Interfacial Delamination Between Through Silicon Vias (TSVs) and Silicon Matrix

2010 ◽  
Author(s):  
Kuan Hsun Lu ◽  
Suk-Kyu Ryu ◽  
Qiu Zhao ◽  
Rui Huang ◽  
Paul S. Ho
Keyword(s):  
Steady State ◽  
Analytical Solutions ◽  
Driving Force ◽  
Heating Process ◽  
Thermal Cycles ◽  
Through Silicon Vias ◽  
Silicon Matrix ◽  
Interfacial Delamination ◽  
Silicon Vias ◽  
The Impact

Recently, three-dimensional (3-D) integration with through silicon vias (TSVs) has emerged as an effective solution for interconnect structures beyond the 32-nm technology node in microelectronics. Among others, thermo-mechanical reliability is a key concern for the development of TSV structures used in 3-D interconnects. This paper examines the thermal stress-induced delamination between through silicon via (TSV) and the silicon matrix. First, the driving force for TSV delamination was derived for a long crack at the steady state, and then the analytical solutions were validated using finite element analysis (FEA). The analytical solutions and simulation results were found to be in good agreement at the steady state, and together they suggested a fracture mechanism to account for the TSV delamination observed. The analytical solution further provided a basic framework for studying the impact of materials, process and structural design on reliability of the TSV structure. In particular, we found that reducing the thermal mismatch and TSV diameter yield definite advantages in lowering the crack driving force for TSV delamination. Such driving force can also be controlled by introducing an annular metal filling or a dielectric liner between TSV and the Si matrix. Finally, the TSV protrusion phenomenon during thermal cycles was investigated. The interfacial delamination was found to initiate during a cooling process and to develop under a subsequent heating process, causing TSVs to protrude from the silicon matrix after repeated thermal cycles.

Driving forces and structural changes of China as a market provider for Korea

2018 ◽  
Vol 22 (3) ◽  
pp. 194-211 ◽  
Author(s):  
Yongqi Feng ◽  
Tianshu Zhang
Keyword(s):  
Steady State ◽  
Driving Force ◽  
Design Methodology ◽  
Structural Changes ◽  
Driving Forces ◽  
Consumption Expenditure ◽  
Input Output ◽  
Content Type ◽  
Fixed Capital Formation ◽  
The Impact

Purpose The purpose of this paper is to provide a better understanding of the driving forces and structural changes of China as a market provider for Korea. This paper gives the answers for the following questions: How do China’s final demands trigger the growth of its imports from Korea? And what’s the impact of China’s final demands on the import in different industries? Design/methodology/approach Based on the Multi-Regional Input-Output model and World Input-Output Table database, this paper constructs the non-competitive imports input-output (IO) table of China to Korea. According to this table, we can calculate the induced imports coefficient and comprehensive induced import coefficients of China’s four final demands for imports from Korea in the 56 industries in China. Findings Among the four driving forces, the strongest one is changes in inventories and valuables. The impact of final consumption expenditure and fixed capital formation is much lower than that of changes in inventories and valuables, but they have a broader impact for the 56 industries. This paper finds out the China’s import induction of the final demands to Korea peaked in 2005 and 2010 and decreased greatly in 2014, so the position of China as market provider for Korea will no longer rise substantially, contrarily it will be in a steady state. Originality/value First, this paper constructs the non-competitive IO table to analyze the market provider issues between two countries and provides practical ways and methods for studies on the issues of imports and market provider. Second, this paper investigates the different roles of four final demands on driving force of China as market provider for Korea and the structural changes of China as a market provider for Korea among 56 industries from 2000 to 2014.

