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Interaction Effect of Voids and Standoff Height on Thermomechanical Durability of BGA Solder Joints Leila J. Ladani and Jafar Razmi
Abstract—This paper documents simulation studies on the interactive effect of standoff height and void volume on the thermomechanical durability of ball-grid-array solder joints using a 3-D viscoplastic finite element analysis. Surface Evolver software was used to find the optimized shape of the solder joints and standoff height by minimizing the surface energy as voids with different sizes were placed in solder balls. A global–local modeling approach was then utilized to model the thermomechanical durability of voided solder joints. Void-area-fraction ranges of 14%–40% were analyzed. A nonmonotonic behavior of durability versus void area fraction was observed. The results showed that, if the void is completely inside the solder ball and has no interface with the boundaries of the joint, it does not have a detrimental effect and even improves the durability as the void size increases. However, voids located at the interface of the solder joint and copper pads were found very detrimental to durability. Factors such as load bearing area, stress concentration factor, and overall compliance of the structure were found responsible for the nonmonotonic behavior of the joints. An analytical micromechanics approach was used to calculate the compliance of the structure, and a nonmonotonic trend in phase with the durability trend was observed. The stress concentration factor also showed the same nonmonotonic trend. The rise of these two factors for the void interfacing with copper pads in addition to the decreased-load-bearing-area effect resulted in a drastic decrease in durability. Index Terms—Cyclic loading, solder joints, thermomechanical durability, voids.
N OMENCLATURE A Af E F g G L L0 K Nf S1 T U
Facet area. Void area fraction. Elastic modulus. Force. Gravitational constant. Shear modulus. Effective stiffness matrix. Stiffness matrix. Bulk modulus. Number of cycles to failure. Eshelby’s tensor. Surface tension. Energy.
Manuscript received November 12, 2008; revised February 11, 2009 and March 19, 2009. First published April 10, 2009; current version published September 2, 2009. The authors are with the Department of Mechanical and Aerospace Engineering, Utah State University, Logan, UT 84322 USA (e-mail: Ladani@ engineering.usu.edu;
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TDMR.2009.2020600
V Wc Wp Z ρ ν Δεp
Volume. Rate-dependent inelastic strain energy. Rate-independent inelastic strain energy. Height. Density. Poisson’s ratio. Plastic strain range on one cycle. I. I NTRODUCTION
V
OIDS are one of several types of defects that may be introduced during the manufacturing processes of microelectronic devices. Manufacturing voids in solders are relatively large and are caused by entrapped air during reflow and outgassing from either the PWB laminates or the solder flux [1]. Voids can cause quality and reliability issues. Very large voids may cause starved joints and premature failures. They may also pose reliability issues depending on the geometry of the joint, void size, location, and frequency. Voids and their effects on durability are reasonably well understood for Sn37Pb solder joints because of their relative maturity in the electronics industry. Assembly processes have been optimized to improve the quality of the processes and the durability of products made with Sn37Pb solders. The manufacturing processes for Pb-free solders, however, have not yet undergone the same level of scrutiny for quality issues. Due to different melting temperatures and wettability, Pb-free solder joints are more prone to voids. The effect of voids on durability and stress concentration in solder joints have been studied by researchers such as Lau et al. [2], [1], Liu and Mei [3], Banks et al. [4], Yunus et al. [5], Doroszuk et al. [6], Zhu et al. [7], Kim et al. [8], and Herzog et al. [9]. Some of these researchers have come up with conflicting results about the effect of voids on durability or stress distribution in solder balls. Some studies have been conducted for Sn–Pb solders and cannot be extrapolated to Pb-free solders such as Lau’s study. In some cases, modeling was conducted for a very simple geometry in 2-D finite elements and under different types of loading such as mechanical and vibration loading. In some cases, such as that of Kim et al., the solder was considered elastic–plastic which does not represent the case of thermomechanical loading (even room temperature is higher than the 0.5 homologous temperature of Pb-free solders, and thus, the solder experiences creep deformation which may exacerbate in case of thermomechanical loading in which the solder may experience temperatures up to 125 ◦ C). Finally, some have used linear elastic fracture mechanics, such as Lau and Jeans [2], to evaluate the solder damage, which is not the best way for thermomechanical loading since
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LADANI AND RAZMI: EFFECT OF VOIDS AND STANDOFF HEIGHT ON DURABILITY OF SOLDER JOINTS
