CALCE EPSC Graduate Student Theses and Dissertation Abstracts (2021)

Deshpande, Abhishek (Ph.D.)
Grain-Scale Anisotropic Study of Tensile Vs. Shear Mechanical Constitutive and Fatigue Behavior in Oligocrystalline SAC305 Solder Joints

Solder joints in microelectronic assemblies experience a multiaxial combination of cyclic extensional and shear loads due to combinations of thermal expansion mismatch and flexure of printed circuit assemblies (PCAs) during thermal cycling or during vibrational loading of constrained PCAs. Although a significant amount of research has been conducted to study cyclic fatigue failures of solder joints under pure-shear loading, most of the current literature on cyclic tensile loading of solders is on long dog-boned monolithic solder coupons. Unfortunately, such coupon specimens do not capture the critical interactions between key micro-scale morphological features (such as grain orientation, grain boundaries, intermetallic compounds [IMCs] and substrates) that are observed to play important roles in the fatigue of functional solder joints under life-cycle loading. Therefore, Part I of this study uses a combination of experiments and finite element analysis to investigate the differences in mechanisms of cyclic fatigue damage in Sn-3.0Ag-0.5Cu (SAC305) few-grained (oligocrystalline) microscale solder joints under shear, tensile and multiaxial loading modes at room temperature. Cyclic fatigue durability test results indicate that tensile loads are more detrimental compared to shear loads. Tensile vs. shear loading modes are found to cause distinctly different combinations of interfacial damage vs. internal damage in the bulk of the solder (transgranular and intergranular damage), which correlates with the differences observed in the resulting fatigue durability. The test results also confirm that this type of multimodal fatigue damage cannot be modeled with the traditional approach of a power-law dependence on the cyclic amplitude of equivalent deviatoric strain. Instead, multiaxial fatigue damage results are seen to be affected not only by the cyclic equivalent strain amplitudes, but also by the severity of the stress-triaxiality, as hypothesized in models such as the Chaboche model. Estimating the true deviatoric strains and triaxiality ratios at the failure sites is not a trivial task in typical oligocrystalline SAC305 solder joints, because the strong anisotropy of the individual grains - and the interactions of such grains with surrounding grains as well as with the interfacial boundaries - make the strain field unique in each joint. Thus, the current approach of modeling solder joints as homogeneous isotropic structures, are clearly inadequate because they fail to capture the true grain-scale stress fields at the failure sites. The joint-to-joint variation in the grain morphology leads to variability in fatigue damage accumulation rates under cyclic loading. Part II of this study thus focuses on grain-scale study of the fatigue results presented in Part I, by: (a) characterizing multi-scale anisotropic elastic-plastic properties of SAC305 single crystals, using a hybrid combination of experiments and finite element simulation, (b) applying a grain-scale parametric study to explain the variability seen in Part I, in the bimodal fatigue failures under multiaxial cyclic loading. The anisotropic elastic-plastic properties in Part IIa were determined by conducting monotonic tensile and shear tests on SAC305 single crystal specimens. The anisotropic elastic behavior is modeled using anisotropic elastic stiffness constants for SAC305, whereas anisotropic plasticity is modeled using Hill’s potential in conjunction with a Holloman-type power-law plastic constitutive model. Microstructurally motivated scaling factors are empirically developed, to assess the effect of dendritic and eutectic microstructural features on single-crystal stress-strain properties. This facilitates extrapolation of constitutive properties across different cooling rates and different isothermal aging protocols. Additional empirical scaling factors are also developed to account for the influence of characteristic grain sizes and grain aspect ratios (relative to principal loading directions). The parametric study in Part IIb, was conducted using the anisotropic properties of Part IIa, to quantify the effect of grain anisotropy on variability in cyclic mechanical fatigue curves of SAC305 solder. This study demonstrates an efficient computational approach for determining variability in mechanical response and fatigue behavior of Sn-rich solder joints, thereby reducing the time and costs associated with physical testing.

