By Cher Ming Tan, Wei Li, Zhenghao Gan, Yuejin Hou
Applications of Finite aspect tools for Reliability experiences on ULSI Interconnections presents an in depth description of the appliance of finite aspect equipment (FEMs) to the research of ULSI interconnect reliability. during the last 20 years the applying of FEMs has develop into common and keeps 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 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 standpoint, incorporating the Monte Carlo method.
A full-scale assessment of the numerical modeling method utilized in the examine of interconnect reliability highlights precious and remarkable recommendations which have been built lately. Many illustrations are used during the e-book to enhance the reader’s knowing of the method and its verification. genuine experimental effects and micrographs on ULSI interconnects also are included.
Applications of Finite aspect tools for Reliability experiences on ULSI Interconnections is an efficient reference for researchers who're engaged on interconnect reliability modeling, in addition to when you need to know extra approximately FEMs for reliability purposes. It supplies readers a radical realizing of the functions 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
In this method, w is defined in the form of Lagrange interpolation polynomials L(u) = 0 with u as unknown function to be solved. An example of a 1D boundary-value problem is given below for easier understanding of the weighted residual approach. Considering a general form of a governing DE: ! d du þ bðxÞ Á u À f ðxÞ ¼ 0; ÀaðxÞ Á dx dx x1 x x2 ð3:14Þ with the following boundary conditions: uðx1 Þ ¼ u1 uðx2 Þ ¼ u2 ÀaðxÞ Á or ÀaðxÞ Á or du dx du dx ! ¼ u1 at x ¼ x1 ¼ u2 at x ¼ x2 x1 ! x2 where x is the independent variable; x1 B x B x2 is the domain; u is the unknown function to be solved; a, b are the material or physical properties of the system; f(x) is the interior load; u ¼ ÀaðxÞ Á du=dx is the flux; du/dx is gradient of the unknown; u1, u2, u1, u2 is the boundary loads (with known values).
Bruynseraede C, Tokei Z, Iacopi F, Beyer GP, Michelon J, Maex K (2005) The impact of scaling on electromigration reliability. In: Proceedings of 43rd IEEE/IRPS conference, pp 7–17 82. Suo Z (2003) Interfacial and Nanoscale Failure. In: Gerberich W, Yang W (eds) Reliability of interconnect structures. Comprehensive Structural Integrity (Milne I, Ritchie RO, Karihaloo B, Editors-in-Chief), 8:265–324 83. Gan ZH, Shao W, Mhaisalkar SG, Chen Z, Gusak A (2006) Experimental and numerical studies of stress migration in Cu interconnects embedded in different dielectrics.
Numerous vacancies are generated thermodynamically in the metal interconnect at high temperatures, and they migrate due to the stress gradient and accumulate at vacancy sinks in the interconnect. The accumulation of the vacancies leads to the formation of voids. Based on the fact that vacancy migration and void growth are enhanced by the thermo-mechanical stress, stressinduced vacancy model was proposed in Aoyagi’s early work . In his work, the vacancy distribution was directly correlated with the thermo-mechanical stress distributions based on the stress-induced vacancy model, and the thermomechanical stress distribution was simulated using FEM.
Applications of Finite Element Methods for Reliability Studies on ULSI Interconnections by Cher Ming Tan, Wei Li, Zhenghao Gan, Yuejin Hou