Ag-(In-Bi) Solid–Liquid Interdiffusion Bonding

Solid–liquid interdiffusion is a metallurgical bonding technique, suitable for assembly of temperature sensitive materials. We identify Ag-(In-Bi) as meeting the low-temperature bonding requirements, theoretically as low as 73°C. This work focuses on understanding the bonding process and the interactions between the metal elements. Ag-(In-Bi) was bonded using an eutectic In-Bi foil at both 150°C and 180°C. The resulting bondlines were layered as Ag/Ag9In4/AgIn2/In-Bi compounds/AgIn2/Ag9In4/Ag. At some sections the phase growth of AgIn2 or Ag9In4 bridged the bond. Because of this bridging of γ-Ag9In4, temperature stability of ~480–570°C, is readily possible. The majority of the remaining Bi was located within large pockets near the middle of the bondline, and the minority as precipitates in protruding arms. Mechanisms for these Bi precipitates and intermetallic arm growth are discussed, and the evidence indicates that dissolution and surface planarity play important roles in their formation.


Introduction
Solid-liquid interdiffusion (SLID) is a metallurgical bonding technique where a layer of a low-melting-temperature (T m ) metal is sandwiched between two layers of a high-T m metal. The formed bonds typically comprise intermetallic compounds (IMCs) which remelt at temperatures higher than the bonding temperature. 1 This makes SLID bonding attractive for high-temperature applications where elevatedtemperature stability is required. SLID bonds are mechanically strong, electrically conductive, hermetic and compatible with die-level and wafer-level manufacturing. Some SLID systems have the ability to bond at temperatures lower than common soldering temperatures. For example, the Au-(In-Bi) SLID system can be bonded with temperatures as low as 115°C. Such a low bonding temperature has been proven successful for the bonding of piezoelectric materials in ultrasound transducers, 2 where bonding at temperatures lower than the Curie temperature of the piezoelectric materials eliminates the need for magnetic re-poling, reducing the fabrication costs. The bonds provide better acoustic coupling than the traditionally used epoxy solutions. 3 The material cost of gold, however, is a deterrent for the final application of the Au-(In-Bi) system.
The Cu-(In-Bi) metal system, being cheaper than Au-(In-Bi), unfortunately showed a significant degree of voiding at the interfaces with the In-Bi foil 4 when bonded under a non-protective atmosphere. Wetting issues between the Cu and the In-Bi have been noted, 5 and may be responsible for this degree of voiding.
Given that Ag is lower in cost than Au, and may have better wetting then Cu, the Ag-(In-Bi) metal system may be a viable SLID bonding solution to piezoelectric materials. Ag has a room temperature asymptotic oxide layer thickness which approaches a maximum value of 20 Å. 6 However, some care is needed to prevent surface reaction with hydrogen sulfides producing Ag 2 S, which if present in small amounts contaminates the bonding surface by acting as impingement points, leading to voiding, 7 or if in large amounts, hinders interdiffusion due to its elevated T m of 842°C.
SLID work on the Ag-In-Bi system is sparse. Roman tested two In-Bi alloys in 1991. 5 The first, with an In-Bi interlayer ~381 µm thick, of 47 at.% In, held for 13 h at 120°C in argon, remelted at 320°C. The second, with ⁓152 µm thickness and 78.5 at.% In, held for 24 h at 110°C in argon, remelted at 580°C. The remelting of the first corresponds with the melting of a bondline containing Bi (T m = 274.4°C), while that of the second corresponds with the melting of a bondline of ζ (T m 675-205°C) (Supplementary Fig. S1 showing the Ag-In phase diagram). 8 For the first test, the high Bi content and thickness of that interlayer likely leaves a continuous layer of Bi between the bonding partners after bonding, whereas the lower Bi content and smaller thickness test did not, indicating that at sufficiently small amounts, Bi does not form a continuous layer.