the solder damage is caused by the accumulation of micro cracks and microvoids resulting in a very ductile fracture, unlike brittle materials in which the crack can develop as a single sharp crack. Therefore, continuum damage models are deemed more appropriate for solder materials under thermomechanical loadings. In a recent study conducted by the author, it was shown that, depending on the location, voids larger than 25% of the area fraction of ball-grid-array (BGA) joints may degrade reliability drastically [12]. Voids, however, may increase the standoff height of solder joints, which has been proven to assist the reliability of the joints [4], [11]. One of the shortcomings of the previous study conducted by Ladani and Dasgupta was that the modeling was conducted such that the joint volume was reduced when the void was introduced. In other words, voids were introduced by taking a portion of the material out of the solder ball. In reality, the volume of the void will be added to the volume of the joint, causing the standoff height to increase. The durability in this case will be a function of competing factors, void size, location, and standoff height. Thus far, no study has been published on the dependence of standoff height and void size and their interaction effect on durability. We have attempted to cover all of the aforementioned shortcomings in this paper by developing a comprehensive model for the case of thermomechanical modeling in 3-D finite element analyses using continuum damage models. One of the objectives of this study is to find the relationship between the void volume and the standoff height. Surface Evolver (SE) was used to find the optimum shape and height of the solder joints with a void inside and to determine the change in the standoff height as a function of void volume. This information was then used in ANSYS to model the durability of solder balls with voids and increased standoff height as a result of void. The main objective of this study was to find the interaction between the standoff height and void on durability as a response variable.
II. S URFACE E VOLVER The SE [13] software is an interactive program to find the optimum surfaces shaped by surface tension, gravity, and other energies that are subject to various constraints by minimizing these energies. The energy in the Evolver can be a combination of surface tension, gravitational energy, squared mean curvature, user-defined surface integrals, or knot energies. A surface is implemented as a union of triangles. The user defines an initial surface in a data file. The Evolver evolves the surface toward minimal energy by a gradient descent method. In the case of the solder joint, the energy consists of surface energy, gravitational energy, and energy due to applied loads. Therefore, the total energy is the summation of the integrals of these energies over the surface or volume [11]
T dA +
U= A
ρgdz +
FV A
(1)
V
where T is the surface tension, A is the facet area, z is the solder height, F is the net force on the molten solder, and V
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Fig. 1. Standoff height versus void volume.
is the solder volume. ρ is the density of solder material, g is the gravitational constant, and U denotes the total energy. In SE, the surface is defined by vertices, edges, and faces. Each edge is defined by its vertices, and each face is defined by its edges. Different types of constraints can be put on the vertices, edges, or surfaces. A data file was used to model a void inside the BGA solder joints. Five different constraints were imposed on the model: two constraints that define the place of upper and lower pads, one constraint that defines the shape of the lower and upper pad as a circle, and two constraints that keep the void inside the surface. The total volume of the solder ball is the summation of the void and initial volumes of the solder without the void. The height of the solder joint was considered as an optimizing parameter, which means that it can vary to minimize the energy. By default, Evolver uses only the first gradient information for moving to an optimal shape using the steepest descent method. Evolver also provides an alternate conjugate gradient methodology that makes use of the past history of the optimization process. In this paper, the default method of the steepest descent algorithm has been used. The Hessian command was used to start the iteration process. This command constructs a quadratic approximation of the energy and solves for the minimum. III. SE R ESULTS A parametric study was conducted for void area fractions varied between 14% and 40%. Area fraction is defined as the ratio of the void area to the solder ball area when viewed from the top (the same way X-ray machines measure the area fraction for voids). In almost all the cases except that of 40% area fraction, the standoff height increase accommodated the void size increase, and the void was formed spherically inside the solder ball. In the case of 40% void area fraction, the void was shaped flat at the top and base. In this case, the void was considered to be truncated by the copper pad when it was modeled in ANSYS, as seen in Fig. 1. The standoff height was extracted from the SE data and was plotted versus the void volume as seen in Fig. 1. Standoff height is the linear function of void volume. The validity of the SE results has been confirmed by Sidharth et al. [11],
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TABLE I THERMOMECHANICAL E-P DAMAGE MODEL CONSTANTS FOR Sn3.8Ag0.7 S OLDER [14]
Fig. 2. Measured versus predicted standoff height [11].
