Thermal Stresses of Through Silicon Vias and Si Chips in Three Dimensional System in Package

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Takahiro Kinoshita ◽  
Takashi Kawakami ◽  
Tatsuhiro Hori ◽  
Keiji Matsumoto ◽  
Sayuri Kohara ◽  
...  

Thermal conduction and mechanical stresses in through silicon via (TSV) structures in three dimensional system in package (3D SiP) under device operation condition were discussed. A large scale simulator, ADVENTURECluster® based on finite element method (FEM) was used to simulate the effects of voids formed inside Cu TSVs on the thermal conduction and mechanical stresses in the TSV structure. The thermal performance that was required in 3D SiP was estimated to ensure the reliability. Simulations for thermal stresses in the TSV structure in 3D SiP were carried out under thermal condition due to power ON/OFF of device. In case that void was not present inside the TSV, the stresses in TSV were close to the hydrostatic pressure and the magnitude of the equivalent stress was lower than the yield stress of copper. Maximum principal stress of the Si chip in the TSV structure for the case without voids was lower than that of the bending strength of silicon. However, the level of the stresses in the Si chips should not be negligible for damages to Si chips. In case that void was present inside the TSV, stress concentration was occurred around the void in the TSV. The magnitude of the equivalent stress in the TSV was lower than the yield stress of copper. The magnitude of the maximum principal stress of the Si chip was lower than that of the bending strength of silicon. However, its level should not be negligible for damages to TSVs and Si chips. The stress on inner surfaces of Si chip was slightly reduced due to the presence of a void in the TSV.

Author(s):  
Takahiro Kinoshita ◽  
Takashi Kawakami ◽  
Tatsuhiro Hori ◽  
Keiji Matsumoto ◽  
Sayuri Kohara ◽  
...  

Thermal conduction and mechanical strength around TSV (Through Silicon Via) structures of 3D SiP (Three Dimensional System in Package) were discussed both cases of with and without void in TSV by using a large scale simulator based on FEM, ADVENTURECluster® for ensuring the reliability of 3D SiP. In the results, the thermal performance that was required in 3D SiP was estimated to ensure the reliability. Simulations for thermal stresses around TSV structure in 3D SiP under thermal cycle condition due to power ON/OFF were carried out. In case that void was not in TSV, stresses in TSV were close to hydrostatic pressure and the magnitude of the equivalent stress was lower than the yield stress of copper. However, the level of the stresses, especially in Si chips, should not be negligible in inducing damages to TSVs and Si single crystals. In case that void was in TSV, stress was concentrated around void in TSV and the magnitude of the equivalent stress was lower than the yield stress of copper. The level of stresses applied to Si chip was slightly reduced due to void in TSV. However, its level should not be negligible in inducing damages to TSVs and Si single crystals.


Author(s):  
Takahiro Kinoshita ◽  
Takashi Kawakami ◽  
Takeshi Wakamatsu ◽  
Shunpei Shima ◽  
Keiji Matsumoto ◽  
...  

Stresses and mechanical strength of brittle materials (Si chip and insulator) around TSV (Through Silicon Via) structures in 3D SiP (Three Dimensional System in Package) were discussed under device operation condition and reflow process condition by using a large scale simulator ADVENTURECluster®, which was based on FEM (Finite Element Method), for ensuring the reliability of 3D SiP. In case of the device operation, the equivalent stress of TSV were lower than yield stress of copper, and the maximum principal stress of Si and insulator were also lower than its bending strength. In case of the reflow process, the equivalent stress of TSV were over the yield stress of copper, and the maximum principal stresses of Si and insulator were closed to its bending strength. In addition, steep stress elevations were shown at edge part of Si and insulator. It will be a singular stress field by stress concentration. Its stress singularity was evaluated and the local strength of Si chip and insulator was discussed.


Author(s):  
Toshiyuki Sawa ◽  
Yuya Hirayama ◽  
He Dan

The stress wave propagation and stress distribution in scarf adhesive joints have been analyzed using three-dimensional finite element method (FEM). The FEM code employed was LS-DYNA. An impact tensile loading was applied to the joint by dropping a weight. The effect of the scarf angle, Young’s modulus of the adhesive and adhesive thickness on the stress wave propagations and stress distributions at the interfaces have been examined. As the results, it was found that the point where the maximum principal stress becomes maximum changes between 52 degree and 60 degree under impact tensile loadings. The maximum value of the maximum principal stress increases as scarf angle decreases, Young’s modulus of the adhesive increases and adhesive thickness increases. In addition, Experiments to measure the strains and joint strengths were compared with the calculated results. The calculated results were in fairly good agreements with the experimental results.


2013 ◽  
Vol 404 ◽  
pp. 365-370 ◽  
Author(s):  
Qi Tao Pei ◽  
Hai Bo Li ◽  
Ya Qun Liu ◽  
Jun Gang Jiang

During the construction of hydropower station, the change of slope gradient in river valleys often takes place. In order to study influence of slope gradient change on distribution rule of geostress field, the three dimensional unloading models under different slope gradients were established by finite difference software (FLAC3D). After numerical simulation, the results were as follows: (1) The phenomenon of stress concentration at the bottom of river valleys was obvious, which appeared the typical stress fold. Both the depth of stress concentration zone and the principal stress values significantly increased with the increment of slope gradient. (2) Maximum principal stress values increased less in shallow part of upper bank slope (low stress zone) but increased more in the nearby slope foot with the increment of slope gradient, causing great difference in geostress field of bank slope. (3) There was some difference in released energy of bank slope due to slope gradient change in river valleys. In order to distinguish the difference, stress relief zone was further divided into stress stably released zone and stress instability released zone. Finally, take Ada dam area of the western route project of South-to-North Water Transfer as an example, the results by numerical simulation were reliable through comparing the distribution rule of geostress field for the dam, which could provide important reference for stability of the design and construction of steep and narrow river valleys.


1996 ◽  
Vol 74 (1-2) ◽  
pp. 4-9
Author(s):  
M. R. M. Witwit

The energy levels of a three-dimensional system are calculated for the rational potentials,[Formula: see text]using the inner-product technique over a wide range of values of the perturbation parameters (λ, g) and for various eigenstates. The numerical results for some special cases agree with those of previous workers where available.


1976 ◽  
Vol 15 (2) ◽  
pp. 197-222
Author(s):  
R. J. Hartman

This paper uses the general solution of the linearized initial-value problem for an unbounded, exponentially-stratified, perfectly-conducting Couette flow in the presence of a uniform magnetic field to study the development of localized wave-type perturbations to the basic flow. The two-dimensional problem is shown to be stable for all hydrodynamic Richardson numbers JH, positive and negative, and wave packets in this flow are shown to approach, asymptotically, a level in the fluid (the ‘isolation level’) which is a smooth, continuous, function of JH that is well defined for JH < 0 as well as JH > 0. This system exhibits a rich complement of wave phenomena and a variety of mechanisms for the transport of mean flow kinetic and potential energy, via linear wave processes, between widely-separated regions of fluid; this in addition to the usual mechanisms for the absorption of the initial wave energy itself. The appropriate three-dimensional system is discussed, and the role of nonlinearities on the development of localized disturbances is considered.


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