Simulation offers speed and cost savings over thermal cycling
BY CEMAL BASARAN, HONG TANG, TERRANCE DISHONG AND DAMION SEARLS

In the microelectronics industry, reliability of a package is usually assessed by the integrity of its solder joints. Tinlead eutectic and neareutectic solder alloys are the most commonly used bonding materials in electronic packaging, providing electrical and thermal interconnection, as well as mechanical support. The temperature fluctuations as a result of device internal heat dissipation and ambient temperature changes, combined with the coefficient of thermal expansion (CTE) mismatch between the solder and packaging materials, result in thermomechanical fatigue of the solder joints. Progressive damage eventually leads to device failure.
The standard practice in the industry to determine the number of cycles to failure is conducting highly accelerated stress testing in a thermal chamber. The process of thermal cycling is expensive and time consuming, but computer simulation is a good alternative to these problems. Simulation can be even more beneficial for new package designs, where cost of manufacturing a prototype test vehicle is very high. The purpose of this article is to show that by using a new plugin special purpose material subroutine in a commercial finite element code, testing can be simulated on a computer screen.
Modeling and Testing
One of the reasons for preferring testing over computational procedures to determine reliability of solder joints is the lack of verified specialized material models and software packages. For example, all of the major commercial finite element analysis codes available in the market are effective for stress analysis but lack the capability to perform number of cycles to failure analysis in a unified manner for solder joints. The process requires a specialized material model based on damage mechanics theory and verification at the actual solder joint level. On the positive side, all major finite element analysis codes allow users to implement their own user defined plugin material subroutines.
Figure 1. Comparison of fatigue life (Solomon's Test vs. FEM). 
Until now, it was not possible to measure strain field in a solder joint during fatigue testing, which is essential for verifying the material model. A Moiréé interferometry system developed at University at Buffalo, Electronic Packaging Laboratory (UBEPL) allows measurement of strain field during fatigue testing up to failure.
Figure 2. Cross section of the BGA package. 
A fatigue life prediction model based on thermodynamic principles has also been developed at UBEPL and used for computer simulations of reliability tests of actual ball grid array (BGA) packaging. The damage within the solder joints, corresponding to the material degradation under cyclic themomechanical loading, is quantified with a thermodynamic framework. The damage, as an internal state variable, is coupled with a creep deformationbased constitutive model to characterize the response of solder joints. The model is implemented into a commercial finite element package through its userdefined subroutine.
Predicting Solder Joint Reliability
Fatigue life prediction of solder joints is critical to the reliability assessment of electronic packaging. The standard state of practice in the microelectronics industry for predicting the number of cycles to failure is based on using empirical relations obtained by testing. If an analytical approach is used, usually empirical curves such as CoffinManson (CM) are employed. Typically, using the CTE differential between the bonded components, the maximum expected elastic and plastic strains in the solder joint are calculated.
Figure 3. Thermal loading profile of one cycle. 
Most of the time, using the plastic strain value, CM curves are used to predict the fatigue life of solder joints. It has been shown by many researchers that this approach yields conservative results for BGA packages. For example, Zhao et al. have shown metallurgically that the
Figure 4. Shear strain distribution after 2 and 4 thermal cycles (with damage model implemented). 
CM approach cannot be used for microstructurally evolving materials, such as tinlead solder alloys.^{1,2} The reason for this is that the CM approach does not take into account any change in material properties during the fatigue process. The CM approach assumes that the plastic strain experienced during each thermal cycle remains constant during the thermal cycling process. In reality, actual plastic strain experienced by the solder joint decreases at each cycle as a result of microstructural coarsening. Consequently, the CM approach significantly underestimates fatigue life of solder joints.
Figure 5. Shear strain distribution after 6 and 8 thermal cycles (with damage model implemented). 
A damage evolution function is used in this study to quantify the degradation in the solder joint. The damage evolution function is based on the second law of thermodynamics and uses entropy as a damage metric. Basaran and Yan have shown that the entropy, which is a measure of disorder in a system, can be used as a damage metric in solid mechanics.^{3} The damage evolution is incorporated into a unified viscoplastic constitutive model (described below) to characterize the cyclic fatigue behavior of solder joints under thermomechanical loading.
