D. Chan

Constitutive Behavior of Sn3.8Ag0.7Cu and Sn1.0Ag0.5Cu Alloys at Creep and Low Strain Rate Regimes

Constitutive models for SnAgCu solder alloys are of great interest at the present. Commonly, constitutive models that have been successfully used in the past for Sn-Pb solders are used to describe the behavior of SnAgCu solder alloys. Two issues in the modeling of lead-free solders demand careful attention: 1) Lead-free solders show significantly different creep strain evolution with time, stress and temperature, and the assumption of evolution to steady state creep nearly instantaneously may not be valid in SnAgCu alloys and 2) Models derived from bulk sample test data may not be reliable when predicting deformation behavior at the solder interconnection level for lead-free solders due to the differences in the inherent microstructures at these different scales. In addition, the building of valid constitutive models from test data derived from tests on solder joints must de-convolute the effects of joint geometry and its influence on stress heterogeneity. Such issues have often received insufficient attention in prior constitutive modeling efforts. In this study all of the above issues are addressed in developing constitutive models of Sn3.8Ag0.7Cu and Sn1.0Ag0.5Cu solder alloys, which represent the extremes of Ag composition that have been mooted at the present time. The results of monotonic testing are reported for strain rates ranging from 4.02E-6 to 2.40E-3 s-1. The creep behavior at stress levels ranging from 7.8 to 52 MPa is also described. Both types of tests were performed at temperatures of 25degC, 75degC and 125degC. The popular Anand model and the classical time-hardening creep model are fit to the data, and the experimentally obtained model parameters are reported. The test data are compared against other reported data in the literature and conclusions are drawn on the plausible sources of error in the data reported in the prior literature.

Microstructurally Adaptive Model for Primary and Secondary Creep of Sn-Ag-Based Solders

Sn-Ag-based solders are susceptible to appreciable microstructural coarsening due to the combined effect of thermal and mechanical stimuli during service and storage. This results in evolution of the creep properties of the solder over time, necessitating the development of a thermo-mechanical history-dependent creep model for accurate prediction of the long-term reliability of microelectronic solder joints. In this paper, the coarsening behavior of Ag3Sn and Cu6Sn5 precipitates in ball grid array-sized joints of Sn-3.8Ag-0.7Cu solder attached to Ni bond-pads with four different thermo-mechanical histories is reported. Because of the substantial numerical superiority of Ag3Sn over Cu6Sn5, it was inferred that the evolution of mechanical properties during aging is controlled largely by the coarsening of Ag3Sn. An effective diffusion length (x̅) for Ag diffusion in Sn was defined, and it is shown to adequately describe the thermo-mechanical history dependence of Ag3Sn particle size. The shear creep behavior of these joints was experimentally characterized, and the entire creep data were fitted to a unified model combining exponential primary creep and power-law steady state creep. The parameter x̅ was then incorporated into the creep equation to produce a unified creep model, which can adapt to thermo-mechanical history-dependent microstructural coarsening in the solder. Predictions using this creep law show very good agreement with experimental creep data for several different test and microstructural conditions.

Maximum-Entropy Principle for Modeling Damage and Fracture in Solder Joints

A maximum-entropy fracture model (MEFM) is derived from concepts of information theory and statistical thermodynamics. Exploiting the maximum-entropy principle enables life predictions for a structure in the presence of microstructural uncertainty. This single-parameter model relates the probability of fracture to accumulated entropic dissipation at a given material point. Using J2 plasticity and equilibrium thermodynamics, entropic dissipation is related to inelastic dissipation. We demonstrate the MEFM by extracting the single damage accumulation parameter for Sn-3.8Ag-0.7Cu solder through cyclical fatigue testing. We then apply the model with the single parameter to numerically predict, in three dimensions, crack initiation and growth in Sn-3.8Ag-0.7Cu solder joints of a wafer-level chip-scale package (WLCSP). The simulated crack fronts are validated against experimentally observed crack fronts obtained by testing 64 packages under conditions identical to those used in the simulations. The model is shown to accurately predict the geometrical profile of the observed crack fronts, and the number of cycles corresponding to the observed crack profile to within 10% of the measured number of cycles.

Maximum entropy fracture model and its use for predicting cyclic hysteresis in Sn3.8Ag0.7Cu and Sn3.0Ag0.5 solder alloys

Abstract Appropriate constitutive, damage accumulation and fracture models are critical to accurate life predictions. In this study, we utilize the maximum entropy fracture model (MEFM) to predict and validate cyclic hysteresis in Sn3.8Ag0.7Cu and Sn3.0Ag0.5 solder alloys through a damage enhanced Anand viscoplasticity model. MEFM is a single-parameter, information theory inspired model that aims to provide the best estimate for accumulated damage at a material point in ductile solids in the absence of detailed microstructural information. Using the developed model, we predict the load drop during cyclic fatigue testing of the two chosen alloys. A custom-built microscale mechanical tester was utilized to carryout isothermal cyclic fatigue tests on specially designed assemblies. The resultant relationship between load drop and accumulated inelastic dissipation was used to extract the geometry and temperature-independent damage accumulation parameter of the maximum entropy fracture model for each alloy. The damage accumulation relationship is input into the Anand viscoplastic constitutive model, allowing prediction of the stress–strain hysteresis and cyclic load drop. The damage accumulation model is validated by comparing predicted and measured load drops after 55 and 85 cycles respectively for Sn3.8Ag0.7Cu and Sn3.0Ag0.5 solder alloys. The predictions agreed to within 10% and 20% of the experimental observations respectively for the two alloys. The damage enhanced Anand model developed in this study will enable the tracking of crack fronts during finite element simulations of fatigue crack initiation and propagation in complex solder joint geometries.

