Critical evaluation of creep behavior of Sn-Ag-Cu solder alloys over wide range of temperatures

Materials Science & Engineering A 703 (2017) 144–153

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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea

Critical evaluation of creep behavior of Sn-Ag-Cu solder alloys over wide range of temperatures Anwesha Kanjilal, Vikas Jangid, Praveen Kumar

MARK

⁎

Department of Materials Engineering, Indian Institute of Science, Bangalore 560012, India

A R T I C L E I N F O

A B S T R A C T

Keywords: Activation energy Compression creep Dislocation climb controlled creep SAC alloys Stress exponent

A critical survey of the current literature on creep behavior of Pb-free Sn based Sn-Ag-Cu (SAC) alloys show that there is considerable discrepancy in the creep parameters, such as activation energy, Qc, and stress exponent, n. Accordingly, this study addresses the underlying reasons for such variability in the existing data by studying the creep behavior in compression of two most commonly used SAC alloys, namely Sn-1 wt.%Ag-0.5 wt.%Cu and Sn3 wt.% Ag-0.5 wt.% Cu, over wide range of temperatures, from 60 to 200 °C, and stresses from 7 to 14 MPa. Analysis of microstructure of SAC alloys reveals that both temperature and stress have pronounced effects on coarsening of precipitates during creep. The steady state strain rate increases with both temperature and stress as well as with decrease in Ag content of the alloys. Irrespective of the composition, SAC alloys show a transition in the creep behavior around 150 °C, with Qc and n changing from 55 kJ/mol and 7, respectively, at low temperatures to 100 kJ/mol and 5, respectively, at higher temperatures. Such a simultaneous change in both Qc and n suggests that creep mechanism in SAC alloys is dislocation climb controlled by the core diffusion at low temperatures and the lattice diffusion at high temperatures.

1. Introduction With the progressive shift towards Pb-free microelectronics over the last decade, Sn based solders like near eutectic Sn-Ag and Sn-Ag-Cu (SAC) alloys, having low melting temperature of ~ 223–226 °C (depending on their composition) [1–3], excellent wettability and mechanical properties, have emerged as the most promising alternatives of eutectic Pb-Sn solders [4]. With continuous miniaturization of microelectronic packages, there has been a transition from the traditional 2-D interconnects using ball grid array (BGA) and flip-chip solder joints towards 3-D integration of die-to-die interconnect bonding using metal filled through silicon via (TSV)-micro-bump assembly. Consequently, the size of the solder balls has also reduced from ≈ 750 µm in BGA and ≈ 100 µm in C4 flip-chip joints to almost 10–20 µm in 3-D integrated circuits, and it is expected to further decrease below 10 µm in near future [5]. In addition to decrease in the open space necessary for efficient heat transfer from the microelectronic chip to the heat sink, the high-density packaging in 3-D devices has also led to high current densities, as high as ~ 3 × 1011 A/m2, passing through these miniaturized solders, resulting in a significant increase in the service temperature [6]. The temperature of interconnects in commercial microelectronic devices can reach 70 °C during regular usage, whereas for industrial and defense applications the service temperature is usually

⁎

Corresponding author. E-mail address: [email protected] (P. Kumar).

http://dx.doi.org/10.1016/j.msea.2017.07.061 Received 4 May 2017; Received in revised form 19 July 2017; Accepted 19 July 2017 Available online 20 July 2017 0921-5093/ © 2017 Elsevier B.V. All rights reserved.

85 °C and 125 °C, respectively [7]. Moreover, while the maximum operating temperature of micro-bump chip assembly in electronic packages of automobiles and aircrafts under harsh service conditions was limited to 150 °C till the last decade, it is now expected to shoot up to 200 °C (≈ 0.95 Tm, where Tm is the melting temperature, for SAC alloys) by 2022 [6]. All of this results in high homologous temperatures in the low melting solder joints, for example, 125 °C is approximately equal to 0.80 Tm. This necessitates study of high temperature behavior of SAC alloys over wide range of temperatures. In particular, the dies containing solder joints and micro-bumps are stacked in multiple layers in 3D integrated circuits, thereby generating significant compressive stresses in the solder micro-bumps. Besides other mechanical behavior of interest, such as thermal fatigue, fracture, impact, etc., creep response of SAC alloys under compression also becomes critical for evaluating the reliability of the solder joints. However, it will become evident in the subsequent discussions that there is lack of a general consensus amongst various researchers about the creep deformation of SAC alloys, with a dearth of data on the creep behavior beyond 160 °C and under uniaxial compression. Moreover, as explained next, a critical examination of the published data on creep of SAC alloys casts doubts on the validity of some of the tests performed in the past for obtaining the creep parameters. Therefore, it is necessary to examine the creep behavior of bulk solder alloys, especially in

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Fig. 1. Schematics showing typical (a) strain versus time and (b) strain rate versus strain curves during compression creep. In (a), different types of broken lines show “perceived” linearized portions, which can be artificially considered to depict steady state, of a non-linear curve with decreasing of slope. The arrows with thin line width are the three lines drawn on the original strain versus time curve, clearly showing a decrease in the strain rate with time or with accumulation of strain. In (b), the two curves show the manifestations of steady state behavior under constant true stress and constant nominal stress or load. The true steady state with a flat strain rate curve is possible only under a constant true stress test, whereas the quasi-steady state showing a linear curve on log-linear plot with a slope equal to the stress exponent is revealed under a constant load or nominal stress test. The broken vertical arrows in (b) show plausible locations for transition from primary to secondary stages of creep.

