scholarly journals Thermally induced deformations in die-substrate assembly

2008 ◽  
Vol 35 (1-3) ◽  
pp. 305-322 ◽  
Author(s):  
Milena Vujosevic
Keyword(s):  
Flip Chip ◽  
Plate Theory ◽  
Contour Plot ◽  
Predictive Capability ◽  
Thermally Induced ◽  
Ball Grid Arrays ◽  
Proposed Model ◽  
Fundamental Understanding ◽  
Numerical Finite Element ◽  
Analytical Expressions

The work focuses on the thermally induced deformations caused by the processing of Flip Chip Ball Grid Arrays (FCBGA). Analytical expressions for substrate displacements are derived based on the Plate Theory and Suhir's solution for stresses in tri-material assembly. The validity of the model is established by comparing the analytical solution to the numerical finite element results as well as to the experimental data. The benefits of the proposed model are twofold: 1) it provides a tool for fundamental understanding of the deformation process of interest, and 2) has a predictive capability. More specifically, an analysis is presented on the nature and degree of influence that different geometric and material parameters have on the substrate deflections, as well as a "Warpage Contour Plot", proposed as a tool for warpage prediction that can be easily utilized in the early stages of the design process.

Warpage of Flip Chip BGA Package

2006 ◽  
Author(s):  
Milena Vujosevic
Keyword(s):  
Flip Chip ◽  
Plate Theory ◽  
Contour Plot ◽  
Thermally Induced ◽  
Ball Grid Arrays ◽  
Fundamental Understanding ◽  
Out Of Plane ◽  
Bga Package ◽  
Plane Displacement ◽  
Analytical Expressions

The work focuses on the thermally induced out of plane displacement of Flip Chip Ball Grid Arrays (FCBGA). Analytical expressions for substrate displacements are derived based on the Plate Theory and Suhir's solution for stresses in tri-material assembly. The validity of the model is established by comparing the analytical solution to the finite element results as well as to the experimental data. The benefits of the model are twofold: 1) it provides a tool for fundamental understanding of the parameters that influence warpage, and 2) has a predictive capability. With respect to 1) an analysis is presented on the nature and degree of influence that different geometric and material parameters have on the FCBGA warpage. With respect to 2) the "Warpage Contour Plot" is proposed as a tool for warpage prediction that can be easily utilized in the early stages of the design process.

Application of an Epoxy Cap in a Flip-Chip Package Design

1989 ◽  
Vol 111 (1) ◽  
pp. 16-20 ◽  
Author(s):  
E. Suhir
Keyword(s):  
Thermal Expansion ◽  
Flip Chip ◽  
Coefficient Of Thermal Expansion ◽  
Preliminary Test ◽  
Elastic Stability ◽  
Thermally Induced ◽  
Package Design ◽  
Silicone Gels ◽  
Low Modulus ◽  
Supporting Frame

In order to combine the merits of epoxies, which provide good environmental and mechanical protection, and the merits of silicone gels, resulting in low stresses, one can use an encapsulation version, where a low modulus gel is utilized as a major encapsulant, while epoxy is applied as a protecting cap. Such an encapsulation version is currently under consideration, parallel with a metal cap version, for the Advanced VLSI package design which is being developed at AT&T Bell Laboratories. We recommend that the coefficient of thermal expansion for the epoxy be somewhat smaller than the coefficient of thermal expansion for the supporting frame. In this case the thermally induced displacements would result in a desirable tightness in the cap/frame interface. This paper is aimed at the assessment of stresses, which could arise in the supporting frame and in the epoxy cap at low temperatures. Also, the elastic stability of the cap, subjected to compression, is evaluated. The calculations were executed for the Advanced VLSI package design and for a Solder Test Vehicle (STV), which is currently used to obtain preliminary information regarding the performance of the candidate encapsulants. It is concluded that in order to avoid buckling of the cap, the latter should not be thinner than 15 mils (0.40 mm) in the case of VLSI package design and than 17.5 mils (0.45 mm) in the case of STV. At the same time, the thickness of the cap should not be greater than necessary, both for smaller stresses in the cap and for sufficient undercap space, required for wirebond encapsulation. The obtained formulas enable one to evaluate the actual and the buckling stresses. Preliminary test data, obtained by using STV samples, confirmed the feasibility of the application of an epoxy cap in a flip-chip package design.

