Creep Behavior of a Sn-Ag-Bi Pb-Free Solder

Compression creep tests were performed on the ternary 91.84Sn-3.33Ag-4.83Bi (wt.%, abbreviated Sn-Ag-Bi) Pb-free alloy. The test temperatures were: −25 °C, 25 °C, 75 °C, 125 °C, and 160 °C (± 0.5 °C). Four loads were used at the two lowest temperatures and five at the higher temperatures. The specimens were tested in the as-fabricated condition or after having been subjected to one of two air aging conditions: 24 hours at either 125 °C or 150 °C. The strain-time curves exhibited frequent occurrences of negative creep and small-scale fluctuations, particularly at the slower strain rates, that were indicative of dynamic recrystallization (DRX) activity. The source of tertiary creep behavior at faster strain rates was likely to also be DRX rather than a damage accumulation mechanism. Overall, the strain-time curves did not display a consistent trend that could be directly attributed to the aging condition. The sinh law equation satisfactorily represented the minimum strain rate as a function of stress and temperature so as to investigate the deformation rate kinetics: dε/dtmin = Asinhn (ασ) exp (−ΔH/RT). The values of α, n, and ΔH were in the following ranges (±95% confidence interval): α, 0.010–0.015 (±0.005 1/MPa); n, 2.2–3.1 (±0.5); and ΔH, 54–66 (±8 kJ/mol). The rate kinetics analysis indicated that short-circuit diffusion was a contributing mechanism to dislocation motion during creep. The rate kinetics analysis also determined that a minimum creep rate trend could not be developed between the as-fabricated versus aged conditions. This study showed that the elevated temperature aging treatments introduced multiple changes to the Sn-Ag-Bi microstructure that did not result in a simple loss (“softening”) of its mechanical strength.


Introduction
Predicting the reliability of solder interconnections, whether subjected to thermal mechanical fatigue (TMF), mechanical shock, or vibration, is depending to a greater extent upon computation modeling techniques. Interestingly, the capabilities of computer facilities and equipment have grown at such a rapid pace over the last 10-15 years that "CPU time" is not always the bottleneck to obtain timely, high-fidelity predictions. Rather, the limiting factor is now having access to the time-dependent (creep) and time-independent (stress-strain) mechanical properties of the materials that comprise the joint structure and, in particular, the solder. These properties are essential towards developing a unified creep-plasticity (UCP) constitutive equation that predicts deformation in the computational model [1,2]. In the study reported here, the creep behavior was evaluated for a Pb-free solder comprised of tin (Sn), silver (Ag), and bismuth (Bi). Although later variants of this material have included Cu additions, this effort examines the commercially-available, ternary alloy, 91.84Sn-3.33Ag-4.83Bi (wt.%, abbreviated Sn-Ag-Bi) [3].
The Sn-Ag-Bi alloy has a number of benefits. It has a relatively low solidus temperature of 212 °C. The Sn-Ag-Bi alloy exhibits exceptionally high strength values when compared to the other Pb-free compositions or the baseline eutectic Sn-Pb alloy. The Bi addition provides for excellent wetting-and-spreading behavior. A multiyear study examined the physical properties of the Sn-Ag-Bi solder as well as its performance in printed wiring assembly (PWA) interconnections [4][5][6][7][8][9][10]. Those studies examined the shear strength of ring-and-plug solder joints as well as the pull and shear strength of actual printed wiring assembly interconnections. Later studies explored the mechanical properties of this Sn-Ag-Bi composition as well as those of similar alloy contents. Kariya and Otsuka examined the isothermal fatigue of this solder [11] Shin and Yu investigated the creep behavior of the Sn-3.5Ag-xBi alloys (×, 2.5 and 7.5 wt.%) at 100 °C [12]. The single lap shear sample (solder joint thickness, 0.39 mm) resulted in shear stresses of 5-9 MPa. Strain rates ranged between approximately 6 × 10 −7 s −1 and 5 × 10 −6 s −1 , resulting in stress exponents of 5.8 (2.5Bi) and 4.4 (7.5 Bi).
The objective of the present study was to obtain a more complete compilation of the time-dependent deformation behavior of bulk Sn-Ag-Bi solder in order to support the development of a computational model for predicting the TMF of both electronic and structural solder joints. The effects of isothermal aging were also evaluated in this work. The methodologies used in the present study were similar to those used to evaluate the creep properties of the 95.5Sn-3.9Ag-0.6Cu solder (Sn-Ag-Cu) that is described in [13,14]. References [15][16][17] are excellent resources for the reader interested in obtaining more detailed information on the mechanical properties of these and other Pb-free solders.