There is limited thermodynamic work on the Ag-In-Bi metal system. 9,10 No stable ternary phases have been discovered. The lack of a ternary phase and the immiscibility of Ag and Bi (illustrated by the Ag-Bi phase diagram 10 ) simplify the thermodynamics of the system. These attributes are shared in previous work in the Au-In-Bi system 2 and in the Cu-In-Bi system. 4 Ag is expected to react with In only, depleting the In-Bi layer as the bonding proceeds. From the Ag-In Phase diagram, we expect the first Ag-In IMCs formed to be In-rich AgIn 2 , continuing with Ag 9 In 4 , then the ζ phase, finalizing with a α-Ag matrix with up to 18 at.% In at room temperature, given a sufficient supply of Ag. With this high solubility limit of In in Ag, the thermodynamically stable configuration is expected to be Bi sandwiched between α-Ag (with all In dissolved in this phase). For realistic bond profiles, the different Ag-In IMCs are expected to be the resulting phases appearing in the bondline. A bond where all In is contained in AgIn 2 will have a theoretical thermal stability of 166°C, whereas further transformation to Ag 9 In 4 (T m ~480-570°C) will give a thermal stability only limited by the remaining Bi.
Though the underlying motivation is low-temperature bonding, the focus of this paper is to experimentally explore the bondline characteristics and phase evolution resulting from SLID bonding of Ag-(In-Bi). Therefore, higher than necessary bonding temperatures will be implemented to expedite phase growth, providing more developed bondlines. This paper does not aim to present a complete process optimization, although it will make suggestions to this larger task.

Bonding
Ag foil (99.9 at.%Ag) with a thickness of 0.28 mm was diced into squares with dimensions of 0.4 cm × 0.4 cm (top) and 0.7 cm × 0.7 cm (bottom). The larger cuts were pressed with 200 bar, while the smaller with 100 bar in order to flatten the surface and edges, improving the mating. The Ag cuts were then polished with 1 μm diamond solution, resulting in a roughness average (Ra) of 250 nm (± 40 nm). Prior to bonding, the Ag cuts were cleaned utilizing hydrochloric acid 37 at.% followed by acetone and isopropanol and dried with N 2 . A eutectic In-Bi 78.5 at.% In foil 120 μm thick was cleaned by scraping the surface with a sterilized carbon steel blade and placed between the cuts. A silicon spacer 525 μm thick was placed on the top of the stack to distribute the pressure applied by the spring plunger of the bonding fixture. The bonding pressure was 0.7 MPa. Bonding was done in ambient atmosphere in a Budatec VS160 UG soldering machine. The temperature was monitored by a thermocouple inserted into the bonding fixture. The heating rate was 49°C/min, while the cooling rate was set to 2°C/ min. Two bonding temperatures were studied: 150°C and 180°C. The temperature of 150°C was selected to obtain a more rapid solid-state transformation of AgIn 2 to γ-Ag 9 In 4 while avoiding the formation of In-Bi IMCs, which all melt at 110°C (Supplementary Fig. S2 In-Bi phase diagram). 11 The temperature of 180°C was selected in order to study the effects of forming γ-Ag 9 In 4 directly from the eutectic melt, as seen in Fig. S1. The holding time (time at bonding temperature) for 180°C was 2 h, while no holding time was used for 150°C. With the heating and cooling rates used in these bonding experiments, the 150°C bonds experience 40 min above the eutectic melting point of 73°C.

Characterization
Samples were cross-sectioned and the bondline surface was prepared by molding, grinding and polishing. Cross-sections are imaged by scanning electron microscopy (SEM) and energy-dispersive x-ray spectroscopy (EDX). ImageJ software was used to measure the cross-sectional area of features representing different IMCs in the micrographs, utilizing tracing and contrast tools where applicable. 12 This area was divided over the length of the analyzed section, to attain the average thickness of the IMC.

