In-situ synchrotron micro-diffraction study of surface, interface, grain structure and strain/stress. evolution during Sn whisker/hillock formation

Transcription

1 In-situ synchrotron micro-diffraction study of surface, interface, grain structure and strain/stress evolution during Sn whisker/hillock formation Fei Pei 1, Nitin Jadhav 2, Eric Buchovecky 3, Allan F. Bower 1, Eric hason 1, Wenjun Liu 4, Jonathan Z. Tischler 4, Gene E. Ice 5, and Ruqing Xu 4 1 School of Engineering, Brown University, Providence, RI, USA 2 IBM, Hopewell Junction, NY Saint-Gobain, Northboro R&D enter, Northborough, MA Advanced Photon Source, Argonne National Laboratory, Argonne, IL, USA 5 Oak Ridge National Lab, Oak Ridge, TN, USA Abstract We have performed X-ray synchrotron micro-diffraction measurements to study the processes controlling the formation of hillocks and whiskers in Sn layers on u. The studies were done in real-time on Sn layers that were electro-deposited immediately before the X-ray measurements were started. This enabled a region of the sample to be monitored from the as-deposited state until after a hillock feature formed. In addition to measuring the grain orientation and deviatoric strain (via Laue diffraction), the X- ray fluorescence was monitored to quantify the evolution of the Sn surface morphology and the formation of intermetallic compound (IM) at the Sn-u interface. The results capture the simultaneous growth of the feature and the corresponding film stress, grain orientation and IM formation. The observations are compared with proposed mechanisms for whisker/hillock growth and nucleation. Keywords: Tin whiskers, X-ray micro-diffraction, microstructure, stress gradient, strain energy density 1

2 Introduction Sn whiskers and hillocks are features that grow spontaneously on the surfaces of Sn coatings. Whisker is a term used to describe long thin filaments that grow primarily out of the surface, typically with a relatively uniform cross-section. Hillock refers to lower aspect-ratio features that are accompanied by lateral grain growth within the layer [1]. Because whiskers can grow long enough to cause system failures [2], there is a strong desire to understand the underlying driving forces and mechanisms behind their formation. A complete understanding of whisker or hillock growth has not been developed, but it has been suggested that similar driving forces and mechanisms control their growth [1, 3-5]. Therefore, although we report in this work specifically on measurements of the evolution of a hillock-like feature, we believe that the results are relevant to the growth of whiskers as well. The driving force behind whisker/hillock growth is generally believed to be stress [3, 6-8], specifically due to the formation of u 6 Sn 5 intermetallic compound (IM) between the Sn and u [1, 9- ]. Yet many of the underlying processes controlling the stress evolution and surface evolution are not understood. To address these issues, we have performed X-ray micro-diffraction experiments at the Advanced Photon Source (APS) synchrotron facility of the Argonne National Lab. The measurements were made on newly-deposited Sn layers so they could be observed while they are still reacting to form IM and the surface morphology is changing. Using a sub-micron X-ray beam, we repeatedly measured the Laue diffraction pattern and the fluorescence intensity from each point in the same 36 µm 36 µm region of the surface. We emphasize that these studies were done in real-time, starting soon after the layer was deposited, so that the simultaneous evolution of the strain, microstructure and surface morphology could be monitored both before and after the surface features start to develop. By real-time, we mean that the features were measured as they were developing, in contrast with other studies where the sample is fabricated long before the measurements are done and the surface is no longer evolving at the time of the measurement. This allows aspects of the growth and stress relaxation processes to be captured that cannot be seen after the features have formed. The results provide insight into the interactions among IM 2

3 growth, stress generation/relaxation and surface evolution on a local level that lead to whisker/hillock formation. There have been many measurements that have studied different features of how the IM volume [11, 14-16], stress [1, 1-, 17, 18] and whisker density [1, 11] evolve with time. Measurements on a series of samples grown with different Sn layer thicknesses and grain sizes [19] demonstrated the correlation among these different parameters and showed that the propensity to form a whisker/hillock is correlated primarily with the stress in the Sn film. These studies were performed with spatially averaging optical techniques so they could not address the question of how and why a particular Sn grain would start to deform into a whisker. Other factors that could possibly affect the tendency of a grain to nucleate a whisker can be the orientation of the grain [1], the orientation of the grains surrounding it [4, 2], the grain structure underneath the grain (i.e., oblique boundaries) [21] or the amount of IM that grew below that grain. A greater fundamental understanding of these micro-scale issues is needed to develop reliable mitigation strategies as well as to develop models to predict whisker/hillock formation. X-ray micro-diffraction capabilities [4,, 2, 22] have been used previously to measure the compressive stress, stress gradient, grain orientation distribution in the finish, and the growth direction of Sn whiskers after the whisker features had formed. hoi et al. [22] found that the Sn-u solder finishes in their studies have a (321) texture and are in a state of compressive stress with a magnitude of less than 1 MPa. They observed a whisker growing along the [1] direction with a grain below the whisker oriented with the (21) planes parallel to the surface. There was a stress gradient around the whisker root, spreading over a few grains with zero stress just below the whisker. Sarobol et al. [4] suggested that high misorientation between the defect grain and the surrounding grains creates highly localized out-of-plane elastic strain and strain energy density, which can determine the potential to form a whisker/hillock. Sobiech et al. [] performed similar experiments in which they measured the strain around the whisker root and along the depth of the whisker root [23]; they found in-plane residual strain gradients around the root of growing Sn whisker as well as vertical strain gradients, which they concluded to be the driving 3

