The role of lengthscale in the creep of Sn-3Ag-0.5Cu solder microstructures

Sn-3Ag-0.5Cu wt.% (SAC305) is widely used as a solder alloy in electronic interconnections, where the life of the components can be limited through thermomechanical failure of the solder joints. Here we assess the effect of secondary dendrite arm spacing ({\lambda}2), eutectic intermetallic spacing ({\lambda}e) and intermetallic compound (IMC) size in SAC305 solder on creep in samples containing a single crystal of b/-Sn with near-<110>orientation along the loading direction. Creep is investigated under constant load tensile testing at a range of temperatures (298 - 473 K) to quantify the role of these lengthscale effects on the secondary creep strain rate and activation energy. The deformation mechanisms are investigated using electron backscatter diffraction (EBSD) and strain heterogeneity is identified between b/-Sn in dendrites and b/-Sn in eutectic regions containing Ag3Sn and Cu6Sn5 particles. This motivates our hypothesis about the role of these microstructural features and creep performance.


Introduction
Sn-3Ag-0.5Cu wt.% (SAC305) is one of the most commonly used solder alloys in electronic interconnections [1] . SAC305 consists of primary -Sn dendrites and eutectic regions with Cu6Sn5 and Ag3Sn embedded within the -Sn matrix. -Sn occupies ~ 96% of the SAC305 solder and exhibits significant anisotropy in physical properties, such as elastic stiffness and thermal expansion resulting from its body-centred tetragonal (BCT) structure [2,3] .
Past work has shown that the creep behaviour of a given solder alloy is affected by the initial microstructure, which can be controlled by the cooling rate [12][13][14][15][16] and the undercooling of -Sn nucleation [17] during solidification; faster cooling rates and deeper undercoolings result in a smaller dendrite arm spacing, eutectic IMC size and spacing.
An increase in creep lifetime, secondary creep strain rate and ductility have been reported for samples cooled at a faster rate [12][13][14][15][16][17] . Among these reports, Wu et al. [12] found that the creep life and creep strain rate of their tested Sn-3.5Ag dog-bone samples changed about 1.5 and 1-2 orders of magnitude respectively between fast and slow cooled samples. Less creep resistance and a reduction in ductility for Sn-Ag/Cu joints solidified at a slower rate were indicated by Yang et al. [13] , who reported it is caused by the brittle nature of the IMCs. Kim et al. [14] pointed out that, under tensile testing SAC305, Sn-3.5Ag-0.7Cu and Sn-3.9Ag-0.6Cu samples formed using faster cooling rate have a greater elongation and ductility with decreasing size of Ag3Sn. Moreover, Ochoa et al. [15] observed a slight decrease of the activation energy, Q from 40 to 35 kJ/mol by increasing the cooling rate from 0.08 to 0.5 °C/s for Sn-3.5Ag bulk solder.
Aging of the solder microstructure can also impact the creep behaviour of solder alloys [18][19][20][21][22][23][24] and similar to the solidification studies, the creep strain rate increases with larger IMC size [18][19][20][21][22][23][24] . Dutta et al. [18] studied Sn-3.5Ag and Sn-4Ag-0.4Cu and concluded that creep is controlled by dislocation climb and the rate is dependent on the IMC size, with evidence of climb at the IMC/Sn interface. In comparing aged and rolled and cut 95.5Sn-3.9Ag-0.6Cu samples, Vianco et al. [20,21] found a decrease in both stress exponent (n) and activation energy (Q) from aged to rolled and cut samples for temperatures in the range of -25 -160 C. This was different to Basit et al. [24] and Talebanpour et al. [25] who found no change in Q as the aging time and temperature increased for pure Sn, SAC105 and SAC305 solders tested between -25 and 125 C.
Plastic deformation is heterogenous for Sn-based solders, resulting from an increase in stored energy and dislocation-dislocation interactions. The stored energy in the crystal lattice is reduced by deformation phenomena, namely polygonisation and recrystallisation, and these are precursors to crack nucleation and propagation in the strain-concentrated regions [26][27][28][29][30][31] .
In service, the SAC305 solder works at a sufficiently high homologous temperature (> 0.6) that deformation results in microstructural evolution, including dynamic recovery and recrystallisation. During recovery processes the solders deform by continuous lattice and rigid body rotation, where the stored energy or the driving force can be released by forming subgrains with misorientation between 2 -15° [27][28][29]32] . With increasing strain, the microstructure of the solder develops continuously and is often found to recrystallise by forming high angle grain boundaries (HAGBs). Discontinuous recrystallisation can also take place because of the presence of grain boundaries and second phase particles (IMCs), which act as obstacles to dislocation movement and cause localised dislocation pile-up [30,31,[33][34][35][36] .
These studies did not include information on crystallographic orientation and microstructural evolution during creep deformation, which may play a significant role. It has been shown by Ma and Suhling [37] that there are large discrepancies in the measurement of mechanical properties for solders between studies and these differences result from the microstructural variations between the tested samples.
In the present work, we simplify the microstructure using directional solidification (DS) to reproduce samples with the same microstructure and controlled crystal orientation and select the microstructural lengthscale through controlling the growth rate. In this work, we explore the effect of secondary dendrite arm spacing (λ2), eutectic IMC spacing (λe) and IMC size on the creep behaviour and microstructural evolution for constant stress creep testing at a range of temperatures. Changes on creep behaviour are explored mechanistically with studies of strain accumulation and recrystallisation (location and magnitude) at different microstructural lengthscales by using two-dimensional digital image correlation (2D DIC) and electron backscatter electron diffraction (EBSD).

