Properties of Lead Free Solder Alloys as a Function of Composition Variation

Qing Wang(1) , William F.Gale(2), R. Wayne Johnson(1), David Lindahl(2)

and Hongtao Ma(1) Laboratory for Electronics Assembly & Packaging Auburn University

(1) Electrical Engineering Department 162 Broun Hall

Auburn, AL 36849 USA 334-844-1880

johnson@eng.auburn.edu (2) Materials Research and Education Center

Abstract While the electronics industry appears to be converging on Sn-Ag-Cu as the alloy of choice for lead free electronics assembly, the exact composition varies by geographic region, supplier and user. Add to that dissolved copper and silver from the printed circuit board traces and surface finish, and there can be significant variation in the final solder joint composition. This paper presents the results of a systematic study of the mechanical and microstructural properties of Sn-Ag-Cu alloys with Ag varying from 2wt% to 4wt% and Cu varying from 0.5wt% to 1.5wt%. Different sample preparation techniques (water quenched, oil quenched and water quenched followed by reflow) were explored and the resulting microstructure was compared to that of a typical reflowed lead free chip scale package (CSP) solder joint. The microstructure obtained by oil quenching produced a microstructure similar to that of the CSP solder joint. The water quenched sample had a finer grain structure, while the water quenched and reflowed sample had a coarser grain structure compared to the CSP solder joint. The sample preparation technique and comparative microstructures are presented. The tensile strength, 0.2% yield strength and the ultimate tensile strength have been measured for the range of alloys at conditions of as-cast, aged for 100h at 125oC and aged for 250h at 125oC. The creep test results and the effect of high temperature aging on mechanical properties are also presented for the oil quenched samples. The results of this work provide necessary data for the modeling of solder joint reliability for a range of Sn-Ag-Cu compositions and a baseline for evaluating the effects of subsequent quaternary additions. Introduction Lead free solders have seen increasing use in interconnection systems for electronic packages due to pending legislation in the European Union, environmental and health concerns, and market competition. The European Commissions (EC) draft directives, Waste Electrical and Electronic Equipment (WEEE) and Restriction of Hazardous Substances (Rohs), have approved the ban of Pb in electronics effective July 2006 in European Union countries. Furthermore, several Japanese electronics manufacturers have successfully created a market differentiation and increased market share based on green products that use Pb-free solders. The conversion to Pb-free solders in the electronics assembly appears imminent [1]. A large number of lead free solder research studies [2-7] have been reported which have focused on microstructural analysis, tensile properties including Youngs modulus, Poissons ratio, tensile strength, creep properties for specified compositions of lead free solders. According to the research report [4] of the National Center for Manufacturing Science (NCMS) and the National Electronics Manufacturing Initiative (NEMI), there is no drop in replacement for SnPb eutectic solder. Sn-Ag-Cu alloy has been proposed as the main option for lead free solder in reflow applications due to its relatively low melting temperature, as well as its superior mechanical properties and solderability compared with other lead free solders.

While the electronics industry appears to be converging on Sn-Ag-Cu as the alloy of choice for lead free electronics assembly, the exact composition varies by geographic region, supplier and user. Add to that dissolved copper and silver from the printed circuit board traces and surface finish, and there can be significant variation in final solder joint composition. Current research reports have not provided a systematic study of Sn-Ag-Cu lead free solder as a function of alloy composition. The dimensions of the specimens used were not close to those of real solder joints in electronic packages such as BGAs and CSPs. This will significantly affect the microstructure of the sample, as well as the mechanical properties. Also, there is little experimental data available on the effect of aging on the mechanical properties including creep and tensile behavior for the wide range of Sn-Ag-Cu ternary alloys. In this study, a new fabrication technique which produces specimens with microstructure very similar to a real CSP solder joint was developed to systematic study the mechanical and microstructural properties of Sn-Ag-Cu alloys with Ag varying from 2wt% to 4wt% and Cu varying from 0.5wt% to 1.5wt%. Tensile and creep properties, as well as the effects of aging on these properties for a selected range of alloy compositions are reported. Specimen Preparation The solder alloy compositions investigated in this study covered Ag from 2.0~4.0 % and Cu from 0.5~1.5% by weight percent. Sn is the base metal of the alloy. In the specimen preparation process, commercial tin shot (purity 99.99 +%, 3mm), silver shot (99.9 +%, 1-5mm) and copper shot (99.5+%, 0.5-0.8mm) were mixed according to the specified composition ratio (Table 1), and then mixed with small quantities of flux (Kester Tacky Flux TSF-6522). The alloy mixture was put in a fused-quartz crucible and heated on a hot plate. The melting process was performed in an inert environment (vacuum was first applied and then the sample was purged with argon gas). The heating profile is shown in Figure 1. Table 1 shows the chemical composition of solder alloys measured by Plasma Emission Spectroscopy.

