary
  • 16. Conclusion and Outlook
  • A. Mathematical Preliminaries
    • A.1 Norms
    • A.2 Means
    • A.3 Inequalities
    • A.4 Analysis
  • B. Multivariate Bernstein Polynomials
  
  
• Bibliography
  • C. Own Publications
  • D. Curriculum Vitae