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In this study, we focus on investigating the nature of the stress and strain behavior in solder joints and their effect on the hybrid damage modeling approach, which is inspired by cohesive zone modeling and Weibull functions [Towashiraporn, et al., 2005, “A Hybrid Model for Computationally Efficient Fatigue Fracture Simulations at Microelectronic Assembly Interfaces,” Int. J. Solids Struct., 42(15), pp. 4468–4483]. We review well understood principles in elastic-plastic fracture mechanics and more recent work in cohesive zone modeling, that address the nature of the singular solutions at the crack tip and provide insight when dealing with the more complex problem of solder joint fracture. Using three-dimensional finite element analysis of a chip scale package, we systematically examine the stress-strain behavior at the edge of the solder joint along the interface. The singular nature of the behavior manifests itself as mesh dependence of the predicted crack front shape and the cycles to failure. We discuss the conditions under which the predicted crack growth rate is of reasonable accuracy by incorporating a characteristic length measure. We validate predictions made by the hybrid damage modeling approach against a companion experimental study in which crack growth was tracked in packages subjected to accelerated thermal cycling.

Extensive failure analysis was performed on identical, isothermally cycled wafer-level chip scale packages with Sn3.8wt%0.7wt%Ag (SAC387) solder joints. Packages were periodically removed during the cycling process to observe crack front progression. The packages were dipped in liquid nitrogen to reduce solder ductility and then pried apart. The crack areas were observed under an optical microscope. The average crack areas on the corner and mid-edge joints of the package were measured using an image processing software. 50 packages were characterized from 240 to 7200 cycles at every 240 cycles. An average of 20 solder joints per cycle was observed to estimate the crack length and area. A finite element model of this package was constructed in ABAQUS. The solder interconnects of the model were given full plastic and creep properties. Using the failure analysis data and the finite element model, the material constant value in a previously developed hierarchal fracture model was calibrated for SAC387. The ability of the model to predict non-intuitive failure initiation sites due to the under bump metallurgy (UBM) geometry is demonstrated. The hierarchal fracture process model was inspired by information theory and continuum thermodynamics. It was earlier proposed to capture the length-scale and temporal hierarchy inherent in quasi-static fracture processes. This single parameter model allows for a non-empirical, geometry independent approach to predicting crack growth by relating equivalent inelastic dissipations and a material constant to the probability of fracture at a material point.

In heterogeneous micro structures that include several grains, secondary phases and interfaces, cracks are known to initiate and grow through different mechanisms. The failure processes however are not well understood. Solder alloys in general, and Pb-free alloys in particular possess complex, heterogeneous microstructures that evolve in fracture in ways that are challenging to model. Often, underlying a fracture observed under a microscope is a hierarchy of fracture-related phenomenon from atomic to macro length-scales. In this paper we develop a failure model inspired by information theory and continuum thermodynamics to capture the multiscale fracture processes in solder joints. We systematically develop measures of dissipation from continuum thermodynamics for materials described by J2 plasticity theory. Crack growth is known to be dissipative and such measures are natural candidates for predicting failure within a mechanics framework. The dissipation estimates, multiple fracture mechanisms and the notions of continuity, monotonicity and composition borrowed from information theory suggest a single model as being capable of predicting both ductile and brittle types of failures.Copyright © 2009 by ASME

The hierarchal fracture process model is a theory derived from continuum thermodynamics and information theory. This single parameter model provides a non-empirical approach able to predict crack growth for solder interconnects regardless of package or solder interconnect geometry. The model relates inelastic dissipations to the probability of failure at a given material point. The hierarchal fracture process model is used to predict crack growth and fatigue lives in a package with atypical solder interconnect geometry: a quad-flat-no-lead (QFN) package. The fracture model uses the material parameter calibrated for Sn3.8wt%0.7wt%Cu solder in a previous study of wafer-level CSP packages. Finite element models of these packages are created in ABAQUS with the solder interconnects given full creep and plastic properties. The results obtained from the hierarchal fracture process model are validated against the experimentally obtained fatigue lives and cross-sectional images of the crack path.Copyright © 2009 by ASME

