**Meng, Jingshi** (Ph.D)

__Multi-scale Dynamic Study of Secondary Impact during Drop Testing of Surface Mount Packages__

This dissertation focuses on design challenges caused by secondary impacts to printed wiring assemblies (PWAs) within hand-held electronics due to accidental drop or impact loading. The continuing increase of functionality, miniaturization and affordability has resulted in a decrease in the size and weight of handheld electronic products. As a result, PWAs have become thinner and the clearances between surrounding structures have decreased. The resulting increase in flexibility of the PWAs in combination with the reduced clearances requires new design rules to minimize and survive possible internal collisions impacts between PWAs and surrounding structures. Such collisions are being termed ‘secondary impact’ in this study. The effect of secondary impact on board-level drop reliability of printed wiring boards (PWBs) assembled with MEMS microphone components, is investigated using a combination of testing, response and stress analysis, and damage modeling. The response analysis is conducted using a combination of numerical finite element modeling and simplified analytic models for additional parametric sensitivity studies.

Drop tests are conducted for PWAs assembled with commercial off-the-shelf (COTS) Micro-Electro-Mechanical Systems (MEMS) microphone components under highly accelerated conditions of 20,000g (“g” is the gravitational acceleration). Under such high accelerations, the stress levels generated are well beyond those expected in conventional qualifications. Furthermore, secondary impacts of varying intensities are allowed by varying the clearance between the PWB and the drop fixture, to mimic unexpected secondary impacts in a product, if design rules fail to avoid such conditions. As a result, there are additional amplifications in stress and accelerations and reduction of repetitive drop durability. The amplification of the test severity is quantified using the characteristic number of drops to failure (η, Weibull distribution) of the population of tested MEMS components at each clearance. Multiple failure modes from drop testing are identified, ranging from package level failures to MEMS device failures. The participation of competing failure modes is also demonstrated via characteristic life representations of each failure mode at various clearances.

A multi-scale, dynamic, time-domain, finite-element analysis (FEA) approach is used to assess the response and stress histories at critical failure sites. A set of fatigue damage models is proposed, to predict the damage accumulation due to competing failure modes in MEMS components when subjected to drops with secondary impacts. The proposed damage accumulation model accounts for hydrostatic stresses and for dynamic post-impact oscillations during each drop event. Based on the failure data and stress/strain outputs from FEA, fatigue damage model constants are determined for each failure mode when the components are facing downwards during the drop test. The proposed damage models not only provide a good fit to the measured lifetimes of the MEMS components, but also provide insights into the transitions in the dominant failure modes. This model (calibrated to failure data from drop durability of downwards facing components) is found to provide reasonable prediction of results for tests with components facing upwards.

Finally, a dynamic sensitivity study is carried out, using a simplified model structure, to gain parametric insights into the influence of secondary impact on the local stress histories at two typical failure sites in surface mount technology (SMT) PWAs. The selected model structure is an idealized representation of the MEMS PWA, to facilitate mechanistic insights using simplified analytic and numerical models. The two typical failure sites of interest included in this simplified model are representative of: (i) interconnects between the SMT component and the PWB; and (ii) miniature structures within the SMT component (e.g. MEMS diaphragm, runners, back-plate, wire bonds). The secondary impact parameters studied include: (i) width, shape, and magnitude of the impact pulse; (ii) laminated structure of the PWB; (iii) geometric constraints such as clearance magnitude and impact site; and (iv) contact stiffness. The results from this parametric study are compatible with the experimental evidence. This study clearly demonstrates the importance of accounting for the through-thickness oscillations of the PWB when considering different failure modes in SMT components due to secondary impacts. In worst case scenarios, modeling the PWB as a shell element can introduce significant errors (5-50X, depending on the magnitude of damping) when predicting the response amplitudes of the internal miniature structures within the SMT component.

**George, Elviz** (Ph.D)

__A Non-Linear Damage Model with Load Dependent Exponents for Solders Under Sequential Cyclic Shear Loads__

Miner’s rule assumes that damage in solder interconnects accumulate linearly under cyclic loading and the damage path independent of the applied load level. Due to these inherent assumptions, Miner’s rule inaccurately estimate solder interconnect life under sequential loading conditions. In this dissertation, a non-linear damage model based on damage curve approach that takes into account the effect of loading sequence under sequential loading conditions is proposed for solders. In the proposed non-linear damage model, damage is related to the cycle ratio using a power law relationship where the power law (damage) exponent is defined as a function of the applied load level (cycles to failure).