A phenomenological model for thermally-induced hysteresis in polycrystalline shape memory alloys with internal loops

2021 ◽  
pp. 1045389X2110482
Author(s):  
Yuxiang Han ◽  
Haoyuan Du ◽  
Linxiang Wang ◽  
Roderick Melnik
Keyword(s):  
Shape Memory Alloys ◽  
Single Crystal ◽  
Shape Memory ◽  
Phenomenological Model ◽  
Landau Theory ◽  
Thermally Induced ◽  
First Order ◽  
Proposed Model ◽  
Crystal Model ◽  
Hysteretic Response

In the current study, a 1-D phenomenological model is constructed to capture the temperature-induced hysteretic response in polycrystalline shape memory alloys (SMAs). The martensitic and austenitic transformations are regarded as the first-order transitions. A differential single-crystal model is formulated on the basis of Landau theory. It is assumed that the transformation temperatures follow the normal distribution among the grains due to the anisotropic stress field developed in the material. The polycrystalline hysteretic response is expressed as the integration of single-crystal responses. Besides, the prediction strategy for incomplete transitions is presented, and the first-order reversal curves are obtained via density reassignment. The proposed model is numerically implemented for validation. Comparisons between the modeling results and the experimental ones demonstrate the capability of the proposed model in addressing the hysteresis in thermally-induced phase transformations.

Aberrations of Volume Cylindrical Holographic Optical Element

2013 ◽  
Vol 8 (3) ◽  
pp. 6-12
Author(s):  
Yuriy Batomunkuev
Keyword(s):  
Refractive Index ◽  
Characteristic Function ◽  
Optical Element ◽  
Thermally Induced ◽  
The Third ◽  
Holographic Optical Element ◽  
Seventh Order ◽  
Chromatic Aberrations ◽  
Cylindrical Volume ◽  
Analytical Expressions

The analytical expressions allowed to calculate the third-, fifth- and seventh-order monochromatic and chromatic aberrations are obtained for the cylindrical volume holographic optical element by method of the characteristic function. The formulas for coefficients of third-, fifth- and seventh-order aberrations are presented. It is noted that coefficients of the aberrations arising because of photo induced, thermally induced and deformation changes of refractive index and of sizes of the cylindrical volume holographic optical element can be isolated in these coefficients. It is shown that width of the working spectral range for reflection cylindrical volume holographic optical element is inversely proportional to its thickness and for transmission holographic element is inversely proportional to square its thickness

Aberrations of Volume Cylindrical Holographic Optical Element

2012 ◽  
Vol 7 (3) ◽  
pp. 15-23
Author(s):  
Yuriy Batomunkuev
Keyword(s):  
Refractive Index ◽  
Characteristic Function ◽  
Optical Element ◽  
Thermally Induced ◽  
The Third ◽  
Holographic Optical Element ◽  
Seventh Order ◽  
Chromatic Aberrations ◽  
Cylindrical Volume ◽  
Analytical Expressions

The analytical expressions allowed to calculate the third-, fifth- and seventh-order monochromatic and chromatic aberrations are obtained for the cylindrical volume holographic optical element by method of the characteristic function. The formulas for coefficients of third-, fifth- and seventh-order aberrations are presented. It is noted that coefficients of the aberrations arising because of photo induced, thermally induced and deformation changes of refractive index and of sizes of the cylindrical volume holographic optical element can be isolated in these coefficients. It is shown that width of the working spectral range for reflection cylindrical volume holographic optical element is inversely proportional to its thickness and for transmission holographic element is inversely proportional to square its thickness

scholarly journals An Analytical Model for Rotation Stiffness and Deformation of an Antiloosening Nut under Locking Force

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
X. J. Jiang ◽  
J. Hong ◽  
G. Q. Shao ◽  
L. B. Zhu ◽  
Y. S. Zhu
Keyword(s):  
Friction Torque ◽  
Design Calculation ◽  
Element Analysis ◽  
Deformation Problem ◽  
Proposed Model ◽  
Rotation Stiffness ◽  
Machine Elements ◽  
Applied Forces ◽  
Numerical Finite Element ◽  
Contact Stress Distribution

Screw fasteners are undoubtedly one of the most important machine elements due to their outstanding characteristic to provide a high clamping force just with a simplified design. However, the loosen vibration is their inherent and inevitable fault. The friction locking approach is one of the basic locking fastener categories by enhancing the bearing load on the contact surface of thread by applying a locking force on an antiloosening nut. This locking force may cause more severe deformation in the nut. The contact stress distribution on the nut would be changed and that can cause the variation of the friction torque for the bolt joint. However, there exists no established design calculation procedure that accounts for the rotation deformation and its stiffness of the antiloosening nut under the locking force. The main objective of the work is to develop an analytical solution to the rotation deformation problem encountered in the antiloosening nut. The proposed model is supported by comparison with numerical finite element analysis of different sizes of joint elements and different applied forces.

scholarly journals A Novel Integrated Approach of Relevance Vector Machine Optimized by Imperialist Competitive Algorithm for Spatial Modeling of Shallow Landslides

2018 ◽  
Vol 10 (10) ◽  
pp. 1538 ◽  
Author(s):  
Dieu Tien Bui ◽  
Himan Shahabi ◽  
Ataollah Shirzadi ◽  
Kamran Chapi ◽  
Nhat-Duc Hoang ◽  
...  
Keyword(s):  
Landslide Susceptibility ◽  
Imperialist Competitive Algorithm ◽  
Relevance Vector Machine ◽  
Support Vector ◽  
Predictive Capability ◽  
Competitive Algorithm ◽  
Susceptibility Modeling ◽  
Gis Database ◽  
Proposed Model ◽  
Soft Computing Techniques

