Creep and Fatigue Behavior of Snag Solders with Lanthanum Doping Min Pei and Jianmin Qu

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712 IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 31, NO. 3, SEPTEMBER 2008 Creep and Fatigue Behavior of SnAg Solders With Lanthanum Doping Min Pei and Jianmin Qu

Abstract—In this paper, extensive testing was conducted to study face/interface energy. They can aggregate at the grain/dendrite the effects of Lanthanum (La) doping on the creep and fatigue boundary and lower the grain/dendrite boundary energy, so as to behavior of SnAg lead free solder alloys. Variables considered in stabilize the boundaries and restrain the moving or sliding of the this paper include doping amount, aging temperature, and aging time. The experimental data show that rare earth element (RE) boundaries. Furthermore, they can remove the impurities, such doping increases SnAg solders creep resistance by about 15%. as sulphur and phosphorus, from the steel liquid, change the Meanwhile, RE doping does not affect thermal aging behavior of property, shape, and distribution of the inclusions and, hence, the solder alloy. A microstructure dependent Anand viscoplastic improve the performance of the steel. RE elements were also model is proposed to capture the RE doping effect on the creep put in lead free solder materials as additives, and similar effects behavior. Good agreement between the model predictions and experimental data are obtained. In addition, fatigue tests were was found. performed with bulk specimen. It is found that La doping increases Several RE doped solder alloys have been studied. For ex- the fatigue life by about five times. The optimal doping level for ample, Ce and La have been added to Sn-9Zn system [2], [3], better fatigue performance is around 0.1%. and Lu has been added to SnAg and AuSn solders [4], etc. Re- Index Terms—Constitutive law, creep, lead free solder, rare earth searchers found that RE doping can significantly increase the element (RE). wetting property of solder [1]; it can reduce IMCs and their growth on solder/pad interfaces, and thus greatly increase the solder joint reliability [5]. RE doping also leads to refined mi- I. INTRODUCTION crostructure of the solder alloys [2], [3], [5]–[8] and improves mechanical behavior of solder joints [2], [3], [5], [6]. EAD-FREE solders such as SnAg and SnAgCu are used In a previous paper, we have shown that Lanthanum (La) L extensively as replacements of SnPb solders in microelec- doping has a significant effect on the microstructure of SnAg tronics packaging. It has been found that, in comparison with alloys and its evolution during thermal treatment [8]. It is well traditional SnPb eutectic solders, these lead-free solders have known that creep behavior, to a large extent, is controlled by the much higher melting temperature and higher elastic modulus microstructure and its evolution. Therefore, it is perceivable that which increase the requirements on both temperature and stress La doping would have an effect on the creep behavior. However, tolerance on the boards and other components. The thermome- the existing results from the literature are limited. Furthermore, chanical behavior of these lead-free solders is much more com- no appropriate constitutive models are available to account for plex. More over, the wetting ability of SnAgCu solders gener- the effect of RE doping. ally is not as good as SnPb solder so special care must be taken In addition, there is virtually no study on the effect of RE on choosing flux and reflow profile. Another major disadvan- on the fatigue behavior of solder alloys. As low cycle fatigue tage of the current lead-free compositions is the formation of in- failure is the main failure mechanism for solder joints in elec- termetallic compounds (IMC) that embrittle the solder/pad and tronic packaging, this property is urgently needed. solder/underbump metallization (UBM) interfaces and make the According to these requests, the research presented in this package prone to shock and vibration failure. Work is therefore paper is aimed at conducting a comprehensive and systematic needed to modify the current lead-free compositions and further study to understand how the La doping affect the thermome- improve their performance. chanical behavior of SnAg solder alloys. The paper is arranged In this work, effects of doping of rare earth element (RE) on as follows. In Section II, we will first describe the experimental the creep and fatigue behavior of SnAg alloys were investigated. program used to conduct the creep tests at various tempera- Rare earth elements have been successfully used in the steel in- tures and strain rates, and the test result will be discussed in dustry as an oxidation resistant additive [1]. REs are well rec- Section III. A microstructure-dependent viscoplastic model is ognized as a surface-active agent because they reduce the sur- proposed in Section IV to simulate the creep tests. The fatigue study is discussed in Section V. Some conclusions are drawn in Manuscript received May 12, 2007; revised August 31, 2007. Current pub- Section VI to summarize the paper. lished date September 17, 2008 . This work was supported by the National Sci- ence Foundation Packaging Research Center, Georgia Tech, an Advanced Micro Devices (AMD) Contract, Beijing University, and the Harbin Institute of Tech- II. CREEP EXPERIMENTS nology. This work was recommended for publication by Associate Editor J. Yu. The authors are with the George W. Woodruff School of Mechanical En- The base material used in this study is Sn3.5Ag lead free gineering, Georgia Institutive of Technology, Atlanta, GA 30332-0405 USA solder alloy and Lanthanum is used as the RE additive. Three (e-mail: [email protected]). level of La doping were used and the final alloy compositions Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. in weight percent are: 96.45Sn3.5Ag0.05La, 96.4Sn3.5Ag0.1La Digital Object Identifier 10.1109/TCAPT.2008.922002 and 96.25Sn3.5Ag0.25La, respectively.