Test Samples
The ternary alloy that was examined in this study had the composition, 91.84Sn-3.33Ag-4.83Bi (wt.%, abbreviated Sn-Ag-Bi). The compression test methodology was used for the creep tests. The test samples were created by first casting the material into cylinders. A density determination was made of each specimen to assure that significant voids were not present in the material. Then, the samples were machined to the nominal dimensions of 10 mm diameter and 19 mm length; the machining step also established parallelism between the end faces. These dimensions conformed to the "short length" ratio of 2.0 per the ASTM E9-89A specification [18]. A more detailed description of the sample fabrication equipment and procedures is available in [19]. The specimens were tested in the as-fabricated (as-cast) condition, that is, after casting and the machining operations. Additional samples were exposed to one of two aging temperature for 24 hours in air: 125 °C or 150 °C prior to the creep test.

Creep Testing
Creep tests were performed on a servo-hydraulic frame using constant load control. The test temperatures were: −25 °C, 25 °C, 75 °C, 125 °C, and 160 °C (± 0.5 °C). The load values were chosen to provide nominal stresses in the range of 20%-80% of the estimated yield stress at that temperature (σ y, T ). Four loads were evaluated at the temperatures of −25 °C and 25 °C while five loads were used at the three higher temperatures. The added loads were of lower values to capture subtle behaviors that could potentially take place under high temperatures and relatively slow strain rates. Duplicate specimens were tested under all stress and temperature combinations.
The duration of the creep tests was limited by either maximum strain reached by the sample, or a maximum time duration for the test. The strain limit was approximately 0.12. The resulting strain range is representative of that experienced by solder in joints that are undergoing TMF. In the event that the sample did not reach the strain limit, the test was halted after 1.73 × 10 5 s (approximately two days). The reader is directed to [11] for additional details regarding the analyses that determined the values of true stress (σ), true strain (ε), and minimum strain rate (dε/dt min ). A visual assessment of the curves was used to determine the presence of one, two, or three stages of creep. This method was determined to be as efficient as attempting to do it with a numerical scheme. Error terms that accompany the stresses and strain rates represent plus-or-minus one standard deviation over the time duration in which those respective data were collected and averaged together. Although standard convention would require the stress and strain rate values to be expressed as negative numbers (compression), they are reported here as positive values.
The deformation rate kinetics were determined from the minimum strain rate, dε/dt min , as a function of stress and temperature and expressed using the "sinh" law Equation (1): dε/dt min = A sinh p (ασ) exp ΔH/RT). (1) The parameters in Equation (1) are: A, a constant (s −1 ); p, the sinh term exponent; α, the stress coefficient (MPa −1 ); σ, the applied stress (MPa); ΔH, the apparent activation energy; R, the universal gas constant (8.314 kJ/mol-K); and T, the temperature (K). The sinh law approach was preferred because it can represent a wider range of applied stresses and thus, avoid "power-law breakdown" that can occur when dε/dt min is expressed using a power-law stress dependency. The parameters A, p, and ΔH were determined by a multivariable, linear regression analysis that was performed on the logarithm of Equation (1) that is represented by Equation (2) below: The parameter, ln(dε/dt min ), was the dependent variable while ln[sinh (ασ)] and 1/T were the independent variables. The regression analysis was performed for different values of the stress coefficient, α. The optimum value of α was determined to within ±0.005 by maximizing the square of the correlation coefficient, R 2 . The error terms on the sinh law parameters were expressed as the ± 95% confidence interval.

Strain-Time Curves
The strain-time curves were analyzed according to sample condition and test temperature. These curves provide critical insight into microstructure changes that are not always readily visible in metallographic cross section, but nonetheless, have a significant role in the mechanical response of the material. The descriptions will be somewhat more detailed for the as-fabricated condition in order to establish the baseline behavior. That narrative will be followed by an analysis of results obtained from the aged samples. It is noted that the elastic strain was not subtracted from the total strain. Although the absence of this step precluded a quantitative comparison from being made between creep strains, qualitative comparisons could still be developed from the curves. Also, this omission did not interfere with an interpretation of the strain rate behavior. Lastly, the term "stress," when alone, refers to the true stress. Nominal stress will be explicitly labeled as such in the discussion.
