Predictive Model for Optimized Design Parameters in Flip-Chip Packages and Assemblies
29 May 2007-IEEE Transactions on Components and Packaging Technologies (IEEE)-Vol. 30, Iss: 2, pp 294-301
TL;DR: In this article, an analytical model is developed to predict the out-of-plane deformation and thermal stresses in multilayered thin stacks subjected to temperature, and a proper formula for effective moduli of solder (C4)/underfill layer, is presented.
Abstract: An analytical model is developed to predict the out-of- plane deformation and thermal stresses in multilayered thin stacks subjected to temperature. Coefficient of thermal expansion mismatches among the components (chip, substrate, underfill, flip-chip interconnect or C4s) are the driving force for both first and second levels interconnect reliability concerns. Die cracking and underfill delamination are the concerns for the first level interconnects while the ball grid array solder failure is the primary concern for the second level interconnects. Inadvertently, many researchers use the so-called rule of mixture in its effective moduli for the flip chip solder (C4)/underfill layer. In this study, a proper formula for effective moduli of solder (C4)/underfill layer, is presented. The classical lamination theory is used to predict the out-of-plane displacement of the chip substrate structure under temperature variation (DeltaT). The warpage and stresses resulting from the analytical formulation are compared with the 3-D finite element analysis. The study helps to design more reliable components or assemblies with the design parameters being optimized in the early stage of the development using closed form analytical solutions.
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TL;DR: In this paper, the warpage of flip-chip PBGA packages subject to thermal loading (from room temperature to 260?C) was measured and simulated using a full-field shadow moirE?.
Abstract: The aim of this paper was to measure and simulate the warpage of flip-chip PBGA packages subject to thermal loading (from room temperature to 260?C). In the experiments, a full-field shadow moirE? was used to measure real-time out-of-plane deformations (warpages) on the substrate and chip surfaces of the flip-chip packages under thermal heating and cooling conditions. A finite-element method (FEM) and Suhir's die-assembly theory, together with the measured material data (elastic moduli and coefficients of thermal expansion (CTEs) for organic substrates), were used to analyze the thermally induced deformations of the packages to gain insight into their mechanics. The strain gauge data used to determine the CTEs of the substrates also indicated that there was nearly no bending strain under thermal loading. The full-field warpages on the substrate surface of the packages from the shadow moirE? were documented under temperature loading. It was also found that there were different zero-warpage temperatures (which resulted in a variation of warpages at room temperature) for the four test packages during thermal loading, but they had similar warpage rates (the slope of warpage with respect to temperature). This might have been due to the creep of the underfill and the solder bumps in the packages at the solder reflow temperature. Regardless of the zero-warpage temperature, the warpage of the packages can be well simulated or predicted by FEM and Suhir's theory. The key material properties (elastic moduli and CTEs for the substrate and underfill) that affect the maximum warpage of the package were thoroughly studied. It was found that, among these material properties, a low elastic modulus for the underfill can significantly reduce the maximum warpage, while its CTE is much less sensitive to warpage. Moreover, the substrate CTE affects the warpage of a package only with noncompliant underfills, while a typical substrate elastic modulus (ranging from 10 to 30 GPa) is insensitive to warpage, unless its value is lower than a few gigapascals.
63 citations
Cites background from "Predictive Model for Optimized Desi..."
...well with the 3-D finite-element analysis [9]....
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...Thus, this radius of curvature cannot be described by the classical lamination theory used in [9], which assumes that the radius of curvature is constant with respect to the Kirchhoff–Love hypothesis....
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...Therefore, the warpage-prediction formulations proposed in [9] will be invalid or suffer more errors as the die attach becomes more compliant....
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01 May 2018
TL;DR: In this article, a 2.5D Field-Programmable Gate Array (FPGA) assembly in both accelerated thermal cycling and power cycling was investigated by computational fluid dynamics (CFD) simulation and finite element analysis.
Abstract: 2.5D packages have been widely used in electronics industry for high performance and product miniaturization. As Through-Silicon-Via (TSV) fabrication methods and multi-level assembly technologies get mature, 2.5D packaging becomes reliable and affordable. In this work, board-level life prediction was performed for a 2.5D Field-Programmable Gate Array (FPGA) assembly in both accelerated thermal cycling and power cycling. Finite element models were built and validated by warpage measurement. Solder fatigue life in power cycling was investigated by computational fluid dynamics (CFD) simulation and finite element analysis. Improved life prediction for power cycling was achieved by mapping temperature results from CFD model to finite element model. Parametric studies regarding geometry and material factors were performed including PCB, substrate, thermal interface material (TIM) and lid adhesive, to give design suggestions to improve board-level thermal reliability. Maximum junction temperature of a 2.5D FPGA package is dependent on application scenarios and working environment. It is found that the designed maximum junction temperature and applied heatsink clamping force have considerable influences on board-level reliability.
