The Creep Parameters of SAC305 Unleaded Solders

The tensile and shear loading creep parameters of unleaded Sn/3.0Ag/0.5Cu solders are extracted from the proposed tensile and shear creep tests in this work. Four creep loading temperatures, that is, 120, 135, 150, and 165C, are employed to extract the corresponding parameters. The creep parameters for tensile and shear loading models, that is, stress exponent, material constant, and activation energy, are curve-fitted by using the least square error and simplex optimization algorithms. The accuracy of the extracted parameters correlated with the measured strain rate versus temperature curves. Results indicate that the proposed measurement setup and extraction algorithm is feasible to extract the tensile and shear type creep parameters with good accuracy.


Introduction
The unleaded Sn/3.0Ag/0.5Cusolders have been used widely in electronic and photonic device packaging.The high operation temperature and on-off thermal cycling introduced in the electronic and photonic devices may introduce the serve thermal creep deformation.The creep deformation may lead to fiber alignment shifts in the transceiver module connectors and reduce the signal efficiency dramatically in the optical communication system.Damage to the encapsulation of electronic components may also be caused by thermal mechanical fatigue (TMF) at the welding point due to creep of the intermetallic compound.Various electronic component materials have different mechanical and thermal properties.Correspondingly, the creep deformation introduced from various temperature distributions may facilitate a redistribution of the stress status around a weld, which may eventually lead to a fatigue failure.A number of studies have investigated thermal stress to make predictions for the timespan of thermal fatigue at the welding areas of components under various thermal cycle loads.
Damage to electronic encapsulations occurs frequently near the solder joint due to thermal fatigue and creep.Creep only occurs when an object is subjected to high temperatures for a prolonged period of time, and creep deformation is generally induced mainly by two factors: temperature and stress.Developing a creep model for electronic encapsulation materials is a very important issue.This study proposed two creep experiments, that is, the tensile and the shear loading creep tests, to derive the corresponding creep equations.Different loading temperatures are applied to initiate the creep for different Sn/3.0Ag/0.5Cusolder specimens.

Creep Experiments on Sn/3.0Ag/0.5Cu Solder Material
Creep deformation and its induced strain and strain rate are tested with a constant loading temperature.The loading temperature is higher than one half of the melting temperature of the specimen material.As noted in many textbooks, the creep deformation can be divided in three stages.In the first stage, that is, the primary creep stage, the more active dislocation sources in the material continue their activities, but they will gradually be blocked thus gradually reducing the strain rate.
In the second stage, that is, the secondary creep stage, the strain hardening and recovery achieve equilibrium, so that the strain rate is maintained at a constant value; the minimum creep rate is reached at this stage.In the third stage, that is, the so-called tertiary creep stage [17], necking, voids, or cracks appear and the material is weakened by overaging and high temperature oxidation, thus increasing the strain rate.The creep rate increases with temperature and stress.
In this study two specimens of Sn/3.0Ag/0.5Cusolder material are used to test the creep phenomena in tensile and shear loading conditions.Four loading temperatures have been applied to measure the elongation variation with a constant load.The corresponding strain and strain rate variations have also been derived.

Creep Model.
As noted [17], the creep strain () in the material is dominated by the loading stress (), stress time (), and temperature (); that is,  =  (, , ) . ( For simplicity, the interaction between these parameters is ignored.
The Norton power law has been used widely to describe the secondary stage creep deformation.In this study, the Norton model has also been employed to describe the secondary stage creep phenomena as the specimen subjected to a tensile or shear type loading.The tensile and shear type creep models are where  and  are the material constant,  is the average normal stress (MPa),  is the average shear stress (MPa),  is the activation energy (J/mol),  is the gas constant (8.3 mol −1 K −1 ),  is the absolute temperature (K), and  and  are the stress exponent under tensile and shear loads, respectively.
Taking the logarithm on both sides of (2), it leads to a linear relation between the ln ε and ln  for a constant loading temperature: Similarly, the shear strain rate can be derived as In the equations,  and  are temperature functions: where (, , , and )and(, , , and ) are creep parameter sets of the tensile and shear models, respectively. and  are the activation energy and gas constant of the solder.From ( 4) and (5), it is observed that the logarithm ln ε (or ln γ ) of strain rate assumes a linear relationship with the logarithm value of average stress ln  (or ln ).The constant slopes of ln ε versus ln  and ln γ versus ln  are the respective stress exponents , and .The natural logarithm of strain rate (ln ε , ln γ ) is proportional to the reciprocal of loading temperature (1/) [18].Therefore, the activation energy parameter  can then be derived from the relationship between the natural logarithm of the strain rate and the reciprocal of the temperature.
Based on the extraction algorithm mentioned in the previous section, the values of creep parameters , , , , , , , , and  can be extracted from the measured strain rate and loading stress by employing the simplex optimization method in this work.