Diao, Weiping (Ph.D.)
Degradation Analysis of Lithium-ion Batteries with Knee Points

The commercialization of lithium-ion batteries has enabled applications ranging from portable consumer devices to high-power electric vehicles to become commonplace. The capacity, which has been used to determine if lithium-ion batteries have reached the end of life, decreases during usage (cycling) and storage (rest). After some charge-discharge cycles, the capacity fade rate has been observed to increase, and the capacity fade curve visibly bends, the onset of which is described as a knee point. The occurrence of the knee point during the useful life of the battery leads a shorter life than expected based on the initial capacity fade rate. Although various degradation mechanisms are generally known in the literature, the degradation mechanisms responsible for the knee point phenomenon have been in contention. Understanding why and when the knee point will appear on the capacity fade curves is valuable to battery manufacturers and device companies to predict or mitigate the knee point. This study presents the degradation behavior with knee point identification algorithms, experimental analysis that identifies the degradation mechanisms for the knee point, and accelerated aging tests and modeling methods to predict the capacity fade trend, including the knee point. Finally, this study discusses how to delay the knee point from chemical design perspectives and how battery users should qualify batteries.

Ravimanalan, Suraj (Ph.D.)
Storage Reliability for Electronic Components and Their Packaging Media

Companies that produce end-products with long-term sustainment requirements undertake long-term storage as one of the measures to overcome the problem of electronic component obsolescence. To protect the components from environmental degradation during storage, they are packed inside vacuum sealed moisture barrier bags along with desiccants and humidity indicator cards. The desiccants have a specific adsorption capacity at a particular temperature / relative humidity condition. They cannot absorb the moisture permeated through the moisture barrier bag beyond that capacity. The relative humidity inside the moisture barrier bag also changes during long-term storage. This thesis provides a methodology to estimate the time to reach the desiccant's adsorption capacity and to estimate the increase in relative humidity inside the moisture barrier bag. The methodology is based on the experimental results and the first principle physical equations used for moisture permeation and adsorption. Based on these estimations, companies can decide on replacement schedules for moisture barrier bags and desiccants, thus protecting the electronic components contained within moisture barrier bags from humidity-related reliability issues.

Jiang, Qian (Ph.D.)
Anisotropic Multi-scale Modeling For Steady-state Creep Behavior Of Polycrystalline Coarse-grain Snagcu (sac) Solder Joints

Heterogeneous integration is leading to unprecedented miniaturization of solder joints. The overall size of solder interconnections in current-generation microelectronics assemblies has length-scales that are comparable to that of the intrinsic heterogeneities of the solder microstructure. In particular, there are only a few highly anisotropic grains in each joint. This makes the mechanical response of each joint quite unique. Rigorous mechanistic approaches are needed for quantitative understanding of the response of such joints, based on the variability of the microstructural morphology. The discrete grain morphology of as-solidified coarse-grain SAC (SnAgCu) solder joints is explicitly modeled in terms of multiple length scales (four tiers of length scales are used in the description here). At the highest length-scale in the joint (Tier 3), there are few highly anisotropic viscoplastic grains in each functional solder joint, connected by visoplastic grain boundaries. At the next lower tier (Tier 2), the primary heterogeneity within each grain is due to individual dendrites of pro-eutectic β-Sn. Additional microscale intermetallic compounds of Cu6Sn5 rods are located inside individual grains. Packed between the dendrite lobes is a eutectic Ag-Sn alloy. The next lower length-scale (Tier 1), deals with the microstructure of the Ag-Sn eutectic phase, consisting of nanoscale Ag3Sn IMC particles dispersed in a β-Sn matrix. The characteristic length scale and spacing of the IMC particles in this eutectic mix are important features of Tier 1. Tier 0 refers to the body-centered tetragonal (BCT) anisotropic β-Sn crystal structure, including the dominant slip systems for this crystal system. The objective of this work is to provide the mechanistic framework to quantify the mechanical viscoplastic response of such solder joints. The anisotropic mechanical behavior of each solder grain is modeled with a multiscale crystal viscoplasticity (CV) approach, based on anisotropic dislocation mechanics and typical microstructural features of SAC crystals. Model constants are calibrated with single crystal data from the literature and from experiments. This calibrated CV model is used as single-crystal digital twin, for virtual tests to determine the model constants for a continuum-scale compact anisotropic creep model for SAC single crystals, based on Hill’s anisotropic potential and an associated creep flow-rule. The additional contribution from grain boundary sliding, for polycrystalline structures, is investigated by the use of a grain-boundary phase, and the properties of the grain boundary phase are parametrically calibrated by comparing the model results with creep test results of joint-scale few-grained solder specimens. This methodology enables user-friendly computationally-efficient finite element simulations of multi-grain solder joints in microelectronic assemblies and facilitates parametric sensitivity studies of different grain configurations. This proposed grain-scale modeling approach is explicitly sensitive to microstructural features such as the morphology of: (i) the IMC reinforcements in the eutectic phase; (ii) dendrites; and (iii) grains. Thus, this model is suited for studying the effect of microstructural tailoring and microstructural evolution. The developed multiscale modeling methodology will also empower designers to numerically explore the worst-case and best-case microstructural configurations (and corresponding stochastic variabilities in solder joint performance and in design margins) for creep deformation under monotonic loading, for creep-fatigue under thermal cycling as well as for creep properties under isothermal aging conditions.