Nevertheless, this is not the correct way of ascertaining steady state creep rate. As a matter of fact, it is strongly recommended to measure the strain rate at every instant (or strain) and plot strain rate versus strain (or time) to accurately ascertain the extent of primary and secondary regions and measure the true steady state creep rate during a constant (true) stress creep test or the quasi-steady state creep rate in case of a constant load or nominal stress test (see Fig. 1b). As shown in Fig. 1b, determination of steady state strain rate under a constant load test, which is the most widely used method for performing compression creep and also used in this study, becomes trickier as the true stress (and hence the true strain rate) never becomes truly constant. Herein, accurate determination of creep rate requires the following: (i) establishing occurrence of quasi-steady state by measuring the slope of the log strain rate versus strain plot (and its being equal to expected stress exponent),1 and (ii) averaging of the strain rate in the region of the identified quasi-steady state regime where the change in true strain rate (and true stress) with strain is negligible or quite small. This gives a small range of strain rate over a small range of stress, thereby having a small box as the representative data instead of a single point on the traditional stress versus strain rate graph. Simple calculation of the slope of the creep strain versus time plot at a single point in the “apparent” secondary stage can lead to erroneous steady state strain rates. Using the approach described above and illustrated in Fig. 1b is physically sound and hence should be preferred. Moreover, for measuring the activation energy (which signifies the effect of temperature on the steady state creep rate or kinetics of creep in general) in Eq. (1), the steady state microstructure of the specimens should be identical throughout the temperature range [17]. This can be ensured by maintaining a constant ratio of the steady state stress and the shear modulus, i.e., σss/G, over the temperature range in which Qc is measured [17]. Using the initial stress during application of load, instead of the steady state true stress normalized with modulus, can lead to overestimation of the apparent Qc or n value. Therefore, (a) steady microstructure, (b) proper calculation of the steady state creep rate, and (c) constant modulus compensated steady state stress are prerequisites for accurate prediction of important creep behavior. Incorporation of the above factors while planning a creep experiment for determination of Qc and n minimizes chances of variability in data. In this context, a thorough examination of the existing works, as enlisted in Table 1, reveals that different testing methodologies have been adopted previously, such as tensile creep, shear creep,

compression, over a wide range of temperatures and stresses to accurately predict the dominant creep deformation mechanism(s) of solder joints. It should be noted that a change in any of the previously mentioned parameters, i.e. temperature and stress, or their combination can change the governing creep mechanism. The most widely used phenomenological creep equation for steady state creep, which is often used to determine the dominant creep mechanism, is given as [8]:

εsṡ =

AD0 Gb σss n ⎛ b ⎞ p Q ⎛ ⎞ exp ⎛− c ⎞ kT ⎝ G ⎠ ⎝ d ⎠ ⎝ RT ⎠

(1)

where εsṡ is the steady state creep rate, A is a dimensionless proportionality constant, D0 is the frequency factor, G is the shear modulus, b is the Burgers vector, σss is the effective stress, n is the stress exponent, p is the grain size sensitivity, Qc is the activation energy for creep, k is Boltzmann constant, T is the absolute temperature, d is the grain size and R is the universal gas constant. Herein, it should be noted that depending on the creep mechanism the values of the creep parameters, namely n, p and Qc, will change; for example, if n, p and Qc are equal to 5, 0 and Qsd (where Qsd is the activation energy for lattice diffusion), respectively, then the dominant creep mechanism is dislocation climb controlled 5-power law, while if n = 1, p = 3 and Qc = Qgb, where Qgb is the activation energy for diffusion through grain boundary, then it is Coble creep and likewise [9]. It is noteworthy to mention that during creep deformation the microstructure continuously evolves with time throughout the primary creep stage till a steady state is attained in the secondary stage, wherein a balance between the rates of hardening and recovery is finally established, signifying a steady microstructure. Hence, while measuring the steady state creep rate it is necessary to ensure development of a statistic steady microstructure also. This is especially critical for SAC alloys as it is widely reported that the precipitates (e.g., Ag3Sn, Cu6Sn5) may coarsen during high temperature exposure [10–12]. It should be noted that here the microstructure not only includes the dislocation based substructures (e.g. cell, subgrain, dislocation density, etc.), but it also includes grain size and precipitate size and their distribution. In addition, as shown in Fig. 1a, in a typical creep test the creep strain in the primary stage increases at a decreasing strain rate, and hence there is a continuous decrease in the slope of the creep strain versus time curve throughout the deformation process. This produces a mirage that the last segment of the primary creep shows a constant slope and hence a transition to secondary stage of creep (see Fig. 1a). Most of the creep studies [13–16] on SAC alloys have performed linear curve fitting to calculate the slope at the very end or in the almost linear portion of the creep curve to obtain the steady state creep rate.

1 The relationship εṫ = C exp(−nεt ) between the true strain rate, εṫ , and true strain, εt in the steady state, gives the slope of log strain rate versus strain plot equal to the stress exponent (i.e., n).

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Table 1 Values of activation energy for creep and stress exponent of different SAC alloys reported by various authors. For the sake of comparison, the most cited values of n and Qc for pure Sn are also listed. Ref.