An experimental approach is proposed to determine the load dependent exponents of the non-linear model under three load levels. The test matrix consisted of a series of ‘standalone’ and sequential cyclic shear tests in a thermo-mechanical micro analyzer. Load dependent exponents were developed for SAC305 (96.5%Sn+3.0%Ag+0.5Cu) solder material and the applicability of these exponents were validated by tests under a new loading condition and reverse loading sequence. Experimental results revealed that the value of damage exponent decreased with the severity of the applied load level. Additionally, taking damage analogous to crack growth, an analytical relationship between the damage exponent and the applied load level was developed from the Paris’ law for crack propagation. This enables determination of non-linear damage curves at different load levels without conducting extensive experimentation. The damage due to crack initiation was assumed to be 10% of the total damage and sensitivity analysis was carried out to determine the effect of this assumption. The load dependence of the Paris’ law exponent (m) was also derived for SAC305 solder material. Analysis of the failed specimens revealed fatigue crack in the solder joints along the tin grain boundaries.

**Menon, Sandeep** (Ph.D)

__An Analytical Approach for Fatigue Life Estimation of Copper Traces for Design Optimization in Electronic Assemblies__

This dissertation investigates the durability of the copper traces using experimental results from a fully reversed four point bend testing using and finite element analysis. The durability data collected from the experiment was used in conjunction with the finite element based critical trace strain, to develop a set of compatible fatigue model constants that best fit the failure behavior observed in the tests. Experimental studies were also conducted in order to determine the impact of assembly variations on the fatigue failures of the traces including the presence of a surface finish, solder mask as well as the presence of assembled components.

Parametric studies using finite element analysis were also conducted in order to determine the relationship between the various geometric and loading conditions and the critical trace strain in the copper traces. Based on these relationships as well as the experiments to determine the impact of assembly variations of failure of the traces, an analytical model was developed in order to determine the copper trace strain.

To understand the crack initiation and crack propagation process in copper traces, experiments were conducted where the crack growth was periodically monitored. Based on these experiments, the constants for the fatigue crack propagation in copper traces based on Paris’s Law were also determined in this study. The experimental data along with finite element analysis was also used to establish the model constants established for a power law based fatigue crack initiation model in copper traces.

Finally in order to validate the established fatigue life model constants further testing was conducted at a different load level. The predicted cycles to failure compare well with the experimentally observed cycles to failure. The analytical model for trace strain developed was also validated by comparing the copper trace strain evaluated using finite element modeling and the analytical modeling at a different load level. The strains estimated based on the analytical model match well with the strains based on the finite element modeling.

**Mukherjee, Subhasis ** (Ph.D)

__Multiscale Modelling of Anisotropic Creep Response of SnAgCu Single Crystal__

The lack of statistical homogeneity in functional SnAgCu (SAC) solder joints due to their coarse grained microstructure, in conjunction with the severe anisotropy exhibited by single crystal Sn, renders each joint unique in terms of mechanical behavior. An anisotropic multiscale modeling framework is proposed in this dissertation to capture the influence of the inherent elastic anisotropy and grain orientation in single crystal Sn on the primary and secondary creep response of single crystal SnAgCu (SAC) solder. Modeling of microstructural deformation mechanisms in SnAgCu (SAC) solder interconnects requires a multiscale approach because of tiered microstructural heterogeneities. The smallest length scale (Tier 0) refers to the Body Centered Tetragonal (BCT) structure of the Sn matrix itself because it governs: (1) the associated dislocation slip systems, (2) dislocation line tension (3) dislocation mobility and (4) intrinsic orthotropy of mechanical properties in the crystal principal axis system. The next higher length scale, (Tier 1), consists of nanoscale Ag3Sn intermetallic compounds (IMCs) surrounded by Body Centered Tetragonal (BCT) Sn to form the eutectic Sn-Ag phase. The next higher length scale (Tier 2) consists of micron scale lobes of pro-eutectic Sn dendrites surrounded by eutectic Sn-Ag regions and reinforced with micron scale Cu6Sn5 IMCs. Unified modeling of above two length scales provides constitutive properties for SAC single crystal. Tier 3 in coarse-grained solder joints consists of multiple SAC crystals along with grain boundaries. Finally, Tier 4 consists of the structural length scale of the solder joint. Line tension and mobility of dislocations (Tier 0) in dominant slip systems of single crystal Sn are captured for the elastic crystal anisotropy of body centered tetragonal (BCT) Sn by using Stroh's matrix formalism. The anisotropic creep rate of the eutectic Sn-Ag phase of Tier I is then modeled using above inputs and the evolving dislocation density calculated for the dominant glide systems. The evolving dislocation density history is estimated by modeling the equilibrium between three competing processes: (1) dislocation generation; (2) dislocation impediment (due to backstress from forest dislocations in the Sn dendrites and from the Ag3Sn IMC particles in the eutectic phase); and (3) dislocation recovery (by climb/diffusion from forest dislocations in the Sn dendrites and by climb/detachment from the Ag3Sn IMC particles in the eutectic phase). The creep response of the eutectic phase (from Tier 1) is combined with creep of ellipsoidal Sn lobes at Tier 2 using the anisotropic Mori-Tanaka homogenization theory, to obtain the creep response of SAC305 single crystal along global specimen directions and is calibrated to experimentally obtained creep response of a SAC305 single crystal specimen. The Eshelby strain concentration tensors required for this homogenization process are calculated numerically for ellipsoidal Sn inclusions embedded in anisotropic eutectic Sn-Ag matrix. The orientations of SAC single crystal specimens with respect to loading direction are identified using orientation image mapping (OIM) using Electron Backscatter Diffraction (EBSD) and then utilized in the model to estimate the resolved shear stress along the dominant slip directions. The proposed model is then used for investigating the variability of the transient and secondary creep response of Sn3.0Ag0.5Cu (SAC305) solder, which forms the first objective of the dissertation. The transient creep strain rate along the [001] direction of SAC305 single crystal #1 is predicted to be 1-2 orders of magnitude higher than that along the [100]/[010] direction. Parametric studies have also been conducted to predict the effect of changing orientation, aspect ratio and volume fraction of Sn inclusions on the anisotropic creep response of SAC single crystals. The predicted creep shear strain along the global specimen direction is found to vary by a factor of (1-3) orders of magnitude due to change in one of the Euler angles (j1) in SAC305 single crystal #1, which is in agreement with the variability observed in experiments. The second objective of this dissertation focuses on using this proposed modeling framework to characterize and model the creep constitutive response of new low-silver, lead-free interconnects made of Sn1.0Ag0.5Cu (SAC105) doped with trace elements, viz., Manganese (Mn) and Antimony (Sb). The proposed multiscale model is used to mechanistically model the improvement in experimentally observed steady state creep resistance of above SAC105X solders due to the microalloying with the trace elements. The third and final objective of this dissertation is to use the above multiscale microstructural model to mechanistically predict the effect of extended isothermal aging on experimentally observed steady state creep response of SAC305 solders. In summary, the proposed mechanistic predictive model is demonstrated to successfully capture the dominant load paths and deformation mechanisms at each length scale and is also shown to be responsive to the microstructural tailoring done by microalloying and the continuous microstructural evolution because of thermomechanical life-cycle aging mechanisms in solders.