4 force behind Sn atom transport to the whisker root (as a strain-relief mechanism). From this they concluded that the compressive strain is not a prerequisite for whisker formation. However, since these measurements were performed after the whisker formed, it is not clear whether the observed gradients may be a consequence of whisker formation rather than a cause. Despite significant study, an important piece of the mechanism what causes whisker/hillock formation to occur at specific grains has still not been answered. Some potential reasons for these grains to deform could be: the higher localized strain (stress) around a grain [4, 1], higher IM formation at the base of the grain, a weaker surface oxide on a grain [24-26], the grain s orientation [1] or the orientation of its surroundings [4, 2], and the sub-surface microstructure [21]. Since previous micro-diffraction studies were performed after the whisker/hillock had already formed, it is difficult to determine the conditions that would make some grains develop into whiskers/hillocks. In order to answer these questions, our studies monitored a sample that was still actively reacting so that the evolution could be recorded in real time. Experiments Sample preparation The Sn-u samples used for the synchrotron micro-diffraction characterization were fabricated by electroplating 3 μm Sn layers on glass substrates that had been previously coated with a 15 nm Ti adhesion layer and a 6 nm u layer by electron-beam evaporation. The u-coated substrates were stored under ambient conditions for over 1 day in order to relax the residual stress from vapor deposition. We used amorphous glass slides (~15 μm thick) as sample substrates so they would not produce additional diffraction features when the sample is scanned by the X-ray beam. The Sn layers were electroplated at the synchrotron shortly before the run started with a threeelectrode plating cell controlled by a potentiostat. The layers were deposited from a SOLDERON S 4

5 chemical bath (manufactured by Dow company) to a thickness of 3 μm in galvanostatic mode. The current density of 1 ma/cm 2 corresponded to a deposition rate of 9.1 nm/s. The resulting Sn microstructure has columnar grains with a diameter of 2-3 µm and predominantly vertical grain boundaries, which is typical of matte Sn platings. X-ray micro-diffraction The X-ray micro-diffraction measurements were performed using Laue Diffraction Microscopy [27, 28] in the 34-ID-E beamline at the APS. A schematic of the experimental set-up is shown in figure 1. A non-dispersive Kirkpatrick-Baez mirror pair (focus independent of wavelength) is used to focus the incident X-ray beam (polychromatic or monochromatic) to a spot with submicron size [29] on the sample surface. Since the X-ray beam probe is much finer than the Sn grains (2-3 µm in diameter), it can be used to resolve the microstructures of different grains and determine the local deformation. In this study, we primarily used a polychromatic X-ray beam (energy range 7 24 kev) to perform Laue diffraction. A non-dispersive monochromator [3] can also be inserted into the X-ray beam for studies under monochromatic conditions [28] which was used for determining the volumetric strain (as described below). The Sn sample was mounted on a precision three-axis translation stage. As shown in figure 1, the sample surface makes an angle of 45 o with respect to the incoming X-ray beam. The sample coordinate is defined so that the x and y axes lie in the Sn film plane, and z is normal to the sample surface. To perform a 2D mapping, the sample was translated in both the x- and y-direction at a step size of.5 µm. At each step the sample dwelled for 1 s to allow for the X-ray sensitive D detector to collect the Laue diffraction patterns generated by each crystalline element illuminated by the incident X-ray beam. At the same time, the fluorescent detector placed near the sample surface captured the characteristic radiation from u (k α ) and Sn (L α and L β ) at the same position. Since the fluorescence intensity is proportional to 5

6 the total volume of each element integrated along the beam direction, it is thus a measure of the integrated thickness of Sn and u along the beam direction in the sample. As described below, by using the measured changes in the fluorescence at different positions we can monitor the evolution of the morphology of the Sn surface and the Sn-u interface. The micro-diffraction measurements were analyzed at each position to determine the crystallographic orientation and deviatoric strain tensor elements. If multiple grains through the thickness of the Sn film are illuminated at the same time, the overlapping Laue patterns from different grains can be separated by the intensity of the reflections. The pattern with the highest intensity is assigned to the position under consideration. For a strained unit cell, the Laue diffraction spots deviate from the reference positions (which correspond to a strain-free Sn unit). By analyzing the displacements of the diffraction spots from the reference, the deviatoric strain tensor at each position can be quantified. The Laue measurement only directly determines the deviatoric strain components averaged over the illuminated volume. In order to determine the volumetric component, Bragg reflections under a monochromatic X-ray beam can be used (further description of this procedure can be found in [28]). From the monochromatic measurement, the actual spacing of a lattice plane that is parallel to the sample surface at a selected position can be determined. By comparing with the theoretical value (i.e. the spacing calculated from the lattice parameters measured from stress/strain free Sn samples), the out-of-plane strain (ε zz ) at this point can be determined. This measurement is time consuming as multiple operations are required, so it was only selectively performed at a few positions on our sample. Alternatively, we can obtain the full strain tensor by making assumptions about the out-of-plane component as described below. Results A goal of this work is to study the morphology, stress and microstructure in the Sn layer both before and after a whisker/hillock formed to understand how these properties are related. Therefore we 6

