Quasi-Static Modeling of the Self-Alignment Mechanism in Flip-Chip Soldering—Part I: Single Solder Joint

1991 ◽  
Vol 113 (4) ◽  
pp. 337-342 ◽  
Author(s):  
S. K. Patra ◽  
Y. C. Lee
Keyword(s):  
Flip Chip ◽  
Three Dimensional ◽  
The Self ◽  
Vertical Loading ◽  
Solder Volume ◽  
Static Modeling ◽  
Restoring Forces ◽  
Alignment Mechanism ◽  
Soldering Technology ◽  
Surface Profiles

A three-dimensional mathematical model simulating the self-alignment mechanism in the flip-chip soldering of a single joint has been developed. Based on the principle of energy minimization, it calculates the quasi-static surface profiles defined by the size of the solder pads, the solder volume, the surface tension coefficient, the vertical loading and the misalignment. The model is capable of calculating initial, intermediate and final profiles and their associated restoring forces during the solder reflow. It can provide the guidelines to improve the assembly yield and the stress-related reliability of the flip-chip soldering technology.

Numerical and Experimental Analysis of Solder Joint Self-Alignment in Fiber Attachment Soldering

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
Wei Zhang ◽  
Chunqing Wang ◽  
Yanhong Tian
Keyword(s):  
Solder Joint ◽  
Low Cost ◽  
Three Dimensional ◽  
Major Axis ◽  
The Self ◽  
Alignment Error ◽  
Surface Evolver ◽  
Confocal Scanning Laser Microscope ◽  
Solder Volume ◽  
Public Domain Software

Fiber attachment soldering is low cost and high-precision technology in direct-coupling optoelectronic packaging. For accurate alignment, it is crucial to understand the self-alignment behavior of solder joint. In this research, the self-alignment method by using surface tension of molten solder and by adopting specific pad shape was proposed. First, the self-alignment model of solder joint in fiber attachment soldering was developed by using the public domain software called SURFACE EVOLVER and the three-dimensional geometry of solder joint with different solder volume was analyzed. Then, the self-alignment behavior of solder joint with an initial yaw misalignment was discussed and the theoretical equilibrium positions of ellipse and square pad were calculated. Next, based on the minimum potential energy theorem and data from geometry simulation, the influences of design and material parameters on the standoff height (SOH) were analyzed. Furthermore, experiments were done to examine the theoretical equilibrium positions of ellipse and square pad and the SOHs of solder joints were measured by using confocal scanning laser microscope. The numerical results show that the theoretical equilibrium positions of ellipse and square pad are the major axis of ellipse and the diagonal of square, respectively. SOH can be controlled by adopting proper solder volume, which is above the critical value for specific pad. The experimental results show that the solder joint with initial yaw angle can be self-aligned to the theoretical equilibrium position of pad and solder joint with ellipse pad substrate demonstrates smaller alignment error than those with square pad substrate. The measurement results of SOH are in agreement with the simulation results.

Nanoscale Self-Assembly Using Ion and Electron Beam Techniques: A Rapid Review

MRS Advances ◽  
2020 ◽  
Vol 5 (64) ◽  
pp. 3507-3520
Author(s):  
Chunhui Dai ◽  
Kriti Agarwal ◽  
Jeong-Hyun Cho
Keyword(s):  
Electron Beam ◽  
Self Assembly ◽  
Ion Beam ◽  
Three Dimensional ◽  
The Self ◽  
Stress Generation ◽  
Rapid Review ◽  
High Yield ◽  
3D Nanostructures ◽  
Self Assembled