32 citations
Cites methods from "Predictive Model for Optimized Desi..."
...The effective material properties (modulus, CTE and Poisson’s ratio) for this layer were calculated using the composite theory [42]....
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TL;DR: In this article, a simulation-based methodology to calculate the equivalent mechanical properties of 3D-ICs through-silicon via (TSV) interposer composed of silicon chip and copper (Cu)-filled metal is presented.
23 citations
TL;DR: To analyze and predict the thermal deformation of the through silicon via (TSV) interposer package during the manufacturing process and to perform a parametric study to minimize the warpage and thermal stress, a validated FEA model was established.
20 citations
Cites background or methods from "Predictive Model for Optimized Desi..."
...[15], the in-plane Young's modulus is given by...
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...[15] were calculated for the C4/underfill layer, micro bump/ underfill layer, and TSV interposer....
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...[15] presented a proper formula for the effective moduli of the solder/underfill layer....
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TL;DR: In this article, the reliability performance of an adhesive flip-chip in the moisture environment was investigated, and the failure modes were found to be interfacial delamination and bump/pad opening which may eventually lead to total loss of electrical contact.
Abstract: A primary factor of anisotropic conductive film (ACF) package failure is delamination between the chip and the adhesive at the edge of the chip. This delamination is mainly affected by the thermal shear strain at the edge of the chip. This shear strain was measured on various electronic ACF package specimens by micro-Moire interferometry with a phase shifting method. In order to find the effect of moisture, the reliability performance of an adhesive flip-chip in the moisture environment was investigated. The failure modes were found to be interfacial delamination and bump/pad opening which may eventually lead to total loss of electrical contact. Different geometric size specimens in terms of interconnections were discussed in the context of the significance of mismatch in coefficient of moisture expansion (CME) between the adhesive and other components in the package, which induces hygroscopic swelling stress. The effect of moisture diffusion in the package and the CME mismatch were also evaluated by using the Moire interferometry. From Moire measurement results, we could also obtain the stress intensity factor K. Through an analysis of deformations induced by thermal and moisture environments, a damage model for an adhesive flip-chip package is proposed.
19 citations
References
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Book•
01 Jan 1959
TL;DR: In this article, the authors describe the bending of long RECTANGULAR PLATES to a cycloidal surface, and the resulting deformation of shels without bending the plates.
Abstract: CONTENTS: BENDING OF LONG RECTANGULAR PLATES TO A CYLINDRICAL SURFACE PURE BENDING OF PLATES SYMMETRICAL BENDING OF CIRCULAR PLATES SMALL DEFLECTIONS OF LATERALLY LOADED PLATES SIMPLY SUPPORTED RECTANGULAR PLATES RECTANGULAR PLATES WITH VARIOUS EDGE CONDITIONS CONTINUOUS RECTANGULAR PLATES PLATES ON ELASTIC FOUNDATION PLATES OF VARIOUS SHAPES SPECIAL AND APPROXIMATE METHODS IN THEORY OF PLATES BENDING OF ANISTROPIC PLATES BENDING OF PLATES UNDER THE COMBINED ACTION OF LATERAL LOADS AND FORCES IN THE MIDDLE PLANE OF THE PLATE LARGE DEFLECTIONS OF PLATES DEFORMATION OF SHELLS WITHOUT BENDING GENERAL THEORY OF CYLINDRICAL SHELLS SHELLS HAVING THE FORM OF A SURFACE OF REVOLUTION AND LOADED SYMMETRICALLY WITH RESPECT TO THEIR AXIS.
10,200 citations
TL;DR: In this article, a general theory of bending of a bi-metal strip submitted to a uniform heating is presented, which is applied in analysis of the operation of a Bi-metal Strip thermostat.
Abstract: The following investigation contains a general theory of bending of a bi-metal strip submitted to a uniform heating. This theory is applied in analysis of operation of a bi-metal strip thermostat. The equations are obtained for calculating the temperature of buckling, the complete travel during buckling, and the temperature of buckling in a backward direction.. By using these equations the dimensions of the thermostat for a given temperature of operation and a given complete range of temperature can be calculated. The results obtained are based on certain ideal conditions. For example, it was assumed that the differ ence in the coefficients of expansion remained constant during heating, that the friction at the supports could be neglected and that the width
2,139 citations
"Predictive Model for Optimized Desi..." refers methods in this paper
...Hence, the out-of-plane Young’s modulus and the Poisson’s ratio can be given by (2) (3) For the in-plane directions ( and ), however, it is more appropriate to assume that the stress is uniform knowing the continuous (serial) loading path of C4 and underfill....
