Contents

• 1. Introduction
  • 1.1 Silicon Technology CAD
  • 1.2 Interconnect Reliability
  • 1.3 IC Fabrication Process Steps
  • 1.4 Components of a Numerical Solution Method
    • 1.4.1 Mathematical Model
    • 1.4.2 Discretization Method
    • 1.4.3 Mesh
    • 1.4.4 Accuracy
  • 1.5 Motivation and Outline of the Thesis
  
  
• 2. Finite Element Method
  • 2.1 The Systems of Partial Differential Equations
  • 2.2 Rayleigh-Ritz Method
  • 2.3 Galerkin's Method
  • 2.4 Time Dependent Problems
  • 2.5 Finite Element Spaces and Meshes
  • 2.6 Newton Methods
    • 2.6.1 Introduction
    • 2.6.2 Basic Newton Method
    • 2.6.3 Simplified Newton Method
    • 2.6.4 Damping
  • 2.7 Assembling
  • 2.8 General Solving Procedure
  • 2.9 Time Step and Mesh Control
  
  
• 3. Diffusion Phenomena in Semiconductors
  • 3.1 The Physics of Diffusion
  • 3.2 Interaction of Dopants with Simple Native Point Defects
    • 3.2.1 Charge Exchange Reactions
    • 3.2.2 Dopant and Point Defect Reactions
  • 3.3 Equilibrium Diffusion
    • 3.3.1 Intrinsic Diffusion
    • 3.3.2 Extrinsic Diffusion
    • 3.3.3 Vacancy-Only Assisted Diffusion
  • 3.4 Nonequilibrium Models
    • 3.4.1 Simple Point Defect Model
    • 3.4.2 Three-Stream Mulvaney-Richardson Model
    • 3.4.3 Five-Stream Dunham Model
  • 3.5 Boundary and Interface Conditions
    • 3.5.1 Dirichlet Boundary Condition
    • 3.5.2 Neumann Boundary Condition
    • 3.5.3 Segregation Interface Condition
    • 3.5.4 Surface Reactions
  • 3.6 The Plus-One Model
  • 3.7 Dopant Diffusion in the Presence of Exdendend Crystal Defects
  • 3.8 Numerical Handling of the Diffusion Models
    • 3.8.1 Discretization of the Simple Diffusion Model
    • 3.8.2 Discretization of the Simple Extrinsic Diffusion Model
    • 3.8.3 Discretization of the Three-Stream Mulvaney-Richardson Model
    • 3.8.4 Analytical Solution of the Segregation Problem for One Dimension
    • 3.8.5 Numerical Handling of the Segregation Model
  • 3.9 Dosis Conservation
  • 3.10 Simulation Results
    • 3.10.1 Equilibrium Diffusion at the Silicon/Silicon-Dioxide Interface
    • 3.10.2 Point Defect Assisted Diffusion
  
  
• 4. Electromigration Problem in the Interconnect
  • 4.1 Integrating Void Pre-Nucleation and Void Evolution
  • 4.2 The Physics of Electromigration
  • 4.3 Electromigration TCAD Solutions
    • 4.3.1 Black's Law
    • 4.3.2 Modeling of the Electromigration Promoting Factors
  • 4.4 Prediction of the Voids Nucleation Sites
    • 4.4.1 Korhonen's Model
    • 4.4.2 Analytical Solution of Korhonen's Equation
    • 4.4.3 The Sink/Source Term
    • 4.4.4 An Explanation of Black's Law
    • 4.4.5 Sarychev's Model
    • 4.4.6 Finite Element Discretization of the Basic Equation
  • 4.5 Void evolution and Interconnect Resistance Change Models
    • 4.5.1 Theoretical Formulation
    • 4.5.2 The Diffuse Interface Model
    • 4.5.3 Numerical Implementation
    • 4.5.4 Setting of the Initial Order Parameter Profile and Initial Grid Refinement
    • 4.5.5 Finite Element Scheme
    • 4.5.6 Maintaining the Grid during Simulation
    • 4.5.7 Grid Adaptation
    • 4.5.8 Solving Procedure
  • 4.6 Simulation Results
    • 4.6.1 Two-Dimensional Void Evolution
    • 4.6.2 Estimating the Void Growth Time and Resistance Change
    • 4.6.3 A Study of Electromigration Promoting Factors and Vacancy Dynamics
  
  
• 5. Summary and Outlook
• A. Vacancies in Solids
• B. Some Tools from Abstract Mathematical Analysis
• Bibliography
• Own Publications