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

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

Applications of Finite aspect tools for Reliability experiences on ULSI Interconnections offers a close description of the applying of finite point equipment (FEMs) to the research of ULSI interconnect reliability. over the last 20 years the appliance of FEMs has develop into frequent and maintains to guide to a more robust figuring out of reliability physics.

To support readers take care of the expanding sophistication of FEMs’ purposes to interconnect reliability, Applications of Finite aspect equipment for Reliability stories 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 functional standpoint, incorporating the Monte Carlo method.

A full-scale assessment of the numerical modeling technique utilized in the examine of interconnect reliability highlights valuable and memorable thoughts which have been built lately. Many illustrations are used during the ebook to enhance the reader’s knowing of the technique and its verification. real experimental effects and micrographs on ULSI interconnects also are included.

Applications of Finite point tools for Reliability stories on ULSI Interconnections is an effective reference for researchers who're engaged on interconnect reliability modeling, in addition to should you need to know extra approximately FEMs for reliability functions. It provides readers a radical knowing of the purposes of FEM to reliability modeling and an appreciation of the strengths and weaknesses of assorted numerical versions for interconnect reliability.

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Extra info for Applications of Finite Element Methods for Reliability Studies on ULSI Interconnections

Example text

2 Review on the Modeling of SIV 29 This effective bulk modulus B is dependent on the cross section of the interconnect as well as dielectric materials, and one can therefore inferred from Eq. 40 that a structure with a smaller B will lead to a longer SIV lifetime, if other things being the same. Fischer et al. proposed another model to formulate the SIV lifetime [47, 74]. Their derivation was based on the assumption that the change in the plastic strain leads to an increase of the void volume which is proportional to the increase of the line resistance.

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. Appl Phys Lett 91:061904 76. Ogawa ET, McPherson JW, Rosal JA, Dickerson KJ, Chiu T-C, Tsung LY, Jain MK, Bonifield TD, Ondrusek JC, Mckee WR (2002) Stress-induced voiding under vias connected to wide Cu metal leads.

3 General Procedure of Finite Element Method 47 where the terms in the stiffness matrix are given by Kij ¼ Zx2 ! 21 is similar to Eq. 8, and with Eq. 21, ai can be solved. A more specific example is given below. Here, we have the temperature distribution T(r) near the core of a reaction tube approximated by the following 1D governing equation ! d dT ¼ 0; ð1 x 2Þ ð3:24Þ ðr þ 1Þ Á dr dr where r is the distance from the center of the tube. The boundary conditions for Eq. 24 are T ð1Þ ¼ 1 and qð 2Þ ¼ 1 where q(r) is the heat flux given by qðrÞ ¼ Àðr þ 1Þ Á dT : dr ð3:25Þ The independent variable is r, and the unknown to be solved is T(r).

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