Contents

1.1 Interconnect Structures in Microelectronics

1.2 Aluminium Based Interconnect Fabrication

1.3 Copper Based Interconnect Fabrication

1.4 Three-Dimensional Integration

1.6 Failure Mechanisms in Interconnects

1.7 Electromigration Induced Failures

2.1 Historic Outline of Electromigration

2.2 Quantum Mechanical Electromigration Description

3.2 Electromigration in Bulk Metals

3.3 Electromigration at Interfaces

3.4 Continuum Mechanical Model

5.3 The Three Phases of the Electromigration Induced Vacancy Accumulation

5.4 Electromigration Induced Stress at the Interfaces of Open TSVs

5.6 Resistance Development due to Void Evolution

A The Asymptotic Limit of the Phase Field Model

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2D | Two-Dimensional |

3D | Three-Dimensional |

CMOS | Complementary Metal-Oxide-Semiconductor |

CVD | Chemical Vapor Deposition |

DRIE | Deep Reactive Ion Etch |

EM | Electromigration |

FEDOS | Finite Element Diffusion and Oxidation Simulator |

FEM | Finite Element Method |

GB | Grain Boundary |

IC | Integrated Circuit |

ILD | Inter-Level Dielectric |

IVD | Inter-Via Dielectric |

KKR | Korringa-Kohn-Rostoker |

LKKR | Layer KKR |

PDE | Partial Differential Equations |

PECVD | Plasma Enhanced CVD |

TCAD | Technology Computer Aided Design |

TSV | Through Silicon Via |

TTF | Time to Failure |

UV | Ultraviolet |

Area | |

Applicable Mechanical Modulus | |

Atom Concentration | |

Specific Heat Capacity | |

Vacancy Concentration | |

Equilibrium Vacancy Concentration | |

Grain Size | |

Atom Diffusion Coefficient | |

Effective Diffusion Coefficient | |

Grain Boundary Diffusion Coefficient | |

Surface Diffusion Coefficient | |

Vacancy Diffusion Coefficient | |

Electric Field | |

Unit Charge | |

Activation Energy | |

Mechanical Force | |

Relaxation Factor | |

Current Density | |

Atom Flux | |

Vacancy Flux | |

Boltzmann Constant | |

Heat of Transport | |

Joule Heat Generated per Time | |

Flaw Radius | |

Temperature | |

Reference Temperature | |

Displacement Field | |

Volume | |

Elastic Strain Energy | |

Effective Valence | |

C | Elastic Tensor |

Grain Boundary Width | |

Kronecker Delta | |

Mechanical Strain | |

Phase Field Interface Thickness Parameter | |

Temperature Induced Mechanical Strain | |

Vacancy Related Mechanical Strain | |

Electric Potential | |

Surface Energy | |

Surface Curvature | |

Lamè Parameter | |

Thermal Conductivity | |

Chemical Potential | |

Specific Electric Resistance | |

Material Density | |

Isotropic Stress | |

Electric Conductivity | |

Threshold Stress for Void Nucleation | |

Characteristic Relaxation Time | |

Atomic Volume |

1.2 Cut through a single and dual-damascene interconnect structure [61].

1.3 Schematic of a chip-to-wafer bonded structure. Stapled dies hold together by solder bumps.

1.5 Schematic of the Bosch process.

3.2 Schematics for the derivation of the segregation model according to [90].

4.1 Example meshing elements for 2D and 3D domains.

4.2 An example mesh for an shaped structure with a fillet.

4.4 The hat test function for a single node located in the middle.

4.5 Flowchart of the EM simulation in FEDOS.

4.6 Flowchart of the EM simulation in COMSOL.

4.7 Flowchart of the EM induced void simulation in COMSOL.

5.1 Schematics of the current crowding calculation at a corner.

5.9 Component of the current density vector normal to the interface.

5.11 Simulation of a highly blocking interface for different time steps in arbitrary units.

5.12 Variation of the equilibrium concentration in the interface region.

5.14 The maximum concentration of vacancies piled up at the interface.

5.15 Maximum Von Mises stress build-up at the interface.

5.20 Maximum Von Mises stress build-up at the interface for different currents.

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