Expected Ratios of Phases
A theoretical assessment of both the expected voiding (caused by changes in molar volumes) and the leftover Bi was conducted so that characterized data could be compared. A situation where all In reacts to form Ag 9 In 4 is considered, which is relevant for the experiments presented in this paper. The volumetric voids will be located anywhere liquid pockets become mechanically constrained by the IMC growth. Planar growth, good mating, and larger bonding pressures leading to significant grain boundary movement are expected to reduce this voiding. Smearing effects during sample preparation 1 3 (polishing) are expected to reduce the amount of voiding observed. The following material properties and equations were used: The volume change can be found as follows: where v i are the stoichiometric coefficients of the reaction, and V m i is the molar volume of components in the reaction. The volumetric change for the formation of AgIn 2 from the In-Bi eutectic is −2.3%: The volumetric change for the formation of Ag 9 In 4 from AgIn 2 is −6.2%: The volumetric change for the formation of Ag 9 In 4 from the In-Bi eutectic is −6.7%: The volumetric change for the formation of Ag 9 In 4 is independent of the pathway (for the above); the reaction route involving (2) + (3) is equivalent to (4). Thus, voids caused by volumetric differences should occupy at most 6.7% of the cross-sectional area of the observed bonded region regardless of the reaction route chosen. The volume fraction of the products Bi and Ag 9 In 4 should be 13.0% and 80.3%, respectively, according to the volume each product contributes to the finalized reaction. This does assume that no further Ag-In reactions occur after Ag 9 In 4 is formed and that no In is left in In-Bi compounds or in AgIn 2 . If volumetric voids are not present, the volume fraction of Bi and Ag 9 In 4 for the system should be 13.9% and 86.1%, respectively. For comparison, the volumetric change associated with the Ag-In SLID system for the formation of Ag 9 In 4(s) is −8.6%: The volumetric contraction for the Ag-In system is −8.6%, compared to −6.7% for the Ag-In-Bi system. The (2) larger contraction is attributed to the lack of Bi. As can be seen in Table I, Bi (l) expands upon solidification by 2.4% (or 3.3% according to Guenther 16 ), which offsets the volumetric contraction. Figure 1 shows micrographs from the same bonded sample, extracted from different positions along the bondline. The overall bondline thicknesses in Fig. 1 (sum of Ag-In IMCs, voids and In-Bi compounds plotted in Fig. 2) vary greatly between the micrographs. There are three different causes which contribute to the overall bondline thickness: the global tilt; the deflection of the top Ag substrate; residual stress in the Ag substrates.

Results
The tilt angle (non-parallelism) between the substrates is indicated by the different bond gaps at each side of the top substrate, as depicted in Fig. 1g. An end-to-end difference in bond gap of 6 µm corresponds to 0.09º in tilt angle (arctan[(12-6) µm/4000 µm]).
Applied pressure from the plunger contributes to the deflection (bending) of the top Ag substrate (depicted in Fig. 1g). COMSOL Multiphysics ®17 was used to estimate the deflection of the Ag caused by the bonding load (0.7 MPa) used in the experiment; a uniform load distribution was used. The top edge of the substrate was constrained mechanically. The Ag was modeled as linear elastic and isotropic.
The maximum deflection obtained by the simulation was 2.5 µm (as shown in Fig. 4). The deflection may be larger if the load is not equally distributed. If the 2.5 µm calculated from the simulation is subtracted from the 6 µm gap created by the tilt, 3.5 µm is left. This is near but not exactly the 1.6 µm minimum gap which was measured in the sample presented in Fig. 1. This means that there is still 1.9 µm unaccounted for.
Residual stresses in the Ag substrates may also cause deflection and bond gap variation. The Ag substrates were pressed with 200 bar (20 MPa) and 100 bar (10 MPa) for the bottom and top substrates, respectively, prior to bonding. This likely introduced some residual stresses which may have deflected the substrate after pressing was finished.
The variation in the distance between the Ag surfaces provides the opportunity to analyze bondline sections  10.043 (l) 15 7.900 (l) a --exposed to different amounts of In-Bi melt with similar temperature profiles. The series of cross-sections show a layering of Ag/Ag 9 In 4 /AgIn 2 /In-Bi compounds/AgIn 2 / Ag 9 In 4 /Ag. The solid In-Bi compounds seen throughout The In-Bi compounds in Fig. 1 have been identified by EDX as BiIn 2 and Bi 3 In 5 . EDX identification of phases with lateral extent in the micrometer range is non-trivial, since the electron beam interaction volume in the sample results in an EDX resolution in the micrometer range (1 µm interaction volume for  Table II. These correspond well to the stoichiometric compositions, as shown in the table. In Fig. 1a, these two different In-Bi IMCs can be distinguished by contrast. The formation of Ag 9 In 4 occurs through solid-state diffusion between the Ag and AgIn 2 layers. The growth shape of both AgIn 2 and Ag 9 In 4 is mostly planar with irregularities that are scallop-crystalline-like. There exists considerable diffusion in the horizontal (z and x) directions once IMC bridging occurs, as can be seen in Fig. 1c-e. Figure 1c shows two points where the AgIn 2 bridges across the In-Bi compounds, implying that the bond at this spatial point has isothermally solidified. Further bridging increases in Fig. 1d and e. The zoomed section of Fig. 1e shows that bridges can be either Ag 9 In 4 or AgIn 2 . It also shows significant diffusion of In into the Ag at a discreet location along the bond, creating a Ag-In IMC arm which penetrates into the Ag substrate. Finally, where the arms occur, small bright pockets are frequently present. EDX measurements indicate these pockets are Bi richer compared to the In-Bi IMCs in the middle of the bondline and are either pure Bi or some combination of Bi and BiIn. The EDX interaction volume in our experiments (15 kV acceleration voltage) is close to 1 µm, making a unique phase identification of these small spots difficult.
