# 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 reviews on ULSI Interconnections presents an in depth description of the appliance of finite point equipment (FEMs) to the examine of ULSI interconnect reliability. during the last 20 years the applying of FEMs has develop into frequent and maintains to steer to an improved realizing of reliability physics.

To aid readers deal with the expanding sophistication of FEMs’ functions to interconnect reliability, Applications of Finite aspect tools for Reliability reviews 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 functional standpoint, incorporating the Monte Carlo method.

A full-scale evaluate of the numerical modeling method utilized in the examine of interconnect reliability highlights worthwhile and memorable options which were constructed lately. Many illustrations are used through the booklet to enhance the reader’s knowing of the method and its verification. real experimental effects and micrographs on ULSI interconnects also are included.

Applications of Finite aspect equipment for Reliability experiences 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 purposes. It provides readers an intensive figuring out 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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Extra info for Applications of Finite Element Methods for Reliability Studies on ULSI Interconnections

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The finite element analysis incorporating the size-dependent effects are still lacking for interconnects below 100 nm. Besides the SIV, large von Mises stress in interconnects may also cause reliability problems, particularly for Cu/low-k interconnects. Paik et al. [63] showed that the von Mises stress in low-k interconnects is larger than that of the SiO2based interconnect, through finite element analysis. A large von Mises stress within the interconnect system would result in failures in the form of plastic deformation.

To list a few: J. Jin, The FEM in Electromagnetics, 1st edn. 1993, Wiley S. J. Salon, Finite Element Analysis of Electrical Machines, 1995, Springer N. Bianchi, Electrical Machine Analysis Using Finite Elements, 2005, CRC Since 1990, FEM is being widely applied to understand the underlying physical mechanisms in VLSI reliability such as electromigration [4–8], stress migration [9–12], and dielectric breakdown [13, 14] Fig. 1 A schematic drawing of the discretization of the domain of interest into elements/nodes Element y x Node 42 3 Introduction and General Theory of Finite Element Method and heat fluxes in heat transfer analysis.

The early analytical models were based on the 26 2 Physics-Based Modeling for ULSI Interconnections Failure Mechanisms Eshelby theory of inclusions in which the line was modeled as an ellipsoidal cylinder embedded in an infinite isotropic matrix of the passivation material [60, 64]. However, these models did not capture the interaction between neighboring lines as well as the elastic properties of the substrate or sharp edges of the line. These two limitations were later overcome by Wikstrom et al.