PEI AND QU: CREEP AND FATIGUE BEHAVIOR 713

Fig. 1. Specimen 2-D geometry. Unit in mm.

Fig. 3. Comparison of results between constant strain rate test and strain rate jump test. The solid lines represent are from the strain rate jump test and the dash-lines with symbols are from the constant strain rate test as indicated in the legend.

Fig. 2. Typical loading curve of the strain rate jump test.

Dog-bone shaped samples were used for the tensile creep test, as shown in Fig. 1. The thermal treatment procedure used in this studyisasfollows.Thesoldermaterialwascastinaluminummold and quenched in 15 C water. The cooling rate near the solidiﬁca- tion point was estimated to be around 85 C/s [9]. Thermal aging was conducted isothermally in a high temperature oven set at either 100 C or 170 C for 20, 100, and 300 h, respectively. Three factors, La doping amount, aging temperature and aging time, were considered in this investigation. The method of full factorial experiment design was used to ensure the validity of the Fig. 4. Creep test stress-strain curves of as-cast alloys. data using a minimum number of tests. Including the case of no thermal aging (as-cast), there are seven combinations of thermal treatment conditions. Since four alloy compositions wereconsid- ered, the test matrix consists of 4 7 28 test conﬁgurations. The tests were performed on a test machine with 220 N load cell. A thermocouple was placed in contact with the specimen to control the temperature of the sample. A non-contact measurement method [10] was used to measure the strain. To investigate the effect of strain rate and temperature, mono- tonic tensile tests were conducted at 4 different temperatures of 55 C, 0 C, 50 C, and 125 C. At each temperature, strain rate jump test was performed as follows. The specimen was elongated to 0.9% strain at a strain rate of 2 10 /s. At this point, the strain rate was increased by a factor of 10 and the specimen was elongated continuously till the strain is increased Fig. 5. Creep test stress-strain curves of samples aged at 170 C for 300 h. by a factor of 2. This procedure was repeated three more times to reach a strain rate of 2 10 /s before stopping the test. With this method, only one test sample was used for each tem- III. CREEP TEST RESULTS perature, instead of 5 as in other convention methods. A typical A. Effect of La Doping stress-strain curve is shown in Fig. 2. This strain rate jump test can drastically reduce the number Effects of La doping on the as-cast samples and for samples of specimen required but the strain-stress behavior may be dis- subjected to 170 C for 300 h are shown in Fig. 4 and in Fig. 5, torted by the loading history at a low strain rate [11]. The loading respectively. From these experimental data it can be seen that history effect on SnAg solder material was studied by com- La doping generally increases the stress under a given strain and paring constant-strain-rate test results with strain-rate-jump test strain rate. The increase is much more pronounced at high tem- results, as shown in Fig. 3. The close result shows that SnAg perature, reaching as high as 15%. This observation is consistent solder has little loading history dependence. with existing results in several other solder alloys [1], [3], [7]. 中国科技论文在线 http://www.paper.edu.cn

714 IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 31, NO. 3, SEPTEMBER 2008

Fig. 6. Steady-state stress levels of as-cast samples, sorted by different temperatures. Fig. 8. Steady-state stress grouped by temperature (a) SnAg solder at 55 C, (b) SnAg0.25La solder at 55 C, (c) SnAg solder 125 C, and (d) SnAg0.25% 125 C.