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Book•
01 Jan 1994
TL;DR: In this paper, the authors present an analysis of the properties of a continuous fiber-reinforced Lamina and its effect on the strength of the composite components, including the elasticity and robustness of the components.
Abstract: Introduction Basic Concepts Constituent Materials for Composites Structural Applications of Composites Multifunctional Applications of Composites Fabrication Processes Elements of Mechanical Behavior of Composites Review of Basic Mechanics of Materials Equations Lamina Stress-Strain Relationships Introduction Effective Moduli in Stress-Strain Relationships Symmetry in Stress-Strain Relationships Orthotropic and Isotropic Engineering Constants The Specially Orthotropic Lamina The Generally Orthotropic Lamina Effective Moduli of a Continuous Fiber-Reinforced Lamina Introduction Elementary Mechanics of Materials Models Improved Mechanics of Materials Models Elasticity Models Semiempirical Models Strength of a Continuous Fiber-Reinforced Lamina Introduction Multiaxial Strength Criteria Micromechanics Models for Lamina Strength Analysis of Lamina Hygrothermal Behavior Introduction Hygrothermal Degradation of Properties Lamina Stress-Strain Relationships Including Hygrothermal Effects Micromechanics Models for Hygrothermal Properties Analysis of a Discontinuously Reinforced Lamina Introduction Aligned Discontinuous Fibers Off-Axis-Aligned Discontinuous Fibers Randomly Oriented Discontinuous Fibers Nanofibers and Nanotubes Particulates Hybrid Multiscale Reinforcements Analysis of Laminates Introduction Theory of Laminated Beams Theory of Laminated Plates with Coupling Stiffness Characteristics of Selected Laminate Configurations Derivation and Use of Laminate Compliances Hygrothermal Effects in Laminates Interlaminar Stresses Laminate Strength Analysis Deflection and Buckling of Laminates Selection of Laminate Designs Application of Laminate Analysis to Composite Structures Analysis of Viscoelastic and Dynamic Behavior Introduction Linear Viscoelastic Behavior of Composites Dynamic Behavior of Composites Nanoenhancement of Viscoelastic and Dynamic Properties Analysis of Fracture Introduction Fracture Mechanics Analysis of Through-Thickness Cracks Stress Fracture Criteria for Through-Thickness Notches Interlaminar Fracture Nanoenhancement of Fracture Toughness Mechanical Testing of Composites and Their Constituents Introduction Measurement of Constituent Material Properties Measurement of Basic Composite Properties Measurement of Viscoelastic and Dynamic Properties Measurement of Hygrothermal Properties Appendix A: Matrix Concepts and Operations Appendix B: Stress Equilibrium Equations Appendix C: Strain-Displacement Equations Index Problems and References appear at the end of each chapter.
1,636 citations
"Predictive Model for Optimized Desi..." refers methods in this paper
...Although we consider that the solder volume fraction does not constitute more than 25% of the entire layer volume, the effective moduli (Young’s modulus and CTE) calculated by the two methods differ as much as 20% each other....
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TL;DR: Timoshenko as mentioned in this paper is one of the outstanding exponents of the mathematical theory of elasticity and of the application of this theory to a variety of practical problems, and has written on these topics for thirty years, and his books have become indispensable to every engineer who has to apply mathematical principles and methods to such problems.
Abstract: PROF. TIMOSHENKO is one of the outstanding exponents of the mathematical theory of elasticity and of the application of this theory to a variety of practical problems. He has written on these topics for thirty years, and his books have become indispensable to every engineer who has to apply mathematical principles and methods to such problems. Theory of Plates and Shells By Prof. S. Timoshenko. (Engineering Societies Monographs.) Pp. xii + 492. (New York and London: McGraw–Hill Book Co., Inc., 1940.) 42s.
1,097 citations
"Predictive Model for Optimized Desi..." refers methods in this paper
...Hence, the out-of-plane Young’s modulus and the Poisson’s ratio can be given by (2) (3) For the in-plane directions ( and ), however, it is more appropriate to assume that the stress is uniform knowing the continuous (serial) loading path of C4 and underfill....
[...]
TL;DR: In this article, the authors derived bounds on effective thermal expansion coefficients of isotropic and anisotropic composite materials consisting of isotropy phases by employing extremum principles of thermoelasticity.
Abstract: Bounds on effective thermal expansion coefficients of isotropic and anisotropic composite materials consisting of isotropic phases are derived by employing extremum principles of thermoelasticity
1,049 citations