Fig. 4. Contour plot of damage based on E-P model in the case without void, showing the maximum damage at the inner corner of the solder ball.
A. E-P Damage Model Fig. 3. Temperature cycle applied to the finite element model.
as seen in Fig. 2, where the SE output is compared against 34 experimental and modeling data sets. IV. T HERMOMECHANICAL D URABILITY M ODELING OF V OIDED S OLDER J OINTS Voids are usually small compared to the size of packages and joints. Modeling voids and their effect on durability is difficult when modeling the full package with finite element analysis. To reduce the degrees of freedom and the size of the finite element model, a global–local finite element modeling strategy was developed. First, a global model of the package on the board was generated. Package symmetry was exploited to model only a quarter of the package. Thermomechanical modeling was conducted by subjecting the model to thermal cyclic loading. The temperature cycle applied to the model is shown in Fig. 3. The critical solder ball was then identified as the one with the highest damage and, therefore, the shortest life (damage and life are calculated using the energy partitioning (E-P) and Coffin–Manson damage models that will be explained in the later sections). Next, all the nodes at the top and bottom of the copper pads at the top and bottom of the critical solder ball were listed in the global model. Then, the time histories of the displacements were recorded for these nodes in the global model for subsequent use in the local model. The local model was error seeded with void, and the displacement histories obtained in the global model were mapped to the corresponding boundaries of the local model. The temperature history of the local model was varied in phase with the displacement history for three consecutive temperature cycles. Damage and life were calculated again using the two aforementioned models.
The E-P damage [10] model seen in the following uses rateindependent and rate-dependent inelastic strain energy released in the first few cycles to obtain the number of cycles to failure 1 = Nf
Wp Wp0
1/c
+
Wc Wc0
1/d .
(2)
In this equation, Wp and Wc are rate-independent and ratedependent inelastic strain energy densities which refer to plastic and creep energy densities in this context. Wc0 , Wp0 , c, and d are damage model constants that are obtained from literature [14] for Pb-free solders and are shown in Table I. To investigate the interaction effect of standoff height and void size on the durability of solder joints, a numerical experiment was designed. In this experiment, a parametric study was conducted for the void area fraction of 14%–40% while the solder volume was kept constant and the standoff height was adjusted using the results obtained from the SE software. The surface area fraction denoted by Af in this context is the area of the void to the area of the solder ball as denoted by IPC-7095 as seen in the X-ray. Two models were built for each case: one with a void in the middle and one with a void close to the upper corner, where the damage was maximum, as seen in Fig. 4 (solder ball without void). Only one case was conducted for a void area fraction of 40%, since there was not enough room in the solder to move the void to the corner. One case with a void area fraction of 14% is shown in Fig. 5. As seen in the figure, as the void moves closer to the maximum damage site, the stress redistributes more uniformly over the solder joint, and less concentration of stress is observed at the interface of the solder ball and the copper pads. The durabilities of all the cases were estimated by averaging the damage in a circular slice around the critical site in the solder ball as mentioned by Zhang who also generated the E-P damage model constants for Pb-free solders [14]. The durability results for the void-area-fraction range are shown in Fig. 6. The
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Fig. 5.
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Damage contour plot of solder ball with (a) the void close to the maximum damage site and (b) the void in the middle.
Fig. 6. Normalized durability using the E-P damage model for a void-areafraction range of 14%–40%.
