Contents

• Kurzfassung
• Abstract
• Resumo
• List of Figures
• List of Tables
• List of Symbols
• 1. Introduction
  • 1.1 Dual-Damascene Fabrication Process
  • 1.2 The Electromigration Failure
    • 1.2.1 Experimental Lifetime Estimation
    • 1.2.2 The Impact of Material Interfaces
    • 1.2.3 Effect of Microstructure
  • 1.3 Empirical and Semi-Empirical Models
    • 1.3.1 Black's Equation
    • 1.3.2 Resistance Increase and Void Growth
    • 1.3.3 EM Lifetime Extrapolation
  • 1.4 TCAD for Electromigration Simulation
  • 1.5 Outline of this Work
  
  
• 2. Physics of Electromigration
  • 2.1 The Electromigration Driving Force
  • 2.2 Diffusivity Paths
  • 2.3 Electromigration Induced Material Transport
  • 2.4 Electromigration and Mechanical Stress
    • 2.4.1 The Blech Effect
    • 2.4.2 Models of Stress Build-up due to Electromigration
  • 2.5 Void Nucleation
  • 2.6 On the Void Evolution
  
  
• 3. A General TCAD Electromigration Model
  • 3.1 Electro-Thermal Problem
  • 3.2 Material Transport Equations
    • 3.2.1 Fast Diffusivity Paths
    • 3.2.2 Anisotropic Diffusivity: Diffusion Dependence on Stress
  • 3.3 Electromigration Induced Stress
    • 3.3.1 Strain due to Vacancy Migration
    • 3.3.2 Strain due to Vacancy Generation/Annihilation
    • 3.3.3 Total Electromigration Strain
  • 3.4 Vacancy Sinks and Sources
    • 3.4.1 Grain Boundary Model
    • 3.4.2 Material Interfaces
  • 3.5 Mechanical Deformation
  • 3.6 Model Summary
  
  
• 4. Numerical Implementation
  • 4.1 The Finite Element Method
    • 4.1.1 Galerkin's Method
    • 4.1.2 Assembly
    • 4.1.3 Shape Function
  • 4.2 Discretization of the Model Equations
    • 4.2.1 Discretization of Laplace's Equation
    • 4.2.2 Discretization of the Thermal Equation
    • 4.2.3 Discretization of the Vacancy Balance Equation
    • 4.2.4 Discretization of the Mechanical Equations
  • 4.3 Simulation in FEDOS
    • 4.3.1 Newton's Method
    • 4.3.2 Assembly of the Electro-Thermal Problem
    • 4.3.3 Assembly of the Vacancy Dynamics Problem
    • 4.3.4 Calculation of the Mechanical Stress
    • 4.3.5 Mesh Refinement at Material Interfaces and Grain Boundaries
  
  
• 5. Simulation Studies of Electromigration
  • 5.1 Material and Simulation Parameters
  • 5.2 Model Calibration and Verification
    • 5.2.1 Vacancy Dynamics
    • 5.2.2 The Role of Mechanical Stress
  • 5.3 Stress Effect on Diffusivity
  • 5.4 Fast Diffusivity Paths
  • 5.5 Redundant Via Structure
  • 5.6 Effect of Microstructure on the Electromigration Lifetime Distribution
    • 5.6.1 Microstructure Generation
    • 5.6.2 Simulation Approach
    • 5.6.3 Sites of Void Nucleation
    • 5.6.4 Electromigration Lifetimes Distribution
  
  
• 6. Conclusion and Outlook
• Bibliography
• List of Publications