By Cher Ming Tan, Wei Li, Zhenghao Gan, Yuejin Hou
Applications of Finite aspect equipment for Reliability stories on ULSI Interconnections offers a close description of the appliance of finite aspect tools (FEMs) to the learn of ULSI interconnect reliability. over the last 20 years the appliance of FEMs has develop into common and maintains to steer to an improved knowing of reliability physics.
To aid readers deal with the expanding sophistication of FEMs’ functions to interconnect reliability, Applications of Finite point tools for Reliability reports 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 viewpoint, incorporating the Monte Carlo method.
A full-scale overview of the numerical modeling technique utilized in the learn of interconnect reliability highlights worthy and remarkable concepts which have been constructed lately. Many illustrations are used in the course of the booklet to enhance the reader’s figuring out of the technique and its verification. genuine experimental effects and micrographs on ULSI interconnects also are included.
Applications of Finite point tools 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 purposes. 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 resources for Applications of Finite Element Methods for Reliability Studies on ULSI Interconnections
83] demonstrated that low-k interconnects suffered more from SIV at via bottom due to a higher stress gradient despite a lower thermo-mechanical stress. Based on the recent SIV model proposed by Tan and Hou , SIV performance for the low-k interconnects depends on the compromise between the confinement and the passivation effects. Since the passivation condition is highly process dependent, if one can assume that the passivation on Cu surface is the same for both Cu/SiO2 and Cu/low-k interconnects, Cu/low-k interconnects will outperform its counterpart in SIV due to a lower thermo-mechanical stress.
As the total potential energy is a function of state variables or a function of functions, which is called ‘‘functional,’’ the next task is to find the minimum through PDE given as oE ¼ 0; oui i ¼ 1; . ; n: ð3:13Þ By solving these series of equations, the values of the state variables at minimum E will be available. While the direct approach can be used to formulate element properties for only the simplest element shapes, the variational approach can be employed for both simple and complex element shapes.
By creating the void, a surface of area of 4pa2 is exposed, raising the free energy of the system by c4pa2. At the same time, atoms occupying the volume of 4pa3/3 is relocated from the void, allowing the remote stress to do the work by r4pa3/3. 10 shows the free energy as a function of the void radius. Based on Eq. 37, the critical void radius is given by a* = 2c/r. One can see from Fig. 10 that when the void is small, the surface energy dominates, and the void will shrink to reduce the free energy, rendering no void formation after some time.
Applications of Finite Element Methods for Reliability Studies on ULSI Interconnections by Cher Ming Tan, Wei Li, Zhenghao Gan, Yuejin Hou