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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 aspect equipment for Reliability experiences on ULSI Interconnections presents an in depth description of the applying of finite aspect equipment (FEMs) to the examine of ULSI interconnect reliability. during the last twenty years the appliance of FEMs has turn into frequent and maintains to steer to a far better figuring out of reliability physics.

To aid readers deal with the expanding sophistication of FEMs’ purposes to interconnect reliability, Applications of Finite aspect equipment for Reliability stories on ULSI Interconnections will:

  • introduce the main 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 standpoint, incorporating the Monte Carlo method.

A full-scale overview of the numerical modeling technique utilized in the examine of interconnect reliability highlights precious and memorable concepts which have been constructed lately. Many illustrations are used during the ebook to enhance the reader’s realizing of the technique and its verification. genuine experimental effects and micrographs on ULSI interconnects also are included.

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

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The typical EM diffusion paths include interface diffusion, grain boundary diffusion, and lattice diffusion inside a grain. Numerical method, such as finite element analysis, is needed to solve the EM equations in a coupled manner with current density, temperature, and stress distributions. Most of the proposed 1D and 2D models investigate the EM within the interconnect material itself, and the effect of the surrounding materials on the interconnect EM is not taken into consideration. However, as the interconnect line width goes into 150 nm and below, and with the use of the low-k dielectric, the impact of the surrounding materials on the interconnect EM becomes significant.

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). Comparing Eq. 24 with Eq. 14, we have the following corresponding parameters: aðrÞ ¼ Àðr þ 1Þ; bðrÞ ¼ 0; f ðrÞ ¼ 0; r1 ¼ 1; r2 ¼ 2: Thus, for this example, Eq. 19 can be expressed as: Z2 ! d dT /i Á Á dr; ðr þ 1Þ Á dr dr i ¼ 1; 2; . ; n ð3:26Þ 1 In order to solve Eq.

Assume an initial flaw exist in a metal line and is large enough that the stress near the flaw is zero. In this case, Eq. 38 is identical to the usual diffusion equation with K acts as the diffusivity. 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.

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