Figure 1- Heating Profile for Alloy Melting

Table 1-Target Alloy Composition Matrix and Chemical Analysis

Target Ag (wt.%) Alloy Chemical Composition 4% 3.5% 3.0% 2.5% 2.0%

1.5% 94.7Sn3.9Ag1.4Cu 95.2Sn3.4Ag1.4Cu 95.6Sn3Ag1.4Cu 96.23Sn2.47Ag1.4Cu 96.58Sn2.02Ag1.4Cu

1.2% 94.7Sn4.06Ag1.24Cu 95.2Sn3.6Ag1.2Cu 95.78Sn3Ag1.22Cu 96.44Sn2.4Ag1.16Cu 96.86S2.01Ag1.13Cu

0.8% 95.23Sn3.92Ag0.85Cu 95.64Sn3.5Ag0.86Cu96.28Sn2.9Ag0.82Cu 96.6Sn2.5Ag0.8Cu 97.28Sn2.02Ag0.8Cu

Target Cu (wt.%)

0.5% 95.52Sn4.0Ag0.51Cu 96.06Sn3.4Ag0.54Cu96.47Sn2.9Ag0.53Cu96.96Sn2.55Ag0.49Cu 97.46Sn2.04Ag0.5Cu

Actual chemical analysis shown in table compared to target composition indicated by row and column headings.

An advanced specimen preparation process was developed using rectangular cross-section small glass tubes and a controlled vacuum system (Figure 2). The solder was melted in a quartz crucible (L=120mm, =19mm) with a heating coil. A thermocouple and temperature control module was used to monitor and control the melting process temperature. After the temperature of the molten solder had maintained the desired temperature for 5 minutes, the glass tube connected to the controlled vacuum system was inserted into the molten solder and the solder was sucked into the glass tube. The glass tube was immersed in oil or cold water immediately after filling. Once the sample cooled to room temperature, the specimen could be extracted due to the lower CTE of the glass compared to the solder (Figure 2). Figure 3 shows the dimension of the specimen made by this process [8]. Compared with the dog-bone or casting specimens used by other researchers [2-5], the thickness of the Auburn uni-axial specimen is close to that of real CSP (0.25~0.5mm) and BGA (0.5mm) solder joints.

(a) Solder Melting System

(b) Specimen solidified in glass tube (c) Specimen after removal from glass tube

Figure 2 - Solder Melting System and Specimen Preparation [8]

Figure 3 - Auburn Uni-axial Specimen [8]

Microstructure of the SnAgCu System The mechanical properties of alloy specimens depend on their microstructure. Hence the challenge is to make a specimen which has a comparable microstructure to a real solder joint. The microstructure is controlled by the cooling profile. In this study, cooling options were: oil quench; water quench; and water quench followed by a 248oC peak reflow in a Heller 1800 reflow furnace (Figure 4). The resulting microstructure was compared with a CSP solder joint (95.5Sn4Ag0.5Cu) reflowed using the CSP quick ramp profile (Figure 4)