results are normalized with respect to the case without void and minimum standoff height. For each point on the solid line on the graph, the durability is obtained by averaging the durabilities of two cases where the void is located at the corner and middle. The graph shows a nonmonotonic function where durability increases as void area fraction increases up to 35%. Only when the void is large enough to be truncated by the copper pads at a void area fraction of 40% does the durability start to decline. An improving effect of voids was also shown by Doroszuk et al. from Raytheon [6]. This confirms the previous study conducted by the author [15] that showed a nonmonotonic trend. However, the previous study did not take the increase in standoff height due to the presence of void into account, and the point of deflection for the durability was shown to be at the area fraction of 25% when the void started to get truncated by the copper pads. As seen in the graph, in the cases where there is no void in the solder ball, shown by the dashed line in the graph, as expected, the durability increases as the standoff height increases [16]. Although an increased standoff height enhances the reliability, the effect of void location and size is a more significant factor. A comparison between the two studies conducted by the author shows that the decline in reliability is severe in the case where the void is located at the interface of the solder joint and copper pad. Comparing the results of the case with a void size of 25% in this study and the previous study [15] shows that, regardless of the void size, as long as the void is completely inside the solder joint and the volume of solder joint is constant, the
durability does not decrease by the presence of a void as large as 35%. It is only when the void is at the interface that the solder-joint reliability starts to decline. In other words, as long as the void is completely inside the solder ball and is not at the interface, voids even up to 35% are not detrimental to reliability and even improve the durability of the solder joints by making the solder ball more compliant. The comparison between the cases with a void at the corner and in the middle shows a slight difference in the predicted durability. Comparing the contour plot of damage for voids at the corner and in the middle shows that the void at the corner increases the compliance of the solder ball, thus decreasing the stress concentration and damage at the maximum site. As seen in Fig. 7, the void at the corner redistributes the damage in the solder, providing a more uniform distribution of damage. The void in the middle shows the same concentration site as the case without the void. B. Coffin–Manson Damage Model To confirm the results obtained from the E-P model, another existing model, namely, the Coffin–Manson [17], [18] model, was also used to predict the durability of solder joints with voids. The Coffin–Manson model uses the plastic strain during the cyclic load to determine the number of cycles to failure through the following: Nfm (Δεp ) = C
(3)
where Nf shows the number of cycles to failure and Δεp is the plastic strain range in one cycle. m and C are damage model constants and are obtained for Pb-free solders from literature as 0.853 and 9.2, respectively [19]. These values are used to calculate the damage in the solder joints with and without void in the same way that it was done for the E-P damage model. Calculating the durability using Coffin–Manson yields the same nonmonotonic trend where the durability increases as the void size increases up to 35% and then starts to decrease when the void is large enough that it is truncated by the copper interface (Fig. 8). This nonmonotonic behavior can be explained in terms of physical parameters including the overall compliance of the solder ball structure, stress concentration factor, and decreased crack path. Overall, the compliance of the solder ball is increasing as the void size increases, resulting in a lower stiffness and easier deformation of the solder ball and thereby decreasing the stress in solder balls (note that this problem is a straincontrolled case, meaning that the CTE mismatch between the
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Fig. 7. Contour plot of damage in solder ball. (a) Void at the corner. (b) Void in the middle.
Fig. 8. Normalized durability using the Coffin–Manson model for a void-areafraction range of 14%–40%.
component and the board is the same in all the cases since ΔT is the same for all the cases). At the same time, an increasing void size results in a decrease in stress concentration factor [22], [23] at the initiation site, resulting in a longer initiation life. The damage propagation path, however, is decreasing as the void size increases. The effect of an increase in overall compliance and decrease in stress concentration factor is higher than the effect of a decreased crack path, resulting in improved durability for larger voids up to 35%. As the void interfaces with the copper pads, the stress concentration increases at the interfaces, resulting in increased stress that causes the failure to initiate faster. At the same time, the damage propagation path is decreased drastically due to large area taken out of the damage path. The combination of these two factors decreases the durability for voids at the interface or large voids that are truncated by the copper interfaces. To understand the complex structural behavior of a solder joint with voids, a deep understanding of how stress and strain are redistributed in the solder structure as the void location and size change is required. This discussion is presented in the next section. V. D ISCUSSION To avoid a complex dependence of stress and strain on the void location, the cases studied are categorized into two groups: cases with the void in the middle and cases with the void close to the corner and damage initiation site. A cluster of elements at the maximum damage site (damage initiation site
Fig. 9. Time history of Von Mises plastic strain for cases with the void at the corner.