Shown in Figure 1a are the duplicate curves for the Sn-Ag-Bi samples tested in the as-fabricated condition; temperature of −25 °C; and stresses of 13.4 MPa. While one of the curves exhibited a small positive strain rate (2.2 × 10 −10 s −1 ), the other curve showed negative creep (open circles). Negative creep could indicate of the simultaneous occurrence of mechano-chemical phenomenon in the material as suggested by Li [20]. The discussion in [20] refers to amorphous metals and specifically, microstructural disorder-to-order processes that occur in such materials leading to negative creep. The occurrence of such a mechano-chemical phenomenon in Sn-Ag-Bi, or similar consequence of DRX due to its associated changes to grain structure and defect density, are certainly possible, but would be only a hypothesis until validated by microstructural analysis.. Negative creep was also observed for both samples tested at −25 °C and the nominal stress of 26.6 MPa. This behavior is shown in Figure 1b and was more distinct in one sample than in the other sample. The stress of 39.8 MPa produced positive strain rates (3.1 × 10 −9 s −1 and 5.0 × 10 −9 s −1 ) as did also the stress of 52.8 MPa (4.0 × 10 −9 s −1 and 4.2 × 10 −9 s −1 ) as indicated in Figure 1c. The remainder of the strain-time curves representing the as-fabricated condition-regardless of stress or temperature-exhibited positive strain rates. The other correspondin creep rates stages of cre      Figure 4b. When averaged together, the curves indicated an increase of strain rate with stress; but, individually, that trend was not entirely monotonic. This behavior suggests that there are significant microstructural differences in the starting Sn-Ag-Bi material because their effects persisted through the relatively long duration of the creep tests rather than impact only at the early stages of deformation. Figure 4c shows the plots obtained at 21.8 MPa and 22.4 MPa (125 °C). These tests were of relatively short durations (10,000 s = 2.7 hours) as the samples quickly reached the maximum strain. The curves exhibited a slight degree of tertiary behavior over, what was largely, secondary creep. Again, despite duplicate test conditions, the minimum strain rates were very different between the samples.
The strain-time curves were examined that originated from (as-fabricated) samples tested at 160 °C. The duplicate strain-time responses are shown in Figure 5a for the nominal stresses of 0.5 MPa, 2.0 MPa, and 4.0 MPa. The lowest stress resulted in only primary creep. The other samples exhibited both primary and secondary stages except for the sample tested at 3.9 MPa, which also exhibited a small degree of tertiary creep. When averaged together, the curves demonstrated the expected increase of strain rate with increasing stress. But, a monotonic trend was not observed when considering all of the individual samples. The latter behavior was also observed at the higher stresses, the creep curves of which are shown in Figure 5b. Interestingly, those curves exhibited either primary creep, only, or a mixture of primary and a small degree of secondary creep. The absence of tertiary creep in Figure 5b, is further evidence that this behavior does not likely originate from a large-scale damage process.
In summary, the strain-time curves were examined for the Sn-Ag-Bi solder when tested in the as-fabricated condition. Tests performed at −25 °C and 25 °C and lower stresses exhibited fluctuations indicative of DRX activity. The overall trend was primary creep. The DRX behavior was not observed at the higher stresses. The DRX fluctuations were recorded in only one other condition at higher temperatures: 75 °C, 4.0 MPa. At 75 °C, primary creep dominated the curves at stresses less than 18 MPa. At the higher stresses, primary, secondary and tertiary stage contributed to the deformation. The creep curves obtained at 125 °C and 160 °C were comprised of largely primary and secondary stages. Only a slight contribution was observed of the tertiary stage, and that occurred at the 125 °C test temperature. The lack of correlation between the presence of the tertiary stage versus strain rate, which determines the extent of strain deformation in the material, suggest that the source of the tertiary behavior is DRX and its related effects rather than microvoid coalescence and crack damage processes.       process. Rather, it originated from DRX or was an effect of DRX (e.g., grain size change). However, other mechanisms, such as precipitation hardening/softening, cannot be completely ruled out. (e) Overall, the strain-time curves did not display a consistent trend that could be attributed to the aging condition.. This behavior is not unexpected because the elevated temperatures provide an opportunity for microstructural phenomenon such as DRX or precipitation hardening/softening to take place simultaneously with the deformation. (f) The individual, minimum strain rate data corroborated the above observations. Further use is made of the strain rate data in the following section that discusses deformation rate kinetics.