Sample microstructure and experimental procedure
Dog-bone samples ( Figure 1a) were produced by DS, using the method given in ref [38][39][40] , with a 350 C hot zone and 25 C cold zone and three different pulling rates: 2, 20 and 200 µm/s. A constant pulling rate through a near-constant positive temperature gradient produces a uniform λ2, λe, and eutectic IMC (Ag3Sn and Cu6Sn5) size, and their lengthscale is controlled by the pulling velocity. This also results in large <110> oriented -Sn dendrites along the long axis during growth. Together these are required for the mechanistic understanding presented in this work. Furthermore, Figure 1e -1j show that the eutectic Ag3Sn undergoes a plate-to-rod transition with increasing growth rate between 2 and 20 µm/s, consistent with [41][42][43] . The eutectic Cu6Sn5 has a rod-like morphology for all three microstructures and a decreasing lengthscale with increasing growth velocity (Figure 1h -1j). Note that the medium microstructure sample was published in ref [38] . The tensile sample surface was polished before testing using broad ion beam (Gatan PECS II) after mechanical polishing (0.05 m colloidal silica) to improve the quality of surface finish for EBSD and to generate long strip speckle patterns for DIC [38] . EBSD scans were performed using Bruker e-Flash HR detector in a FEI Quanta SEM. The sample was then replaced within the loading frame to resume the creep test between the two EBSD scans without polishing. The EBSD maps were scanned with a step size of 6 µm and 0.4 µm [38] .
Creep strain was measured by 2D optical DIC using DaVis (LaVision), from which the surface strain field was extracted and the average value of each strain field map was recorded for each time-step. A subset size of 16 × 16 pixels, window size of 65 pixels and field of view of 10 × 2 mm were set to achieve a strain map with an effective pixel size of 11.5 m/pixel [38] .

Creep behaviour of DS SAC305 solder
Maps of crystal orientation, depicted using inverse pole figure  The creep curve data is analysed using a simple constitutive model: where R is the ideal gas constant of 8.314 J·Kmol -1 , A is a constant, n and Q are measured through the slope of ln () vs. ln (σ) and ln () vs. 1/T plot respectively by rearranging Analysis of the creep data across different temperatures using linear fitting is presented in Table 3. Exploring the high and low temperature creep data, shown in Figure 2e, indicates a 'nose' that separates these two temperature domains highlighting a change in creep mechanism, consistent with prior work [20,21,38,44,45] . At low temperatures a climbcontrolled dislocation mechanism operates and at higher temperatures potentially this is controlled by lattice-associated vacancy diffusion [38,44,45] . Table 3 collates that the activation energy, Q, decreases for samples with a finer lengthscale in the low temperature range and slightly increase in the high temperature range, and this is supported by Table 4 which indicates the lengthscale for each of these mechanisms.   Figure S2-3 and in ref [38] ).  [38] . There is no transition in the observed creep mechanism for the coarsescaled samples ( 2 ≈ 120 ± 4 µ and ≈ 7.95 ± 0.05 µ ), within the testing temperature range. While the intersection of two linear fits has been used to assess this mechanism change, it is more likely that the transition between mechanisms is asymptotic with a transition range of

