Accumulated Strain Energy Density Research Articles

Packaging Parameters Analysis for the Fatigue Reliability of Stacked Chip Ball Grid Array by Using the Optimal Equivalent Solder Balls

A global/local method with the modified sub‐modeling approach of the two‐parametric optimal equivalent volume solder balls is introduced to predict the deformation and reliability of the package. The equivalent solder balls as exhibit in this method can obviously reduce the required elements/nodes quantities to enhance computing efficiency. A package model of wire‐bonded stacked chip ball grid array under cyclic thermal loading is used as a test vehicle to verify the influences of design factors by fatigue life indicator. Comparing the proposed method with the global fine mesh model, it is found that the difference in the accumulated strain energy density is merely 5.77%, but the optimal equivalent model has highly saved 90% finite element analysis required elements, which means the adopted method can effectively replace the global fine mesh model because both results are in accordance with each other. Using design of experiments to efficiently verify each factor influence with their cross‐coupling effects, this paper adopts two kinds of response surface methods that confirm the fatigue life of the proposed approach can be improved by as much as 123.7% for the dual response surface method and 126.3% for the mixed response surface method when comparing with the baseline model. In addition, the optimization of generic algorithm for both response surface methods is demonstrated in this study. From the reviews of factor coupling effects, it is concluded that the response surface method is eligible to achieve the optimum design for package reliability improving. Copyright © 2013 John Wiley & Sons, Ltd.

Application of Optimal Design on Twin Die Stacked Package by Reliability Indicator of Average SED Concept

ABSTRACTThis paper deals with the optimal design for a twin die stacked package. Firstly, the numerical model is built up in terms of a three-dimensional slice model along the diagonal direction of the package. The material behavior of the solder balls is a consequence of the viscoplastic property which can be described by the Anand's model. Secondly, the Darveaux model is applied to predict the solder ball reliability of the stacked die package under a cyclic temperature loading. Since simulation analysis found an obvious relation is found between the fatigue life of the solder ball and the distribution of the accumulated strain energy density (SED) on the critical solder ball of the package through the simulation analysis, the average value of the strain energy density for all solder balls is adopted as the optimization indicator of reliability. With such a viewpoint, the critical solder ball position can be ignored, and accordingly an efficient analysis can be obtained. Finally, the Box-Behnken regression model is adopted to construct all the experiments. Each experiment analyzes the reliability of the package under varying parameters. Subsequently, the pattern search algorithm is applied to search for optimal factors.Through optimal analysis with the fatigue reliability indicator of an average SED, the fatigue life is found to be 59% lower than that of the original design. The fatigue life had clearly improved and the lowest ball fatigue life is found to be 2.859 times longer than the original one.

Packaging parameter analysis and optimization design on solder joint reliability for twin die stacked packages by variance in strain energy density (SED) of each solder joint

In accordance with vigorous development of the electronic product market as well as the consumers’ preference for smaller scales, the structure of 3D stacked die package rapidly becomes popular. Hereafter the stacked process of the silicon dies always makes the coupling effect among materials more complicated. Such an issue has been seriously paid attention to and becomes a critical problem to be solved for the product reliability. In this paper, the ANSYS software is adopted to analyze a twin die stacked package under a cyclic thermal loading condition. The viscoplastic finite element analysis and the Darveaux theory are applied to investigate the solder joint reliability (SJR) of the stacked die package. This research will verify a significant dependence between the solder joint fatigue life of the stacked die package and the distribution of the accumulated strain energy density (SED) on the solder joints by proposing a viewpoint of the variance of the strain energy density among solder joints for a 3D-Slice model.

Estimation of fatigue crack growth retardation due to crack branching

Quantitative analysis is provided to estimate the reduction of fatigue crack growth rate due to overload crack branching. A recent mixed-mode fatigue crack growth model based on the dilatational component of the accumulated strain energy density near the crack tip is modified to quantify the retardation factor of crack growth rate following an overload. It is found that crack branching due to an overload results in considerable reduction of fatigue crack growth rate. The retardation factor estimated by the proposed methodology is correlated with test results for the 2090-T8E41 aluminum–lithium alloy indicating encouraging agreement.

Estimation Of Fatigue Crack Growth Retardation Due To Crack Branching

Quantitative analysis is provided to estimate the reduction of fatigue crack growth rate due to overload crack branching. A recent mixed-mode fatigue crack growth model based on the dilatational component of the accumulated strain energy density near the crack tip is modified to quantify the retardation factor of crack growth rate following an overload. It is found that crack branching due to an overload results in considerable reduction of fatigue crack growth rate. The retardation factor estimated by the proposed methodology is correlated with test results for the 2090-T8E41 aluminum-lithium alloy indicating encouraging agreement.

Relaxation of strain during solid phase epitaxial growth of Ge + ion implanted layers in silicon

Formation of Si 1− x Ge x -alloy layers by solid phase epitaxial growth (SPEG) of Ge + ion implanted silicon has been studied. The ion implantations were performed with 40, 100, 150, 200 and 300 keV 74Ge + ions and various ion doses. The SPEG of the ion implanted layers was carried out in a conventional furnace at 850°C for 20 min under a flow of nitrogen gas. The Si 1− x Ge x -alloy layers were characterised by Rutherford backscattering spectrometry and transmission electron microscopy (TEM). For a given ion energy, a Si 1− x Ge x -alloy layer with no observable extended defects can be manufactured if the ion dose is below a critical value and strain-induced defects are formed in the alloy layer when the ion dose is equal to or above this value. The critical Ge + ion dose increases with ion energy, while the critical maximum Ge concentration decreases. For ion energies ⩽150 keV, the defects observed in the alloy layers are mostly stacking faults parallel to the {1 1 1} planes. For higher ion energies, 200 keV and above, the majority of defects in the alloy layer are hairpin dislocations. In the whole ion energy range, the critical ion dose and the depth position of the nucleation site for the stacking faults obtained from the measurements are in good agreement with theoretical predictions. Extended defects are formed in the alloy layer during the SPEG when the regrowth of the crystalline/amorphous interface has reached the depth position in the crystal where the accumulated strain energy density is equal to the critical value of 235 mJ/m 2.

Strain induced defects in Si 1− xGe x-alloy layers formed by solid phase epitaxial growth of 40 keV Ge + ion implanted silicon

High-dose Ge + ion implantation, together with Solid Phase Epitaxial Growth (SPEG), has been used to form Si 1− x Ge x -alloy layers in silicon crystals. The microstructure and crystal quality of the alloy layers were studied for 40 keV Ge + ion implantations in the dose range 9.3 × 10 15 to 3.4 × 10 16 ions/cm 2. The SPEG was carried out in a conventional furnace at 850°C in a flow of nitrogen gas. A regrowth of the ion implanted amorphous layer is achieved for all ion doses and a single crystal Si 1− x Ge x -alloy layer with no observable extended defects is obtained when the Ge + ion dose is lower than a critical value of about 2.3 × 10 16 ions/cm 2. This gives a critical areal strain energy density of about 235 mJ/m 2. Above the critical ion dose, extended defects are formed in the Si 1− x Ge x material during the recrystallisation process and the density of the defects increases with Ge + ion dose. Most of the defects are stacking faults lying parallel to the {111} planes. The defects are bound at the surface of the crystal in one end and with dislocations in the other end. The depth position of the dislocations obtained from the measurements agrees with a theoretical prediction based on the assumption that the defects are nucleated at the SPEG process when the crystalline/amorphous interface advances to the depth position in the crystal where the accumulated strain energy density in the recrystallised layer reaches the critical value. No appreciable glide of the dislocations into the already recrystallised layer is detected.