Constitutive Model
Experimental results indicate that the contribution of the elastic strain component to lowcycle fatigue life is negligible compared to the contributions of creep, or viscoplastic, strain. The time dependent creep strain dominates the lowcycle fatigue life of solder joints.^{1,2} This is because eutectic and neareutectic solder alloys are regularly expected to perform at high homologous temperature (0.50.8 Tm) due to their low melting point (183°C). At high homologous temperatures, materials experience significant creep deformation. A thermoviscoplastic constitutive model is, therefore, essential for modeling solder behavior.
Figure 6. Shear strain distribution after 10 thermal cycles (with damage model implemented). 
To model primary, secondary and tertiary creep stages of neareutectic solder, a creep rate function is needed. Steadystate plastic deformation kinetics of most metals and alloys at high homologous temperatures can be described by the Dorn creep equation.^{4} Kashyap and Murty have experimentally shown that grain size can significantly affect creep behavior of tinlead solder alloys.^{5} Based on their laboratory test data results, they proposed a creep law that is a modified version of the Dorn equation. The strain rate is described as a function of temperature, diffusion coefficients, and material parameters, such as Young's modulus and grain size. Activation energies vary with temperature, and are determined based on published creep data. Similarly, the grain size is exponentially related to the strain rate by an experimentally determined grain size exponent.
To simulate cyclic fatigue behavior of materials, there is a need for a progressive degradation model. Damage mechanics provides us a basic framework to develop damage evolution models. An internal damage variable is introduced into the stressstrain relationship. As degradation of the solder increases, the value of the damage variable goes from zero to one, which represents total failure. Basaran and Yan have shown that entropy is the most accurate and simplest damage metric for solder joints.^{3} The entropy can be described in terms of a disorder parameter. Change in disorder parameter yields degradation in the solder joint. More details on the damage mechanics model are available in the references.^{3,6}
Figure 7. Comparison of finite element simulation results with Moiré interferometry test data. 
Using the damage mechanics based constitutive model briefly presented above eliminates the need for a twostep process to estimate the number of cycles to failure, which is the traditional way of performing fatigue analysis. A finite element analysis typically calculates the plastic strain for one thermal cycle and then a CM curve is used to predict the fatigue life for that plastic strain value. The model proposed above directly yields the fatigue life of each solder joint, as well as providing a visual presentation of the degradation process that take place in a solder joint.
Finite Element Simulations and Laboratory Tests
Several numerical simulations of simple cyclic shear tests were made by the damage mechanics based model, and compared with the fatigue test results of Pb40/Sn60 solder joints. Solomon performed cyclic simple shear tests on Pb40/Sn60 solder joints under isothermal displacement controlled conditions, with different plastic strain ranges.^{9} The author reported the number of cycles to failure for each plastic strain range, defining failure as a 90percent load drop in ultimate stress. Figure 1 shows the comparison between the number of cycles to failure for Solomon's test data and the finite element simulations.
Figure 8. Damage distribution after 10 thermal cycles (with damage model implemented). 
Computer simulation was also performed for the fatigue behavior of Pb37/Sn63 solder joints in an actual BGA package that was subjected to thermal cycling. The cross section of the BGA package tested is shown in Figure 2. An FR4 printed circuit board (PCB) and polymer connector layer are connected by Pb37/Sn63 solder joints. Only half of the package is plotted and meshed for simulation because of the structural symmetry.
Testing was performed to validate the model and implementation into the finite element program. An actual BGA package was subjected to thermal cycling in a SuperAGREE thermal chamber and the plastic strain field was measured by means of high sensitivity Moiré interferometry. Using the finite element program, with the implemented constitutive model, the same thermal cyclic tests were simulated and results were compared.
The BGA package was subjected to the thermal loading profile shown in Figure 3. A Super AGREE thermal chamber was used for thermal cycling. Specimens were periodically taken out to measure inelastic strain accumulation in each solder joints using the Moiré interferometry system. Details of this testing are given in Zhao et al.^{1.2} During testing and finite element analysis (FEA) simulation, the package is fixed at the both ends of the middle FR4 PCB layer. In finite element simulations, the FR4 PCB and polymer layers are considered as linear elastic and solder joints as nonlinear elasticviscoplastic with damage evolution.
Figure 9. The evolution of maximum damage under 10 thermal cycles (with damage model implemented). 