The problem of solder joint fatigue is essentially one of fatigue crack growth. However, little work has been done that enables fatigue life predictions by means of tracking the crack front and its growth. Most popular fatigue life models are empirical and therefore, limited in their applicability and in the insight they provide. Analytical fracture mechanics approaches such as the Paris law and the J-integral are of questionable validity due to the fact that several assumptions made in these approaches are not appropriate in the context of solder joint fatigue. Failure in solder joints involves large plastic deformation in a viscoplastic material along with crack growth which is not self-similar and is significantly large relative to the size of the joint. Accurate descriptions of crack growth in solder joints can thus be obtained only by means of an approach that includes (a) the complete constitutive behavior of solder and (b) a non-empirical failure model that does not make the limiting assumptions of small cracks or self-similar crack growth. One such promising approach is the hybrid damage modeling approach, which is inspired by cohesive zone modeling and Weibull functions. In this study, we focus on investigating the nature of the stress and strain behavior in solder joints and its effect on the hybrid model. We review well understood principles in elastic-plastic fracture mechanics and more recent work in cohesive zone modeling, that address the nature of the singular solutions at the crack tip and provide insight when dealing with the more complex problem of solder joint fracture. Using three dimensional finite element analysis of a chip scale package (CSP), we systematically examined the stress-strain behavior at the edge of the solder joint along the interface. The singular nature of the behavior manifests itself as mesh dependence of the predicted crack front shape and the cycles to failure. We discuss the conditions under which the predicted crack growth rate is of reasonable accuracy, by incorporation of a characteristic length measure. We validate predictions made by the hybrid damage modeling approach against a companion experimental study in which crack growth was tracked in packages subjected to accelerated thermal cycling. In the first part, we discussed the effects of choice of constitutive model (elasticity, deformation and incremental plasticity and creep) and finite deformation on the nature of the singularity at the crack tip and the resulting mesh sensitivity. We used a conventional crack-in-plate analysis to first study the effects and then investigate similar effects in the more complex problem of a solder joint. In the second part, presented here, a characteristic length is introduced in an attempt to mitigate the mesh dependence, and shown to improve results for the predictions of crack growth in both, the crack-in-plate and the solder joint models.

Predicting the fatigue life of solder interconnections is a challenge due to the complex nonlinear behavior of solder alloys and the importance of the load history. Long experience with Sn–Pb solder alloys together with empirical fatigue life models such as the Coffin–Manson rule have helped us identify reliable choices among package design alternatives. However, for the currently popular Pb-free choice of SnAgCu solder joints, designing accelerated thermal cycling tests and estimating the fatigue life are challenged by the significantly different creep behavior relative to Sn–Pb alloys. In this paper, a hybrid fatigue modeling approach inspired by nonlinear fracture mechanics is developed to predict the crack trajectory and fatigue life of a solder interconnection. The model is shown to be similar to well accepted cohesive zone models in its theoretical development and application and is anticipated to be computationally more efficient compared to cohesive zone models in a finite element setting. The approach goes beyond empirical modeling in accurately predicting crack trajectories and is validated against experiments performed on lead-free as well as Sn–Pb solder joint containing microelectronic packages. Material parameters relevant to the model are estimated via a coupled experimental and numerical technique.

The need for predicting fatigue life in solder joints is well appreciated at the present time. Currently, however, there are very few experimentally validated material parameters for popular SnAgCu alloys. Furthermore, the validity of Coffin-Manson life models, being empirical, also needs to be explored for these alloys which creep in a manner significantly different from SnPb solder alloys. In this paper, we present a modeling approach inspired by cohesive zone theory of modern fracture mechanics and Weibull distributions of material failure. The approach relies on the accurate estimation of inelastic strains at the crack tip estimated through finite element analysis, which are then used to make decisions on crack propagation. Like most popular cohesive zone models, the modeling approach presented here requires the estimation of two parameters. Unlike most cohesive zone models however, no special elements are needed in the finite element model and estimation of the parameters is more straightforward. We demonstrate the applicability of the modeling approach via the simulation of fatigue crack growth in Sn3.8Ag0.7Cu solder joints subjected to anisotropic thermal cycling. Anisotropic thermal cycling conditions were created experimentally using a simulated power cycling testing device and fatigue crack fronts were tracked at different life cycles using traditional dye-and-pry methods. The experiments were repeated for varying temperature profiles. Experimental results were coupled with numerical analysis to obtain fracture parameters for Sn3.8Ag0.7Cu. The model and the parameters were then validated by verifying their predictive ability against a variety of temperature profiles. In a separate study, the authors have developed a time hardening creep model for describing the behavior of Sn3.8Ag0.7Cu. The time hardening model accounts for primary and secondary creep and does not restrict itself to the assumption of steady state creep. The need for accurate estimation of inelastic strains in the finite element model is thus met using a valid constitutive model to describe solder creep behavior. The ability of the model to predict three dimensional crack fronts for a variety of fatigue loading environments, with sufficient accuracy, is a key result of this work.