We do not observe the ζ phase (which has 20-25% In content in equilibrium at room temperature) in the bondline. Nor do we observe significant amounts of In dissolved in the Ag phase. It is challenging to quantify small amounts of In in a Ag matrix by EDX, since the atomic number of the two elements differ by one, and the stronger In EDX peaks are superimposed on weaker Ag peaks. With the signal-to-noise ratio we have in our measurement, an In level of 6% would still be detectable. Since Ag 9 In 4 was then the most Ag-rich Ag-In IMC we observed, we used the thickness of Ag 9 In 4 as an indicator for the bonding progression and sorted the sections accordingly.
Voids of significant size can be observed in Fig. 1b, d and e. All voids tend to be located at either the original bonding interfaces or the middle of the bond. Grinding/ polishing was seen to dislodge the (In) phase (if present), due to its low hardness (⁓15 on Brinell Hardness 18 ) leaving behind voids. 19 This is most readily seen in Fig. 1b, where pullout has occurred to the right of the analyzed   section. This effect to varying degrees, contributes to the observed voiding in the other micrographs. Figure 3a shows a typical cross-section of the bond formed at 180°C for 2 h. The entire bondline showed similar growth and shape with some localized irregularities as depicted in Fig. 3b. The variability was lower compared to the bonding at 150°C (Fig. 1), and a similar layer structure was formed. The In-Bi phases measured by EDX are the same as for Fig. 1 (BiIn 2 and Bi 3 In 5 ), despite the higher bonding temperature and longer bonding time. AgIn 2 is visible in this sample even though the bond spent significant time above the T m of AgIn 2 . AgIn 2 is formed during cooling of the bond, where sufficient time is spent in the temperature window where AgIn 2 is stable. See the Discussion, section "Bonding at 180°C," for a detailed discussion. It is seen that no significant Bi precipitation occurred at the top and bottom substrates. Voiding is seen close to the interfaces where the In-Bi preform had initiated contact with the Ag substrates. Figure 5 shows a growth model of bonding at 150°C. The model assumes homogeneous diffusion of elements in the vertical direction, no horizontal diffusion of elements, and no restrictions on the relative movement of the bonding partners. The volumetric contraction will be compensated through shrinkage of the bondline thickness rather than generating voids. The model does not go beyond the formation of Ag 9 In 4 , treating the Ag/Ag 9 In 4 /Bi/Ag 9 In 4 /Ag as the final structure. The further conversion to ζ phase and diffusion of In into the α phase (Ag) is not covered in this paper, as it is not observed in our experiments. A future study including high-temperature storage might reveal such transitions.

Discussion
Once the In-Bi eutectic melts, it begins to dissolve the Ag reaching a Ag composition of ~ 1.7 at.%, according to the ternary liquids projection seen in the supplementary begins to precipitate. After some time, Ag 9 In 4 begins to precipitate (d). In stage (e), the In-Bi-Ag (l) is sufficiently depleted such that Bi precipitation occurs and the bond begins to isothermally solidify.
Finally, (f) shows the isothermally solidified bond. Fig. S3 taken at 150°C isotherm. Eventually, the Ag-In-Bi liquid will become saturated with Ag, and then AgIn 2 will form followed by Ag 9 In 4 . As the In reacts with Ag during bonding, the Bi content in the liquid layer will increase, and when the Bi content goes above ~ 60 at.%, Bi will precipitate since Bi has almost no solubility with the Ag-In phases nor any stable IMCs. 10,20 Precipitation is shown in Fig. 5e as solid particles within the Ag-In-Bi liquid. This violates the model assumptions on homogeneous layer set above, but is a more realistic description of this stage. Isothermal solidification of the entire bond will occur when all In is consumed to form Ag 9 In 4 . This model will have a theoretical remelt temperature of 271°C (T m of Bi). For bonding at 180°C, the Ag saturation is higher ~ 2.9% and only Ag 9 In 4 will grow from the melt.