7 could not identify and characterize a feature that had already formed as was done in previous synchrotron micro-diffraction studies. Instead, based on our previous work we chose an area of the surface to monitor (36 µm 36 µm) that was large enough to have a high probability for a whisker or hillock to develop in it. Multiple measurements were made on the same region of the sample at different times. Starting at 4 h after the Sn layer deposition, we acquired 4 consecutive scans of approximately 2.5 h duration over the same region. After these runs, the sample was removed from the experiment system and stored in ambient conditions. In the following days, this same area was re-examined in two additional scans performed at 51 h and 114 h after Sn plating, respectively. As described below, a hillock-like feature was observed to form in this region. Scanning electron microscope (SEM) images of the surface after the synchrotron run indicated that there were higher aspect ratio whisker features at other positions on the surface, but these were not in the region that we measured with micro-diffraction. In figure 2 we present the results obtained from 4 of the micro-diffraction measurements described above. The start time for each scan is indicated on the top of each column. The results from the 2 nd and 3 rd scans are not shown due to limitations of space. The different rows in the figure show (starting from the top of figure 2) the Sn fluorescence (figure 2a), u fluorescence (figure 2b), grain orientation (figure 2c) and biaxial deviatoric strain (figure 2d). The maps acquired in different scans have been aligned so that each image in figure 2 shows the same area with a size of 35 µm 3 µm. 1. Sn fluorescence and surface morphology Figure 2a shows the Sn fluorescence maps obtained at different times after Sn deposition. To eliminate variation between each fluorescence scan due to beam intensity variation, the intensity in the figure is normalized by dividing the value at each position by the average of the intensity over the entire measured region. This normalization keeps the total intensity the same for each scan, since the total amount of Sn measured in each scan is essentially the same. We interpret the variation in the normalized fluorescence to correspond to the variation of Sn thickness relative to the average film thickness. Further 7

8 discussion of the basis for this interpretation is contained in section 3 of the discussion. The color scheme (shown below the Sn fluorescence maps) is chosen in such a way that the spot with strong (weak) Sn fluorescence intensity appears bright (dark) in the maps. The first measurement shows a fairly uniform distribution of Sn (the 1 st image in figure 2a), with the variation presumably corresponding to the surface roughness of the Sn electrodeposits. No significant morphology change is observed in the following 1 hours, i.e., the Sn fluorescence map at 14 h (the 2 nd image in figure 2a) shows a featureless distribution just like the 1 st image. At 51 h after Sn deposition, however, a large bright spot is observed in the Sn fluorescence map (the 3 rd image in figure 2a). The significantly increased Sn signal is due to Sn accumulation in this area, indicating that a hillock-like feature has formed at this place (the height of the feature is estimated to be approximately 1.5 µm). The dark area adjacent to the bright spot is due to shadowing of the fluorescence radiation from the Sn grains in this region by the protruding hillock. The hillock continues to grow after this scan as shown by the increased size of the bright spot and shadowed areas in the subsequent measurement (after 114 h). 2. u fluorescence and IM formation u maps were similarly constructed from the u fluorescence signal at each point (also normalized to have the same total intensity) on the surface (figure 2b), acquired at the same time intervals and same positions as for Sn. The color coding of the intensity is indicated in the color bar below the maps; the points which are darker have a larger amount of u than the light orange regions. The magnitude of the u fluorescence varies over the interface and the degree of variation increases with time. The RMS variation is equal to 4.7, 6.7, 9.7 and 11.4% for the different times from 4 to 114 h in figure 2b. For comparison, the as-grown u layer had relatively uniform thickness with roughness on the order of 5 nm (i.e., ~1 % of the average u thickness) as determined by atomic force microscopy (AFM). We attribute the spatial distribution and increasing variation of the u intensity with time to the inhomogeneous growth of IM particles at the interface. Other measurements of IM formation have 8

9 shown that in these early stages it does not grow as a uniform layer but instead primarily forms particles that are irregular in shape [1, 16]. Therefore, regions of higher u intensity are interpreted to correspond to accumulation of u into the growing IM particles. Since u reacts readily with Sn at room temperature, there is already noticeable interface roughening and IM accumulation within 4 h after Sn plating, as seen by the dark areas in the 1 st image in figure 2b. The u-accumulating areas continued to increase in the subsequent measurements, consistent with continuous formation of the IM with time [11, 14-16]. AFM and SEM measurements [14-16, 31] have also found that the IM particles grow preferentially in the Sn grain boundaries at the Sn-u interface. To examine this for these samples, we superimpose the Sn grain boundaries (determined from the orientation measurements shown in figure 2c) as blue lines over the u fluorescence map measured after 114 h. Greater accumulation of u (dark regions) is seen to occur along the Sn grain boundaries. Note that the fluorescence measurement identifies the IM growth that is spatially non-uniform (i.e., particles); IM that grows as a uniform layer cannot be measured by this technique. A low u intensity (bright spot) is also observed in the u maps measured after the hillock has formed on the surface (i.e., the 3 rd and 4 th images in figure 2b). This feature correlates with the low intensity area adjacent to the hillock site observed in figure 2a, indicating that the decrease in u intensity is due to shadowing of the u fluorescence signal by the surface feature (similar to the shadowing observed in the Sn fluorescence). 3. Grain orientation The Laue diffraction pattern collected during each step in the scan was indexed [32] to determine the crystallographic orientation of the Sn grain at each point within the selected area. Figure 2c shows the orientation maps of the Sn surface measured at different times after Sn deposition. Each Sn grain in the 9