Constitutive Models for Intermediate- and High-Strain Rate Flow Behavior of Sn3.8Ag0.7Cu and Sn1.0Ag0.5Cu Solder Alloys

In much of the existing research, SnAgCu solder alloys are characterized at low strain rates, typically in the 10-6 to 1 s-1 range. In this paper, we report experimental results and constitutive models for two popular SnAgCu solder alloys at intermediate and high strain rates, ranging from 10-2 to 103 s-1 at room temperature. These experiments were performed using two different experimental setups: a MTS 810 uniaxial compression tester, and a split-Hopkinson pressure bar. In conjunction with our previous work at lower strain rates (10-6 to 10-3 s-1), these results yield the plastic flow response of these solders over nine decades of strain rate, and demonstrate a remarkably consistent relationship between the yield stress and the strain rate over the entire nine decades. We also develop the Anand viscoplastic constitutive model, and demonstrate that fit parameters for the low-strain rate regime can be extrapolated to accurately predict the experimental response at high strain rates. Thus, the model presented here proffers the capability of modeling solder deformation under a wide range of loading conditions using most commercially available finite element (FE) programs. To illustrate the validity of the model parameters, we develop idealized FE models together with cohesive zone failure descriptions at the interface between the solder and the intermetallic compound. We demonstrate that when used in conjunction with appropriate failure models, the constitutive model developed here accurately captures the empirically observed shift in failure modes from bulk failure to interfacial failure under tensile loading at higher strain rates.

Aging-informed behavior of Sn3.8Ag0.7Cu solder alloys

Predicting reliability of solder joints requires a thorough understanding of solder constitutive behavior. Recent studies on SnAgCu solder alloys have reported that pre-test conditions of aging-time and aging-temperatures can be factors that significantly affect solder constitutive behavior. The results presented here are a part of ongoing efforts to construct constitutive models that can predict aging affects on behavior of SnAgCu solder alloys. In this work, creep test results on aged Sn3.8Ag0.7Cu samples are reported, and aging effects are discussed primarily on secondary creep behavior and on microstructure. Aging effects on primary creep are observed, and will be discussed, and modeled in a future work. Experiments to characterize behavior were carried out using double-lap shear tests on specimens specifically prepared to represent realistic microstructures, and mitigate effects of joint geometry, and stress heterogeneity during test conditions. Aging temperatures of -10deg C, 25deg C, 75deg C and 125deg C, and aging times of 15, 30, 60 and 90 days (at each aging temperature) were selected as different levels of factors in a statistically designed experiment. Previous studies have focused on developing constitutive models without due considerations to aging effects, the results presented herein augment aging-informed constitutive model development efforts that are currently in progress.

A Nonlinear Fracture Mechanics Approach to Modeling Fatigue Crack Growth in Solder Joints

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.

Fatigue Crack Growth and Life Descriptions of Sn3.8Ag0.7Cu Solder Joints: A Computational and Experimental Study

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.

Effects of Dwell Time on the Fatigue Life of Sn3.8Ag0.7Cu and Sn3.0Ag0.5Cu Solder Joints During Simulated Power Cycling

Compared to Sn-Pb solder joints, our understanding of the fatigue of SnAgCu solder joints is far from complete. The challenges to achieving a complete understanding of SnAgCu solder joint fatigue arise partly from their significantly different creep behavior and vulnerability to micro structure evolution (aging). In this paper, we present results from thermal fatigue tests carried out with the help of a simulated power cycling tester. The test specimens were 1.27 mm pitch Ceramic Ball-Grid Array (CBGA) components with two lead-free solder alloy compositions - Sn3.8Ag0.7Cu and Sn3.0Ag0.5Cu. The components were subjected to hot dwells at 100degC for 10, 30 and 60 minutes to study the effect of dwell time on the fatigue life -a total of 48 components were tested. The resulting failure data was fit to a Weibull distribution. The packages were stored at room temperature prior to testing and the effect of the time of storage on the fatigue life was also studied. Finite element analyses were performed to study the effect of hot dwell time on the fatigue life of the CBGA component.

Maximum entropy fracture model and fatigue fracture of mixed SnPb/Sn3.0Ag0.5Cu solder alloys

During the transition from Pb-containing solders to Pb-free solders, joints composed of a mixture of SnPb and SnAgCu often result from either mixed assemblies or rework. Comprehensive characterization of the constitutive and fatigue fracture behavior of these mixed solder alloys is necessary to predict the life of mixed alloy solder joints. Three alloys of 1, 5 and 20 weight percent Pb were selected so as to represent reasonable ranges of Pb contamination expected from different 63Sn37Pb components mixed with Sn3.0Ag0.5Cu alloy. In recent, related, work we developed constitutive relations for these alloys; this work focuses on the fatigue failure behavior. One recent approach to modeling fatigue fracture in ductile solids is the maximum entropy fracture model. The maximum entropy fracture model is a thermodynamically consistent and information theory inspired (non-empirical) damage accumulation theory for ductile solids, validated on both area array and peripheral array packages. The model uses a single damage accumulation parameter to relate the probability of fracture to accumulated entropic dissipation. A custom-built microscale mechanical tester capable of submicron displacement resolution was utilized to carryout isothermal cyclic fatigue tests on specially designed assemblies using the three mixed alloys. The resultant relationship between load drop and accumulated entropic dissipation was used to extract the temperature and geometry-independent damage accumulation parameter of the information theoretic model for each alloy. Combining our knowledge of the constitutive behavior with the damage accumulation behavior, life predictions can be made for a wide variety of package types and mixed metallurgical conditions.