Creep Experiment Setup and Specimens.
The tensile and shear creep specimens are illustrated in Figures 1(a) and 1(b).Two round copper solid bars are welded with the Sn/3.0Ag/0.5Cusolder between the orthogonal or parallel connecting surfaces.Figures 2(a) and 2(b) show the preparation and geometries of the specimens used in the tensile and shear creep tests.An appropriate amount of the Sn/3.0Ag/0.5Cusolder paste was placed at the middle section of two 5 mm in diameter copper rods.About 3-4 mm gap is designed for the Sn/3.0Ag/0.5Cusolder layer.These two copper rods were then, respectively, placed on a vertical clamp or a "V" shape bed, as shown in Figure 1(a) or Figure 1(b), respectively.A torch was then used to heat the area around the Sn/3.0Ag/0.5Cusolder paste until it was completely molten.Extra care was taken not to directly expose the solder paste to the flame.The dimensions of eight Sn/3.0Ag/0.5Cusolder specimens are listed in Table 1.The size parameters , , , and  of eight solder specimens (specimens numbers 1a∼8a) indicate the diameters of top, bottom, waist, and the height of the solder layer in the tensile specimens.Due to the surface tension introduced in the melting process, the waist diameter  in the tensile specimens always has the smallest value.The corresponding size parameters , , and  for the eight shear specimens (specimens numbers 1b∼8b) values, respectively, indicate the length, width, and height of the solidified solder paste.Two constant loads, that is, 7.35 and 29.4 N, are applied for the tensile and shear creep tests, and four loading temperatures, that is, 120, 135, 150, and 165 ∘ C (393, 408, 423, and 438 K), are measured in this study.Since the melting temperature of the copper is much higher than that of the Sn/3.0Ag/0.5Cusolder, the creep deformation of the copper bar can be ignored in these measurements.In other words, the measured end  displacements are considered to be introduced from the creep deformation of the solder layer.Figure 2(c) is the scheme of the creep test setup.The specimens are arranged in a temperature controlled box and loaded vertically with a constant disc weight.Three displacement sensors are located at three measured points.The measured elongation variation in the loading direction is recorded periodically.The corresponding true stress, strain, and strain rate are calculated simultaneously.correlation between ln ε and 1/ of tested specimens under the loads of 7.35 N and 29.4 N. Based on Norton power law, that is, (4), the slope value is equal to −/.By applying the least square error method, the linear slope values of measured specimens under loads of 7.35 N and 29.4 N can be derived as −8318.02and −7257.00,respectively.The average value −7737.51 of these two slopes and an activation energy value 64221.32(J/mol) can be derived with the gas constant (8.3 mol −1 K −1 ).

