Applications of Finite Element Methods for Reliability by Cher Ming Tan, Wei Li, Zhenghao Gan, Yuejin Hou

By Cher Ming Tan, Wei Li, Zhenghao Gan, Yuejin Hou

Applications of Finite point equipment for Reliability stories on ULSI Interconnections presents a close description of the applying of finite point tools (FEMs) to the learn of ULSI interconnect reliability. during the last twenty years the appliance of FEMs has develop into frequent and keeps to steer to a far better figuring out of reliability physics.

To support readers deal with the expanding sophistication of FEMs’ functions to interconnect reliability, Applications of Finite aspect tools for Reliability reports on ULSI Interconnections will:

  • introduce the primary of FEMs;
  • review numerical modeling of ULSI interconnect reliability;
  • describe the actual mechanism of ULSI interconnect reliability encountered within the electronics undefined; and
  • discuss intimately using FEMs to appreciate and enhance ULSI interconnect reliability from either the actual and useful viewpoint, incorporating the Monte Carlo method.

A full-scale evaluation of the numerical modeling method utilized in the research of interconnect reliability highlights important and memorable innovations which have been built lately. Many illustrations are used during the e-book to enhance the reader’s realizing of the method and its verification. real experimental effects and micrographs on ULSI interconnects also are included.

Applications of Finite point tools for Reliability reports on ULSI Interconnections is an effective reference for researchers who're engaged on interconnect reliability modeling, in addition to in the event you need to know extra approximately FEMs for reliability purposes. It offers readers an intensive realizing of the purposes of FEM to reliability modeling and an appreciation of the strengths and weaknesses of assorted numerical types for interconnect reliability.

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At nearly the same time as Mahadevan and Bradley, Bhate et al. [39] reported their own version of the phase field model for simulating the process of electron wind force migration, curvature-driven surface migration, and the stress-driven migration. In their work, Bhate et al. [39] briefly discussed the theory of the sharp interface model and its limitations and disadvantages. They then proposed their own phase field model. Their approach is based on the introduction of an order parameter field to characterize the damaged state of an interconnect.

Korhonen MA, Black RD, Li C-Y (1993) Stress evolution due to electromigration in confined metal lines. J Appl Phys 73:3790–3799 73. Zhai CJ, Blish RC (2005) A physically based lifetime model for stress-induced voiding in interconnects. J Appl Phys 97:113503 74. Fischer AH, Zitzelsberger AE (2001) The quantitative assessment of stress-induced voiding in process qualification. In: Proceedings of 39th IEEE/IRPS conference, Orlando, Florida, IEEE, New York, pp 334–340 75. Tan CM, Hou Y (2007) Lifetime modeling for stress-induced voiding in integrated circuit interconnections.

Finite element formulation can be derived using this variational formulation as long as there exists a variational principle corresponding to the problem of interest. An example is a very important physical principle to describe a deformation process of an elastic body, namely the Principle of Minimum Total Potential Energy, which can be summarized as follows. The total potential energy of an elastic body is given in E ¼ X þ Y : Total Potential Energy ð3:12Þ where X is strain energy, and Y is potential energy, they are from external loads.

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