This research aims at proposing a new artificial intelligence approach (namely RVM-ICA) which is based on the Relevance Vector Machine (RVM) and the Imperialist Competitive Algorithm (ICA) optimization for landslide susceptibility modeling. A Geographic Information System (GIS) spatial database was generated from Lang Son city in Lang Son province (Vietnam). This GIS database includes a landslide inventory map and fourteen landslide conditioning factors. The suitability of these factors for landslide susceptibility modeling in the study area was verified by the Information Gain Ratio (IGR) technique. A landslide susceptibility prediction model based on RVM-ICA and the GIS database was established by training and prediction phases. The predictive capability of the new approach was evaluated by calculations of sensitivity, specificity, accuracy, and the area under the Receiver Operating Characteristic curve (AUC). In addition, to assess the applicability of the proposed model, two state-of-the-art soft computing techniques including the support vector machine (SVM) and logistic regression (LR) were used as benchmark methods. The results of this study show that RVM-ICA with AUC = 0.92 achieved a high goodness-of-fit based on both the training and testing datasets. The predictive capability of RVM-ICA outperformed those of SVM with AUC = 0.91 and LR with AUC = 0.87. The experimental results confirm that the newly proposed model is a very promising alternative to assist planners and decision makers in the task of managing landslide prone areas.

Prediction of Vibration Properties of Sandwich Panel Using Thick Plate Theory

2001 ◽  
Author(s):  
Qunli Liu ◽  
Yi Zhao
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Variational Principle ◽  
Free Vibration ◽  
Thick Plate ◽  
Sandwich Panel ◽  
Plate Theory ◽  
Vibration Properties ◽  
Proposed Model ◽  
Thin Plate Theory

Abstract The vibration of a sandwich panel with two identical isotropic facesheets and an orthotropic core was studied. The governing partial differential equation was derived using variational principle. Kirchhoff’s theory was applied to describe the deformation of the panel, and the rotational effect was taken into consideration. The frequencies of free vibration of a rectangular panel can be predicted based on the proposed analytical model. Results based on the proposed model were compared with those from thin plate theory. The effect of orthotropic core on frequencies was also discussed.

Failure Prediction of Flip Chip Packages Using Finite Element Technique

2002 ◽  
Author(s):  
Abm Hasan ◽  
H. Mahfuz ◽  
M. Saha ◽  
S. Jeelani
Keyword(s):  
Finite Element ◽  
Flip Chip ◽  
Thermal Loading ◽  
Failure Modes ◽  
Element Model ◽  
Thermally Induced ◽  
Operational Life ◽  
Flip Chip Assembly ◽  
The Individual ◽  
Element Technique

Flip-chip electronic package undergoes thermal loading during its curing process and operational life. Due to the thermal expansion coefficient (CTE) mismatch of various components, the flip-chip assembly experiences various types of thermally induced stresses and strains. Experimental measurement of these stresses and strains is extremely tedious and rigorous due to the physical limitations in the dimensions of the flip-chip assembly. While experiments provide accurate assessment of stresses and strains at certain locations, a parallel finite element (FE) analysis and analytical study can complementarily determine the displacement, strain and stress fields over the entire region of the flip-chip assembly. Such combination of experimental, finite element and analytical studies are ideal to yield a successful stress analysis of the flip-chip assembly under the various loading conditions. In this study, a two-dimensional finite element model of the flip-chip consisting of the silicon chip, underfill, solder ball, copper pad, solder mask and substrate has been developed. Various stress components under thermal loading condition ranging from −40°C to 150°C have been determined using both the finite element and analytical methods. Stresses such as (σ11, σ12, ε12 etc. are extracted and analyzed for the individual components as well as the entire assembly, and the weakest positions of the flip-chip have been discovered. Detailed description of FE modeling is presented and the different failure modes of chip assembly are discussed.

Evaluation of Bare Die Chip Reliability Due to Underfill Materials During Mechanical Actuation and Thermal Cycling

2005 ◽  
Author(s):  
Arv Sinha
Keyword(s):  
Flip Chip ◽  
Coefficient Of Thermal Expansion ◽  
Bond Line ◽  
Thermal Interface Material ◽  
High Power Density ◽  
The Finite Element Method ◽  
Chip Design ◽  
Thermal Interface ◽  
Ball Grid Arrays ◽  
Mechanical Actuation

Use of underfill materials to encapsulate ball grid arrays (BGAs) or chip scale packages (CSPs) have become very important in increasing the reliability of area array packages [1]. Underfill enhances the reliability of flip-chip devices by distributing the thermo-mechanical stresses [2, 3]. These stresses are generated due to mechanical actuation and coefficient of thermal expansion mismatch (CTE) [3]. They are required due to high power density of the current chip design to achieve fine bond line at the thermal interface material in order to dissipate heat. In this paper, details of reliability assessment using the finite element method and actual test data will be presented and discussed.

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