Material

Specimen type

Testing method

T (°C)

σ (MPa)

Qc (kJ/mol)

n

[18] [15]

Machined to dimension BGA solder balls

Tensile creep Impression creep

23–100 25–150

1–30 19–108

60.7 ± 6.6 61

[19]

Sn-3.5 wt.% Ag Sn-1.0 wt.% Ag-0.5 wt.% Cu (SAC 105) Sn-4.0 wt.% Ag-0.5 wt.% Cu (SAC 405) SAC 105

BGA array

Tensile Creep

24.2

40.7

[16]

Sn-3.9 wt.% Ag-0.6 wt.% Cu

Cylindrical sample

Compression creep

2–45

[20] [21] [22]

Sn-3.8 wt.% Ag-0.7 wt.% Cu (SAC387) Sn-3.9 wt.% Ag-0.6 wt.% Cu Sn-3.5 wt.% Ag

Bulk cylindrical samples Solder joints Solder joints with Cu

Tensile creep Shear creep Shear creep

[26]

Pure Sn single crystal

Wires of single crystal

Tensile creep

[27]

Polycrystalline Sn

–

[28]

Pure Sn

Single crystals machined as tensile specimens

Tensile Creep

[29]

Pure Sn

Single crystal

Compression creep

25 70 110 −25–75 75–160 25–125 25–125 25–95 95–130 25–130 > 130 25–100 150–224 70–150 150–200 < 121 > 121

25 ± 7 95 ± 14 45 63 58 135 46.2 92.4 46 108 40–52 98–118 50.4 115

5 ± 0.2 5 6 7 6 5.3 4.4 ± 0.7 5.2 ± 0.8 4.96 3.8 6 4 5.1 4.6 12 4.5 –

2–40 4–30 2–13 1–15

1.57 6.3

–

of n ranging in between 5 and 7 in most of the studies at temperatures below 150 °C. A more careful examination of Table 1 shows that for the same SAC alloy, say SAC 105, two different Qc values of 40 kJ/mol [19] and 61 kJ/mol [15] have been reported at similar temperature and stresses, which is quite puzzling. Furthermore, it is observed that there is no change in the value of Qc between SAC 105 and SAC 405, whereas the stress exponent increases from 5 to 6 with this change in composition [15]. Although the authors [15] proposed that such a change in the value of n was due to the transition of the creeping constituent from the core diffusion controlled dislocation creep through β-Sn in SAC 105 to Ag3Sn dispersed eutectic Sn in SAC 405 (due to the high Ag content in SAC 405), they have not rationalized the proposed hypothesis with direct microstructural evidence and also corresponding effect on the value of activation energy was not noted. Another study [19] focused on SAC 105 reported a range of stress exponents that decreased from 7 to 5 with an increase in the test temperature; however, a corresponding change in Qc was not observed over the temperature range. Such a change in the stress exponent was attributed to microstructural instability, a feature which the authors argued to be common during high temperature deformation. However, it is not clear if such a phenomenon would impact only the value of n (and not Qc). Interestingly, at least in a couple of studies [16,22], both these creep parameters, i.e., Qc and n, seem to change with change in the temperature and stress, with a transition occurring below 100 °C accompanied by a change in the creep mechanism from pipe diffusion to lattice diffusion controlled dislocation climb. However, there is a considerable mismatch in the values of Qc and n as well as in the transition temperature reported by them. For example, Vianco et al. [16] have observed a change in both Qc and n with temperature, wherein Qc increases by almost a factor of 4 (from 25 to 95 kJ/mol), whereas the corresponding change in n was minor. Such a drastic jump in the value of Qc with temperature with insignificant change in n is not very realistic, especially as the values of activation energy for diffusion through dislocation core (or pipe) and lattice generally differ by a factor of 2. Overall, from the large range of values of Qc and n reported for SAC alloys, as highlighted in Table 1, it is apparent that there is a confusion regarding their exact values and a comprehensive understanding about the creep behavior of SAC solders is still lacking. As discussed previously, variability in the creep parameters relevant to SAC alloys, i.e., Qc and n may arise if steady state microstructure is not attained as well as if the creep parameters are not calculated in the steady state region. As mentioned previously, most of the earlier studies

compression creep, etc., to study the creep deformation behavior of the SAC alloys [15,16,18–22]. It is important to note that in all these studies the experiments were performed under constant load conditions and hence the standard creep strain versus time curves obtained from such tests will show similar behavior as depicted in Fig. 1, with or without the presence of tertiary stage. It should be noted that tertiary stage may not show up in compression tests. However, while some of the studies have provided the standard creep strain plots [15,16], none of them have used the strain rate versus strain curves to show the attainment of a bona fide steady state during the tests and the correct calculation of the corresponding steady state strain rates. Compression creep tests performed in an earlier study [16] on Sn3.9 wt.% Ag-0.6 wt.% Cu did not exhibit a monotonous increase in the slope of the creep strain versus time plots with stress, denoting lack of consistency in the obtained representative (steady state) strain rates. This variability was attributed to the differences in the initial microstructure of the specimens tested, which is a major issue that is extremely important to consider as the microstructure of SAC alloys are known to coarsen even under room temperature storage [23,24]. Therefore, 2 samples stored for different periods after reflow (or soldering) may have quite different microstructure and hence different creep curves. This raises considerable doubts regarding the reliability of the creep parameters, i.e., n and Qc, reported in this study [16]. On a similar note, another study [18] performing constant load tensile creep tests on Sn-3.5 wt.% Ag also did not provide any information about the nature of tensile creep strain versus time plots or equivalent strain rate versus strain plots. An interesting study [22] performing shear creep tests on small Sn-3.5 wt.% Ag/Cu solder joints (with ~ 500 µm joint thickness) under constant load up to fracture showed a transition in creep mechanism above a certain temperature; however, it has come under scrutiny due to the non-uniform deformation of very small solder joints under shear [25]. Herein, the Cu substrates are known to delay the transfer of shear strain to the solder as they are not very rigid and in the process, absorb some deformation, an effect which becomes even more prominent as the solder joint thickness is reduced [25]. Besides some ambiguity with the validity of the test methodologies and the data analysis as well as reporting, there is also a lack of a clear consensus amongst various researchers regarding the values of important creep parameters, e.g. n and Qc, for these alloys in moderate stress regime over wide range of temperature (see Table 1). For example, while some authors have reported Qc of ~ 60 kJ/mol [15,18], others have obtained a lower Qc of ~ 45 kJ/mol [16,19,20], with values 146