10 map is shaded according to the position of its (1) pole in the pole figure color scheme that is shown at the bottom of figure 3. The color corresponds to the azimuthal orientation of the grain while darker hues correspond to the tilt of the (1) pole relative to the surface normal. For example, Sn grains with their (1) poles normal to the sample surface would be shown as white in the maps. The grains whose orientations cannot be indexed from the Laue patterns are shown as black. It is apparent from figure 2c that the Sn film is polycrystalline with most of the grains having sizes within the range of 2-3 µm. omparison of the orientation maps measured at different times shows that the average grain structure does not change significantly. This is consistent with our previous study [25], in which large scale grain growth was not observed on similar Sn electrodeposits when their surfaces were monitored by SEM over a period of 5 days. One obvious exception is the large grain that forms at the same position as the bright spot in the Sn fluorescence map after 51 h. The growth of this grain is further evidence that it corresponds to the formation of a hillock on the surface. Smaller amounts of grain growth can also be observed at other regions on the surface, as highlighted by the circles in the leftmost image in figure 2c. To understand the distribution of grain orientations in the sample, we display the same data plotted as (1) pole figures in figure 3. The pole figure represents how the (1) pole in each Sn grain is oriented with respect to the axes of the sample coordinate system. The color code of each pole is the same as used for the individual Sn grains on the surface (figure 2c). The distribution of orientations suggests a fiber texture, with the (1) orientations (c-axis) of most Sn grains distributed azimuthally around the surface normal and tilted from it at an angle in the range of 61 ± 8. This fiber texture remained essentially unchanged over the measured time period. We do not observe the formation of many grains with new orientations in the Sn layer and most of the measured Sn grains were found to retain their asdeposited orientations till the end of the study. To understand the degree of texture, in figure 4 we plot a normal-direction inverse pole figure constructed from the orientation data obtained at 4 h after Sn deposition. The inverse pole figure shows 1

11 the distribution of crystallographic directions parallel to the surface normal. The contour coloring is chosen so that the darker color indicates a higher fraction of grains having that orientation. A band of orientations is found to have intensity higher than the average; the most common orientations are ~1 from the (311) pole. This is similar to the results of hoi et al. [22], who found that (321) was the most common orientation for their Sn coating. However, the film texture can be affected by the preparation conditions (i.e., plating bath, growth rate, etc). Sarobol et al. [2] reported that change in current density as well as film composition can lead to significant variations in the resulting Sn textures. 4. Strain measurements The deviatoric strain tensor was derived from the indexed Laue diffraction pattern of each point by measuring the shift in peak positions from their expected positions in a strain-free Sn crystal with the same orientation [32]. The mean biaxial deviatoric strain ( ε b ) was calculated from the measured deviatoric strain tensor as: ε b = 1 (ε 2 xx + ε yy ). (1) where ε xx and ε yy are the xx and yy components of the deviatoric strain tensor respectively in the sample coordinate (as described in figure 1). Figure 2d shows the biaxial deviatoric strain maps measured at the same time and positions as the other data in the figure. The strain maps are color-coded according to the sign and magnitude of the strain measured at each position, as indicated by the color bar below figure 2d. The areas having compressive strain are colored with shades of red while those with tensile strain use shades of blue. The intensity of each color increases with the magnitude of the measured strain, up to a value of.1 %. Above that value, the saturation colors of dark red or dark blue are used to shade the points. The black points correspond to the grains whose Laue patterns could not be indexed. To make it easier to recognize the features in the strain maps, the Sn grain boundaries extracted from the orientation map (figure 2c) are superimposed on 11

12 the strain map as black lines. The measured deviatoric strain tensor and crystal orientation at each point were used as input for calculation of local stress, as described below. 5. Stress distribution Since stress is believed to be the driving force for whisker/hillock formation, we would like to know how the stress is distributed and how it evolves within the layer, especially around the growing hillock. Determination of the stress requires all the elements of the strain tensor which includes the volumetric strain (e). As discussed above, this component of the strain cannot be determined directly by the Laue diffraction technique. However, we have obtained an estimate for the full stress tensor by assuming that the stress component normal to the sample surface is zero everywhere (i.e., σ zz = ). This is the same assumption that has been used previously by hoi et al. [22] and Sarobol et al. [4] to analyze their synchrotron micro-diffraction measurements. Although this condition is only satisfied exactly at the surface or if the stress is averaged over the entire film, the approximation assumes that it can be applied locally. Use of this approximation makes it possible to estimate the volumetric strain at each point even though it was not directly measured in the Laue measurements. A description of how the volumetric strain and full stress tensor are calculated from the deviatoric strain components is given in Appendix A. Once the volumetric strain is determined, we can calculate the mean biaxial strain (ε b ) from the deviatoric strain: ε b = ε b + e (2) A map of the mean biaxial strain is plotted in figure 5a using the same graphic scale and color scheme as the deviatoric strain (figure 2d). The similarity of the two plots indicates that the addition of the volumetric strain component does not significantly change the strain distribution within the layer. Based on the estimated volumetric strain, we can also calculate the out-of-plane strain (i.e., ε zz = ε zz + e). The average value of ε zz determined by the calculation is ± The large