Deformation Rate Kinetics
The creep deformation rate kinetics were calculated from the minimum strain rate, stress, and temperature as expressed in equation (1) The confidence intervals on the coefficient, A, were ±20, ±20, and ±30, respectively. These values are very small, relative to the mean values in the equations, because the regression analyses delivered the logarithms of the mean and standard errors, which were then converted to their nominal values. Lastly, the respective R 2 values are 0.906, 0.865, and 0.840. These values indicate that the sinh law expression provided a satisfactory fit to the respective experimental data sets.
Observations are made with respect to the values of stress coefficient, α, (in the sinh argument); the sinh term exponent, n; and the apparent activation energy, ΔH. The value of α is relatively small, which tends to de-amplify the effect of stress on the minimum strain rate. A similar effect can be attributed to n, that is, a smaller value of n causes the minimum strain rate to be less sensitive to stress. Comparing the three equations above, the minimum strain rate was most sensitive to stress when Sn-Ag-Bi was tested in the as-fabricated condition. The reduced stress sensitivities that were observed for the samples of the two aged conditions, were identical to one-another.
It is possible to draw a correlation between the value of n and possible deformation mechanisms because the product of ασ is less than 0.8 so that the sinh law representation can be approximated by the common power law expression, σ n . Given this similarity, it is possible to exploit the following established correlations between n and specific deformation mechanisms:  n = 1, diffusion mechanisms (Coble or Nabarro-Herring creep);  n > 3, dislocation mechanisms (glide, climb, or climb-assisted glide).
Besides supporting their own respective deformation processes, diffusion, dislocation or both mechanisms in combination, can be rate-controlling for the grain boundary sliding deformation process. Lee and Stone demonstrated that the value of n can be in the range of 1 < n < 2.5 for grain boundary sliding in Pb-Sn alloy [21]. However, the value is highly dependent on grain size as well as other microstructural features and can significantly exceed this range in other materials [22].
Based on these two limiting mechanisms indicated by n, it appears that Sn-Ag-Bi creep is controlled by dislocation activity (glide or climb) when in the as-fabricated condition. This trend would also corroborate with the higher value of α, which indicates a greater effect by stress that is expected when dislocation activity is present. However, the magnitude of n is near the lower limit considered indicative of dislocation activity, implying that a diffusion-based mechanism may have a contributing role in the creep behavior. After either aging treatment, the still lower value of n implies that a diffusion mechanism has an increased role in creep behavior of Sn-Ag-Bi. A microstructure analysis would be required to confirm the process actually responsible for the creep deformation (e.g., simple dislocation motion or the more complex grain boundary sliding) The third parameter in the sinh law Equations (3)(4)(5) is the apparent activation energy, ΔH. Per the 95% confidence interval, ΔH was statistically the same between all three sample conditions. The values are indicative of a short-circuit diffusion process rather than bulk diffusion (which would have ΔH values of 90-110 kJ/mol for these materials). Given that the values of n, above indicated the likelihood that diffusion contributed to the creep of Sn-Ag-Bi, the ΔH values would certainly support that observation. The diffusion-based mechanism would support a Coble creep process, which is based on grain boundaries providing the short-circuit path, as opposed to Nabarro-Herring creep, which is controlled by bulk diffusion.
A comparison was made between the experimental creep data and the sinh law predictions. The discussion is categorized according to sample condition. Shown in Figure 15 is a plot of the natural logarithm of the minimum strain rate (dε/dt min ) as a function of the natural logarithm of the applied stress, σ, for the as-fabricated condition. The symbols are the experimental data. The solid lines are the predicted trends generated according to Equation 3. The accompanying dashed lines represent the 95% confidence intervals. The sinh law slightly under-predicted the strain rates at −25 °C. This discrepancy was not unexpected, given the relatively small strains and strain rates experienced by the Sn-Ag-Bi alloy at this temperature.
On the other hand, the sinh law model significantly over-predicted the strain rates observed at 25 °C. Although negative creep was not observed in these samples, moderate fluctuations, which are indicative of cyclic DRX, were superimposed on the strain-time curves at all but the highest nominal stress. It was concluded that the grain growth stage of DRX, which increases grain size, was responsible for the lower-than-expected experimental strain rate.  As was the case in Figures 15 and 16, the sinh law model over-predicted the strain rates at 25 °C compared to the experimental data. The "knee" in the test data is very prominent; the best fit occurred at the highest stresses where the data were within the 95% confidence interval.