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significantly smaller than the creep strain recorded in this study) and (ii) by aligning the samples against a square steel scale with no gap in between the sample and the square scale. The initial as-cast microstructure was characterized using a scanning electron microscope (SEM). The samples were metallographically polished up to 40 nm of colloidal silica before observing the microstructure in SEM using back scattered electrons (BSE). Compression creep tests under constant load using a dead-weight type of creep machine were conducted in air at various temperatures and stresses to obtain the creep parameters Qc and n. The creep tests were conducted over temperature and stresses ranging from 60 to 200 °C (0.71–0.95 Tm) and 7–14 MPa, respectively. The stress range corresponds to σ/G values of 4 × 10−4 to 9 × 10−4. The variation of the shear modulus with temperature was obtained using the equation: G (MPa) = 20,632 − 37.67 T (°C) [15]. The samples were placed in between two smooth Al2O3 platens for avoiding formation of any eutectic between the sample and the loading rods at the highest of the test temperatures. Also, boron nitride powder was used as a solid lubricant between the sample and the Al2O3 platens to minimize the friction between these surfaces and hence to minimize the extent of low stress regimes (or friction cone) inside the sample. A small steel ball was introduced above the top platen so that the load can be applied uniformly and normally onto the sample. In order to quickly stabilize and maintain the temperature of the sample, a ceramic rod was introduced in the compression rod load train to minimize the heat loss to the surroundings via conduction through the metallic loading rods. In addition, the samples were soaked at the test temperature for 1 h at a very small load of 0.04 MPa before the start of the actual creep test. The temperature of the sample was recorded continuously using a K-type thermocouple and the temperature during the test period did not vary by more than ± 1 °C. The variation of strain with time was constantly recorded and a plot of strain rate versus strain was plotted real time to ensure the attainment of a genuine steady state before terminating a test. The microstructures of a few of the samples were observed after creep test, especially to highlight coarsening of precipitates. Tests under a couple of conditions were repeated for ascertaining repeatability of the experiments.

have neither explicitly considered the need for using strain rate versus strain plots for an unambiguous determination of steady state creep rate nor have they clearly elucidated the role of microstructural evolution of SAC alloys during creep test on the (steady state) creep behavior. Hence, a closer inspection of the creep behavior of these SAC alloys, by considering all these factors which can lead to large scatter in data, is required to get a comprehensive understanding of the overall creep deformation kinetics. Accordingly, in light of the existing confusion, the present work tries to address these issues and develop a clearer picture of the creep behavior of SAC 105 and SAC 305 alloys within a temperature range of as low as 60 °C to as high as 200 °C (i.e., homologous temperature of 0.67–0.95 Tm), covering the range of temperature useful for regular as well as extreme usage of SAC solders in wide range of applications. In addition to this, the effect of creep on the microstructure of solders has also been observed. Furthermore, as evident from Table 1, since there is serious lack of data on compressive creep response of SAC solders, especially Sn-1.0 wt.% Ag-0.5 wt.% Cu (SAC 105) and Sn-3.0 wt.% Ag-0.5 wt.% Cu (SAC 305), we have investigated the creep behavior of these commercially useful alloys in compression, thereby making this work relevant in the context of their actual application. 2. Experimental procedure Solder alloys in this study include SAC 105 and SAC 305. Solder bars of these two alloys were obtained from Hiflo Solders Private Limited, Chennai (India) and were machined into small cylinders. These cylinders were then vacuum-sealed in quartz tubes, imparting a pressure of ≤ 10−4 mbar. The samples were then reflowed in the furnace at a temperature of 300 °C, followed by quenching in water bath maintained at room temperature. This process of sample preparation ensures that all the specimens to be tested have identical initial microstructure because of the same reflow process used (and hence no dependence on the storage history), and it also minimizes the porosity in the samples by removing the air from the tube during vacuum sealing. Care was taken to avoid microstructural coarsening at room temperature by storing the prepared samples in deep freezer (i.e., at −20 °C ~ 0.5Tm) and all creep tests were conducted within a few days of the sample preparation. Prior to a creep test the samples were cut to final dimensions of 6 mm diameter and 10 mm height, (i.e., an aspect ratio of ~ 1.7) and both ends were metallographically polished up to 0.5 µm diamond paste. Plane planarity of samples was ensured as follows: (i) the maximum difference in the height of sample along any vertical line was limited to < 30 µm, corresponding to a nominal strain of ~ 0.3% (which is

(a)

3. Results 3.1. Effect of creep on microstructure of solders The representative microstructures of as-cast SAC 305 before and after creep are shown in Fig. 2. The as-reflowed (i.e., as-cast)

(b)

Colloidal silica

Colloidal silica

Fig. 2. Representative SEM micrographs of SAC 305 (a) before creep (i.e., just after reflow) and (b) after creep at 11 MPa and 85 °C for 20 h. The SEM micrographs were obtained using BSE and hence the brighter phase represents Ag3Sn precipitates. The black spots are colloidal silica embedded into soft Sn. It was not possible to discern Cu6Sn5 precipitates as they were fewer and farther than Ag3Sn precipitates.