shown in Fig. 4) is monitored as the void size increases in both of these categories. The results of the time histories of Von Mises stress and plastic strain are shown in Figs. 9–12. As seen in Figs. 11 and 12, in the category with the void in the middle, the void-size change does not have a significant effect on stress and strain magnitudes at this maximum damage site. In the case where the void is located close to the corner, as the void size becomes larger, the magnitudes of Von Mises stress and plastic strain become smaller in the site. Looking more closely, we observe that the maximum site is moving and, now, is not located at the corner as the void size becomes larger. As seen in Fig. 9, the maximum damage site turns away from the corner. Durability predictions are functions of many factors such as the magnitudes of stress and strain, their distribution, and the time histories of these factors. The magnitudes of stress and strain depend on factors such as load bearing area, stress concentration factor, and compliance of the structure. The durability result will change depending on how these factors change as the size and location of the void change. To understand the trend observed in this study, the trend of each individual factor and how the size and location of voids affect that trend is needed. This discussion is intended to provide some analytical relations to analyze the trend of each factor individually and to relate the final trend of durability prediction to the size and location of voids. The first factor that clearly changes as the size of the void changes is the overall compliance of the structure that can be
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353
where T1 is a tensor derived from Eshelby’s inclusion tensor as follows: −1 T1 = I + S1 L−1 (5) 0 (L1 − L0 ) where S1 is Eshelby’s tensor for spherical inclusion. This equation shows a linear relationship between the effective stiffness tensor and the volume ratio of inhomogeneity c1 . A more familiar representation of the structural compliance or stiffness is the elastic modulus that can be calculated analytically using Eshelby’s equation after substituting zero for the elastic modulus of air as follows: E= Fig. 10.
Time history of Von Mises stress for cases with the void at the corner.
18(K0 + f c1 )(G0 + gc1 ) 2(G0 + gc1 ) + 6(K0 + f c1 )
(6)
f=−
K0 1−3γ0
(6a)
g=−
G0 1−2δ0
(6b)
where
Fig. 11. Time history of Von Mises plastic strain for cases with the void in the middle.
K0 =
E0 3(1 − 2υ0 )
(6c)
G0 =
E0 2(1 + υ0 )
(6d)
γ0 =
1 + υ0 9(1 − υ0 )
(6e)
δ0 =
4 − 5υ0 . 15(1 − υ0 )
(6f)
Subscript 0 denotes the matrix or, in this case, the solder material. In the case where the void becomes so large that it cannot fit inside the solder ball and is truncated by the copper interface, the previous assumptions of spherical inhomogeneity are no longer valid. This case is more similar to a cylindrical cell with a cylindrical inhomogeneity inside; therefore, a modified approach is used to calculate the stiffness of the structure using the following [21]: E = Em cm + Ei ci +
Fig. 12.
Time history of Von Mises stress for cases with the void in the middle.
estimated using available analytical techniques of micromechanics. Eshelby’s estimate of the effective stiffness tensor [20] for spherical inhomogeneities for one type of inhomogeneity with a volume fraction of c1 and stiffness of L1 in a matrix with a stiffness of L0 under the assumption of no interactions between inhomogeneities yields the following for the effective stiffness L: L = L0 + c1 (L1 − L0 )T1
(4)
4(νi − νm )2 cm ci cm ci 1 . k i + k m + Gm
(7)
Subscripts i and m denote inhomogeneity (in this case, air) and matrix (solder), respectively. All the parameters used in this equation are defined in the nomenclature. The values of Young’s modulus calculated as a function of void size through (6) and (7) are shown in Fig. 13. The other factor that affects the durability-prediction results is the stress concentration factor. A plot of the stress concentration factor for a circular cavity of elliptical cross section [22], [23] shows that stress concentration is an inverse function of cavity or void radius. The plot of the stress concentration factor as a function of void size is shown in Fig. 13. The load bearing area for the solder is also calculated and is shown in the same figure. As seen in the figure, all of the factors show a decreasing trend up to a void area fraction of 35%. Decreasing two of the factors, elastic modulus and stress concentration factor are in favor of durability. Decreasing
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the joint. The decrease in load bearing area as the void crossed the interface was added to the detrimental effect of overall compliance and stress concentration effects. The critical size of the void is found to be 35% for this study. However, this critical size may change based upon the size and shape of the joint, since it was found that the downfall of the durability is caused by the truncation and not the size of the void. The results of this study are believed to be more accurate for thermomechanical cyclic fatigue, since the mechanism of damage may be different in other regimes such as vibration. ACKNOWLEDGMENT Fig. 13. Analytical values of elastic modulus, normalized load bearing area, and stress concentration factor with respect to nonvoided joint.