Experimental Results and Creep Parameters Extraction
Figure 7 shows the correlation between the logarithm strain rate (ln ε ) and the logarithm stress (ln ) in the tensile creep experiment.The four left points and the four right points in this figure are related to the measured data for the load of 7.35 N and 29.4 N, respectively.Therefore, four linear equations can be derived for these tensile specimens to describe the power law relation between the strain rate and average stress with different loading temperatures.Initially, an average slope value of  (1.954) is approximated from these four equations by ignoring its loading temperature effect.Similarly, a constant value of −14.22 is approximated by averaging the four constant values in (8).Then an approximated initial trial power relation for these tensile specimens is proposed; that is, ln ε = 1.954 ln  − 14.22.
From ( 4) and ( 9) and the approximated activation energy value 64221.32(J/mol) mentioned previously, the relationship between the material constant  and temperature can be derived in Figure 8.By using the least square error method and the definition of material constant  in (6), the set of parameters in the tensile creep equation can be derived as  = 15.40, = 6.39 × 10 11 , and  = (−1/18.04).To improve the accuracy of these extracted parameters, the simplex optimization algorithm has been employed in this study to minimize the difference between measured strain rate and the strain rate data estimated from the initial trial parameters.All the extracted creep parameters mentioned previously are considered as the initial trial parameters in the optimization process.In the optimization procedure the following is assumed: strain rate : ε = (, , , , ) , object function: min.(Δ 2 ), Δ: deviation between the estimated and experimental values,   ) .
The tensile creep parameters, that is, , , , , and , for the Sn/3.0Ag/0.5Cusolder specimens converged from the simplex optimization method are  = 1.8640,  = 52154.52, = 1.2507,  = 6.3131 × 10 A comparison between the temperature and estimated strain rate results for the specimens 1(a) to 8(a) reveals a difference between 0.19% and 43.6% for the specimens with a loading of 7.35 N and a difference between 2.1% and 17.3% for the specimens with a loading of 29.4 N as shown in Figure 9.   Figure 13 shows the correlation between the strain rate in the shear creep tests and the average shear stress.Four linear equations can be derived for the shear creep test results.They are ln γ = 0.92 ln  − 16.00 when  = 393 K, ln γ = 0.94 ln  − 15.57 when  = 408 K, ln γ = 0.97 ln  − 15.01 when  = 423 K, ln γ = 0.99 ln  − 14.52 when  = 438 K. (13) Figure 14 shows the correlation between shear creep material constant and temperature.Following the process mentioned in the tensile creep test, the creep parameters in the shear creep equation can be approximated as  = 0.084,  = 7.27, and  = (−1/21.47).All these approximated parameter values are considered as the initial trial values in the simplex optimization process to minimize the difference between the measured and estimated shear strain rates.The following is assumed: object function: min.(Δ 2 ), γ  : estimated shear strain rate, γ ie : shear strain rate from the experimental results.A set of parameters is generated from the simplex optimization method; they are  = 0.9515,  = 58494.91, = 2.3705,  = 2.4639 × 10 9 , and  = (−1/17.99).Therefore, the following shear creep equation for the Sn/3.0Ag/0.5Cusolder can be derived:  From a comparison between the experimental and the estimated strain rates for the shear creep specimens, that is, 1(b) to 8(b), a difference between 0.43 and 8.1% is found for the specimens with a load of 7.35 N as shown in Figure 15.A difference between 1 and 6% has been found for the specimens with a load of 29.4 N.

Conclusions
The solder joint reliability is strongly affected by creep.This was validated by both simulation and experimental results, which show significantly higher occurrence of thermal failures of solder joints in high temperature aging tests.The high operation temperature induced creep phenomenon is the major cause of solder joint failure.Therefore, the reliability of solder packages under high operation temperature is highly dependent on solder joint creep property.The tensile and shear creep models of lead-free Sn/3.0Ag/0.5Cusolder material have been proposed in this study.Simplified tensile and shear tests can be used as a quick way of modeling the lead-free solder.Due to the diversity of the measured data, an optimization algorithm is proposed to extract the creep parameters in these creep equations.Experimental measurements and estimated strain rate results reveal that the proposed creep equations can provide reasonable accuracy.
The processes of extracting the creep parameters are specifically presented for illustrating the versatility of creep equation formulation.This result is useful for packaging reliable lead-free solder jointed assembly of high power laser or LED module packages.A wide variety of other applications of this proposed lead-free Sn/3.0Ag/0.5Cusolder creep model are expected.

Figure 7 :
Figure 7:  The correlation between logarithm strain rate and logarithm stress.

Figure 8 :
Figure 8: Correlation between tensile creep material constant and temperature.

Figure 9 :
Figure 9: Correlation between strain rate and temperature in the tensile creep equation.

Figure 10 :
Figure 10: Correlation of displacement-time in the shear creep experiment under different loads: (a) 7.35 N load disc and (b) 29.4 N load disc.

Figure 11 :
Figure 11: Correlation between strain-time and strain rate under a temperature of 408 K and a load of 7.35 N in the shear creep experiment.

Figure 12 :
Figure 12: Correlation between the natural logarithm of the strain rate and the reciprocal of temperature in the shear creep experiment.

Figure 13 :Figure 14 :
Figure 13:  The correlation between the logarithm of strain rate and average stress for the shear creep test.

Figure 15 :
Figure 15: Correlation between shear creep equations strain rate and temperature.
To compensate the possible displacement measurement error, the vertical displacements   ,   , and   measured at disk rim as shown in Figure3are averaged.The vertical displacement of the specimens is averaged as Two sets of creep specimens, that is, eight specimens for the tensile creep test and the other eight specimens for the shear creep test, are measured with two constant loads (7.53 3.1.Tensile Creep Experiment. Figure 4 shows the variation of displacement of tensile specimens subjected to the loads

Table 2 :
Results of tensile creep specimen experiment.

Table 3 .
Similarly, the correlation between ln γ and 1/ under loads of 7.35 N and 29.4 N is shown in Figure12.From the slope values the −/ values can be derived as −6879.823and −5569.58.

Table 3 :
Results of the shear creep specimen experiment.