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Fig. 3. The distribution of the precipitate size in SAC 305 alloy: (a) in as-cast condition, (b) after isothermal aging at 125 °C for 20 h, (c) after creep deformation at 125 °C and 7.7 MPa for 20 h and (d) after creep deformation at 125 °C and 11 MPa for 20 h. There is a consistent increase in the median particle size and decrease in the variance with increase in the stress at which the sample is creep deformed.

at 125 °C, the size of the precipitates increased with the applied stress also, suggesting that there was a noticeable evolution of microstructure during creep. As shown in Fig. 3, the median particle size increased from 270 nm in the as-reflowed sample to 420 nm and 480 nm in samples creep deformed at 7.7 and 11 MPa at 125 °C for 20 h, respectively. On the other hand, static aging (i.e., without any applied load) at 125 °C for 20 h produced Ag3Sn precipitates with a median diameter of only 390 nm, clearly indicating significant role of applied stress (besides temperature) on the coarsening of precipitates. Moreover, it is evident from Fig. 3 that the distribution becomes more like the classical bell shaped Gaussian distribution after aging or creep with increase in the number of large size precipitates and decrease in the smaller ones. This is consistent with Ostwald ripening, during which the larger precipitates coarsen at the expense of the smaller ones, thereby explaining the change in the distribution of the particle size. The significant effect of stress on coarsening of the particles in SAC alloys has been reported in previous studies in the context of thermomechanical cycling [32,33]; however, it has never been reported in the context of creep. This enhanced growth of the precipitates shown in Fig. 3 in presence of applied stress is attributed to the change in the vacancy concentration, as reported by Dutta [32]. Herein, the presence of hydrostatic stress increases the effective diffusivity of the vacancies or atoms and hence accelerates the coarsening rate of the precipitates via Ostwald ripening. This explains the increase in the precipitate size, as shown in Fig. 3, with increase in the severity of the creep test conditions. Such enhanced coarsening during creep testing condition not

microstructure of SAC 305 shows a continuous network of the eutectic mixture of Ag3Sn (and Cu6Sn5) and Sn, surrounding the primary β-Sn grains which appear as discrete islands (see Fig. 2a). A few dark black particles, as indicated by arrows in Fig. 2, are the colloidal silica particles, which were embedded in the soft Sn matrix during the last stage of metallographic polishing. As shown in Fig. 2, all Ag3Sn precipitates were not exactly circular and did not have the same initial size. Nevertheless, a comparison of Fig. 2a and b readily reveals that the eutectic precipitates underwent considerable coarsening during creep. SAC 105 also showed similar microstructure and microstructural evolution due to creep; however, it had fewer Ag3Sn precipitates which were sparsely distributed. The evolution of the precipitate size was quantified to study the effect of creep test conditions on the overall precipitate size. From the SEM micrographs, as shown in Fig. 2, the representative size of the precipitates was calculated using Image-J software according to the formula d = (6Ap/π)0.5, where Ap is projected area of the precipitate [30]. It should be noted that the 2-D projection of most of the precipitates was elliptical and the above relationship aims to represent all precipitates as spheres. Fig. 3 shows the variation of the particle size distribution with stress at a fixed test temperature of 125 °C. It should be noted that an attempt to distinguish between Ag3Sn and Cu6Sn5 precipitates was not made while measuring the precipitate sizes shown in Fig. 3. Nevertheless, the statistics on precipitate size here is more representative of Ag3Sn as its number fraction is considerably larger than that of Cu6Sn5 [31]. Interestingly, besides isothermal (static) aging 148

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Fig. 4. Variation of nominal creep strain of SAC 305 with (a) temperature at a nominal stress of 11 MPa and (b) stress at constant temperature of 85 °C. Similar curves were obtained for SAC 105 also. Shown curves are the smooth curves passing though all datum points, whereas shown symbols are a few representative datum points.

steady state will be larger in the sample tested at higher stress and hence the steady state strain rate will be relatively greater than that expected from the standard power-law equation assuming constant particle size (or interparticle distance). Therefore, such microstructural coarsening significantly affects the creep behavior of SAC alloys, and necessitates analysis of steady state creep rate using the methodology described in Fig. 1b, especially in absence of in situ measurement of precipitate size (and its evolution as well as saturation) during creep. However, all previous studies discussing creep behavior of SAC solders have neither accounted for such coarsening of microstructure during creep deformation nor followed the methodology shown in Fig. 1b, which makes it all the more important to examine the creep behavior of the SAC alloys afresh.

only results in wider inter-particle spacing, but also decreases total number of particles. A combination of these leads to longer mean free path for the dislocations to glide, with a fewer number of obstacles. The resultant effect of this is the easy dislocation movement, leading to an enhanced creep rate and a decrease in the creep resistance. This effect of particle coarsening on the creep behavior will be prominent if the creep mechanism is mainly controlled by the climb of the dislocations. Interestingly, the creep behavior of SAC alloys is primarily governed by the power law creep, controlled by dislocation climb (see Section 3.2 for detailed discussion), of the eutectic Sn phase dispersed with Ag3Sn precipitates. Therefore, it can be expected that the coarsening of the Ag3Sn precipitates, with a net decrease in their overall number, will have a pronounced effect on the steady state creep behavior of SAC alloys. The aforementioned effect of particle coarsening on steady state creep response can be quantified by incorporating a microstructural parameter, such as the particle size, the inter-particle spacing, etc., in the standard creep equation. There are a few existing creep models, which account for the microstructural length scale; one of them is the Ansell-Weertman model for dislocation creep in dispersion strengthened alloys [34]. According to this model, the creep rate is directly proportional to λ2/dp, where λ is the inter-particle spacing and dp is the particle size; this can be further simplified for simple cases (e.g., constant volume of precipitates, uniform/regular distribution of precipitates, etc.) such that the creep rate becomes directly proportional to the precipitate size. On a similar note, another model, which is worthwhile to mention particularly in the context of SAC alloys, has addressed the effect of coarsening of the Ag3Sn precipitates during an arbitrary thermo-mechanical excursion prior to a creep test, on the creep response of differently aged SAC alloys [24]. In this study [24], a direct correlation was established between the creep rate and the interparticle spacing. For developing it as a microstructurally adaptive model, both the particle size and the inter-particle spacing were expressed in terms of an effective diffusion distance [24]. However, it should be noted that the latter model (i.e. described in Ref. [24]) neglects the microstructural evolution occurring during creep test as compared to the significant coarsening taking place during severe thermo-mechanical excursion prior to onset of creep experiment. Both of the aforementioned models suggest that steady state creep deformation of the SAC alloys will be significantly affected by the size of Ag3Sn particles (and hence the inter-particle spacing), and they seem to agree well with the qualitative picture discussed here. A closer inspection of the behavior depicted in Fig. 3 suggests that if two creep tests are conducted at the same temperature and for the same time duration but at different stresses, the Ag3Sn particle size in the