13 scatter in the average strain values is a consequence of fluctuations in strain resulting from random variations in orientations of the grains, which result in a highly heterogeneous stress and strain state in the film. We also performed monochromatic measurements at 5 selected points to determine ε zz ; these resulted in an average value of ± The average value is within 15% of the average value obtained from x-ray measurements, providing some confirmation of the assumption, σ zz = used to reconstruct the three dimensional state of strain. The mean biaxial stress (σ b ) at each position can also be calculated once the full stress tensor has been determined: σ b = 1 2 (σ xx + σ yy ). (3) Figure 5b shows σ b at different times, calculated from the measurements in figure 2d. The Sn grain boundaries are shown as black lines in the figure. The stress maps are colored using a similar scheme to the strain measurements as indicated below the figure, i.e., red represents areas with compressive stress while blue is used for those with tensile stress. The stress distribution is not uniform across the Sn surface and not constant over time. For instance, some regions that have high stress in the measurement made at 4 h do not have large stress at later times. We attribute these variations to processes of stress generation (e.g., due to IM growth) and stress relaxation (e.g. power law creep [33]) within the layer that occur over time. For comparison with our previous measurements of the stress evolution using wafer curvature [14], we calculated the average biaxial stress (area-weighted) over the entire region. Results from measurements on this and another similar Sn-u sample (shown in figure 6 as samples 1 and 2, respectively) indicate that the average biaxial stress in the Sn film becomes increasingly compressive soon after Sn deposition and then reaches a maximum of approximately -15 MPa. In some measurements, the compressive stress decreased after several days, even though the IM was still growing, suggesting extensive relaxation within the Sn film. The stress evolution in figure 6 is consistent with curvature

14 measurements on similar Sn samples with thickness of 2.9 µm [14]. We will discuss below whether the surface deformation or other mechanisms are responsible for the stress relaxation. It has been suggested by Sarobol et al. [4] that strain energy density (SED) is the driving force for whisker/hillock growth. The strain energy density is defined as SED = 1 2 σ ijε ij. (4) The SED at each point is shown in figure 5c, measured at the same time intervals as the other figures. The color scale is shown below the images. The SED of certain grains is much higher than the average value in the scanned area. By comparing with other measurements, we can examine whether defect formation or microstructural change preferentially occurs at grains with high SED, as discussed in the following sections. Discussion 1. IM growth, stress evolution and whisker/hillock formation IM growth has been proposed to produce the driving force for whiskers/hillocks by inducing compressive stress in the Sn grains as it grows [1, 9-]. However, there is not an understanding of how the resulting stress is distributed over the layer, or how the local stress distribution is related to the whisker/hillock growth. The simultaneous measurement of the surface/interface morphology (via fluorescence) and the local stress/strain distribution (via Laue diffraction) enables the relationship between the IM formation, stress and whisker/hillock formation to be studied directly. Importantly, these measurements are done in real-time so that they capture the effects both before and after the formation of a whisker/hillock surface feature has occurred. We consider first the relationship between the distribution of IM particles and the development of a whisker/hillock feature. If IM growth provides the driving force, we can examine whether there is more IM around the site where a whisker/hillock forms than at other sites. Figures 2a and b show that 14

15 there is no greater growth of IM particles (i.e., higher u fluorescence) around the root of the grain that forms a hillock (bright spot in figure 2a after 51 h) than around other grains that do not change into hillocks. This observation is consistent with previous work that measured the IM structure around the whisker-forming grains after chemical removal of the Sn layer [31]. However, the micro-diffraction results also show that this is true even before the hillock starts to form. Similarly, we can consider the relationship between the spatial distribution of the IM and the resulting biaxial stress in the Sn layer (figure 5b). The non-uniform particles highlighted by the fluorescence measurement would be expected to generate more stress in the Sn than the growth of a uniform IM layer at the Sn-u interface. However, this is mitigated by stress relaxation processes that determine whether the stress remains localized around the IM particle growth that generates it or spreads out into the surrounding regions. If there is not much relaxation, we would expect to see large compressive stress in the regions where the IM formation is greatest. onversely, if there is significant stress relaxation (e.g., by creep or dislocation-mediated plasticity) then we would not expect to see a strong correlation between the stress and the IM maps. The measurements indicate that the biaxial stress is distributed relatively uniformly across the surface. Although we observe hot spots in the stress maps (i.e., regions with high compressive stress), these do not coincide with the areas that show significantly higher IM accumulation. We also do not observe large stress gradients across the individual grains even though the IM growth occurs preferentially near the grain boundaries. These observations are consistent with the results from finite element analysis (FEA) calculations [34] that simulated the stress around growing IM particles with the inclusion of elasticity, grain boundary diffusion and ideal plasticity. Although the compressive stress is initially localized around the IM particles, the relaxation process (grain boundary diffusion and plasticity) act to spread out the stress and make its distribution more uniform throughout the Sn film. 15

16 Measurements of the surface morphology (via the Sn fluorescence, figure 2a) show that the hillock did not appear to initiate from a region where the biaxial compressive stress is significantly higher than others. Furthermore, many grains with high compressive stress did not deform into whiskers/hillocks. This suggests that the local stress is not the only factor that determines whisker formation and that other issues such as the underlying grain microstructure must be considered. 2. Local microstructure, stress and strain energy density within the deforming region To look at the local stress and microstructure around the developing hillock, we show a sequence of enlarged images (15 µm 15 µm) that represent the grain structure (figure 7a), mean biaxial stress (figure 7b) and strain energy density (figure 7c) before and during the surface morphology change that we infer from the Sn fluorescence measurement (figure 2a). The grain that formed into the hillock is indicated by the arrow in figure 7a after 114 h. Looking at earlier times shows that this grain orientation was present in the first measurement (at 4 h), though it was much smaller. The results indicate that this grain starts to grow laterally (at 6 and 14 h) before there is any observable change in the Sn thickness based on the fluorescence map. This lack of growth outward from the surface suggests that this grain is initially growing beneath the surface of the Sn (although small amounts of surface deformations such as cracking of the oxide may occur that are below the measurement sensitivity). However, since the microdiffraction cannot observe the vertical height of the grain boundary, we do not know if the growing grain extends throughout the thickness of the layer or if there is another grain beneath it. ross-sectional measurements in other systems show that in many cases where whiskers/hillocks form, there are oblique boundaries between grains underneath the surface [1, 21]. It has been proposed that the oblique boundary allows the addition of atoms at these sites to induce stresses that lead to grain boundary sliding and growth of the whisker/hillock [21]. 16