Reflow profile (Peak temp = 248C) CSP quick ramp reflow (peak temp=245 C)

Figure 4 - Specimen Cooling Options and CSP Reflow Profile

Specimens with the different cooling options were polished with SiC papers, diamond paste and finally with Al2O3 paste to a 0.1 micrometer finish. All samples were etched for a few seconds with 5% volume of hydrochloric acid in methanol. A scanning electron microscope (SEM) was used to analyze the microstructure. Figure 5 compares the SEM microstructures (95.5Sn4Ag0.5Cu) from the different cooling conditions with the CSP solder joint. With the aid of energy dispersion x-ray analysis (EDS), it is found that the dark areas are a Sn rich phase and the bright areas, which are needle-like, elongated or spherical, are the Ag3Sn intermetallic phase. Both the oil quenched specimen and CSP solder joint shown the eutectic region of Sn and moderately dispersed Ag3Sn intermetallic surrounded by a dentritic Sn-rich phase. The microstructure of the water quenched specimen consists of a mixture of eutectic regions of dense Ag3Sn intermetallic within a tin rich matrix surrounding large equiaxed crystals of tin-rich solid solution [9]. The specimen made by water quenching followed by a reflow cycle has a more coarse tin eutectic structure with irregular dispersed Ag3Sn intermetallic precipitates. Based on the microstructure evaluation, the water quenched specimen shown has a more fine microstructure than the CSP solder joint, while the specimen that was water-quenched followed by reflow cycle showed a more coarse microstructure than the CSP solder joint. The specimen prepared by oil quenching had a microstructure close to that of the CSP solder joint after reflow. Based on these results, oil quenching was selected for fabrication of specimens for the tensile and creep tests in the following section. Tensile Properties of the SnAgCu System Tensile tests were performed with an MT-200 tension/torsion thermo-mechanical test system made by Wisdom Technology Inc. shown in Figure 6. The system provides an axial displacement resolution of 0.1 micrometer and a rotation resolution of 0.001o. The testing machine is under displacement control. Load and displacement data were recorded and used to determine the true stress/true strain curve. True stress and true strain were calculated from the engineering stress and strain by the conventional constant volume assumption. Figure 7 indicates the Youngs modulus, 0.2%-strain yield stress and ultimate tensile strength on a typical strain-stress testing curve measured at a strain rate of 10-3 (1/sec) at 25oC.

Figure 5 -Microstructure comparison between CSP Solder Joint and Specimens with Different

Cooling Options

Figure 6 - Micro Tension Tester

Figure 7 - Stress-strain Tensile Curve for 96.5Sn-3.5Ag-1.5Cu

A group of stress-strain tensile test curves for 96.5Sn-3.5Ag-1.5Cu is shown in Figure 8 to represent the general test results. At least five specimens were tested for each alloy composition at each test condition. Figure 8 shows that the tensile test data fits well with the elastoplastic model for 96.5Sn-3.5Ag-1.5Cu. The elastoplastic model of lead free solder exhibits an elastic phase until a critical stress is reached (the yield point), after which plastic behavior becomes dominant. It is normally used to predict the deformation of the alloy on the stress-stain curve.

(a) Tensile measurement curves (b) Elastoplastic model

Figure 8-Stress - strain Tensile Curve for 96.5Sn-3.5Ag-1.5Cu Youngs modulus, 0.2% strain yield stress and ultimate tensile strength were measured for all 20 selected alloy compositions (Table 1) at three conditions (as-cast, aged for 100h at 125 oC, aged for 250h at 125 oC). The distribution of tensile properties as a function of alloy composition and their change with aging time are shown in Figures 9-11. Youngs modulus (Figure 9) as a function of alloy composition (Ag=2%~4%, Cu=0.5%~1.5%) ranged from 37-41 GPa and decreased to 30-32 GPa after aging for 100 hours and 250 hours at 125oC. There is no significant difference in Youngs Modulus as a function of alloy compositions. After the initial decrease in modulus after 100 hours at 125oC, there was insignificant change with further aging.

