By Cher Ming Tan, Wei Li, Zhenghao Gan, Yuejin Hou
Applications of Finite point equipment for Reliability reports on ULSI Interconnections offers an in depth description of the applying of finite aspect tools (FEMs) to the examine of ULSI interconnect reliability. during the last 20 years the appliance of FEMs has develop into frequent and keeps to steer to a far better realizing of reliability physics.
To aid readers do something about the expanding sophistication of FEMs’ functions to interconnect reliability, Applications of Finite aspect equipment 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 sensible standpoint, incorporating the Monte Carlo method.
A full-scale evaluation of the numerical modeling technique utilized in the research of interconnect reliability highlights invaluable and remarkable recommendations which were built lately. Many illustrations are used during the publication to enhance the reader’s figuring out of the technique and its verification. real experimental effects and micrographs on ULSI interconnects also are included.
Applications of Finite aspect equipment for Reliability reviews on ULSI Interconnections is an effective reference for researchers who're engaged on interconnect reliability modeling, in addition to if you happen to need to know extra approximately FEMs for reliability functions. It offers readers a radical realizing of the purposes of FEM to reliability modeling and an appreciation of the strengths and weaknesses of varied numerical versions for interconnect reliability.
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Extra resources for Applications of Finite Element Methods for Reliability Studies on ULSI Interconnections
The physical mechanism of the stress development and relaxation have been studied [41, 42]. For example, chip with electroplated Cu interconnects consists of small grains initially. If the lines are not annealed properly before encapsulation, subsequent annealing will cause grain growth, resulting in grain growth-induced stress in the line . The stress-induced voids can deteriorate the EM lifetime of an interconnect as observed experimentally . The failure site varies in interconnects under thermo-mechanical stress.
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. The order parameter takes on distinct uniform values within the material and the void, varying rapidly from one to the other over narrow interfacial layers associated with the void surface. They derived the field equations for the order parameters based on the microforce balance principle of Gurtin . Accordingly, they expressed the free energy of the line as ' Z & Z 2cs 1 2 2 Fð/; r/; uÞdV ¼ f ð/Þ þ u jr/j þ Wðu; /Þ dV Fð/; uÞ ¼ 2 R R up ð2:33Þ where f(/) is the bulk free energy, cs is the isotropic surface energy, u is a parameter that controls the thickness of the interfacial layer associated with the void surfaces, and W is the elastic strain energy.
1D EM modeling is only capable of simulating the simplified scenarios of EM due to its limitation on dimensionality. The influence of the triple points of the multiple grain textures, the surrounding materials and the induced thermomechanical stress, the shape of the metal line or the microstructure of the interconnects were poorly addressed in the 1D modeling. The consideration of the EM from thermodynamics aspect, such as the various diffusion paths for atoms diffusion, was highly simplified in the 1D model.
Applications of Finite Element Methods for Reliability Studies on ULSI Interconnections by Cher Ming Tan, Wei Li, Zhenghao Gan, Yuejin Hou