3.2. Stress exponent and activation energy From the compression creep tests, strain versus time curves for SAC 105 and SAC 305 at several combinations of temperature and stress were obtained. A few representative creep curves are shown in Fig. 4, wherein an increase in the total creep strain as well as the apparent creep rate with increase in both temperature and stress is clearly revealed. Since the tests were performed under compression, only primary and secondary stages of creep were observed. The visual inspection of the samples after compression creep tests did not reveal noticeable barreling, thereby confirming the efficacy of lubrication used in between the sample and the Al2O3 platens, as well as limited extent of friction cone in the sample. Fig. 5 shows a couple of representative plots of true strain rate versus true strain on semi-log scale, which can be used to determine the steady state creep rate following the procedure outlined in Fig. 1b. As mentioned earlier, steady state can be characterized by either a constant strain rate or variation of ln ε ̇ with ε with a constant slope over a sufficiently large strain (~ 5–10%). Since the tests were conducted at constant loads (and hence had decreasing true stress), the strain rate did not become truly constant, and it decreased very slowly in the steady state, giving an impression of quasi-steady state. It can also be observed from Fig. 5 that the slope of both the curves over a sufficiently large strain (of > 5%) in the steady state region was equal to 7, which, as it will be shown later, is equal to the value of stress exponent of creep at the shown test temperature.2 This confirms the attainment of steady 2 The slope was obtained by curve fitting the equation, ε ̇ = C exp(−7εt ) , where ε ̇ is the true strain rate, C is a constant and εt is the true strain. Here, 7 is the stress exponent value for both the SAC alloys at 85 °C with regression parameter R, for curve fitting greater than 0.95.

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semi-log plot, for SAC 105 and SAC 305. The data shown in Fig. 6 were obtained at constant value of σss/G of ~ 5.5 × 10−4 at low temperatures and ~ 6.5 × 10−4 at higher temperatures, thereby satisfying one of the main requirements of meaningful calculation of activation energy. Fig. 6 readily reveals that the activation energy, Qc, represented by the slope of the curves, changed from 55 kJ/mol to 100 kJ/mol across temperature of ~ 145–150 °C for both the alloys. This clearly indicates that there was a change in the creep mechanism over the range of temperatures (i.e., 60–200 °C) used in this study. However, observation of a corresponding change in the stress exponent is also required to fully quantify and establish a physically meaningful transition in the creep mechanism. In order to evaluate the values of stress exponents of creep in both the high and the low temperature regimes, normalized creep rate, ̇ / Gb exp(−Qc / RT ) , was plotted against the normalized stress, σss/G. εkT The temperature dependence of the shear modulus was taken into account while calculating normalized stress and normalized strain rate. The activation energy, as obtained from Fig. 6, for each temperature regime was used for normalizing the strain rate. Fig. 7 shows the variation of normalized creep rate with the normalized stress for SAC 105 and SAC 305 at 85 and 180 °C. Fig. 7 shows that the stress exponent changed from 7 at 85 °C to 5 at 180 °C for both the alloys. From the plot of normalized creep rate versus normalized stress, as shown in Fig. 7, it is evident that the stress exponent was ~ 7 for both SAC alloys at 85 °C, while it decreased to ~ 5 at 180 °C. Moreover, the activation energy plot, as shown in Fig. 6, clearly indicates a simultaneous transition in the value of Qc from 55 kJ/mol to 100 kJ/mol with increase in the temperature. These two observations suggest that there is a change in the creep mechanism for both SAC alloys with temperature. It has been widely accepted that there is an excellent correlation between the activation energies for creep (Qc) and self-diffusion (Qsd) with Qc = Qsd in case of 5-power law creep, wherein the dislocation climb is controlled by the lattice diffusion [17]. On the other hand, a stress exponent of 7 (i.e., +2 more than the stress exponent at higher temperatures), a simultaneous decrease in the activation energy by approximately 50% and its dominance at lower temperatures suggests a creep mechanism based on dislocation climb controlled by diffusion through dislocation core at lower temperature [9]. The change in n by +2 with change in the diffusion mechanism from the lattice to the core of dislocation arise due to the dependence of the dislocation density on the stress, as dislocation density has often been observed to be proportional to the square of stress under steady state creep conditions. Based on the above set of arguments and the mutually consistent values of Qc and n obtained in the study, it is reasonable to conclude that creep of SAC alloys, irrespective of Ag content, is controlled by diffusion through the lattice at high temperatures (> 150 °C) and the core at low temperatures.

Fig. 5. A couple of representative true strain rate versus true stain plots using semi-log scheme. Slope of the curve in the steady state region, as shown by the curve fitting, was equal to 7 for both SAC 105 and SAC 305. The curve fitting parameters for obtaining slopes were 0.98 and 0.96 for SAC 105 and SAC 305, respectively, which are reasonable.