17 To investigate the microstructure below the surface, it is possible to perform depth profiling along a single line in the layer by scanning a wire over the surface [28]. This is very time-consuming so it could not be done often during these experiments. This technique was used to characterize the structure underneath the hillock feature after the other measurements were completed (at a time of 1 h after deposition) The line scan indicates that the grain boundaries underneath it are not vertical but inclined at an angle of approximately 25 o from the normal. The grain of the hillock extends through the depth of the film to the Sn-u interface, similar to what has been observed in other hillock features [1, 21]. In many cases, whiskers/hillocks have another Sn grain underneath them but that is not the case here. The orientation of the grain that develops into the hillock is indicated by the arrows on the pole figure (figure 3). The initial orientation is within the band of texture found for the other grains. In other micro-diffraction measurements (not shown here), whiskers and hillocks were also found to grow from common orientations on the surface, i.e., the whiskers/hillocks did not form from grains with unusual orientations. During the period up to 14 h (before the surface morphology changes), the grain retains its same orientation. At later times, as the grain grows into a hillock (at 51 and 114 h), the orientation changes. The deviation in the (1) pole from the initial position corresponds to rotation of the average grain orientation (i.e., the (1) pole further tilted from the surface normal by ~7 after 114 h). Because the micro-diffraction averages over the thickness of the grain, it cannot be determined if this corresponds to rotation of the entire grain or if there are a distribution of orientations due to rotation of the growth direction from the surface normal. Although we cannot specify how the orientation changes exactly, rotation of the growing hillock has been seen in other work [31]. The observed roatation highlights the importance of characterizing the grain orientation before whisker/hillock formation since the orientation after growth is not necessarily the same. The observation of grain growth before hillock extrusion might suggest that the features nucleate via dynamic recrystallization, as proposed by Vianco et al. [35, 36]. To further examine this issue, we refer to the SED maps of the layer for additional information. As shown in figure 7c, the SED of the grain 17

18 that turned into the hillock was initially higher than the surrounding grains and then decreased after it expanded. This is different from what would be expected if hillocks nucleated by a recrystallization mechanism. In recrystallization, the growing grain would be expected to have lower SED than its neighbors so that it would grow at the expense of neighboring grains. This suggests that recrystallization may not be the source of the observed nucleation behavior. We also observe that other grains with high SED do not necessarily develop into whiskers/hillocks. At some sites, grains with high SED were seen to be consumed by surrounding grains, such as those pointed out by the circles in figure 2c. Sarobol et al. [4] have suggested that high strain energy density can promote defect formation, which is consistent with our observations. To determine what causes the growth of hillocks, we consider the biaxial stress and SED in the region surrounding them (figure 7b and c). The biaxial stress in the hillock grain is less than the average compressive stress in the layer. Similarly, the SED of the hillock grain is less than the surrounding area. This difference in stress and SED can drive diffusion from the neighboring regions into the hillock grain and cause its growth on the surface. Note that there are not any long-range gradients in the stress or SED around the growing hillock (similar situations were observed around other whisker and hillock sites that are not shown). hoi et al. [22] also found that the stress gradients around the root of a whisker were small and spanned only a few grains. This is somewhat different than the picture that is suggested by some models for whisker growth (e.g., by Tu [3] and Hutchinson et al. [37]). In these, it is proposed that the relaxation of stress at the base of the whisker leads to stress gradients that drive a flux of atoms to the whisker base. In Tu s model, the range of the gradient is determined by the spacing between the whiskers. However, such long range gradients are not seen in the measurements. Other calculations using finite element analysis [38] based on the model of Buchovecky [39] predict that the stress gradients may have a much shorter range. These calculations include effects of stress relaxation by other processes than whisker formation (e.g., powerlaw creep) which lead to a more rapid drop-off in the stress away from the whisker. 18