AbstractNanoscale self-assembly, as a technique to transform two-dimensional (2D) planar patterns into three-dimensional (3D) nanoscale architectures, has achieved tremendous success in the past decade. However, an assembly process at nanoscale is easily affected by small unavoidable variations in sample conditions and reaction environment, resulting in a low yield. Recently, in-situ monitored self-assembly based on ion and electron irradiation has stood out as a promising candidate to overcome this limitation. The usage of ion and electron beam allows stress generation and real-time observation simultaneously, which significantly enhances the controllability of self-assembly. This enables the realization of various complex 3D nanostructures with a high yield. The additional dimension of the self-assembled 3D nanostructures opens the possibility to explore novel properties that cannot be demonstrated in 2D planar patterns. Here, we present a rapid review on the recent achievements and challenges in nanoscale self-assembly using electron and ion beam techniques, followed by a discussion of the novel optical properties achieved in the self-assembled 3D nanostructures.

Towards Predicting Relative Belt Edge Endurance With the Finite Element Method

1990 ◽  
Vol 18 (4) ◽  
pp. 216-235 ◽  
Author(s):  
J. De Eskinazi ◽  
K. Ishihara ◽  
H. Volk ◽  
T. C. Warholic
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Shear Deformations ◽  
Element Analysis ◽  
Vertical Loading ◽  
Predicted Values ◽  
Element Method

Abstract The paper describes the intention of the authors to determine whether it is possible to predict relative belt edge endurance for radial passenger car tires using the finite element method. Three groups of tires with different belt edge configurations were tested on a fleet test in an attempt to validate predictions from the finite element results. A two-dimensional, axisymmetric finite element analysis was first used to determine if the results from such an analysis, with emphasis on the shear deformations between the belts, could be used to predict a relative ranking for belt edge endurance. It is shown that such an analysis can lead to erroneous conclusions. A three-dimensional analysis in which tires are modeled under free rotation and static vertical loading was performed next. This approach resulted in an improvement in the quality of the correlations. The differences in the predicted values of various stress analysis parameters for the three belt edge configurations are studied and their implication on predicting belt edge endurance is discussed.

Simulating Self-Regeneration and Self-Replication Processes Using Movable Cellular Automata with a Mutual Equilibrium Neighborhood

2020 ◽  
Vol 29 (4) ◽  
pp. 741-757
Author(s):  
Kateryna Hazdiuk ◽  
◽  
Volodymyr Zhikharevich ◽  
Serhiy Ostapov ◽  
◽  
...  
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Three Dimensional ◽  
Computer Models ◽  
The Self ◽  
Model Construction ◽  
Natural Phenomena ◽  
Different Types ◽  
Movable Cellular Automata ◽  
Self Replication

This paper deals with the issue of model construction of the self-regeneration and self-replication processes using movable cellular automata (MCAs). The rules of cellular automaton (CA) interactions are found according to the concept of equilibrium neighborhood. The method is implemented by establishing these rules between different types of cellular automata (CAs). Several models for two- and three-dimensional cases are described, which depict both stable and unstable structures. As a result, computer models imitating such natural phenomena as self-replication and self-regeneration are obtained and graphically presented.

scholarly journals Detecting the Mechanism behind the Transition from Fixed Two-Dimensional Patterned Sika Deer (Cervus nippon) Dermal Papilla Cells to Three-Dimensional Pattern

2021 ◽  
Vol 22 (9) ◽  
pp. 4715
Author(s):  
Guanning Wei ◽  
Hongmei Sun ◽  
Haijun Wei ◽  
Tao Qin ◽  
Yifeng Yang ◽  
...  
Keyword(s):  
Culture Condition ◽  
Sika Deer ◽  
Three Dimensional ◽  
Cervus Nippon ◽  
Dermal Papilla ◽  
Growth Patterns ◽  
The Self ◽  
Dermal Papilla Cells ◽  
Aggregative Behavior ◽  
Cell Pattern

