Contents
List of Abbreviations
List of Symbols
List of Figures
List of Tables
1 Introduction
 1.1 Integrated Circuits
 1.2 Interconnect Structures
  1.2.1 2D Integrated Circuit
  1.2.2 2.5D and 3D Integrated Circuit
 1.3 Through Silicon Vias
  1.3.1 TSV Fabrication
  1.3.2 TSV Metalization
  1.3.3 Current and Future TSV Applications
 1.4 Reliability of Interconnect Structures
 1.5 FEM Approach for Reliability
 1.6 Outline of the Thesis
2 Overview of Solid Mechanics and the Finite Element Method
 2.1 Continuum Mechanics
  2.1.1 Deformation and Strain
  2.1.2 Stress
  2.1.3 Constitutive Laws
   2.1.3.1 Elasticity
 2.2 Plane Strain and Plane Stress
  2.2.1 Plane Strain
  2.2.2 Plane Stress
 2.3 Source of Residual Stress in Thin Films
  2.3.1 Intrinsic Stress
  2.3.2 Thermal Strain and Thermal Stress
 2.4 Virtual Work
 2.5 Fracture Mechanics
 2.6 FEM
  2.6.1 Weighted Residual Method
  2.6.2 Weak Formulation
  2.6.3 Spatial Discretization
 2.7 FEM for Solid Mechanics
3 Stress Evolution during 3D IC Stacking using Open TSVs
 3.1 Stress Generation during 3D IC Stacking
 3.2 Nanoindentation
 3.3 FEM Approach
  3.3.1 Simulation Setup
  3.3.2 Plasticity Simulation
 3.4 Results and Discussions
 3.5 Summary
4 Fracture Mechanics and Delamination in Open TSVs
 4.1 Basis of Fracture Mechanics
  4.1.1 Crack-Tip Field
  4.1.2 Delamination
  4.2.0 Energy Release Rate
  4.2.1 Failure Criterion
 4.3 Energy Release Rate Calculation
  4.3.1 J-Integral
  4.3.2 Regression Analysis
 4.4 Delamination Prediction at TSV Bottom
  4.4.1 Studied System
  4.4.2 Approach
  4.4.3 Results
   4.4.3.1 Residual Stress Analysis
   4.4.3.2 Thickness Analysis
   4.4.3.3 Force Analysis
  4.4.4 Discussion
 4.5 Experimental Analysis
  4.5.1 Experiment - Four Point Bend Technique
  4.5.2 Simulation
  4.5.3 Simulation Results
  4.5.4 Discussion
 4.6 Comparison between J-Integral and
Regression Analysis
  4.6.1 Structure
  4.6.2 Results and Discussion
 4.7 Summary
5 Simulation of Intrinsic Stress Build-Up in Thin Metal Films
 5.1 Introduction
 5.2 Theoretical Background
  5.2.1 Volmer-Weber Growth
  5.2.2 DRIE Scallop Formation
 5.3 Volmer-Weber Model for Thin Films
  5.3.1 Geometry
  5.3.2 First Step: Compressive Stress
  5.3.3 Second Step: Island Coalescence Process
  5.3.4 Third Step: Thickening
 5.4 Results
  5.4.1 Low Adatom Mobility Analysis
   5.4.1.1 Sample Description
   5.4.1.2 Island Nucleation and Expansion
   5.4.1.3 Island Coalescence and Grain Formation
   5.4.1.4 Effects of the Island Shapes
   5.4.1.5 Influence of Scallops
   5.4.1.6 Effects of the Scallop Geometry (Width & Height)
   5.4.1.7 Overtaking of Grains
  5.4.2 High Adatom Mobility Analysis
   5.4.2.1 Temperature Effects
   5.4.2.2 Growth Rate Effects
 5.5 Summary
6 Summary and Outlook
A Kolosov-Muskhelishvili Formulas
 A.1 Airy Stress Function
 A.2 Analytic Function and Complex Variable
 A.3 Complex Representation of the Airy Stress Function
 A.4 Stress and Displacement described by
Airy Stress Function
B Westergaard Approach
Bibliography