Test Temp: 25 oC Strain Rate: 0.001 s-1

Figure 9(a) - Distribution of Youngs Modulus as a Function of Alloy Composition (As-cast)

Figure 9(b) - Distribution of Youngs Modulus as a Function of Alloy Composition (125oC, 100h Aging)

Figure 9(c) - Distribution of Youngs Modulus as a Function of Alloy Composition (125oC, 250h

Aging) The distribution of 0.2% strain yield stress and ultimate tensile strength as a function of alloy composition was more significant as compared to the variation in Youngs modulus. Both were significantly higher with higher levels of silver and copper. The 0.2% strain yield stress was 56 MPa for the Sn-4Ag-1.5Cu alloy and 34 MPa for the Sn-2Ag-0.5Cu alloy. After 100h aging at 125oC, the 0.2% strain yield stress for these alloys decreased to 32 and 23 MPa, respectively. The maximum ultimate tensile stress was (61 MPa) for the Sn-4Ag-1.5Cu alloy and only 38 MPa for the Sn-2Ag-0.5Cu alloy (Figure 11(a)). After 100 hours of aging at 125oC, the ultimate tensile stress for these two alloys decreased to 37 and 27 MPa, respectively. The absolute values of the yield stress and the ultimate tensile stress, as well as the difference between values for the different alloy compositions decreases during the aging process. There is no significant change in the 0.2% strain yield stress and the ultimate tensile stress distribution for the different alloys after 100hours of aging at 125oC.

Figure 10(a) - Distribution of 0.2% Strain Yield Stress as a Function of Alloy Composition (As-cast)

Figure 10(b) - Distribution of 0.2% Strain Yield Stress as a Function of Alloy Composition (125oC,

100h Aging)

Figure10(c) - Distribution of 0.2% Strain Yield Stress as Function of Alloy Composition (125oC, 250h Aging)

Figure 11(a) - Distribution of Ultimate Tensile Strength as a Function of Alloy Composition (As-cast)

Figure 11(b) - Distribution of Ultimate Tensile Strength as a Function of Alloy Composition (125oC,

100h Aging)

Figure 11(c) - Distribution of Ultimate Tensile Strength as a Function of Alloy Composition (125oC,

250h Aging)

Creep properties of selected lead free solders The creep data available in the literature for Sn-Ag-Cu ternary alloys are very limited. This hinders reliable predictions using finite element analysis of electronic assemblies [3]. The systematic analysis of creep properties over a wide range of Sn-Ag-Cu ternary alloy compositions after thermal aging is very important for FEM analysis. If the creep properties of the alloy changes as a function of storage time at elevated temperature, this must be included in the model for accurate predictions. Furthermore, there is little data available for strain rates less than 10-6/sec, stress levels less than 10 MPa and temperatures above 75 oC or combinations thereof [4]. However, the creep data at these conditions are very important as they represent the real stress conditions of solder joints in electronic assemblies in service. In this study, creep tests were performed with an MT-200 tension/torsion thermo-mechanical test system for selected alloy compositions (Sn-4Ag-1.5Cu, Sn-4Sg-0.5Cu, Sn-2Ag-1.5Cu, Sn-2Ag-0.5Cu, Sn-3.5Ag-0.8Cu) for three conditions: as-cast; aged for 100 hours at 125oC; and aged for 250 hours at 125oC. The selection of Sn-4Ag-1.5Cu, Sn-4Sg-0.5Cu, Sn-2Ag-1.5Cu, Sn-2Ag-0.5Cu represent the four corners of the alloy range previously characterized for tensile properties, while the Sn-3.5Ag-0.8Cu represents a mid-point and is close to the eutectic composition of the SnAgCu ternary alloy. Tests were conducted for three different temperatures (22oC, 100oC and 150oC) at different constant stress levels. A thermal chamber was used for creep test at different temperature. The temperature of the specimens was monitored and controlled by a thermocouple placed close to the center of the specimen. The creep curves display typical primary creep, quasi-steady state (constant strain rate) and tertiary rupture stages (Figure 12). The quasi-steady state is dominant in the creep process. The creep strain rate was determined by differentiating the creep strain with respect to time. Each test was continued until the minimum true strain rate was identified. The creep specimens will fail earlier at high applied stress and have a long quasi-steady-state at low applied stress (Figure 13).