the load bearing area is, however, against durability. The sum effect of these three factors is in favor of durability up to 35%. After 35%, the form of the structure changes completely, and a sudden increase in stress concentration factor and elastic modulus is observed. At the same time, the load bearing area continues its declining trend. The net result of these factors is a sudden decrease in durability as was observed in finite element results. VI. C OMPARISON W ITH A VAILABLE E XPERIMENTAL D ATA A few researchers studied the effect of voids experimentally. Banks et al. investigated the effect of voids on the reliability of BGAs and found no negative effect caused by voids up to 24% of the pad area [4]. They observed that standoff height was measurably higher in the voided joint. They attributed the reliability improvements of voided joints to this increased standoff height. Herzog et al. studied the effect of voids on the shear strength of the joints with different void volume ratios and found no significant difference between the joint strength of the cases with different void area fractions. Doroszuk et al. [6] also studied the thermomechanical durability of voided joints and found that voids larger than 30% were, in fact, more reliable than the voids smaller than 30%. No discussion of the void location was given; therefore, there is no indication that the voids have been at the interface. The study conducted by Yunus et al. showed the same characteristic life for joints with and without voids for chip-scale packages. All of these results indicate no negative effect with a tendency to the positive effect of voids, which confirms the finding of this study that indicates that, as the void size increases, the thermomechanical reliability increases as long as the void is not at the interface of the joint. VII. S UMMARY AND C ONCLUSION The interaction effect of voids and standoff height has been studied using SE software and finite element analysis. The results show a nonmonotonic trend as the void size and standoff height increase. The deflection point was observed when the void became so large that it got truncated by the copper pad and thus caused increased stress concentration and stiffness of
The authors would like to thank Prof. K. Brakke of the Mathematics Department of Susquehnna University for his help with the SE software and codes. R EFERENCES [1] J. Lau and S. Erasmus, “Effect of voids on Bump Chip Carrier (BCC++) solder joint reliability,” in IEEE Electron. Compon. Technol. Conf., 2002, pp. 992–1000. [2] J. H. Lau and A. H. Jeans, “Effects of voids on SMT solder joint reliability,” in Proc. 2nd ASM Int. Electron. Mater. Process. Congr., 1989, pp. 177–187. [3] S. Liu and Y. H. Mei, “Effects of voids and their interactions on SMT solder joint reliability,” J. Soldering Surf. Mount Technol., no. 18, pp. 21–28, Oct. 1994. [4] D. R. Banks, T. E. Burnette, Y. C. Cho, W. T. Demarco, and A. J. Mawer, “The effect of solder joint voiding on plastic ball grid array reliability,” in Proc. Surf. Mount Int., 1996, pp. 121–126. [5] M. Yunus, A. Primavera, and K. Srihari, “Effect of voids on the reliability of BGA/CSP solder joints,” Microelectron. Reliab., vol. 43, no. 12, pp. 2077–2086, Dec. 2003. [6] A. Doroszuk, E. Simeus, M. Mehrotra, S. Stegura, B. Bowers, J. Wickersham, K. Ladera, and M. W. Lyons, “BGA solder joint void and its effect on thermal fatigue,” in SMTA Int., Chicago, IL, Sep. 2000. [7] W. H. Zhu, S. Stoeckl, H. Pape, and S. L. Gan, “Comparative study on solder joint reliability using different FE models,” in IEEE Electron. Packag. Technol. Conf., 2003, pp. 687–694. [8] D. S. Kim, Q. Yu, and T. Shibutani, “Effect of void formation on thermal fatigue reliability of lead-free solder joints,” in 9th Intersoc. Conf. Therm. Thermomech. Phenom. Electron. Syst., Las Vegas, NV, Jun. 1–4, 2004, vol. 2, pp. 325–329. [9] T. Herzog, K. J. Wolter, and F. Poetzsch, “Investigations of void forming and shear strength of Sn42Bi58 solder joints for low cost applications,” in Proc. 53rd Electron. Compon. Technol. Conf., New Orleans, LA, 2003, pp. 