Fig. 9. Steady-state stress grouped by strain rate: (a) SnAg solder 2E-6/s, (b) SnAg0.25La solder 2E-6/s, (c) SnAg solder 2E-2/s, and (d) SnAg0.25La solder 2E-2/s. Fig. 7. Steady-state stress levels of as-cast solder materials, sorted by different strain rates. this is a signiﬁcant enhancement. The improvement in creep re- One of the important characteristics of creep deformation is sistance can also be illustrated in a different way. From Fig. 6 the steady-state (saturation) stress as a function of strain rate. it can be seen that to reach the same steady-state stress (dead To obtain this steady-state stress vs. strain rate curve from the load), the corresponding strain rate of La doped samples can be stain rate jump test data, it is assumed that the stress at the end of an order of magnitude less than that of the undoped samples. each strain rate has reached its saturation, e.g., toward the end of each strain rate, the creep is becoming steady-state at that strain B. Effect of Aging rate. The measured stress-strain curves, Fig. 4, show that this After casting, samples were aged at either 100 C or 170 C assumption is very good at higher temperature and lower strain for 20, 100, and 300 h, respectively. The strain rate jump tests rate, which are the conditions most relevant to solder joints were then performed on these samples at various temperatures. in electronic packaging. Therefore, by taking the stress at the The steady-state stress versus strain rate curves were obtained end of each strain rate, the steady-state stress versus strain rate using the same approach discussed in the preceding section. Re- curves can be obtained for samples with various doping levels sults obtained at 55 C are shown in Fig. 8(a)–(b) for the un- and aging condition at different temperature. The same infor- doped and doped samples, respectively. Similarly, results ob- mation is plotted in Fig. 6 as a function of temperature for the tained at 125 C are shown in Fig. 8(c)–(d). It is seen from these as-cast samples (see Fig. 7). data that thermal aging leads to similar effect in both doped and From Figs. 4 and 6, it can be seen that at the same strain rate, undoped samples indicating that La doping does not affect the the steady-state stress in the doped samples is about 5–10 MPa aging behavior of SnAg alloy. higher than that in the undoped samples. Considering the soft Shown in Fig. 9 are the steady-state stress versus tempera- nature of the solder materials, especially at high temperature, ture curves for a given strain rate. It is seen that both the doped 中国科技论文在线 http://www.paper.edu.cn

PEI AND QU: CREEP AND FATIGUE BEHAVIOR 715

TABLE I TABLE II ANAND MODEL CONSTANTS [13] MICROSTRUCTURE DEPENDENT ANAND MODEL CONSTANTS FOR DIFFERENT PROCESSING CONDITIONS

and undoped samples behave similarly, conﬁrming again that La doping does not affect the aging behavior of the SnAg alloy.

IV. CONSTITUTIVE MODELING The Anand model, widely used in Sn based solder materials [10], is a phenomenological constitutive model that does not explicitly account for the microstructure of the alloys. To account for the La doping induced microstructure changes, a microstructure dependent constitutive model is proposed here. The new model is based on the Anand model, but incorporating a power law particle size-dependent term

(1) Fig. 10. As-cast condition. where the diameters of the Ag Sn particles are in units of m and the initial particle size of undoped alloy is m; A one step model constants extraction method [10] was used is the particle size exponent. Particle sizes can be obtained to ﬁt the solder material tensile test data. Together with mi- from quantitative microstructure studies [8], or calculated with crostructure dependent Anand model, a linear temperature de- the following model [8]: pendent elastic model was also used

(6)

where is the Young’s modulus at 0 C and the measures the temperature dependence. Temperature in this equation will be in the unit of C. (2) To study the La doping effect on solder material creep be- where RE is the rare earth doping in percent, is coarsening havior, the model was fitted with tensile test data from samples constant, is aging time, 42.1 kJ/mol is the coarsening that have different La doping levels but with the same thermal activation energy in the undoped sample, and is the isothermal treatment. As a result, each thermal process condition has aging temperature. one set of corresponding model constants, which are listed in The evolution rules of the internal variable in (1) are un- Table II. Two examples of the model predictions comparing changed from the Anand model with tensile test data are shown in Fig. 10 for the as-cast condition and in Fig. 11 for the 170 C 300 h aged condition. Good (3) fit can be observed from these two figures. It can be seen from Table II that the particle size-dependent (4) powers are around 5.5 for most of the cases. This is a much high particle-size dependence compared with a similar model where (5) linear particle size dependence was used [8]. In this phenomenological model, only particle size effect on The physical meanings of the parameters is these equations are creep behavior is considered. Other creep enforcing mecha- listed in Table I, [13]. Other constants that are not listed in the nisms, such as the distribution of the particles, are not explicitly table have the usual meanings. accounted for in the model. A more sophisticated model based 中国科技论文在线 http://www.paper.edu.cn

716 IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 31, NO. 3, SEPTEMBER 2008

Fig. 13. Deﬁnition of average shear strain for fatigue test.