Initial strain(Elastic +plastic)

t (time)

Stra

in

PrimaryCreep

Secondary creep Tertiarycreep

RuptureQuasi-steady state:d/dt = constant

Initial strain(Elastic +plastic)

t (time)

Stra

in

PrimaryCreep

Secondary creep Tertiarycreep

RuptureQuasi-steady state:d/dt = constant

Figure 12 - Conventional Steady Strain Rate Creep Curve [4]

As a benchmark, the authors data is compared with reported reference creep data [4] in Figure 14. It shows the quasi-steady state creep rates plotted against applied stress in the log-log format. In general, the creep data from these sources are in the same range even though the sample dimensions, sample preparation and exact compositions vary (Table 2).

Figure 13 - Experimental Creep Curves for 94.5Sn-4Ag-1.5Cu (100h, 125oC Aging) at T=150oC at

Different Stress Levels

Figure 14 - Comparison of Creep Data [4]

Table 2 - Comparison of Creep Specimens

Source Alloy Composition Specimen shape

Specimen/Gauge length

Cross-section Specimen treatment

Auburn Univ. 95.7Sn3.5Ag0.8Cu Uni-axial rectangular

60mm/50~60mm 3mm x 0.5mm rectangular

Oil quench

Schubert et 95.5Sn3.8Ag0.7Cu Dog-bone 60mm/30mm 3mm x 3mm Not reported Neu et 96.2Sn2.5Ag0.8Cu Cylinder 127mm/12.7mm 13mm square Air-cooled

Karriya et 95.5Sn3.8Ag0.7Cu 96.5Sn3.0Ag0.5Cu

Dog-bone 60mm gauge 11.28mm square

Water quenched

The creep curves for the five selected alloy compositions at the different aging conditions are shown in Figures 15-17 for test temperatures of 22oC, 100oC and 150oC respectively. The creep curves shift from right to left, indicating that the creep resistance decreases as the test temperature is increased for all five alloy compositions. For each alloy composition, the creep resistance decreases as the aging time at 125oC increases. Sn4Ag1.5Cu has the highest creep resistance and Sn3.5Ag0.5Cu ranks second. The creep resistance for Sn2Ag0.5Cu, Sn4Ag0.5Cu and Sn2Ag1.5Cu are similar and lower.

Figure 15 - Comparison of Creep Data at T=22 oC (As-cast, and Aging 100h, Aging 250h at 125oC)

Figure 16 - Comparison of Creep Data at T=100oC (As-cast, and Aging 100h, Aging 250h at 125oC)

Figure 17 - Comparison of Creep Data at T=150oC (As-cast, and Aging 100h, Aging 250h at 125oC)

Creep constitutive models The quasi-steady state creep constitutive model can be simply characterized by a power law relationship,

kTQ

neA

= (1) where the quasi-steady state creep strain rate is , A is a material constant, is the applied stress, n is the stress exponent, Q is the creep activation energy, k is Boltzmans constant, and T is absolute temperature [6]. The activation energy, Q, and the stress exponent, n, depend on the creep mechanism, and have different values at different temperature and applied stress. Equation (1) prescribes a linear relationship in logarithmic coordinates between the creep strain rate and the applied stress for a specified temperature. However, the simple power-law model cannot describe the non-linear experimental creep curves over large stress ranges. A hyperbolic-sine power-law relationship has been proposed and found to predict the observed behavior at low and high stresses [10,11,12]. At low and medium stresses, the creep strain rate depends on stress to the power n. At high stresses, the strain rate is an exponential function of stress [3].