Microsystems present several challenging reliability-related issues on account of their micron-scale dimensions. Many of these micron sized devices consist of compliant beam- or plate-like microstructures that are in close proximity to a substrate or other structural parts. If such structures come into contact, short-range adhesive forces can pin them together if they cannot be overcome by the elastic restoring forces of the deformed microstructures. This phenomenon of adhesion, often called stiction, depends on the structural response of the micro structure itself, as well as on the nature of the adhesive forces between the contacting surfaces. In this study we develop an approach to model adhesion in microsystems in a computationally feasible finite element environment, and demonstrate its capability via a companion experimental study. The modeling approach adopts the principles of three dimensional linear elastic fracture mechanics (LEFM) and extends it to thin-film plate-like microstructures. Extensive experimental work is done to study the behavior of adhesion in micro structure cantilever beams and square and circular plates. The finite element code is validated against analytically predicted and experimentally observed behavior to corroborate its effectiveness

Predicting the fatigue life of solder interconnections is a challenge due to the complex nonlinear behavior of solder alloys and the load history. Long experience with Sn-Pb solder alloys together with empirical fatigue life models such as the Coffin-Manson rule have helped us identify reliable choices among package design alternatives. However, for the currently popular Pb-free choice of SnAgCu solder joints, designing accelerated thermal cycling tests and estimating the fatigue life are challenged by the significantly different creep behavior relative to Sn-Pb alloys. This study is divided into two parts: In the first part, a hybrid fatigue modeling approach inspired by nonlinear fracture mechanics is discussed. The hybrid fatigue model has been shown to predict the crack trajectory and fatigue life of a Sn-Pb solder interconnection subjected to both isothermal accelerated thermal and anisothermal power cycling conditions. In the second part, results of experimental characterization via fatigue testing of microelectronic packages with SnAgCu solder interconnections subjected to anisothermal power cycling conditions are described. Packages of different geometries were tested to study the effects of these variations on the estimation of fatigue life. The afore mentioned hybrid model relies on the estimation of two fracture parameters which are to be determined experimentally. In this study, a novel technique involving tracking crack fronts in solder interconnections as a function of number of fatigue cycles is proposed to estimate these fracture parameters that can be then used to model fatigue crack growth using the hybrid modeling technique.

Predicting the fatigue life of solder interconnections is a challenge due to the complex nonlinear behavior of solder alloys and the load history. Long experience with Sn-Pb solder alloys together with empirical fatigue life models such as the Coffin-Manson rule have helped us identify reliable choices among package design alternatives. However, for the currently popular Pb-free choice of SnAgCu solder joints, designing accelerated thermal cycling tests and estimating the fatigue life are challenged by the significantly different creep behavior relative to Sn-Pb alloys. In this paper, a hybrid fatigue modeling approach inspired by nonlinear fracture mechanics is developed to predict the crack trajectory and fatigue life of a solder interconnection subjected to both isothermal accelerated thermal and anisothermal power cycling conditions. The model is shown to be similar to well accepted cohesive zone models in its approach and application and is anticipated to be computationally more efficient in a finite element setting. The approach goes beyond empirical modeling in accurately predicting crack trajectories. It is argued that such non-empirical models that capture the physics of material degradation and failure can form the basis for determining meaningful Pb-free solder environmental testing conditions as well as the acceleration factors relative to field use