Modeling diffusional coarsening in eutectic tin/lead solders: a quantitative approach

Dreyer, Wolfgang; Müller, Wolfgang

doi:10.1016/s0020-7683(00)00103-7

Cited by 46 publications

(41 citation statements)

References 24 publications

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“…The responses of the microstructures to stress and EM can be summarized as follows: (Single column image) a D is the interdiffusion coefficient [36], C ij is the stiffness tensor in Voigt notation [35], [40], [41], r r r is the electrical resistivity [37]- [39], Z Sn and Z Cu are the effective charge numbers of Sn and Cu, respectively [36].…”

Section: Discussionmentioning

confidence: 99%

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Effects of Stress and Electromigration on Microstructural Evolution in Microbumps of Three-Dimensional Integrated Circuits

Xiong

Huang

Conway

2014

IEEE Trans. Device Mater. Relib.

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Section: Discussionmentioning

confidence: 99%

“…The material parameters of the model are set in reference to the published experimental data [28], [35]- [41] and are listed in Table II. An isotropic interdiffusion coefficient for Sn, D, is used in studies of the interaction between external stresses and microstructural evolution.…”

Section: Materials Parametersmentioning

confidence: 99%

Effects of Stress and Electromigration on Microstructural Evolution in Microbumps of Three-Dimensional Integrated Circuits

Xiong

Huang

Conway

2014

IEEE Trans. Device Mater. Relib.

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“…As a detailed example to show the general applicability of our method, the phase field model developed by Dreyer and Müller [15] is employed in this work to simulate the phase separation and coarsening processes in ultrafine Sn37Pb solder joints. This model incorporates the strain energy as a driving force for microstructural evolution, and thus can predict the microstructure in solder joints under shear load when the joints are in service.…”

Section: Modeling Methodologymentioning

confidence: 99%

“…The distribution of the mass fraction of Sn, denoted as C Sn , is used as an order parameter to represent the morphology of the Sn-rich and Pb-rich phases. The evolution of the morphology is obtained by solving the following governing equation with the finite element method [15]:…”

Section: Modeling Methodologymentioning

confidence: 99%

A Method for Quantification of the Effects of Size and Geometry on the Microstructure of Miniature Interconnects

Xiong

Huang

Conway

2013

Journal of Elec Materi

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The heterogeneity of microstructure has significant impacts on the material properties of ultrafine interconnects, and thus should be quantified and used to facilitate high-fidelity reliability predictions. In order to address this challenge, a method based on autocorrelation and singular value decomposition for quantitative microstructural characterization is proposed in this work. The method is applied to study the size and geometry effects on the microstructure and the stress state in ultrafine Sn37Pb solder joints. The degree of the microstructural heterogeneity related to the preferred growth directions of the phases is quantified with a scalar microstructural index by using this method. It is found that the degree of microstructural heterogeneity increases with the decrease of the standoff height, and is higher in the hourglass-shaped solder joints. The maximum von Mises stress is lower in the hourglass-shaped joints in most cases studied in this work, which indicates a higher strength and longer lifetime than the barrel-shaped joints. The average von Mises stress increases almost monotonically with the degree of the microstructural heterogeneity. The strong correlation between the microstructural index and the average von Misse stress is confirmed by a nonlinear regression analysis using artificial neural network. Based on the microstructural index, the mechanical behavior of the ultrafine interconnects can be predicted more accurately.

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“…We refer e.g. to the work by Dreyer and Müller [5] and by Leo, Lowengrub and Jou [18] and the references therein. Due to the highly nonlinear structure of the Cahn-Larché system, approaches based on spectral methods loose their efficiency.…”

Section: Introductionmentioning

confidence: 99%

Numerical approximation of the Cahn-Larché equation

Garcke

Weikard

2005

Numer. Math.

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Abstract. Spinodal decomposition, i.e., the separation of a homogeneous mixture into different phases, can be modeled by the Cahn-Hilliard equation -a fourth order semilinear parabolic equation. If elastic stresses due to a lattice misfit become important, the Cahn-Hilliard equation has to be coupled to an elasticity system to take this into account. Here, we present a discretization based on finite elements and an implicit Euler scheme. We first show solvability and uniqueness of solutions. Based on an energy decay property we then prove convergence of the scheme. Finally we present numerical experiments showing the impact of elasticity on the morphology of the microstructure.

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Modeling diffusional coarsening in eutectic tin/lead solders: a quantitative approach

Cited by 46 publications

References 24 publications

Effects of Stress and Electromigration on Microstructural Evolution in Microbumps of Three-Dimensional Integrated Circuits

Effects of Stress and Electromigration on Microstructural Evolution in Microbumps of Three-Dimensional Integrated Circuits

A Method for Quantification of the Effects of Size and Geometry on the Microstructure of Miniature Interconnects

Numerical approximation of the Cahn-Larché equation

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