SEMI-ANALYTICAL SOLUTIONS FOR THE BRUSSELATOR REACTION–DIFFUSION MODEL

2017 ◽  
Vol 59 (2) ◽  
pp. 167-182 ◽  
Author(s):  
H. Y. ALFIFI
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Partial Differential ◽  
Analytical Results ◽  
Transient Solutions ◽  
The Impact

Semi-analytical solutions are derived for the Brusselator system in one- and two-dimensional domains. The Galerkin method is processed to approximate the governing partial differential equations via a system of ordinary differential equations. Both steady-state concentrations and transient solutions are obtained. Semi-analytical results for the stability of the model are presented for the identified critical parameter value at which a Hopf bifurcation occurs. The impact of the diffusion coefficients on the system is also considered. The results show that diffusion acts to stabilize the systems better than the equivalent nondiffusive systems with the increasing critical value of the Hopf bifurcation. Comparison between the semi-analytical and numerical solutions shows an excellent agreement with the steady-state transient solutions and the parameter values at which the Hopf bifurcations occur. Examples of stable and unstable limit cycles are given, and Hopf bifurcation points are shown to confirm the results previously calculated in the Hopf bifurcation map. The usefulness and accuracy of the semi-analytical results are confirmed by comparison with the numerical solutions of partial differential equations.

Synchrotron-based measurement of the impact of thermal cycling on the evolution of stresses in Cu through-silicon vias

2014 ◽  
Vol 115 (24) ◽  
pp. 243509 ◽  
Author(s):  
Chukwudi Okoro ◽  
Lyle E. Levine ◽  
Ruqing Xu ◽  
Klaus Hummler ◽  
Yaw Obeng
Keyword(s):  
Thermal Cycling ◽  
Through Silicon Vias ◽  
Silicon Vias ◽  
The Impact

scholarly journals The Landslide Velocity

2021 ◽  
Author(s):  
Shiva P. Pudasaini ◽  
Michael Krautblatter
Keyword(s):  
Analytical Solutions ◽  
Driving Force ◽  
Dissipative System ◽  
Viscous Drag ◽  
Breaking Wave ◽  
Physical Point ◽  
Technical Problems ◽  
Non Linear ◽  
Applied Forces ◽  
The Impact

Abstract. Proper knowledge of velocity is required in accurately determining the enormous destructive energy carried by a landslide. We present the first, simple and physics-based general analytical landslide velocity model that simultaneously incorporates the internal deformation (non-linear advection) and externally applied forces, consisting of the net driving force and the viscous resistant. From the physical point of view, the model stands as a novel class of non-linear advective – dissipative system where classical Voellmy and inviscid Burgers' equation are specifications of this general model. We show that the non-linear advection and external forcing fundamentally regulate the state of motion and deformation, which substantially enhances our understanding of the velocity of a coherently deforming landslide. Since analytical solutions provide the fastest, the most cost-effective and the best rigorous answer to the problem, we construct several new and general exact analytical solutions. These solutions cover the wider spectrum of landslide velocity and directly reduce to the mass point motion. New solutions bridge the existing gap between the negligibly deforming and geometrically massively deforming landslides through their internal deformations. This provides a novel, rapid and consistent method for efficient coupling of different types of mass transports. The mechanism of landslide advection, stretching and approaching to the steady-state has been explained. We reveal the fact that shifting, up-lifting and stretching of the velocity field stem from the forcing and non-linear advection. The intrinsic mechanism of our solution describes the fascinating breaking wave and emergence of landslide folding. This happens collectively as the solution system simultaneously introduces downslope propagation of the domain, velocity up-lift and non-linear advection. We disclose the fact that the domain translation and stretching solely depends on the net driving force, and along with advection, the viscous drag fully controls the shock wave generation, wave breaking, folding, and also the velocity magnitude. This demonstrates that landslide dynamics are architectured by advection and reigned by the system forcing. The analytically obtained velocities are close to observed values in natural events. These solutions constitute a new foundation of landslide velocity in solving technical problems. This provides the practitioners with the key information in instantly and accurately estimating the impact force that is very important in delineating hazard zones and for the mitigation of landslide hazards.

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