Thermally induced shear strain in the solder joints, because of the CTE mismatch between FR4 PCB and polymer layer, are cyclic in nature, and they result in thermomechanical fatigue of solder joints. Experiment results show that shear strain dominates creepfatigue in solder joints. Numerical simulations of shear strain are shown in Figures 4 through 6. In practice, testing to failure can require 1,000 cycles or more. For the purpose of verifying the computer model, however, simulating 10 cycles is sufficient. The FEA results of shear strain of the solder joint are in good correlation with the Moiré interferometry test data. During testing, highest strain was always observed in solder joint number 1. Therefore the results of inelastic strain accumulation from FEA and Moiré interferometry methods are plotted for that joint (Figure 7). It should be pointed out that, in our testing and analysis, it was observed that plastic strain accumulation is not linear from cycle to cycle. Plastic strain accumulation in each cycle decreases as solder coarsening progresses. On the other hand, with the CM approach, it is assumed that plastic strain accumulation is linear. Therefore, in practice, the fatigue life of BGA packages obtained from lab tests is usually longer than the fatigue life predicted by CoffinManson based models.
The simulation of damage distribution among solder joints is shown in Figure 8. The damage distribution provides important information for design optimization and reliability, because it can be used to predict where and when packages will fail. Figure 9 shows the simulation of damage evolution of the critical solder joint. The damage evolution is an intrinsic reflection of material degradation under fatigue loading, rather than just an indirect measure, such as electrical open. Using the damage evolution function, the accurate fatigue life prediction can be made and the material degradation progress can be predicted for each point in the solder joint by means of computational simulations.
Conclusions
A computational tool with damagecoupled viscoplastic constitutive model has been proposed and implemented into the finite element package through a userdefined material subroutine. Using computational simulations, the cost of reliability evaluations for new generation packages can be reduced significantly. The FEA simulation of thermomechanical response of Pb37/Sn63 solder joints in a BGA electronic package under thermal cyclic loading was compared with the test data. A comparison of FEA results with Moiré interferometry measurements shows good correlations. The objective of the implementation is to provide a computational tool for fatigue life predictions of reallife solder joints in electronic packages. This work can facilitate numerical simulation of the progressive degradation of eutectic solder interconnections in electronic packages under thermomechanical fatigue loading without need for extensive costly testing.
AP
Acknowledgments
This research project is partially sponsored by a grant from the National Science Foundation GOALI program, CMS division and by the DoD Office of Naval Research PEBB program.
References
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 C. Basaran and C.Y. Yan, "A Thermodynamic Framework for Damage Mechanics of Solder Joints," Journal of Electronic Packaging, Trans. ASME, Vol.120, 1998, pp. 379384.
 D.S. Stone and M.M. Rashid, "Constitutive Models," The Mechanics of Solder Alloys, Interconnect, ChapmanHall, 1994.
 P. Kashyap and G.S. Murty, "Experimental Constitutive Relations for the High Temperature Deformation of a PbSn Eutectic Alloy," J. Mater. Sci. Eng., Vol. 50, 1981, pp. 205213.
 L.M. Kachanov, Introduction of Continuum Damage Mechanics, Nijhoff (Martinus), Dordrecht, 1986.
 I. Boltzman,1898, Lectures on Gas Theory, U of California Press, Berkley, CA (translation by S. Brush, 1964).
 H.D. Solomon, "StrainLife Behavior in 60/40 Solder," ASME Journal of Electronic Packaging, Vol. 111, 1989, pp. 7582.
 P.J. Adams, "Thermal Fatigue of Solder Joints in MicroElectronic Devices," M.S. Thesis, Department of Mechanical Engineering, MIT, Cambridge, MA, 1986.
 Basaran, C., and Chandaroy, R., "Mechanics of Pb40/Sn60 Neareutectic Solder Alloys Subjected to Vibration," Applied Mathematical Modeling, Vol. 22, 1998, pp. 601627.
CEMAL BASARAN is associate professor and director, and HONG TANG is a Ph.D. candidate at the Electronic Packaging Laboratory at the University at Buffalo, SUNY. TERRANCE DISHONG is a path finding architect, and DAMION SEARLS is manager of microprocessor packaging Q&R; at Intel Corporation.
For more information, contact Cemal Basaran at 212 Ketter Hall, North Campus, Buffalo, NY 142604300; 7166452114; Fax: 7166453733; Email: [email protected].
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