19 Finally, we note that our measurements suggest that whisker/hillock formation is not the only mechanism of stress relaxation in the Sn films. Large compressive stress at certain grains was effectively relieved without the formation of any surface features. In addition, there was considerable relaxation over the entire area, i.e., the average stress changed from ~ - MPa (at 51 h) to ~ -5 MPa (at 114 h) while the growth of the hillock was insufficient to account for this amount of relaxation and the additional strain from IM growth in this interval. These observations imply that other relaxation mechanisms besides whisker/hillock formation are active in the Sn film. 3. Interpretation of fluorescence measurements Our observations indicate that variations in the Sn and u fluorescence from a Sn-u bilayer can be measured in real-time. We have interpreted the fluorescence changes in terms of the thickness of the layers at each point and used this to infer changes in the surface and interface morphology. Although previous synchrotron studies of solder joints [4] used microfluorescence to measure the evolution of the Sn and Pb concentrations, these did not try to determine the morphology of the interfaces. It would be desirable to compare the fluorescence measurement of the surface/interface with other techniques (e.g., SEM or AFM), but it was not possible to measure the exact region monitored in figures 2a and 2b by other methods within a short time. Therefore, the quantitative accuracy of this method remains to be verified. However, other measurements can be invoked to support the interpretation of the fluorescence measurements as indicating morphology evolution. The lateral size of the grain underneath the hillock feature (in figure 2c) is comparable to the size estimated from the fluorescence. Similar correspondence between the hillock diameter and the underlying grain structure has been seen by others [1] in crosssectional measurements. The line scans that probe the depth dependence of the grain structure (described above) also indicate that the feature protrudes out of the surface to a height of 1-2 m, consistent with the estimate from the fluorescence measurement. The presence of the shadowed region in the Sn and u fluorescence measurements also supports the interpretation of the increased Sn fluorescence as protruding 19

20 from the surface. SEM scans of the sample surface after the synchrotron run (not at the same position) show that there are many features with similar morphology to that observed in figure 2a. For the IM measurements, the increasing spatial variations of the u intensity within the layer is indicative of the inhomogeneous growth of IM particles into the Sn layer. The alignment of the fluorescence with the microstructure measurements further indicates that the growth occurs at the grain boundaries between Sn grains. These results are consistent with AFM [16] and SEM [14, 15, 31, 41] measurements of IM formation at the Sn-u interface. onclusions Although it is believed that Sn whiskers/hillocks are the result of compressive stress, the origin of the stress, how it is distributed within the Sn layer and how it relaxes (locally or uniformly) due to the whisker/hillock formation are issues that are not well understood. We have performed in-situ synchrotron micro-diffraction with complementary fluorescence measurements to determine simultaneously the surface and interface morphology, local microstructure and deviatoric strain in Sn-u systems. Repeated measurements over the same 36 µm 36 µm area shortly after the Sn layer was plated enabled us to observe how the microstructure, IM particles and stress fields evolve before and after surface features form. One large hillock feature was observed to form within the measured region that allowed us to monitor the evolution around this feature for comparison with regions where there were no surface morphology changes. The Sn film was polycrystalline and exhibited a fiber texture, with the [1] axis tilted by an average of 61 ± 8 from the normal. Aside from the formation of a hillock, the average grain size and orientation did not change significantly over time. The fluorescence measurements show that there was not excessive IM accumulation at the site where the hillock formed. Similarly, comparison of the IM and stress maps show that the biaxial stress is distributed relatively uniform across the surface although IM grows preferentially along the Sn grain boundaries. 2

21 The hillock grew from an existing grain with an orientation that was similar to the average texture. Other whiskers/hillocks were also seen to initiate from orientations that were common on the surface; there was no evidence showing that whiskers/hillocks grow from certain preferred orientations. Importantly, local high compressive stress or high strain energy density does not necessarily lead to whisker/hillock nucleation. The hillock grain had lower biaxial stress and strain energy density than the surrounding areas which may provide the driving force for their growth. We did not observe long-range gradients within the film which suggests that the gradients controlling growth may occur over short distances. Other relaxation mechanisms besides whisker/hillock growth are believed to be active in the Sn film in order to explain the large amount of stress relaxation observed as well as the additional strain from the IM growth. Acknowledgements FP and E gratefully acknowledge the support of the NSF-DMR under contract DMR68 and DMR The work of AFB, EB and NJ was supported by the Brown MRSE program (DMR79964). This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under ontract No. DE-A2-6H157. The work of WL, JZT, GEI, and RX was supported by the US DOE Office of Science Figure captions Figure 1 Schematic of synchrotron micro-diffraction set up. The incident X-ray beam is focused by a Kirkpatrick-Baez mirror pair to a fine probe on the sample surface. The diffraction pattern is measured by 21

22 an X-ray sensitive D detector. A fluorescent detector is placed near the sample surface in order to collect the characteristic fluorescence radiation from Sn and u in the different layers. Figure 2 Distribution of (a) Sn fluorescence intensity, (b) u fluorescence intensity, (c) grain orientation and (d) biaxial deviatoric strain measured at 4 h, 14 h, 51 h and 114 h after the Sn electro-deposition. Each indexed grain in (c) is colored according to the orientation of the (1) pole in the sample coordinate system. The corresponding color scheme can be found in figure 3. The black points indicate the spots that were not indexed in the scan. Dashed circles are used to point out where grain growth occurred later. The blue lines in (b) and black lines in (d) correspond to Sn grain boundaries determined from the orientation measurement at the same time (as shown in (c)). Figure 3 (1) pole figures corresponding to the orientation maps in figure 2c. The color of each point is specified according to its position in the pole figure color scheme shown below the images. The arrows point to poles from which hillock growth was observed. Figure 4 The normal direction inverse pole figure constructed from the orientation data obtained at 4 h after Sn electro-deposition. The contour coloring is chosen so that the darker color indicates a larger fraction of grains having that orientation, as shown by the color scale in the figure. Figure 5 Distribution of (a) biaxial strain, (b) biaxial stress and (c) strain energy density calculated from the measured deviatoric strain components. In each map, the dark points indicate the grains that were not indexed in the scan. The black lines correspond to Sn grain boundaries determined from the orientation measurements (figure 2c). 22