Fig. 11. 170 C aged at 300 h.

Fig. 12. Geometry of the fatigue test sample (unit mm). Fig. 14. Fatigue test data for as-cast samples at room temperature, 0.1 Hz.

on micromechanics that considers particle distribution has also been developed, and reported elsewhere [12].

V. F ATIGUE STUDIES Mechanical fatigue tests were performed on bulk solder material specimens. Bulk samples were chosen to avoid any inter- facial effect in fatigue test and the pre-notched sample drawing is shown in Fig. 12. The samples are 4 mm wide, 0.9 mm thick, with 1 mm pre-notch on the each size. When in-plane shear fatigue load was applied, the shear deformation will be concentrated in the pre-notch portion of the sample. Similar to the tensile test specimen, fatigue samples were cast in an aluminum mold. The mold with liquid solder was quenched in 5 C water. Quenched specimens were aged in room temperature for about 24 h before testing. In this paper, only results from as-cast specimens are reported. A fixture was made to clamp the sample in the same test ma- Fig. 15. 3-D FEM mesh of the fatigue test sample model. chine used in the creep test. The average shear strain applied on the sample was measured with a non-contact method [10]. The average shear strain was calculated from the relative displace- which were found to have great importance in the fatigue ments over the notch width, as illustrated in Fig. 13. The tests are behavior of SnAg solder materials. It was found that Sn3.5Ag done by controlling the applied displacement . A frequency of has relatively low crack growth resistance compared to other 0.1 Hz (10 s per cycle) was used in the test. A test sample is con- solder alloys and the fatigue life depends on the resistance to sidered fatigue failed when the load measured from the load-cell fatigue crack initiation rather than to crack propagation [14]. drops to half of initial value. Before crack initiation, an orientation imaging study [15], The strain range vs. number of cycles to failure (fatigue life) [16] confirmed that at a strain concentrated region, thermo- is shown in Fig. 14. It can be seen that the La doped specimens mechanical fatigue causes heterogeneous refinement of the have about five times longer fatigue life than the undoped spec- microstructure that accounts for the localized grain boundary imens. This difference is not very obvious at the higher strain sliding. Microscopy on cracked samples found that the cracks levels 0.1 , but becomes obvious at lower strain levels will propagate along grain/sub-grain boundaries [17]–[19]. 0.01 . After fatigue failure, small grains can be observed along the The most likely reason for La doping to prolong fatigue life fracture surface [17]–[19] and near the crack path region [20], may come from the grain/sub-grain boundaries in the alloy, [21]. 中国科技论文在线 http://www.paper.edu.cn

PEI AND QU: CREEP AND FATIGUE BEHAVIOR 717

Fig. 16. Contour plots of FEM results simulating the fatigue test (a) XY shear stress, (b) ﬁrst principal stress, (c) total equivalent strain, and (d) plastic work.

As REs are surface active agents, La doping yields several ment loading is applied by fixing the bottom of the model and benefits on solder fatigue through grain/sub-grain boundaries. setting a uniform displacement on the top. Although Anand First, La refines the grain size, provides more boundaries for model has some draw backs on modeling cyclic behaviors due stress release to reduce the damage on each grain and prevent to the lack of back stresses, it is nevertheless used here for its crack formation. In addition, the pinning effect from the La simplicity. The material constants for the Anand model come atoms helps to form stronger bonds at grain boundaries [22]. from Section IV. This FEM model has been validated with ex- These better bonded grain boundaries will have higher resis- perimental tests [9]. tance to damage and thus prevent cracks from initiating. One of the cases will be shown here as a typical result. This One should bear in mind that this discussion is based on bulk specimen is loaded at room temperature with frequency of 0.01 solder specimens. In solder joints, La doping has been proven to Hz. Ten cycles were simulated in this FEM model, and several improve interface bonding as well, as discussed in the introduc- contour plots of the FEM result are shown in Fig. 16. These tion section. Combining these two effects together, the La doped images are at the last time step, with max displacement at top solder joints can be expected to have much longer fatigue life. to be 0.093 mm. It can be seen in Fig. 16(a) that the shear Because of the geometry of the sample, the applied strain deformation is uniformly distributed near the center of the spec- range is not the same as the strain in the notch region. To corre- imen, although the most severe deformation happens at the inner late the fatigue life with the plastic strain range near the notch, corner of the notch. During fatigue shear loading, these corners a 3-D FEM model was built with ANSYS to simulate the de- were cycles between tensile and compression loadings. formation of the fatigue samples. The model uses 8-Node el- The Coffin–Manson fatigue model ement VISCO107 with large strain mode and transient ramp loading. The mesh of the model is shown in Fig. 15. Displace- (7) 中国科技论文在线 http://www.paper.edu.cn