**Mathew, Sony ** (Ph.D)

__An Analytical Model for Developing a Canary Device__

Solder joint fatigue failure is a prevalent failure mechanism for electronics subjected to thermal cycling loads. The failure is attributed to the thermo-mechanical stresses in the solder joints caused by differences in the coefficient of thermal expansion of the printed circuit board (PCB), electronic component, and solder. Physics of failure models incorporate the knowledge of a product's material properties, geometry, life-cycle loading and failure mechanisms to estimate the remaining useful life of the product. Engelmaier's model is widely used in the industry to estimate the fatigue life of electronics under thermal cycling conditions. However, for leadless electronic components, the Engelmaier strain metric does not consider the solder attachment area, the solder fillet thickness, and the thickness of the PCB. In this research a first principles model to estimate the strain in the solder interconnects has been developed. This new model considers the solder attachment area, and the geometry and material properties of the solder, component and PCB respectively. The developed model is further calibrated based on the results of finite element analysis. The calibrated model is validated by comparing its results with results of testing of test assemblies under different thermal cycling loading conditions. Further, the calibrated first principles model is used to design reduced solder attachment areas for electronic components so that under the same loading conditions they fail faster than components with regular solder attachment areas. Such structures are called expendable Canary devices and can be used to predict the solder joint fatigue failure of regular electronic components in the actual field conditions. The feasibility of using a leadless chip resistor with reduced solder attachment area as a canary device to predict the failure of ball grid array (BGA) component has been proven based on testing data. Further, a methodology for the developing and implementing canary device based prognostics has been developed in this research. Practical implementation issues, including estimating the number of canary devices required, determination of appropriate prognostic distance, and failure prediction schemes that may be used in the actual field conditions have also been addressed in this research.