While the model in Fig. 5 describes the phase formation and growth during the SLID bonding, the observations in Figs. 1 and 3 show clear deviations: The interfaces between phases have a complex topography, resulting from a nonhomogeneous diffusion of elements. For Fig. 1c-e, the growing Ag-In IMC layers have bridged at certain locations, while other locations still have In-Bi compounds. Figure 1 and Fig. 3 both show SLID bonds reaching the bonding stage of Fig. 5d, with the liquid containing ~63-67 at.% In. Solidification of this remaining liquid happened through cooling of the bond, not by isothermal solidification. Figure 1c has two locations of AgIn 2 bridges, indicating that the bond will be solid up to the T m of AgIn 2 166°C. For Fig. 1d-e, Ag 9 In 4 bridges the bond, implying a T m of ~480-570°C. In these cases, upon reheating, the In-Bi inclusions pass their liquidus temperatures, and the In-Bi would liquefy but be contained by the Ag-In IMCs. For longer bonding times, all In is expected to be depleted from the In-Bi liquid, and the bond would be similar to Fig. 5f with only Bi pockets rather than a Bi layer. The pockets of pure Bi will have a T m of ⁓271°C. For the bonds in Figs. 1a,b and 3a where a continuous layer of BiIn 2 and Bi 3 In 5 exists, the thermal stability will be ~90°C.

Bondline Thicknesses
The measurements for the Ag-In IMCs, In-Bi compounds and bondline thicknesses, are presented in Fig. 2. For the entire bondline of the bond in Fig. 1 the bondline thickness varies significantly. For the samples measured in Fig. 2, a minimum and maximum bondline thickness of 4.1 μm and 14.2 μm were measured (these measurements include the IMC diffusion into the substrate). Where the squeeze-out is most intense, there is less supply of total In, limiting the possible thickness of AgIn 2 . A thinner layer of AgIn 2 means a shorter diffusion path for In resulting in faster Ag 9 In 4 growth. Additionally, the pressure applied to the top of the Ag foil cuts, is transferred unevenly through load bearing regions along the bondline. It is well known in sintering that higher pressures increase diffusion. 21 This concentrated pressure delivers increased grain boundary movements leading to more rapid diffusion. It also changes the thermodynamics of the system influencing the energy needed to form phases. From Fig. 2 the result of all this is a correlation: decreasing overall bondline thickness, decreasing AgIn 2 thickness, and increasing thickness of Ag 9 In 4 . Figure 6 shows how the sections in Fig. 1 approach the theoretically predicted values calculated for Bi and Ag 9 In 4 in the bondline (ignoring voids) of 13.9% and 86.1%, respectively. This is relative for when a bondline approaches Ag/ Fig. 5 Thickness of Ag 9 In 4 , AgIn 2, their summation, In-Bi compounds, and the overall bondline in the (y) direction (including voids) are extracted from Fig. 1 and Fig. 3a. All values are averaged for the phases on the top and bottom of the bond, but then halved to represent the "half-bondline" thickness. It is assumed that the layer uniformity is representative across longer cross-sections. The average absolute deviations for the measurements were calculated to be < ± 0.2 µm. Ag 9 In 4 /Bi. The significance of these values is that they act as an indicator to a quasi-equilibrium state, where isothermal solidification has appeared when all In has been depleted from the liquid. Figure 6d-e has good agreement with the theoretical prediction. Ignoring voids, the measured In-Bi compound occupation for d and e was 16.2% and 11.4%, respectively. The measured Ag 9 In 4 occupation was 69.3% and 82.3% for d and e, respectively, the rest being made up by AgIn 2 . When considering voids, the void occupation of the bonded region was 5.2% and 2.7% for d and e, respectively, both below the theoretical value of 6.7%. At other sections, the voiding measured is significantly above the theoretical value. This is not surprising since there are many sources of voiding. Contaminations and oxidation, high vacancy drift (Kirkendall effect), lack of intimate contact and sequent wetting, and finally, moisture or entrapped gases such as air. A significant amount of the voids observed arise from the sample preparation. The soft nature of the In-Bi alloy was seen to significantly cause dislodgement during cross-sectional preparation. This again can be seen in Fig. 1b, to the right of the analyzed section (indicated by the black box). The voids seen in Fig. 1c-e, which are located at the In-Bi to Ag-In IMC interfaces, on the other hand, exhibit more circular shapes and a varied frequency which is dissimilar to the dislodgement voids, indicating causes other than dislodgement. Cross-section sample preparation using ion milling is challenging since ion milling causes sufficient heating which melts the In-Bi compounds; hence, the cross-section will no longer represent the as-bonded status. We do not have access to ion milling machines equipped with cooling systems.