718 IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 31, NO. 3, SEPTEMBER 2008

TABLE III [3] C. M. L. Wu, D. Q. Yu, C. M. T. Law, and L. Wang, “Microstructure FATIGUE MODEL CONSTANTS and mechanical properties of new lead-free Sn-Cu-Re solder alloys.,” J. Electron. Mater., vol. 31, no. 9, pp. 928–932, 2002. [4] S. M. Hutson, “Rare-earth solders make better bonds,” Photon. Spectra., vol. 36, no. 5, p. 139, May 2002. [5] X. Ma, Y. Qian, and F. Yoshida, “Effect of La on the Cu-Sn inter- metallic compound (IMC) growth and solder joint reliability,” J. Alloys Compounds, vol. 334, no. 1–2, pp. 224–227, 2002. [6] Y. Zhu, H. Fang, and Y. Qian, “Study of Sn-Pb-RE solder,” in Proc. Mater. Res. Soc. Symp., Electron. Packag. Mater. Sci. VII, 2002, vol. 323, pp. 137–143. [7] Z. Chen, Y. Shi, Z. Xia, and Y. Yan, “Properties of lead-free solder SnAgCu containing minute amounts of rare earth.,” J. Electron. Mater., vol. 32, no. 4, pp. 235–243, 2003. [8] M. Pei and J. Qu, “Effect of rare earth elements on lead-free solder mi- was used to predict the fatigue life of La doped SnAg solder. The crostructure evolution,” in Proc. 57th Electron. Comp. Technol. Conf., Reno, NV, 2007, pp. 198–204. plastic inelastic strain range in (7) was obtained at the inner [9] M. Pei, “Effects of Lanthanum Doping on the Microstructure and Me- corner of the notch where crack-initiation takes place. Experi- chanical Behavior of a SnAg Alloy,” Ph.D. dissertation, Georgia Inst. mentally obtained fatigue life is then fitted into (7) to obtain the Technol., Atlanta, 2007. [10] M. Pei and J. Qu, “Constitutive modeling of lead-free solders,” ASME: constants and . Their values are listed in Table III for var- Adv. Electron. Packag., pp. 1307–1311, 2005. ious La doping amounts. The values for the undoped samples [11] R. W. Neu, D. T. Scott, and M. W. Woodmansee, “Thermomechanical obtained here are very close to the existing values [23], [24]. behavior of 96Sn-4Ag and castin alloy.,” J. Electron. Packag., Trans. ASME., vol. 123, no. 3, pp. 238–246, 2001. It is seen from Table III that the effects of La doping is well [12] M. Pei and J. Qu, “Hierarchal modeling of Sn/Ag solder alloys.,” correlated with the change in the Coffin-Manson coefficients. in Proc. 57th Electron. Comp. Technol. Conf., Reno, NV, 2007, pp. The exponent decrease as La doping level increases up to 273–277. [13] “User manual of ANSYS,” ver. Release 7.1. about 0.1%. Further increase of doping will not reduces fur- [14] J. Glazer, “Microstructure and mechanical properties of Pb-free solder ther. Since the fatigue life is primarily determined by the expo- alloys for low-cost electronic assembly. a review,” J. Electron. Mater., nent , one may conclude that higher La doping (up to 0.1%) vol. 23, no. 8, pp. 693–700, 1994. [15] A. U. Telang, T. R. Bieler, S. Choi, and K. N. Subramanian, “Orien- leasd to longer fatigue life. However, further increase of doping tation imaging studies of Sn-based electronic solder joints,” J. Mater. amount will not add any more benefit. On the contrary, the slight Res., vol. 17, no. 9, pp. 2294–2306, 2002. decrease in may produce a detrimental effect. [16] A. U. Telang, T. R. Bieler, D. E. Mason, and K. N. Subramanian, “Com- parisons of experimental and computed crystal rotations caused by slip in crept and thermomechanically fatigued