Kordell, Jonathan (Ph.D.)
Parametric Design and Experimental Validation of Conjugate Stress Sensors for Structural Health Monitoring

In this dissertation, conjugate stress (CS) sensing is advanced through a parametric evaluation of a surface-mounted design and through experimental validation in monotonic and cyclic tensile tests. The CS sensing concept uses a pair of sensors of significantly different mechanical stiffness for direct query of the instantaneous local stress-strain relationship in the host structure, thus offering measurement of important health indicators such as stiffness (modulus), yield strength, strain hardening, and cyclic hysteresis. In this study, surface-mounted CS sensor designs are parametrically evaluated with finite element modeling, with respect to the sensors’ location, thickness, and modulus and the external loading state. An analytic pin-force model is developed to infer the host structure’s stress-strain state, based on the strain outputs of the CS sensor-pair. Two CS sensor designs are fabricated – one employs resistive foil strain gauges and the second employs fiber optic sensors – and paired with the pin-force model for experimental demonstration of the measurement of: (i) stress-strain history of three different metal bars (aluminum, copper, and steel) as they experience monotonic tensile loads well into plasticity and (ii) stress-strain hysteresis of a steel bar as it is subject to cyclic tensile fatigue. In the cyclic tests, two machine learning algorithms – anomaly detection and neural net classification – are used in conjunction with the estimated host stiffness from the CS sensor and pin force model to predict the failure time of the steel beams.

Gaonkar, Aishwarya (M.S.)
Assessment of the Fides Reliability Prediction Methodology

The FIDES Guide is a reliability prediction handbook published by a group of European defense and aerospace manufacturers under the supervision of the French Ministry of Defense. FIDES assumes the hazard rates of electronic systems follow a bathtub curve, and only predicts reliability for the useful life period using a constant failure rate metric. The inapplicability of the bathtub model to predict the hazard rate of electronic components, products, and systems is examined. The appropriateness of FIDES model factors as inputs to a reliability prediction is assessed. It is shown that FIDES uses inappropriate reliability prediction metric and combines reliability prediction with supply chain risk assessment. The claim of FIDES being based on the physics-of-failure is assessed and shown to be false. FIDES guide is evaluated using the questionnaire provided by the IEEE Standard 1413 and it is shown that FIDES lacks the key attributes that make a reliability prediction useful and accurate.

Lee, Hyun Seop (Ph.D.)
Time-Temperature Dependent Characterization of Polymers for Accurate Prediction of Stresses in Electronic Packages

Epoxy molding compound (EMC) is a thermosetting polymer filled with inorganic fillers such as fused silica. EMC has been used extensively as a protection layer in various semiconductor packages. The warpage and the residual stress of packages are directly related to the thermomechanical properties of EMC. As the size of semiconductor packages continues to shrink, prediction of the warpage and residual stress becomes increasingly important. The viscoelastic properties of EMC are the most critical input data required for accurate prediction. In spite of the considerable effort devoted to warpage prediction, accurate prediction of warpage remains a challenging task. One of the critical reasons is the inappropriate assumption about the bulk modulus – time and temperature “independent” bulk modulus, which is not valid at high temperatures. In this thesis, a novel experimental method, based on an embedded fiber Bragg grating (FBG) sensor, is developed, and implemented to measure a complete set of linear viscoelastic properties of EMC just from a single configuration. A single cylindrical EMC specimen is fabricated, and it is subjected to constant uniaxial compression and hydrostatic pressure at various temperatures. Two major developments to accommodate the unique requirements of EMC testing include: (1) a large mold pressure for specimen fabrication; and (2) a high gas pressure for hydrostatic testing while minimizing a temperature rise. The FBG embedded in the specimen records strain histories as a function of time. Two linear viscoelastic properties, Young’s modulus and Poisson’s ratio, are first determined from the strain histories, and the other two elastic properties, Shear modulus and Bulk modulus, are calculated from the relationship among the constants. The master curves are produced, and the corresponding shift factors are determined. Validity of three major assumptions associated with the linear viscoelasticity – thermorheological simplicity, Boltzmann superposition and linearity – are verified by supplementary experiments. The effect of the time-dependent bulk modulus on thermal stress analysis is also discussed.

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