The hair follicle dermal papilla is critical for hair generation and de novo regeneration. When cultured in vitro, dermal papilla cells from different species demonstrate two distinguishable growth patterns under the conventional culture condition: a self-aggregative three dimensional spheroidal (3D) cell pattern and a two dimensional (2D) monolayer cell pattern, correlating with different hair inducing properties. Whether the loss of self-aggregative behavior relates to species-specific differences or the improper culture condition remains unclear. Can the fixed 2D patterned dermal papilla cells recover the self-aggregative behavior and 3D pattern also remains undetected. Here, we successfully constructed the two growth patterns using sika deer (Cervus nippon) dermal papilla cells and proved it was the culture condition that determined the dermal papilla growth pattern. The two growth patterns could transit mutually as the culture condition was exchanged. The fixed 2D patterned sika deer dermal papilla cells could recover the self-aggregative behavior and transit back to 3D pattern, accompanied by the restoration of hair inducing capability when the culture condition was changed. In addition, the global gene expressions during the transition from 2D pattern to 3D pattern were compared to detect the potential regulating genes and pathways involved in the recovery of 3D pattern and hair inducing capability.

scholarly journals Investigation of Pressure Oscillation and Cavitation Characteristics for Submerged Self-Resonating Waterjet

2021 ◽  
Vol 11 (15) ◽  
pp. 6972
Author(s):  
Lihua Cui ◽  
Fei Ma ◽  
Tengfei Cai
Keyword(s):  
Sudden Change ◽  
Three Dimensional ◽  
Pressure Oscillation ◽  
Experimental Tests ◽  
Low Pressure ◽  
The Self ◽  
Two Phase ◽  
Cavitation Phenomenon ◽  
Pressure Zone ◽  
Unsteady Characteristics

The cavitation phenomenon of the self-resonating waterjet for the modulation of erosion characteristics is investigated in this paper. A three-dimensional computational fluid dynamics (CFD) model was developed to analyze the unsteady characteristics of the self-resonating jet. The numerical model employs the mixture two-phase model, coupling the realizable turbulence model and Schnerr–Sauer cavitation model. Collected data from experimental tests were used to validate the model. Results of numerical simulations and experimental data frequency bands obtained by the Fast Fourier transform (FFT) method were in very good agreement. For better understanding the physical phenomena, the velocity, the pressure distributions, and the cavitation characteristics were investigated. The obtained results show that the sudden change of the flow velocity at the outlet of the nozzle leads to the forms of the low-pressure zone. When the pressure at the low-pressure zone is lower than the vapor pressure, the cavitation occurs. The flow field structure of the waterjet can be directly perceived through simulation, which can provide theoretical support for realizing the modulation of the erosion characteristics, optimizing nozzle structure.

Self-assembled three-dimensional hierarchical graphene hybrid hydrogels with ultrathin β-MnO2 nanobelts for high performance supercapacitors

2015 ◽  
Vol 3 (4) ◽  
pp. 1540-1548 ◽  
Author(s):  
Sheng Zhu ◽  
Hui Zhang ◽  
Ping Chen ◽  
Lin-Hui Nie ◽  
Chuan-Hao Li ◽  
...  
Keyword(s):  
Self Assembly ◽  
High Performance ◽  
Three Dimensional ◽  
The Self ◽  
Mass Loading ◽  
Hybrid Hydrogel ◽  
Precise Control ◽  
Ultrafine Structure ◽  
Hybrid Hydrogels ◽  
Self Assembled

A facile protocol for the self-assembly of the rGO/β-MnO2 hybrid hydrogel with ultrafine structure and precise control of mass-loading for high performance supercapacitors is reported.