Phase Fractions
Since all the In comes from the In-Bi preform, by using the measured thicknesses in Fig. 2 Table I, the liquid In-Bi eutectic thickness which was present during the bonding can be calculated. Even though Fig. 1a was representative of the 180°C bondline, bridging was seen at discreet locations as shown in Fig. 1b. Thus, even though Fig. 1a shows no bridging, it must be assumed that given longer sections with the same controlled thickness, bridging may appear at discreet locations. Given the large amount of bridging in Fig. 1d and e, it can safely be said that bridging will occur at a controlled thickness of less than 2 µm given a cross-section bond length (x) of 80 µm, when bonding at the conditions employed. Thus, with the bonding parameters used in our experiments, a controlled eutectic liquid layer thickness of ~ 2 µm on each of the bonding partners (giving a total of ~ 4 µm) will satisfy the requirements for high-temperature stability. This thickness can be achieved by deposition techniques such as evaporation, sputtering or electrodeposition, all being suitable for producing patterned metallization for device manufacturing.

Bi Precipitation and IMC Arms
The majority of the Bi is contained within the In-Bi compounds occupying the middle of the bondline. These large pockets are broken up by the bridging of the Ag-In IMCs. The minority of the Bi, collects into pockets which are surrounded by Ag-In IMC arms as indicated in Fig. 1c. These arms are also present in Fig. 1b-e and clearly show that the diffusion of In into the substrate is more significant where the arms are present. The arms and Bi precipitates could be explained by uneven dissolving of the Ag. Etched pockets filled with In-Bi liquid will form, and gradually the liquid will deplete of In. Bi will then precipitate out, due to the limited Bi flux into the Ag.
A systematic study by Zou et al. on the Cu-Sn-Bi system 22 showed that the imbalance of Bi flux across the Cu-IMC Fig. 6 Plotting the In-Bi compounds and Ag-In IMCs as a percentage of the "half-bondline" thickness in Fig. 1, ignoring the void contribution. Theoretical values are taken from Section III, where it is assumed we reach the state depicted in Fig. 4f. interface would cause Bi accumulation leading to precipitation. This explanation couples well to the Ag-In-Bi system, since Bi has low solubility in Ag and thus the flux of Bi into Ag is likely to be small.
As shown in Fig. 3 Ag-In IMC arms were not readily seen and almost no Bi precipitates were seen. If the meltback of the Ag and following growth of Ag 9 In 4 is planar and uniform, it may hinder the entrapment of the liquid pockets since precipitating Bi is ejected towards the middle of the bond instead of becoming entrapped. Bonding at 180°C would have a larger melt-back of Ag since the solubility of Ag in the In-Bi eutectic would be ~ 2.9% according to the ternary diagram. 18 This may improve the planarity of the Ag surface during the melt-back.
To better understand the mechanism, one could bond below the T m of the In-Bi eutectic (72.7°C) preventing dissolution. If the Bi precipitates and the arms are still seen, then the precipitation is not limited by dissolution mechanics and can be attributed additionally to solid-state diffusion. We have conducted such solid-state bonding at 65°C. Results show no protruding arms nor Bi precipitates, giving evidence that dissolution is a necessary condition. These experiments will be elaborated on in a later publication.
Bi precipitation has been observed in Cu-In-Bi and Cu-Sn-Bi systems. 4,[22][23][24] In comparison to Ag-In-Bi, Cu-In-Bi showed a much greater dispersion of the precipitated Bi into the IMC adjacent the (Cu) substrate, as can be seen by comparing Fig. 1c-e with Fig. 7: The cross-sectional area of the Bi precipitates for the entire bondline partially shown in Fig. 1 was measured as 20.4 µm 2 of Bi (within 129 pockets) on the top and nearly half, 11.5 µm 2 Bi (within 90 pockets), on the bottom of the bond. This is in contradiction with the claims by Hu et al., that the density of Bi would influence the degree to which Bi would segregate on the top and bottom of the bond due to gravity. 23 We hypothesize that the asymmetry in Bi distribution, observed in both ours and Hu's results, may be due to statistical fluctuations in different cross-sections rather than indicative of a significant trend.