dual-shear eutectic Sn-Ag solder joints.,” J. Electron. Mater., vol. 32, no. 12, pp. 1455–1462, VI. CONCLUSION 2003. [17] C. Kanchanomai, S. Yamamoto, Y. Miyashita, Y. Mutoh, and A. J. In this paper, extensive creep tests were performed on SnAg McEvily, “Low cycle fatigue test for solders using non-contact digital solder materials with up to 0.25% of La doping. It was found image measurement system.,” Int. J. Fatigue., vol. 24, no. 1, pp. 57–67, 2002. doping increases the creep resistance of SnAg alloys by as [18] C. Kanchanomai, Y. Miyashita, and Y. Mutoh, “Low-cycle fatigue be- much as 15%. Higher RE doping tends to benefit creep resis- havior and mechanisms of a lead-free solder 96.5Sn/3.5Ag.,” J. Elec- tance more. Meanwhile, La doping does not seem to change tron. Mater., vol. 31, no. 2, pp. 142–151, 2002. [19] C. Kanchanomai, Y. Miyashita, and Y. Mutoh, “Low-cycle fatigue be- the thermal aging behavior of the SnAg alloys. havior of Sn-Ag, Sn-Ag-Cu, and Sn-Ag-Cu-Bi lead-free solders.,” J. A modified Anand model incorporating particle-size depen- Electron. Mater., vol. 31, no. 5, pp. 456–465, 2002. dence is proposed to account for La doping effect on the creep [20] J. Zhao, Y. Miyashita, and Y. Mutoh, “fatigue crack growth behavior of 96.5Sn-3.5Ag lead-free solder.,” Int. J. Fatigue, vol. 23, no. 8, pp. behavior. This model was fitted for each thermal aging condi- 723–731, 2001. tion with good fitting result. [21] J. Zhao, Y. Mutoh, Y. Miyashita, and L. Wang, “Fatigue crack growth A preliminary fatigue study was also performed. La doping behavior of Sn-Pb and sn-based lead-free solders,” Eng. Fract. Mech., vol. 70, no. 15, pp. 2187–2197, 2003. was found to increase the fatigue life by approximately five [22] J. Buban, K. Matsunaga, J. Chen, N. Shibata, W. Ching, T. Yamamoto, times. The deformation fields of the fatigue samples were simu- and Y. Ikuhara, “Grain boundary strengthening in alumina by rare earth lated with a 3-D FEM model. It is found that fatigue life is well impurities,” Science, vol. 311, no. 1, pp. 212–215, 2006. [23] J. Pang, B. S. Xiong, and T. H. Low, “Creep and fatigue characteriza- correlated with the inelastic strain and inelastic work near the tion of lead-free 95.5Sn-3.8Ag-0.7Cu solder,” in Proc. 54th Electron. fatigue crack initiation site. It seems that 0.1% La doping is the Comp. Technol. Conf., Las Vegas, NV, 2004, pp. 1333–1337. optimal amount for better fatigue life. [24] A. Syed, “Accumulated creep strain and energy density based thermal fatigue life prediction models for Sn-Ag-Cu solder joints.,” in Proc. 54th Electron. Comp. Technol. Conf., Las Vegas, NV, 2004, pp. 737–746. REFERENCES Min Pei received the Ph.D. degree from the School of Mechanical Engineering, [1] Z. Chen, Y. Shi, Z. Xia, and Y. Yan, “Study on the microstructure of Georgia Institute of Technology, Atlanta. a novel lead-free solder alloy SnAgCu-RE and its soldered joints,” J. He is currently a Quality Engineer with Intel Corporation. Electron. Mater., vol. 31, no. 10, pp. 1122–1128, 2002. [2] D. Yu, C. Law, L. Wang, and C. Wu, “The properties of Sn-9Zn lead- free solder alloys doped with trace rare earth elements,” J. Electron. Jianmin Qu is a Professor in the School of Mechanical Engineering, Georgia Mater., vol. 31, no. 9, pp. 921–927, 2002. Institute of Technology, Atlanta.