23 Figure 6 Evolution of average biaxial stress with respect to time. Stress corresponding to the data in figure 2 is plotted as circular symbols (referred to as sample 1). Results from measurements on another similarly-prepared Sn-u sample (referred to as sample 2) are presented from three different 5 µm 5 µm areas (represented by other symbols). Figure 7 Evolution of (a) local microstructure, (b) biaxial stress and (c) strain energy density before and during the hillock growth. The hillock grain is indicated by the arrow in (a). In each map, the dark points indicate the grains that were not indexed in the scan, whereas the black lines correspond to Sn grain boundaries. Appendix A alculation of stress from deviatoric strain measurements The procedure for stress calculation is described as follows. The deviatoric strain components quantified from the indexed Laue pattern are specified in the sample coordinate, which can be expressed in terms of strain tensor as: ε ij ε ij 1 ε kkδ 3 ij, (A1) where ε ij and ε ij represent the full strain tensor and deviatoric strain tensor in the sample coordinate, respectively. Firstly, the deviatoric strain tensor is transformed to the crystal coordinate (defined by the crystal orientations of [1], [1] and [1] in the β-sn unit) by 23

24 ε ij = A ip A jq ε pq = ε ij 1 ε 3 kkδ ij, (A2) where ε ij and ε ij are the full strain tensor and deviatoric strain tensor in the crystal coordinate, respectively. A represents the transformation matrix from the sample coordinate to the crystal coordinate, and it can be constructed from the orientation measurements. The full stress tensor in the crystal coordinate (σ) can be calculated using the following equation: σ ij = ijkl ε kl = ijkl (ε kl + eδ kl ) = ijkl ε kl + ijkk e, (A3) where is the elastic modulus tensor for β-sn, and e is the volumetric strain: e = 1 3 ε kk. (A4) Eq. A3 can be written in Voigt notation as: ' 11e ' 22 e ' 33e. (A5) 2 ' 23 2 ' 66 2 ' The values of ij are taken from [42] (the unit for ij is GPa). We can express eq. A5 as: ' ' ' ' ' 48 ' e 167.5e 16.e. (A6) On the right side of eq. A6, the first part corresponds to the results that can calculated from the deviatoric strain ε ij, whereas the second part is unknown as the value of e is not determined yet. Similarly, it is convenient to keep the unknown part separated from the part that can be calculated when we rewrite eq. A6 in terms of 3 3 matrix: 24

25 * * * e 167.5e 16.e, (A7) in which * 72.3 ' 59.4 ' 35.8 (A8) ' 33 * 59.4 ' 72.3 ' 35.8 (A9) ' 33 * 35.8 ' 35.8 ' 88.4 (A1) ' ' (A11) 44 ' (A) ' 23 (A) Since the Sn film is polycrystalline, i.e., Sn unit cell (crystal coordinate) orients differently at different positions on the surface, it is therefore necessary to transform the stress tensor to the sample coordinate so that the stress at different grains can be directly compared within the same coordinate. We use B to denote the rotation matrix from the crystal coordinate to the sample coordinate; it is related to the transformation matrix A by B=A T. The stress tensor in the sample coordinate (σ ) can then be written as ˆ ˆ ˆ 11 ˆ ˆ ˆ ˆ ˆ B 23 ˆ B 33 T (A14) ombining eq. A14 with eq. A7 gives us ˆ ˆ ˆ 11 ˆ ˆ ˆ ˆ * ˆ B 23 ˆ * * 33 B T 167.5e B 167.5e B 16.e T (A15) 25

26 Since the stress component normal to the sample surface is assumed to be zero everywhere: ˆ33, we can therefore determine the volumetric strain e from eq. A15. Inputting the value of e into eq. A15, the full stress tensor in the sample coordinate can then be calculated. References [1] W. J. Boettinger,. E. Johnson, L. A. Bendersky, K. W. Moon, M. E. Williams and G. R. Stafford, Acta Mater. 53, 19(25) pp [2] NASA. Multiple examples of whisker-induced failures are documented on the NASA website. Available: [3] K. N. Tu, Phys. Rev. B 49, 3(1994) pp [4] P. Sarobol, W.-H. hen, A. E. Pedigo, P. Su, J. E. Blendell and. A. Handwerker, J. Mater. Res. 28, 5(2) pp [5] P. T. Vianco, M. K. Neilsen, J. A. Rejent and R. P. Grant, J. Electron. Mater. 44, 1(215) pp [6] R. M. Fisher, L. S. Darken and K. G. arroll, Acta Metall. 2, 3(1954) pp , [7]. H. Pitt and R. G. Henning, J. Appl. Phys. 35, 2(1964) pp [8] X. hen, Z. Yun, F. honglun and J. A. Abys, IEEE Trans. Electron. Packag. Manuf. 28, 1(25) pp [9] K. N. Tu, Acta Metall. 21, 4(1973) pp [1] B. Z. Lee and D. N. Lee, Acta Mater. 46, 1(1998) pp [11] E. hason, N. Jadhav, W. L. han, L. Reinbold and K. S. Kumar, Appl. Phys. Lett. 92, 17(28) p [] W. Zhang and F. Schwager, J. Electrochem. Soc. 153, 5(26) pp [] M. Sobiech, M. Wohlschlögel, U. Welzel, E. J. Mittemeijer, W. Hügel, A. Seekamp, W. Liu and G. E. Ice, Appl. Phys. Lett. 94, 22(29) p

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