Bonding at 180°C
It was expected (from observing the Ag-In phase diagram) that bonding at 180°C for 2 h would prevent the formation of AgIn 2 , since Ag 9 In 4 should form directly from the locally saturated melt as seen in reaction (4). However, as seen in Fig. 3, AgIn 2 was still present. The formation of AgIn 2 comes from the lack of quenching in order to rapidly cool the bond and prevent thermodynamic equilibriums, opting instead for air cooling at a slow cooling rate of (2°C/ min). The Ag-In phase diagram shows that AgIn 2 may form between 166°C (T m of AgIn 2 ) and ~ 90°C (T m of BiIn 2 and Bi 3 In 5 ). At the cooling rate mentioned above, this gives a 38-min time window where the rapid formation (through solid-liquid reactions) of AgIn 2 may occur.
Thus, the slow cooling resulted in thermodynamically favorable conditions for the formation of AgIn 2 . Depending on the amount of solid and liquid phase present, two different peritectic reactions may occur. For phase fractions greater than 53.6% liquid (at composition ~95 at.%In), Eq. 6 is the peritectic reaction, while for systems less than 53.6% liquid, Eq. 7 is the reaction: Both involve the consumption of Ag 9 In 4 . If there is available Ag, reaction (2) is also a possible route. In our experiments, the observation of In-Bi IMCs indicates a surplus in liquid In and suggests Eq. 6 is the reaction route. This consumption of Ag 9 In 4 to form AgIn 2 during cooling explains why the thickness of Ag 9 In 4 for Fig. 1e (1.7 µm) is similar to Fig. 3a (1.7 µm), despite the higher bonding temperatures and times. This mechanism has already been observed and elaborated on for the Ag-In SLID system. 25 From the above discussion we can conclude that, when bonding at 180°C, the rate of cooling is a relevant parameter that will affect which IMCs are present and their growth. The enhanced Ag 9 In 4 growth expected from bonding at 180°C was small compared to that obtained by reducing the original liquid In-Bi eutectic thickness. Where a variation in original liquid In-Bi eutectic of 5.2 µm produced a variation in Ag 9 In 4 thickness of 4.8 µm. Bonding at 180°C increased (6) Ag 9 In 4(s) + L 95at%In ↔ AgIn 2(s) + L 95at%In (7) Ag 9 In 4(s) + L 95at%In ↔ AgIn 2(s) + Ag 9 In 4(s) Fig. 7 Plotting the original liquid eutectic "half-bondline" in Fig. 1 and Fig. 3. Calculations assume all In is contained within Ag 9 In 4 , AgIn 2 , and In-Bi compounds.
The location of the voids seen in Fig. 3a, near the original bonding interfaces suggests this to be Kirkendall or oxidation/impurity type voiding. Kirkendall voids (i.e. voids resulting from unequal atomic fluxes, being compensated by vacancy creation, then migration, and eventual saturation into voids. A certain degree of grain boundary impingement at the void accumulation spots, through trace impurities or inherent, may be necessary for their formation 7 ). Oxidation/impurity voids, tend to remain at the original interface, whereas Kirkendall voids tend to drift along with the phase growth. As can be seen in Fig. 3a, the voids seem more independent of the phase growth than not, suggesting them to be more oxidative/impurity in origin. Inert markers can be deposited upon the bonding interfaces before bonding, to indicate the original bonding interface.

Conclusions
Bonding of Ag-(In-Bi) using an In-Bi eutectic foil was conducted at both 150°C and 180°C. The degree of squeeze-out was seen to have the largest impact on the thickness of AgIn 2 and γ-Ag 9 In 4 present, more so than bonding at the higher temperature of 180°C. This indicates that the gap distance between the bonding substrates is a critical process parameter to obtain more even growth. Because of Ag-In IMC bridging across the middle of the bond, the resultant bonds may in theory have a temperature stability of ⁓480-570°C, even though the bond does not fully reach the state of In depletion of the low-temperature In-Bi IMCs. The majority of the Bi is located within large pockets near the middle of the bondline in the form of In-Bi IMCs, and the minority as precipitates within the protruding Ag-In IMC arms. Initial In-Bi thickness at each bonding partner of less than 2 µm should give bridging at the bonding conditions employed, and with longer bonding times we expect all the AgIn 2 to be converted to γ-Ag 9 In 4 , and all the In-Bi IMCs in the middle of the bondline to be converted to Bi. Evidence indicates that dissolution and the resulting planarity of the surface is the main cause. The density of Bi was not seen to impact its distribution, and so gravity is not seen as a significant process parameter.