Minimization of the Local Residual Stress in 3D Flip Chip Structures by Optimizing the Mechanical Properties of Electroplated Materials and the Alignment Structure of TSVs and Fine Bumps

2011 ◽  
Author(s):  
Kohta Nakahira ◽  
Hironori Tago ◽  
Fumiaki Endo ◽  
Ken Suzuki ◽  
Hideo Miura
Keyword(s):  
Mechanical Properties ◽  
Residual Stress ◽  
Thermal Deformation ◽  
Flip Chip ◽  
Flexural Rigidity ◽  
Three Dimensional ◽  
Strain Gauges ◽  
Copper Interconnection ◽  
Induced Stress ◽  
Alignment Structure

Since the thickness of the stacked silicon chips in 3D integration has been thinned to less than 100 μm, the local thermal deformation of the chips has increased drastically because of the decrease of the flexural rigidity of the thinned chips. The clear periodic thermal deformation and thus, the thermal residual stress distribution appears in the stacked chips due to the periodic alignment of metallic bumps, and they deteriorate the reliability of products. In this paper, the dominant structural factors of the local residual stress in a silicon chip are discussed quantitatively based on the results of a three-dimensional finite element analysis and the measurement of the local residual stress in a chip using stress sensor chips. The piezoresistive strain gauges were embedded in the sensor chips. The length of each gauge was 2 μm, and an unit cell consisted of 4 gauges with different crystallographic directions. This alignment of strain gauges enables to measure the tensor component of three-dimensional stress fields separately. Test flip chip substrates were made by silicon chip on which the area-arrayed tin/copper bumps were electroplated. The width of a bump was fixed at 200 μm, and the bump pitch was varied from 400 μm to 1000 μm. The thickness of the copper layer was about 40 μm and that of tin layer was about 10 μm. This tin layer was used for the rigid joint formation by alloying with copper interconnection formed on a stress sensing chip. The measured amplitude of the residual stress increased from about 30 MPa to 250 MPa depending on the combination of materials such as bump, underfill, and interconnections. It was confirmed that both the material constant of underfill and the alignment structure of fine bumps are the dominant factors of the local deformation and stress of a silicon chip mounted on area-arrayed metallic bumps. It was also confirmed experimentally that both the hound’s-tooth alignment between a TSV (Through Silicon Via) and a bump and control of mechanical properties of electroplated copper thin films used for the TSV and bump is indispensable in order to minimize the packaging-induced stress in the three-dimensionally mounted chips. This test chip is very effective for evaluating the packaging-process induced stress in 3D stacked chips quantitatively.

Finite Element Analysis of Stress Singularities in Attached Flip Chip Packages

2000 ◽  
Vol 122 (4) ◽  
pp. 301-305 ◽  
Author(s):  
A. Q. Xu ◽  
H. F. Nied
Keyword(s):  
Contact Angle ◽  
Finite Element ◽  
Glass Fiber ◽  
Flip Chip ◽  
Three Dimensional ◽  
Stress Singularity ◽  
Local Stress ◽  
Stress Singularities ◽  
Element Analysis ◽  
Three Dimensional Finite Element

Cracking and delamination at the interfaces of different materials in plastic IC packages is a well-known failure mechanism. The investigation of local stress behavior, including characterization of stress singularities, is an important problem in predicting and preventing crack initiation and propagation. In this study, a three-dimensional finite element procedure is used to compute the strength of stress singularities at various three-dimensional corners in a typical Flip-Chip assembled Chip-on-Board (FCOB) package. It is found that the stress singularities at the three-dimensional corners are always more severe than those at the corresponding two-dimensional edges, which suggests that they are more likely to be the potential delamination sites. Furthermore, it is demonstrated that the stress singularity at the upper silicon die/epoxy fillet edge can be completely eliminated by an appropriate choice in geometry. A weak stress singularity at the FR4 board/epoxy edge is shown to exist, with a stronger singularity located at the internal die/epoxy corner. The influence of the epoxy contact angle and the FR4 glass fiber orientation on stress state is also investigated. A general result is that the strength of the stress singularity increases with increased epoxy contact angle. In addition, it is shown that the stress singularity effect can be minimized by choosing an appropriate orientation between the glass fiber in the FR4 board and the silicon die. Based on these results, several guidelines for minimizing edge stresses in IC packages are presented. [S1043-7398(00)00904-X]

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