Analytical Thermo-Mechanical Model for Non-Underfilled Area Array Flip Chip Assemblies

2004 ◽  
Vol 126 (3) ◽  
pp. 351-358 ◽  
Author(s):  
Bart Vandevelde ◽  
Eric Beyne ◽  
Dirk Vandepitte ◽  
Martine Baelmans

An analytical model is derived for the calculation of thermo-mechanical induced stresses in area array flip chip assemblies. This analytical model is based on structural mechanics and has the ability to characterize the nature and to estimate the magnitude of the induced stresses. The extension of this model compared to existing procedures is its applicability to area array systems, which behave significantly different from peripheral assemblies. The model is compared to finite element simulations. The model calculates accurately the forces and bending moments acting on the flip chip connections. The transformation of these forces and moments into stresses is less accurate as the model does not include stress concentrations near the corners. The model simulates very well the different parameter trends such as chip size and is therefore well suited for understanding parameter sensitivity studies.

1998 ◽  
Vol 120 (4) ◽  
pp. 336-341 ◽  
Author(s):  
E. Madenci ◽  
S. Shkarayev ◽  
R. Mahajan

In this study, the effect of underfill on the level of stress concentrations is investigated and possible failure sites are identified by using a global/local finite element approach. The global elements capture the exact singular behavior of the stresses near the geometric and material discontinuities. Application of the strain energy density criterion indicates the possible failure sites and how they shift due to the presence of underfill.


1998 ◽  
Vol 516 ◽  
Author(s):  
Sven Rzepka ◽  
Matt A. Korhonen ◽  
Che-Yu Li ◽  
Ekkehard Meusel

AbstractFollowing the general tendency of downsizing in microelectronic packages, the interposing layer between silicon chip and organic board is constantly reduced while the differences in thermal expansion stay constant. Consequently, thermal stresses have become the most important reliability concern in advanced packages. Finite element analysis is known as an effective way of theoretically studying the mechanical situation in multi-component systems with complex material behavior. The paper presents results of finite element simulations that provide practical guidance for design, process and material developments of chip size packaging (CSP), flip chip (FC), and direct chip attach (DCA) modules. Using realistic and efficient models, a low-cost CSP concept is assessed, the effects of underfill, underfill imperfections, and underfill defects on the reliability of FC modules are studied, and an optimum set of mechanical properties for underfill materials is proposed. Finally, reliability risk factors in DCA modules are identified and preliminary design guidelines are given.


2000 ◽  
Vol 123 (3) ◽  
pp. 295-301 ◽  
Author(s):  
Yu Gu ◽  
Toshio Nakamura ◽  
William T. Chen ◽  
Brian Cotterell

Using detailed finite element models, a fracture analysis of solder bumps and under bump metallurgy (UBM) in flip-chip packages is carried out. Our objective is to identify likely fracture modes and potential delamination sites at or near these microstructural components. In order to study flip-chips, whose dimension spans from sub-micron thickness UBM layers to several millimeters wide package, we have applied a multi-scale finite element analysis (MS-FEA) procedure. In this procedure, initially, deformation of whole thermally loaded package is analyzed. Then, the results are prescribed as the boundary conditions in a very detailed cell model, containing a single solder bump, to investigate micro-deformation surrounding UBM. Using the models with two different scales, accurate stress fields as well as fracture parameters of various interface cracks can be determined. The MS-FEA is ideally suited for the flip-chip packages since they contain many identical solder bumps. A cell model can be repeatedly used to probe stress and fracture behaviors at different locations. The computed results show high stress concentrations near the corners of solder bumps and UBM layers. Based on the energy release rate calculations, solder bumps located near the edge of chip are more likely to fail. However, our results also suggest possible delamination growth at solder bumps near the center of chip. In addition, we have observed increasing energy release rates for longer cracks, which implies a possibility of unstable crack growth.


Author(s):  
Jordan Roberts ◽  
M. Kaysar Rahim ◽  
Safina Hussain ◽  
Jeffrey C. Suhling ◽  
Richard C. Jaeger ◽  
...  