Macroscopic evolution of strain field and microstructure
The DIC strain field figures at the onset of secondary creep (Figure 3b, 3g, 3i) show that the samples deformed relatively homogenously from primary to secondary creep. Strain localisation is observed within the samples and shown as hot spots in Figure 3b, 3g, 3i at the early stage of secondary creep.
The spatial distribution of strain heterogeneity revealed in the DIC maps is not correlated with the microstructural unit sizes. However, differences as a function of lengthscale in strain prior to secondary creep can be observed i.e. εcoarse = 2.4% > εmedium = 1.8% > εfine = 0.85% (Figure 3b, 3g, 3i).
As the strain continues (Figure 3c, 3h, 3m), instability develops within the gauge section and flow localisation develops (highlighted in the red square in Figure 3c, 3h, 3m). This continues to develop in secondary and beyond into tertiary stage creep where necking forms (Figure 3d, 3i, 3n) and this is where fracture occurs.
The fine-scaled sample has greater reduction in cross-sectional area within the necked region combined with the greatest total elongation. This indicates that the finest lengthscale stabilises hardening and promote an increase in ductility.
EBSD-based orientation mapping (Figure 3e, 3j, 3o) reveals that crystal lattice orientation spreads and rotates during the deformation, and larger changes are found near the fracture surface. Recrystallisation and new grains are found in the highly strained regions in the neck (Figure 3e) and near the fracture surface (Figure 3j, 3o). The size of the formed recrystallised grains decreases significantly when the microstructure is refined (Figure 3e, 3j, 3o).
The variation in strain heterogeneity is illustrated in Figure 4a, 4c, 4e (extracted from Figure 3c -d, 3h -i, 3m -n). The strain level in the highly-strained regions (necked regions in Figure 3d, 3i, 3n) is significantly higher than the average strain level across the samples, while the uniformly-deformed regions have much lower strain level, and these have not reached tertiary creep at the end of the tests.
The corresponding pole figures (PFs) in Figure 4b,  consideration of the macroscopic loading direction, the crystal orientation, and the critical resolved shear stress ratios estimated from Zamiri et al. [46] (Calculation of Schmid factors are presented in supplementary Table S4). Figure 5 shows the micrographs within the uniformly-deformed regions of each sample in the as-solidified condition. The FSD images indicate the contrast between dendrite and IMC-containing eutectic regions (Figure 5a, 5h, 5o). The IMCs, Ag3Sn and Cu6Sn5, are the protruding features in the eutectic regions. The λ2, λe and size of the IMCs decrease significantly from coarse-to fine-scaled microstructures (as noted in Table 2).

Microscopic evolution of microstructure
EBSD mapping indicates the evolution of the lattice orientation and the lattice misorientations with increasing strain within the (macroscopically) uniformly straining regions ( Figure 5) and the necked region ( Figure 6, Figure 7).
In all microstructures, the EBSD data reveals that heterogeneity of lattice misorientations develops depending on the presence of the IMCs, and the range of this heterogeneity (by comparing the misorientation to average maps in Figure 5e, 5l, 5s to Figure 5f, 5m, 5t) is controlled by the size and distribution of the IMCs. This is reasonable as the IMCs are elastic and hard as compared to the matrix. Subgrains are observed in β-Sn around the IMCs for the coarse-scaled microstructure, near the dendrite-eutectic interfaces for the medium-and fine-scaled microstructures and at grain boundaries for the fine-scaled microstructure (indicated with red arrows in Figure 5f, 5m,5t). There is no obvious orientation change in the IPF-LD maps for the coarse-and medium-scaled microstructures from the as-solidified condition (Figure 5b, 5i) to the onset of secondary creep (Figure 5c, 5j). For the fine-scaled microstructure, the number of pink grains increases and they grow in size within the IPF-LD map (indicated with red arrows in Figure 5q).
At the end of tertiary stage creep (Figure 5d, 5g, 5k, 5n, 5r, 5u), within the mapped regions the lattice is rotated and this is more obvious in the fine-and medium-scaled microstructures (Figure 5n, 5u). In the coarse-scaled microstructure the average orientation does not change (Figure 5d) but significant heterogeneity is observed near the IMCs (Figure 5g).
In all samples the subgrain structures start to grow into the primary β-Sn dendrites, and the size of the subgrains is controlled by IMCs (Figure 5g, 5n, 5u). Furthermore, the magnitude of the misorientations in the fine-scaled subgrains is larger, which correlates with the total strain developed in each sample (Figure 4a, 4c, 4e). The magnitude of the misorientation here is related to the stored energy and this hints at why recrystallisation, and ultimately failure, is changed by the IMC and dendrite lengthscale.  Figure 7e). In the eutectic region, the recrystalised grains (yellow) are rotated towards [001] orientation (indicated with black arrows in Figure 7e).
For the fine-scaled microstructure, the 'rainbow' recrystallised grains are formed in dendritic β-Sn (Figure 7f), which deforms by gradual lattice rotation with continuous development of polygonisation and causes recrystallisation in the highly strained region [38] . The constrained stored energy is released at the fracture surface showing decrease in misorientation (Figure 7g -7i).