Unlike the previous two samples conditions, the lack of correlation between the sinh law fit and empirical data persisted through the higher test temperatures. At 75 °C, a "knee" in the empirical data resulted in the latter having a lower-than-predicted minimum strain rate at 9.0 MPa and 18.0 MPa nominal stresses. At 125 °C and 160 °C test temperatures, the best fit between the test results and sinh law predictions occurred at the mid-range stresses. The sinh law slightly over-predicted the strain rate at the lowest stresses. But, more so, the sinh law under-predicted the strain rates at the highest stresses. This trend was similar to the earlier observations that the Sn-Ag-Bi alloy was susceptible to a breakdown event when creep tested under the higher stress values. Although the breakdown was observed under all three sample conditions, it was most pronounced in samples that were aged at 150 °C.
Recall that the plots in Figures 7-9, 11, and 14 compared experimental, minimum strain rate values between the three sample conditions according to each of the test temperatures. A similar comparison was made of the predictions provided by the sinh law Equations (3)(4)(5) in Figure 18. In this case, the trend lines were combined on a single plot that included test temperature and sample condition dependencies. (The confidence intervals were left off the plots for clarity.) The following observations were made from Figure 18: (a) The slope of the as-fabricated condition is steeper than those of the aging treatments, indicating a greater sensitivity of minimum strain rate to stress. The slopes were nearly identical between the two aging conditions. There are two scenarios to explain this trend. The first scenario is that the aging treatments add obstacles to the motion of existing dislocations. Such a case would prevail if the aging treatments caused solute precipitation. The second scenario would have the aging treatments annihilate dislocations. Thus, the deformation rate would be limited after the aging treatment until there could be an increase in the dislocation density. Certainly, it is possible that both scenarios contributed to the observed trend. (b) It was not possible to develop a consistent trend of minimum strain rates between as-fabricated versus aged sample conditions because the traces crossed over one-another at different stresses, depending upon the temperature. Over the range of stresses used in this study, that inconsistency occurred to the least extent at −25 °C and 160 °C. In those instances, the as-fabricated condition was predicted to have a lower strain rate than are predicted for the two aging conditions. (c) Comparing the two aging conditions, samples annealed at 150 °C (24 hours) caused a lower, minimum strain rate than was observed for samples aged at 125 °C. This result further supports the inference made above with respect to Figures 15-17: The aging treatments cause changes to the Sn-Ag-Bi microstructure other simply decreasing its strength due to recovery and/or static recrystallization mechanisms. Alternative processes include the DRX concept described in this analysis as well as the roles of solute precipitation and changes to the dislocation density (dynamic recovery). fluctuations, the latter suggesting that DRX was active during creep. The evidence was most obvious at the slower strain rates. 3. The tertiary strain-time behavior, which was observed usually at faster strain rates, was not the consequence of a traditional damage accumulation process. Rather, it was proposed that it originated from DRX. However, it is recognized that other mechanism such as precipitation hardening/softening have not been completely ruled out in the absence of a microstructural analysis. 4. Overall, the strain-time curves did not display a consistent trend that could be attributed to the aging condition. 5. The sinh law equation, dε/dt min = Asinh n (ασ) exp (−ΔH/RT), was used to analyze the creep rate kinetics. The values of α, n, and ΔH had these ranges across sample aging conditions: α, (0.010-0.015) ± 0.005 MPa −1 ; n, (2.2-3.1) ± 0.5; and ΔH, (54-66) ± 8 kJ/mol. The rate kinetics parameters indicated that short-circuit diffusion was a contributing mechanism to that of dislocation motion in the creep of this alloy. 6. The sinh law representations did not show a consistent trend of between minimum creep rate between the as-fabricated versus aged conditions. However, there is evidence that the 125 °C, 24 hour aging treatment provided a slightly greater degree of stabilization to the minimum creep rate behavior of the Sn-Ag-Bi alloy. 7. Discrepancies between the sinh law prediction and empirical test data were observed at the lowest temperatures, −25 °C and 25 °C, which were likely due to the effects of DRX. A breakdown event was observed at the highest temperatures and highest stresses.