Thermal cycling accelerated life testing is often used to qualify area array packages (e.g. Ball Grid Arrays and Flip Chip) for various applications. Finite element life predictions for thermal cycling configurations are challenging due to the complicated temperature/time dependent constitutive relations and failure criteria needed for solders and encapsulants and their interfaces, aging/evolving material behavior (e.g. solders), difficulties in modeling plating finishes, the complicated geometries of typical electronic assemblies, etc. In addition, in-situ measurements of stresses and strains in assemblies subjected to temperature cycling is difficult because of the extreme environmental conditions and the fact that the primary materials/interfaces of interest (e.g. solder joints, die device surface, wire bonds, etc.) are embedded within the assembly (not at the surface). For these reasons, we really know quite little about the evolution of the stresses, strains, and deformations occurring within sophisticated electronic packaging geometries during thermal cycling. In our research, we are using test chips containing piezoresistive stress sensors to continuously characterize the in-situ die surface stress during long-term thermal cycling of several different area array packaging technologies including plastic ball grid array (PBGA) components, ceramic ball grid array (CBGA) components, and flip chip on laminate assemblies. The utilized (111) silicon test chips are able to measure the complete three-dimensional stress state (all 6 stress components) at each sensor site being monitored by the data acquisition hardware. The die stresses are initially measured at room temperature after packaging. The assemblies are then subjected to thermal cycling over various temperature ranges including 0 to 100 °C, −40 to 125 °C, and −55 to 125 °C, for up to 3000 thermal cycles. During the thermal cycling, sensor resistances at critical locations on the die device surface (e.g. the die center and die corners) are recorded. From the resistance data, the stresses at each site can be calculated and plotted versus time. The experimental observations show significant cycle-to-cycle evolution in the stress magnitudes due to material aging effects, stress relaxation and creep phenomena, and development of interfacial damage. The observed stress variations as a function of thermal cycling duration are also being correlated with the observed delaminations at the die surface (as measured using scanning acoustic microscopy (C-SAM)) and finite element simulations that include material constitutive models that incorporate thermal aging effects.


2013 ◽  
Vol 41 (2) ◽  
pp. 127-151
Author(s):  
Rudolf F. Bauer

ABSTRACT The benefits of a tire's equilibrium profile have been suggested by several authors in the published literature, and mathematical procedures were developed that represented well the behavior of bias ply tires. However, for modern belted radial ply tires, and particularly those with a lower aspect ratio, the tire constructions are much more complicated and pose new problems for a mathematical analysis. Solutions to these problems are presented in this paper, and for a modern radial touring tire the equilibrium profile was calculated together with the mold profile to produce such tires. Some construction modifications were then applied to these tires to render their profiles “nonequilibrium.” Finite element methods were used to analyze for stress concentrations and deformations within all tires that did or did not conform to equilibrium profiles. Finally, tires were built and tested to verify the predictions of these analyses. From the analysis of internal stresses and deformations on inflation and loading and from the actual tire tests, the superior durability of tires with an equilibrium profile was established, and hence it is concluded that an equilibrium profile is a beneficial property of modern belted radial ply tires.


Author(s):  
Manish Kumar ◽  
Pronab Roy ◽  
Kallol Khan

From the recent literature, it is revealed that pipe bend geometry deviates from the circular cross-section due to pipe bending process for any bend angle, and this deviation in the cross-section is defined as the initial geometric imperfection. This paper focuses on the determination of collapse moment of different angled pipe bends incorporated with initial geometric imperfection subjected to in-plane closing and opening bending moments. The three-dimensional finite element analysis is accounted for geometric as well as material nonlinearities. Python scripting is implemented for modeling the pipe bends with initial geometry imperfection. The twice-elastic-slope method is adopted to determine the collapse moments. From the results, it is observed that initial imperfection has significant impact on the collapse moment of pipe bends. It can be concluded that the effect of initial imperfection decreases with the decrease in bend angle from 150∘ to 45∘. Based on the finite element results, a simple collapse moment equation is proposed to predict the collapse moment for more accurate cross-section of the different angled pipe bends.


Author(s):  
J. R. Beisheim ◽  
G. B. Sinclair ◽  
P. J. Roache

Current computational capabilities facilitate the application of finite element analysis (FEA) to three-dimensional geometries to determine peak stresses. The three-dimensional stress concentrations so quantified are useful in practice provided the discretization error attending their determination with finite elements has been sufficiently controlled. Here, we provide some convergence checks and companion a posteriori error estimates that can be used to verify such three-dimensional FEA, and thus enable engineers to control discretization errors. These checks are designed to promote conservative error estimation. They are applied to twelve three-dimensional test problems that have exact solutions for their peak stresses. Error levels in the FEA of these peak stresses are classified in accordance with: 1–5%, satisfactory; 1/5–1%, good; and <1/5%, excellent. The present convergence checks result in 111 error assessments for the test problems. For these 111, errors are assessed as being at the same level as true exact errors on 99 occasions, one level worse for the other 12. Hence, stress error estimation that is largely reasonably accurate (89%), and otherwise modestly conservative (11%).


2008 ◽  
Vol 59 ◽  
pp. 299-303
Author(s):  
K. Mergia ◽  
Marco Grattarola ◽  
S. Messoloras ◽  
Carlo Gualco ◽  
Michael Hofmann

In plasma facing components (PFC) for nuclear fusion reactors tungsten or carbon based tiles need to be cooled through a heat sink. The joint between the PFC and the heat sink can be realized using a brazing process through the employment of compliant layer of either a low yield material, like copper, or a high yield material, like molybdenum. Experimental verification of the induced stresses during the brazing process is of vital importance. Strains and residual stresses have been measured in Mo/CuCrZr brazed tiles using neutron diffraction. The strains and stresses were measured in Mo tile along the weld direction and at different distances from it. The experimental results are compared with Finite Element Simulations.


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