Applications of Finite Element Methods for Reliability Studies on ULSI Interconnections

by Tan, Cher Ming; Gan, Zhenghao; Li, Wei; Hou, Yuejin

• ISBN13: 9780857293091
• ISBN10: 0857293095
• Format: Hardcover
• Copyright: 2011-03-07
• Publisher: Springer Verlag

Summary

Applications of Finite Element Methods for Reliability Studies on ULSI Interconnections provides a detailed description of the application of finite element methods (FEMs) to the study of ULSI interconnect reliability. Over the past two decades the application of FEMs has become widespread and continues to lead to a much better understanding of reliability physics.To help readers cope with the increasing sophistication of FEMs#xE2;#xAC;" applications to interconnect reliability, Applications of Finite Element Methods for Reliability Studies on ULSI Interconnections will:introduce the principle of FEMs;review numerical modeling of ULSI interconnect reliability;describe the physical mechanism of ULSI interconnect reliability encountered in the electronics industry; anddiscuss in detail the use of FEMs to understand and improve ULSI interconnect reliability from both the physical and practical perspective, incorporating the Monte Carlo method.A full-scale review of the numerical modeling methodology used in the study of interconnect reliability highlights useful and noteworthy techniques that have been developed recently. Many illustrations are used throughout the book to improve the reader#xE2;#xAC;"s understanding of the methodology and its verification. Actual experimental results and micrographs on ULSI interconnects are also included.Applications of Finite Element Methods for Reliability Studies on ULSI Interconnections is a good reference for researchers who are working on interconnect reliability modeling, as well as for those who want to know more about FEMs for reliability applications. It gives readers a thorough understanding of the applications of FEM to reliability modeling and an appreciation of the strengths and weaknesses of various numerical models for interconnect reliability.

Table of Contents

Introduction	p. 1
References	p. 3
Development of Physics-Based Modeling for ULSI Interconnections Failure Mechanisms: Electromigration and Stress-Induced Voiding	p. 5
Electromigration (EM) Modeling Review	p. 5
One-Dimensional (1D) Analytical Modeling	p. 5
Two-Dimensional (2D) Modeling	p. 13
Summary	p. 21
Review on the Modeling of the Stress-Induced Voiding (SIV)	p. 22
Thermo-mechanical Stress Modeling	p. 23
Analytical Modeling of SIV	p. 26
Vacancy and Atomic Migration Model	p. 30
SIV for Nano-interconnects	p. 32
Summary	p. 34
References	p. 34
Introduction and General Theory of Finite Element Method	p. 39
History of Finite Element Method (FEM)	p. 39
Principle of FEM	p. 40
General Procedure of Finite Element Method	p. 42
Direct Approach	p. 42
Variational Approach	p. 44
Weighted Residual Approach	p. 44
Application Categories of Finite Element Method	p. 52
Commercial Software for Finite Element Method	p. 53
Methodology of Finite Element Method for Interconnect Study	p. 55
Thermal Analysis	p. 57
Stress Analysis	p. 60
Electrical Analysis	p. 63
Coupled-Field Analysis	p. 65
ANSYS Parametric Design Language (APDL)	p. 67
Conclusion	p. 70
References	p. 70
Finite Element Method for Electromigration Study	p. 73
Introduction	p. 73
A Review on the Electromigration Modeling Using FEM	p. 73
Computation Methods for Atomic Flux Divergence	p. 74
Voiding Mechanism Simulation	p. 77
Lifetime Prediction	p. 78
Summary	p. 79
Enhanced Finite Element Method Through Matlab	p. 80
Finite Element Model	p. 80
Simulation Methodology	p. 82
Simulation and Experimental Result	p. 83
Improved EM Simulation Methodology Based on the Green Function	p. 85
Derivation of Atomic Flux Divergence Using Green Function	p. 86
Finite Element Model of EM Using Green Theorem-Based AFD Formula	p. 89
Summary	p. 96
Monte Carlo Method for Electromigration Simulation	p. 97
The Application of Monte Carlo Method in EM Study	p. 97
A Holistic EM Modeling Using Monte Carlo Method and Finite Element Method	p. 99
Description of Simulation Methodology	p. 100
Result and Discussion of the Holistic Modeling	p. 104
Summary	p. 108
Conclusion	p. 109
References	p. 110
Finite Element Method for Stress-Induced Voiding	p. 113
Introduction	p. 113
FEM Model Description	p. 113
Finite Element Method Results	p. 116
Effect of Dielectric Materials on SIV	p. 119
Effect of Lower Layer Line Width on SIV	p. 123
Effect of via-Misalignment on SM	p. 127
Conclusion	p. 129
References	p. 129
Finite Element Method for Dielectric Reliability	p. 131
FEM on k-Value Extraction for Low-k Material	p. 131
FEM for Process-Induced Damage Evaluation	p. 135
FEM for k-Drift of Low-k Dielectric Materials	p. 138
FEM for Electric Field Simulation	p. 139
References	p. 145
Index	p. 147
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