Fig. 6. Arrhenius plot of creep showing variation of steady state strain rate of SAC 105 and SAC 305 with inverse of temperature, used for calculating activation energy for creep. The curve fitting parameter, R, is equal to 0.99 for each of the alloys in both the temperature regimes.

state creep in the SAC alloys. Hence, it can be inferred with reasonable certainty that the strain rates measured in this study are indeed representative of the steady state behavior, and the microstructure of the specimen, including the size of precipitates, also becomes steady in the identified steady state regime. It should be noted that the as-described nature of the strain rate versus strain curves is mandatory in confirming the attainment of steady state and hence a meaningful analysis could not be performed without such a plot. It is evident from Fig. 5 that for the same stress and temperature, SAC 105 creeps significantly faster than SAC 305. Owing to the larger volume fraction of the dispersed Ag3Sn precipitates in SAC 305 as compared to that of SAC 105, the number of pinning sites for dislocations increases in SAC 305 compared to SAC 105, thereby reducing the mean free path for dislocation movement. This improvement in the creep resistance of SAC alloys by addition of Ag is consistent with earlier reports [15]. However, although the Ag content plays a significant role in improving the creep resistance, it will become evident later that composition of the solder does not noticeably affect the creep mechanism. Fig. 6 shows the variation of (true) steady state creep rate as function of the inverse of the absolute temperature, i.e., the Arrhenius type

4. Discussions 4.1. Comparison of creep parameters with pure Sn A comparison of the stress exponent values obtained in this work (i.e., 7 at 85 °C and 5 at 180 °C) with earlier studies on creep of pure Sn, as listed in Table 1, and the observation that the creep rates change significantly with variation in Ag content suggest that creep behavior of SAC alloys is governed primarily by eutectic Sn in which the Ag3Sn and Cu6Sn5 precipitates, which act as strengthening elements, are dispersed. Thus, the observed n values suggest that the creep behavior of the two SAC alloys was more similar to that of pure Sn. Furthermore, the activation energies of both SAC 105 and SAC 305 obtained in this study were around 55 kJ/mol between 60–150 °C and 100 kJ/mol between 150–200 °C, with the transition occurring around 150 °C. Similar change in the activation energy value has also been reported in the previous works of Weertman and Breen [26,27] on creep of polycrystalline Sn, where Qc changed from 110 kJ/mol at high temperatures 150

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Fig. 7. Variation of normalized strain rate with normalized stress for SAC 105 and SAC 305 alloys at (a) 85 °C and (b) 180 °C. The curve fitting parameter, R, is equal to 0.99 for each of the alloys at both the temperatures.

situation occurs at very low temperatures and high stress with σ/ G > 10−3 [9]. The experiments in this study were conducted at much lower σ/G values, thereby eliminating such effects on the creep behavior of the SAC alloys and hence PLB as well as threshold behavior is not expected. This further corroborates limited role of precipitates in altering the creep mechanisms of these SAC alloys at lower and moderate stresses.

(i.e., > 130 °C) to 46 kJ/mol at low temperatures (i.e., < 130 °C). It should be noted that addition of fine precipitates increases the dislocation pinning points and hence, probably, the overall dislocation density also. In this scenario of enhanced dislocation density, it is reasonable to expect a transition from the core diffusion dominated creep mechanism to the lattice diffusion dominated creep mechanism at relatively higher temperatures in SAC alloys as compared to pure Sn; this is consistent with observations made in this study. Suh et al. [28] have also reported a similar behavior of creep in Sn single crystals with Qc ~ 118 kJ/mol at temperature greater than 150 °C and 55 kJ/mol at temperature less than 150 °C. It should, thus, be noted that the value of Qc obtained in this work is consistent with Qsd ~ 100 kJ/mol for pure Sn [26–29] at high temperatures. Furthermore, the value of activation energy for pipe diffusion is generally 0.4–0.6 Qsd, with the transition from volume or lattice diffusion to pipe diffusion occurring around 0.7–0.85 Tm for Sn [35]. This further supports the results obtained in this study where Qpipe (55 kJ/mol) is 0.55 times Qlattice (100 kJ/mol). Thus, the values of Qc obtained in this work is also similar to that of pure Sn both in the high and the low temperature regimes, suggesting that creep behavior of these SAC alloys is similar to that of pure Sn with the creep mechanism changing from lattice diffusion to core diffusion around 145–150 °C, with Qc value changing from 100 to 55 kJ/mol. It is noteworthy to mention here that the transition from the dislocation core to the lattice diffusion also depends on the value of σss/G as observed in the standard deformation mechanism maps [9]. Interestingly, the transition temperature obtained in this work is in the range of 145–150 °C (i.e., 0.84–0.86 Tm at σss/G ~ 6 × 10−4) and is similar to that widely reported for Sn for the given stress range [26–29,35,36]. Since the solubility of Ag in Sn is negligible (~ 0.04 wt%) even at ~ 180 °C [37], it can be assumed that all of Ag is precipitated as Ag3Sn in the eutectic Sn in SAC alloys. In such cases, the diffusion of atoms through the soft Sn phase of SAC alloys can be considered to be analogous to that in pure Sn, with dissolved Ag having a limited role on the diffusion mechanism. Nevertheless, presence of fine precipitates can lead to a threshold, a behavior often observed in case of power law breakdown (PLB), wherein n values are very high. However, such a