**Habtour, Ed ** (Ph.D)

__Structural Health Monitoring of Nonlinear Beam under Combined Translational and Rotational Vibration__

This study presents a nonlinear dynamic methodology for detecting fatigue damage precursor in an isotropic metallic cantilever beam exposed to harmonic transverse, rotation or combined ¬– transverse and rotation – base excitations. The methodology accounts for important dynamic nonlinearities due to the complex loading generated by uniaxial and multiaxial nonlinear oscillations. These nonlinearities include: 1) structural stiffening due to gyroscopic motion and high-response amplitude at the structure fundamental mode, 2) structural softening due to inertial forces and gyroscopic loads, and localized evolution in the material microstructure due to fatigue damage and 3) cross-axis coupling due to multiaxial loading. The loading intensity and number of vibration cycles intensified these nonlinearities. The damage precursor feature is acquired by quantifying the reduction in the nonlinear stiffness term in the equation of motion due to localized evolution in the material micromechanical properties at high stress concentration regions. Nanoindentation studies near high stress concentration sites confirmed the evolution in the local micromechanical properties, as a function of loading cycles. The nonlinear analytical approach tracks the degradation in the structural stiffness as a function of the nonlinear dynamic response for the uniaxial transverse or rotation base excitation. The change in the dynamic response due to damage precursor is captured experimentally. The nonlinear stiffness terms are found to be sensitive to fatigue damage precursor for translational or rotational excitation. Therefore, the nonlinear stiffness sensitivity to fatigue damage precursor appeared to be a promising metric for structural health monitoring applications. This method is applicable to a cantilever beam only. Additional investigations will be required to extend its applicability to more complex structures. For the combined transverse and rotation base excitation, the experimental and analytic results demonstrated the importance of cross-axis coupling. The Experiments are performed using a unique multiaxial electrodynamic shaker with high controllability of phase and base excitation frequencies. The analytical model captures the modulation in the nonlinear dynamic response behavior seen in the experiments as a function of cross-axis coupling and the phase relation between the axes. Although the model is successful in capturing these general trends, it does not agree with the beam deflection absolute values obtained from the experiments. The discrepancy is due to fatigue damage accumulation during the experiments, which is manifested by a shift in the resonance frequency and an increase in the response amplitude.

**Mahadeo, Dinesh Michael ** (M.S.)

__Copper Corrosion in the Flowers of Sulfer Test Environment__

Sulfur, present in the environment in the form of sulfur dioxide and hydrogen sulfide, can produce failure in electronics. In particular, copper, which is used extensively in electronic products, is subject to corrosion in the presence of sulfur. This thesis examines the corrosion of copper under the Flowers of Sulfur (FoS) test at varying temperatures and durations. The FoS test setup, described in ASTM B809, was initially designed to evaluate surface finish porosity, but this setup may have boarder application. To expand the applicability of the FoS test, it is important to characterize the test environment. To this end, a systematic study of copper corrosion was conducted through weight gain measurements of copper coupons that were subjected to FoS test environments. From the test results, a model was developed that correlates copper sulfide thickness to temperature and time under the FoS test. This model can be used to determine test conditions given a target field environment.

**Khanna, Sumeer ** (M.S.)

__Structural Reliability of Novel 3-D Integrated Thermal Packaging for Power Electronics__

Thermal management has become increasingly important to ensuring the reliability of power electronics components due to the continuing increase of device power and integration levels. New approaches to provide the necessary thermal management include the development of embedded two-phase cooling systems. However, the reliability of such devices and that of their integration into the power electronics package have yet to be studied. This thesis details a Physics of Failure (PoF) based structural reliability analysis of novel 3-D integrated thermal packaging for next generation Power Electronics. The cooling technology aims to combine two-phase embedded manifold microchannel cooling in thin film evaporation mode with thermoelectric hot-spot cooling using a high conductivity Mini-contact. This study will focus on thermo-mechanical stress analysis of three different Mini-contact structures, micro-fin structure and reliability prediction of solder joint at various levels in Power Electronics package based on Engelmaier's failure model for SAC 305.

**Mifsud, Mark ** (M.S.)

__A Simplified Model for Interconnect Stresses Induced by Bending of Printed Wiring Boards__

A simplified model is developed for analysis of interconnect stresses induced by changes in the curvature of printed wiring boards. The model utilizes the Rayleigh-Ritz variational approach and can be used for rapid assessment and is well-suited for parametric studies because it does not need any numerical meshing. This simplified model represents the component as an equivalent shell and the interconnects as deformable beams. As a simplification, any initial warpage of the component has been neglected in this study. Finite element models are used to verify the simplified model: a simplified FEA model that utilizes the same shell idealization as the proposed Rayleigh-Ritz model and a more detailed 3D solid model. The proposed simplified model provides a faster, more versatile alternative to FEA and can be used to estimate the interconnect stresses caused by PWB warpage under a variety of thermomechanical, vibration, and shock/drop loading conditions. This thesis focuses on demonstrating the use of this simplified modeling approach for area array surface mount components (e.g. stud-grid array, land-grid array, column grid array, and ball grid array). In particular, the example problem addressed in this thesis is the pre-stress induced in surface mount area-array interconnects during the solder reflow process used for attaching surface mount packages to printed wiring boards (PWBs). The possibility exists for the PWB and component to warp during the reflow process and therefore exhibit some concave or convex curvature once the process has been completed. If the PWB is then straightened during the assembly process, the act of straightening the PWB can cause pre-stresses to develop in the interconnects between the PWB and the component package. It is important to understand these pre-stresses because unaccounted for interconnect pre-stresses can result in premature wear-out failures or unexpected overstress failures of the assembly.