( )[ ]

=

kTQC n expsinh (2)

where C and are materials constants. The steady state creep data for all selected alloy composition at three aging conditions (as-cast, and 100h and 250h at 125oC) were fitted to equation (2). The fitted creep model parameters for the alloy compositions are given in Table 3:

Table 3 The Creep Model Parameters for Selected Alloy Compositions at Different Aging Conditions

Aging conditions

Alloy compositions

Hyperbolic-sine power-law model parameters

C n Q (J/mole) Sn-4Ag-1.5Cu 0.48 0.05 5.9 53000 Sn-4Ag-0.5Cu 0.17 0.14 4.2 55000 Sn-2Ag-1.5Cu 2.1 0.09 5.6 55000 Sn-2Ag-0.5Cu 0.3 0.19 4.0 66000

As-cast

Sn-3.5Ag-0.8Cu 1.46 0.09 4.9 60000 Sn-4Ag-1.5Cu 1.6e-3 0.14 4.9 55000 Sn-4Ag-0.5Cu 0.04 0.21 4.4 54000 Sn-2Ag-1.5Cu 0.014 0.25 4.1 55000 Sn-2Ag-0.5Cu 1.42 0.2 4.6 65000

100h at 125 oC

Sn-3.5Ag-0.8Cu 6.54E-4 0.27 4.3 60000 Sn-4Ag-1.5Cu 5.7E-4 0.2 4.2 54000 Sn-4Ag-0.5Cu 5.1E-3 0.25 5.6 55000 Sn-2Ag-1.5Cu 1.4E-2 0.27 4.3 55000 Sn-2Ag-0.5Cu 8 0.2 4.8 66000

250h at 125 oC

Sn-3.5Ag-0.8Cu 8.68E-2 0.22 4.2 60000

Taking the Sn-4Ag-0.5Cu alloy in the as-cast condition as an example; the curve-fitted hyperbolic-sine creep model is given below:

( )[ ]

=

kT55000exp14.0sinh17.0 2.4D (3)

Figure 18 shows the calculated data using the above creep model equation. The model agrees with the experimental data at the different test temperatures. The presented model parameters in Table 3 provide a description for the selected alloy compositions at different aging conditions. Comparison of the hyperbolic-sine creep model data for these selected Sn-Ag-Cu alloys, show that the stress exponent n varies from 4.1

to 5.9, while the activation energy Q varies from 53000 J /mol to 66000 J/mol. The fitted value of parameters C and varied with alloy composition at different temperature and aging times. The physical meaning of these parameters needs further investigation.

Figure 18 - Comparison of Mmodel and Experimental Creep Data for Ascast Sn-4Ag-0.5Cu

Conclusions The mechanical and microstructural properties of Sn-Ag-Cu alloys with Ag varying from 2wt% to 4wt% and Cu varying from 0.5wt% to 1.5wt% were systematically studied. An advanced specimen preparation process was developed using rectangular cross-section small glass tubes. The oil quenched specimen microstructure was comparable to that of a reflow soldered CSP solder joint. Youngs modulus as a function of alloy composition only ranged from 37-41 GPa as-cast and decreased to 30-32 GPa after aging for 100h and 250h at 125 oC. The distribution of 0.2% strain yield stress and ultimate tensile strength as a function of alloy composition was more significant. Both are significantly higher for the high level of silver and copper composition and gradually decreased to the lowest value for low silver and copper compositions. The absolute value of yield stress and ultimate tensile strength both decreased during the high temperature aging process. The tensile creep behavior was investigated at three temperatures (22oC, 100oC 150oC) for five selected alloy compositions (Sn-4Ag-1.5Cu, Sn-4Sg-0.5Cu, Sn-2Ag-1.5Cu, Sn-2Ag-0.5Cu, Sn-3.5Ag-0.8Cu) as-cast, after aging at 125OC for 100 hours and after aging at 125OC for 250 hours. The creep resistance decreased as the testing temperature increased for all alloy compositions. For each alloy composition, the creep resistance decreased as the aging time at 125oC increased. Sn4Ag1.5Cu had the highest creep resistance and Sn3.5Ag0.5Cu ranked second, while the curves for Sn2Ag0.5Cu, Sn4Ag0.5Cu and Sn2Ag1.5Cu were similar. A hyperbolic-sine power-law creep constitutive model was developed to provide an acceptable description for all selected alloy compositions at different aging conditions over wide applied stress ranges. Comparison of the hyperbolic-sine creep model data for selected Sn-Ag-Cu alloy shows that the stress exponent n varies from 4.1 to 5.9, while the activation energy Q varies from 53000 J /mol to 66000 J/mol.