4.2. Comparison with previous works on SAC alloys Most of the previous studies on SAC alloys have obtained n ~ 4–5 and have attributed this to core diffusion controlled creep due to simultaneous observation of the lower activation energies (~ 40–60 kJ/ mol) [15,16,18–21]; this imply that a stress exponent of 2–3 should be expected for the condition when the power law creep is controlled by the lattice diffusion. Such low values of n have never been reported for power law creep of SAC, Sn or other M-class alloys. Daly et al. [19] have reported n ~ 7 at 25 °C and 5 at 110 °C, although a change in Qc along with such a transition in stress exponent value was not observed with temperature. Nevertheless, as mentioned previously in Introduction section, both Qc and n seem to change with variation of temperature in at least a few studies [16,22]. For example, compression creep tests performed by Vianco et al. [16] have reported sinh-law stress exponent n and activation energy Qc of around 4.4 and 25 kJ/mol below 75 °C, respectively, and 5.2 and 95 kJ/mol above 75 °C, respectively. Although Qc and n values obtained in the high temperature regime in the above study [16] were similar to that obtained in this work, the values of these creep parameters at lower temperatures are quite different between these two studies. Moreover, temperatures used in the above study [16] were as low as −25 °C and stresses were very high ~ 40 MPa, due to which PLB can also occur and a transition between the two mechanisms can occur at a different temperature. In addition, a change of stress exponent by only +0.8 upon transition to the core diffusion and the corresponding lower transition temperature of 75 °C at relatively higher stresses (with respect to studies on pure Sn and this

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Acknowledgements

study) are not well supported. Therefore, it becomes difficult to understand the physical implication of such a transition in values of n and Qc. Interestingly, Kerr et al. [22] reported a similar observation about creep of small sized Sn-3.5 wt.% Ag solder joints (with Cu substrate) with Qc and n changing from 58 kJ/mol and 6, respectively, between 25 and 95 °C to 128 kJ/mol and 4, respectively, between 95 and 135 °C at stresses of 2–13 MPa. Herein also, the change in the creep parameters was attributed to a change in the creep mechanism from dislocation climb controlled by the lattice diffusion at high temperatures to the core (or pipe) diffusion at low temperatures [22]; however, the transition temperature from the core diffusion to the lattice diffusion in the above study [22] was significantly lower (< 100 °C) than that obtained in this study as well as that reported for creep deformation of pure Sn. However, there are a few ambiguities in the above study [22] primarily because of the following reasons: (a) an evidence confirming the attainment of steady state during the creep tests was not provided, (b) the creep tests were conducted under shear mode on small sized solder joints, having ~ 500 µm thickness, between Cu substrates, which, as mentioned in Section 1 and also elaborately discussed by one of the authors of the above study [22] in a later work [25], suffers from highly non-uniform distribution of stress and strain fields, thereby leading to inaccurate computation of creep parameters, (c) the reason for obtaining 2 different values of Qc depending on the test methodology, i.e., Qc equal to 42 kJ/mol and 135 kJ/mol at low and high temperatures, respectively, under “constant temperature - constant stress” tests and ~ 58 kJ/mol and 120 kJ/mol in the case of "incremental temperature" tests, is not very well understood; probable reasons for such a discrepancy can be the failure to maintain a constant σss/G during the creep tests in each temperature zone and ambiguity in reaching steady state. Moreover, in the former case (i.e., under “constant temperature – constant stress” test condition) Qc increased almost by a factor of 3, which is significantly large for a transition from the core diffusion to the lattice diffusion to occur. Therefore, from the values of activation energy and stress exponent obtained in this study, which for the first time in the context of SAC alloys used strain rate versus strain plots to ascertain the existence of steady state that is not affected by microstructural coarsening, it can be concluded that creep in the SAC solders, irrespective of Ag content, occurs by the core diffusion controlled dislocation climb at temperatures < 150 °C and the lattice diffusion controlled climb at temperatures > 150 °C. The present study highlights that there is a simultaneous and physically meaningful transition in the values of both Qc and n with change in the temperature, unambiguously indicating a change in the creep mechanism during compression creep of SAC alloys; this is in contrast to most of the previous works which have reported change in either only Qc or only n with temperature.

Authors would like to acknowledge Indian Space Research Organization (ISRO) – Indian Institute of Science (IISc) Space Technology Cell (STC) (Project # ISTC 0367) for the financial help. Authors also like to thank Professor S. Karthikeyan of Indian Institute of Science, Bangalore for meaningful discussions. References [1] A.A. El-Daly, A.E. Hammad, A. Fawzy, D.A. Nasrallh, Microstructure, mechanical properties, and deformation behavior of Sn-1.0Ag-0.5Cu after Ni and Sb additions, Mater. Des. 43 (2013) 40–49. [2] D.A. Shnawah, S.B.M. Said, M.F.M. Sabri, I.A. Badruddin, F.X. Che, Microstructure, mechanical, and thermal properties of the Sn-1.0Ag-0.5Cu solder alloy bearing Fe for electronics applications, Mater. Sci. Eng. A 551 (2012) 160–168. [3] A.A. El-Daly, W.M. Desoky, T.A. Elmosalami, M.G. El-Shaarawy, A.M. Abdraboh, Microstructural modifications and properties of SiC nanoparticles-reinforced Sn-3.0 Ag-0.5 Cu solder alloy, Mater. Des. 65 (2015) 1196–1204. [4] K. 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5. Conclusion

• Creep tests of SAC 105 and SAC 305 solders were conducted under •

•

constant compressive load at stresses varying from 7 to 14 MPa and temperature varying from 60 to 200 °C. At any combination of stress and temperature, SAC 305 was more creep resistant than SAC 105. The activation energy and the stress exponent values for creep for both SAC 105 and SAC 305 were around 55 kJ/mol and 7, respectively, below 150 °C and 100 kJ/mol and 5, respectively, above 150 °C. Simultaneous change in values of both Qc (by ~ 50%) and n (by +2) indicates a transition in the dominant diffusion mechanism for dislocation climb from the core diffusion at low temperatures to the lattice diffusion at high temperatures. Ag content affects the net creep rate with no fundamental change in the dominant creep mechanism. The rate determining creep mechanism as well as possible transition in it with temperature in SAC solders is same as that usually observed in polycrystalline pure Sn.

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