1738–1745. [10] A. Dasgupta, C. Oyan, D. Barker, and M. Pecht, “Solder creep-fatigue analysis by an energy-partitioning approach,” ASME J. Electron. Packag., vol. 114, no. 2, pp. 152–160, Jun. 1992. [11] Sidharth, R. Blish, and D. Natekar, “Solder joint shape and standoff height prediction and integration with FEA-based methodology for reliability evaluation,” in IEEE Electron. Compon. Technol. Conf., 2002, pp. 1739–1744. [12] L. J. Ladani and A. Dasgupta, “Damage initiation and propagation in voided Pb-free solder joints: Modeling and experiment,” ASME J. Electron. Packag., vol. 130, no. 1, p. 011 008-1, Mar. 2008. [13] K. A. Brakkein Surface Evolver Manual. Selinsgrove, PA: Susquehanna Univ., Math. Dept., 2008. Ver. 2.30c. [Online]. Available: http://www. susqu.edu/brakke/evolver/evolver.html [14] Q. Zhang, “Isothermal mechanical and thermo-mechanical durability characterization of selected Pb-free solders,” Ph.D. dissertation defense, Dept. Mech. Eng., Univ. Maryland, College Park, MD, 2004. [15] L. J. Ladani and A. Dasgupta, “Effect of voids on thermo-mechanical durability of Pb-free BGA solder joints: Modeling and simulation,” ASME J. Electron. Packag., vol. 129, no. 3, pp. 273–277, Sep. 2007. [16] X. Liu, S. Xu, G. Q. Lu, and D. A. Dillard, “Stacked solder bumping technology for improved solder joint reliability,” Microelectron. Reliab., vol. 41, no. 12, pp. 1979–1992, Dec. 2001.
LADANI AND RAZMI: EFFECT OF VOIDS AND STANDOFF HEIGHT ON DURABILITY OF SOLDER JOINTS
[17] L. F. Coffin, “A study of the effects of cyclic thermal stresses on a ductile metal,” Trans. ASME, vol. 76, pp. 931–950, 1954. [18] S. S. Manson, “Low cycle fatigue,” in NASA Technical Note. Cleveland, OH: NASA: Lewis Res. Center, 1954, p. 2933. [19] J. H. L. Pang, B. S. Xiong, and T. H. Low, “Low cycle fatigue models for lead-free solders,” Thin Solid Films, vol. 462/463, pp. 408–412, Sep. 2004. [20] J. Qu and M. Cherkaoui, Fundamentals of Micromechanics of Solids. New York: Wiley, 2006. [21] A. F. Avila and T. K. Krishina, “Non-linear analysis of laminated metal matrix composites by an integrated micro/macro-mechanical model,” J. Braz. Soc. Mech. Sci., vol. 21, no. 4, pp. 622–640, Dec. 1999. [22] H. Neuber, Kerbspannungslehre, 2nd ed. Berlin, Germany: SpringerVerlag, 1945. Translation, Theory of Notch Stresses, Office of Technical Services, Dept. of Commerce, Wash. D.C., 1961. [23] W. D. Pilkey, Peterson’s Stress Concentration Factors. New York: Wiley-Interscience, 1997.
Leila J. Ladani received the M.S. degree in heat and fluid mechanics (with honors) from Isfahan University of Technology, Isfahan, Iran, and the M.S. and Ph.D. degrees in mechanical engineering from the University of Maryland, College Park. She is currently an Assistant Professor with the Department of Mechanical and Aerospace Engineering, Utah State University, Logan. She has several publications in the area of electronic packaging. Her research is focused on mechanics and manufacturing of electronic materials with emphasis on fatigue, fracture, failure, and damage behavior of materials at microscale and nanoscale levels. Dr. Ladani is currently the Chair of the electronic materials subdivision of the American Society of Mechanical Engineers (ASME) Materials Division, as well as a Cochair for the emerging technologies subdivision of the ASME Electronic and Photonic Packaging Division. She was a recipient of several awards for her work in the area of electronic materials and reliability, such as the Hutchins’ Educational Award, Zonta International Amelia Earhart Award, Goldhaber Award, and APSIH Academic Achievement Award from the University of California, Los Angeles.
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Jafar Razmi received the M.S. degree from the University of Maryland, College Park. He is currently working toward the Ph.D. degree in civil engineering at Utah State University, Logan. He has worked in the area of mechanical and material systems quality and reliability for more than 12 years. He has several publications in this area. Mr. Razmi is a member of the Golden Key International Honor Society.