Discussion: The role of lengthscale on creep mechanisms
In secondary creep, the two competing processes of strain hardening and dynamic recovery are in balance and no localised creep damage is obtained in the macroscopic scale ( Figure 2a). As the sample starts to yield, the high strain gradient regions are generated by the IMCs and/or dendrite -eutectic interfaces and create unstable regions through the gauge section (DIC strain field maps in Figure 3b, 3g, 3i) and change the accumulation of stored energy (shown with the EBSD maps in Figure 5c, 5f, 5j, 5m, 5q, Failure of the fine-scaled sample results in a sharper neck (Figure 3o) as the total amount of strain in the neck is large before the onset of tertiary creep (Figure 2a). This supports the idea that there is less instability, and the volume of material that recrystallised is smaller.
In the present work, the ex-situ tests with repeat imaging of the same area indicate that recrystallisation occurs during deformation and this creates crystallographic texture. This is supported by our recent prior work [38] . This is important as it highlights that critical to the present work is the establishment of strain gradients near the IMCs during deformation ( Figure 5). The strain gradients result in local subgrains which can be thought of as regions of low dislocation content separated by dislocation walls, resulting in substantive changes in lattice orientation. These subgrains store energy as the deformation progresses and likely act as nucleation sites for recrystallisation. This is associated with the concept of particle stimulated nucleation (PSN) [47] .
By comparing the results of the three samples with different microstructural lengthscales ( Figure 5 -Figure 7), the effect of initial lengthscale on the formed recrystallised β-Sn grains is shown and there is a strong correlation, i.e. with λ2, λe and IMC size. This is plotted in Figure 8g, 8h to quantify the change in size of recrystallised grains within dendrite and eutectic regions separately. Furthermore, the recrystallised grains in the eutectic β-Sn regions have much smaller grain size than in the β-Sn dendrites for all three microstructural lengthscales (Figure 8), as also described in ref [38] .
In addition to recrystallisation around the IMCs, recrystallisation can occur within the dendrite. This is important for the coarse-scaled sample, where the IMCs are fewer and more widely spaced, so the recrystalised grains propagate relatively easily and are quick to deform through the β-Sn matrix in the dendrite (annotated in Figure 8d). In this sample, the creep failure is related to propagation of the recrystallisation bands in the β-Sn dendrites (Figure 3e). This is related to where the neck and the ultimate crack form.
As the microstructural lengthscale becomes coarser, there is a significant strain partitioning between the primary β-Sn dendrites and the eutectic regions ( Figure 5 -Figure 7). The macroscopic deformation of the sample (Figure 3) becomes less stable once the recrystallisation bands start to form and these recrystallisation bands extend relatively quickly through the entire gauge section being evidenced by significant strain localised within the necked region, and in turn during the final stages of necking and failure, this leads to a large volume of recrystallisation (Figure 3e, 3j, 3o).

Conclusions
Creep strain patterning, stored energy accumulation, recrystallisation and ultimately failure of SAC305 solders are controlled by the size and distribution of IMCs and the size of dendrites. This has been studied using reproducible samples with controlled microstructural lengthscales, namely crystal orientation (close to [110] and [100]), secondary dendrite arm spacing (λ2), eutectic spacing (λe) and Ag3Sn and Cu6Sn5 size.
The following conclusions can be drawn from this work. Deformation changes the mechanism at higher temperature and this is likely a transition from climb-controlled dislocation to lattice-associated vacancy diffusion creep. These behaviours imply that creep deformation is obstacle-controlled, which becomes more prominent below the transition temperature.
2. As the microstructural lengthscale changes, the microstructure of the samples evolves differently at the macroscopic scale. Heterogeneous deformation occurs during creep.
The sample with a finer lengthscale forms a more stable neck than the sample with a coarser lengthscale. The ductility of the sample increases with refining lengthscale and the deformation becomes less localised, i.e. more homogenous deformation is introduced.
3. At the microscopic scale, the heterogeneous evolution of microstructure is caused by the presence of two distinct microstructural regions, i.e. primary β-Sn dendrites and IMC-containing eutectic β-Sn regions as described in ref [38] . The initial deformation starts in the β-Sn within the eutectic region near IMCs because dislocations often concentrate against the hard particles (IMCs), which becomes highly localised around the IMCs for a coarse-scaled sample, whereas more spatially extensive deformation for a fine-scaled sample. The soft phase, β-Sn, deforms by lattice rotation to form subgrains with continuous development of misorientation (polygonisation) and generates recrystallisation with large accumulation of strain at tertiary creep and this is enhanced with a finer microstructural lengthscale. The size of the formed subgrains and recrystalised grains decreases with increasing lengthscale of the sample, i.e.
polygonisation and recrystallisation are controlled by λ2 and λe.

Author Contributions:
TG drafted the initial manuscript and conducted the experimental work. CG and TBB supervised the work equally. All authors contributed to the final manuscript.

Data Statement:
Data from this manuscript is available at: <link to be included upon final acceptance>.   Figure S2-3 and in ref [38]