Contents

• List of Figures
• List of Tables
• List of Abbreviations
• List of Symbols
  
  
• 1. Introduction
  • 1.1 Integration Technology
    • 1.1.1 Semiconductor Fabrication
    • 1.1.2 Shrinking Features
    • 1.1.3 Interconnects in Integrated Circuits
    • 1.1.4 New Research Domains
  • 1.2 Three-Dimensional Integration
    • 1.2.1 Interconnect Hierarchy
    • 1.2.2 Classification and Designs
  • 1.3 Interconnect Technologies
    • 1.3.1 Through Silicon Vias Approaches
    • 1.3.2 Solder Bumps
    • 1.3.3 Reliability Issues
  • 1.4 Electromigration Failure
    • 1.4.1 Failure Phases
    • 1.4.2 Accelerated Lifetime Test
    • 1.4.3 Black's Equation
    • 1.4.4 Test Data Analysis and Lifetime Extrapolation
    • 1.4.5 Impact of Microstructure and Material Interfaces
    • 1.4.6 Electromigration Modeling
  • 1.5 Outline of the Thesis
  
  
• 2. Physical Description of Electromigration
  • 2.1 The History of Electromigration
    • 2.1.1 1960s: Black's Equation
    • 2.1.2 1970s: Blech Effect
    • 2.1.3 1980s: Modification of Black's Equation
    • 2.1.4 From 1990s to Modern Times
  • 2.2 Electromigration Driving Force
  • 2.3 Electromigration Induced Vacancy Transport
  • 2.4 Effect of Diffusion Paths
  • 2.5 Stress Build-up due to Electromigration
    • 2.5.1 Kirchheim Back Stress
    • 2.5.2 Korhonen's Model
    • 2.5.3 Mechanical Constitutive Equations
  • 2.6 Void Initiation Condition
  • 2.7 Void Evolution
  
  
• 3. Modeling Electromigration Using TCAD
  • 3.1 Electro-Thermal Problem
  • 3.2 Vacancy Dynamics Problem
    • 3.2.1 Vacancy Sources and Sinks
  • 3.3 Solid Mechanics Model
    • 3.3.1 Effect of Vacancy Transport
    • 3.3.2 Effect of Vacancy Generation/Annihilation
    • 3.3.3 Stress-Strain Relation
    • 3.3.4 Mechanical Deformation
    • 3.3.5 Model Equations
    • 3.3.6 Void Nucleation
  • 3.4 Void Evolution Models
    • 3.4.1 Sharp Interface Model
    • 3.4.2 Diffuse Interface Model
    • 3.4.3 Semi-Empirical Method
  • 3.5 Model Summary
  
  
• 4. Numerical Implementation with Finite Element Method
  • 4.1 General Theory of Finite Element Method
    • 4.1.1 Introduction to Finite Element Method
    • 4.1.2 Principles of Finite Element Method
  • 4.2 Finite Element Analysis for a 1D Problem
    • 4.2.1 1D Boundary Value Problem
    • 4.2.2 Discretization of the Domain
    • 4.2.3 Derivation of Equations over an Element
    • 4.2.4 Assembly of Elements
    • 4.2.5 Imposition of the Boundary Conditions
    • 4.2.3 Solution of the Linear Equations System
  • 4.3 Simulation Implementation in COMSOL Multiphysics
    • 4.3.1 Finite Element Method Procedure in COMSOL Multiphysics
    • 4.3.2 Finite Element Analysis for Electromigration Study
  
  
• 5. Case Studies of Electromigration in Interconnects
  • 5.1 Electromigration Failure in Open TSVs
    • 5.1.1 TSV Design and Simulation Parameters
    • 5.1.2 Void Nucleation Analysis
    • 5.1.3 Void Growth Analysis
    • 5.1.4 Lifetime Estimation
  • 5.2 Electromigration Reliability of Solder Bumps
    • 5.2.1 Geometry and Simulation Parameters
    • 5.2.2 Location of Void Nucleation
    • 5.2.3 Compact Model for Lifetime Estimation
  • 5.3 Effect of Current Crowding and Microstructure
    • 5.3.1 Geometries and Model Parameters
    • 5.3.2 Current Crowding
    • 5.3.3 Impact of Microstructure
  
  
• 6. Summary and Outlook
  
  
• Bibliography
• List of Publications
• Curriculum Vitae
• About this document ...