Acknowledgements The author would like to acknowledge the research funding support from NASA Marshall Space Flight Center. References [1] Qian, Z.; Abhijit, D.; Peter, H.; Creep and High-temperature Isothermal Fatigue of Pb-free Solders, Proc. IPACK2003-35361, International Electronic Packaging Technical Conference, July 6-11, 2003 Maui Hawaii, USA. [2] Steffen, W.; Ekkehard, M.; Klause-Juergen W.; Microstructure Dependence of Constitutive Properties of Eutectic SnAg and SnAgCu Solders, Electronic Components and Technology Conference, 2003, pp. 197-205. [3] Qiang, X.; Luu, N.; William, D.; Aging and Creep Behavior of Sn3.9Ag0.6Cu Solder Alloy, Electronic Components and Technology Conference, 2004, pp1325-1332. [4] Jean, P.; Sn-Ag-Cu Properties and Creep data, National Institute of Standards and Technology, http://www.metallurgy.nist.gov/solder/clech/introduction.htm [5] Schubert, A.; Walter, H.; Dudek, R.; Michel, B.; Thermo-Mechanical Properties and Creep Deformation of Lead-Containing and Lead-Free Solders, International Symposium on Advanced Packaging Materials, 2001, pp. 129-134. [6] John, H.; Pang, L.; Xiong, B.S.; Low, T.H.; Creep and Fatigue Characterization of Lead Free 95.5Sn-3.8Ag-0.7Cu Solder, Electronic Components and Technology Conference, 2004, pp. 1333-1337. [7] Yoshiharu, K.; Mashes, O.; William, J.P.; The Constitutive Creep Equation for a Eutectic Son-Ag Alloy Using the Modified Theta-Projection Concept, Journal of Electronic Materials, Vol. 32, No.12, 2003, pp. 1398-1442. [8] Hecham, A.; Haongtao, M; etc., Measurement of the constitutive behavior of lead free solders, Technical report of CAVE (Center for Advanced Vehicle Electronics), Auburn University, 2004 [9] Qiang, X.; Harold, J.; William, D.; Aging Effects on Microstructure and Tensile Property of Sn3.9Ag0.6Cu Solder Alloy, Transaction of the ASME, Vol.126, June 2004, pp. 208-212. [10] Shi, X. Q.; Wang, Z.P.; Yang, Q. J.; and Pang, H. L. J., Creep Behavior and Deformation Mechanism Map of Sn-Pb Eutectic Solder Alloy, J. Eng. Mat. Tech., 125(1), 2003, pp. 81-88. [11] Lau, J. H.; Ricky, L. S., Modeling and Analysis of 96.5Sn-3.5Ag Lead free Solder Joint of Wafer Level Chip Scale Package on Buildup Microvia Printed Circuit Board, IEEE Transactions on Electronics Packaging Manufacturing, 25(1), 2002, pp. 51-58. [12] Darveaux, R.; Banerji, K., Constitutive Relations for Tin-based Solder Joints, IEEE Transactions on Components, Hybrids, and Manufacturing Technology, 15(6), 1992, pp.1013-1024.