Ag metallizations in solder joints

Acta mater. 49 (2001) 2609–2624 www.elsevier.com/locate/actamat

DISSOLUTION AND INTERFACIAL REACTIONS OF THIN-FILM Ti/Ni/Ag METALLIZATIONS IN SOLDER JOINTS G. GHOSH† Department of Materials Science and Engineering, Robert R. McCormick School of Engineering and Applied Science, Northwestern University, 2225 N. Campus Dr, Evanston, IL 60208-3108, USA ( Received 21 March 2001; received in revised form 3 May 2001; accepted 8 May 2001 )

Abstract—The dissolution and interfacial reactions involving thin-film Ti/Ni/Ag metallizations on two semiconductor devices, diode and metal-oxide-semiconductor field-effect transistor (MOSFET), a Sn–3.0Ag– 0.7Cu solder, and a Au-layer on the substrates are studied. To simulate the dissolution kinetics of the Aglayer in liquid solder during the reflow process, the computational thermodynamics (Thermo-Calc) and kinetics (DICTRA: DIffusion Controlled TRAnsformations) tools are employed in conjunction with the assessed thermochemical and mobility data. The simulated results are found to be consistent with the observed asreflowed microstructures and the measured Ag contents in the solder. In the as-reflowed joints two different intermetallic compounds (IMC) are found near the diode/solder interface. Both are in the form of particles of different morphologies, not a continuous layer, and are referred to as IMC-I and IMC-II. The former corresponds to Ni3Sn4 with Cu atoms residing in the Ni sublattice. It is uncertain whether IMC-II is Cu6Sn5 phase with Ni atoms residing in the Cu sublattice or a Cu–Ni–Sn ternary phase. Near the as-reflowed MOSFET/solder interface, both particles and a skeleton-like layer of Ni3Sn4 are observed. The primary microstructural dynamics during solid state aging are the coarsening of IMC particles and the reactions involving the unconsumed (after reflow) Ni- and the Ti-layer with Sn and Au. While the reaction with the Ni-layer yields only Ni3Sn4 intermetallic, the reaction involving the Ti-layer suggests the formation of Ti–Sn and Au– Sn–Ti intermetallics. The latter is due to the diffusion of Au from the substrate side to the die side. It is postulated that the kinetics of Au–Sn–Ti layer is primarily governed by the diffusion of Au through the Ni3Sn4 layer by a grain boundary mechanism.  2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Kinetics; Thin-films; Interdiffusion; Interface; Intermetallic compounds

1. INTRODUCTION

Bare Si die can be attached to leadframes for use in packaged components or attached to circuit boards for use in chip-on-board (COB) applications. The advantages of the COB approach is the reduction in circuit area required compared to using a packaged die. Furthermore, for power applications the COB approach allows for the elimination of at least two interfaces that can act as paths of increased thermal resistance. The die can be attached using epoxy, “hard” solders such as Au–3Si and Au–20Sn, or “soft” solders such as low melting Pb and Sn based solders. For power applications that require the dissipation of heat from the die it is necessary to use one of the solders, of which the “soft” solders are the most economical. For COB applications where the die is soldered directly to an organic circuit board the only options are the

† Fax: +1 847 491 7820. E-mail address: [email protected] Ghosh)

(G.

Sn or Pb based solders, specifically those with a melting point well below 300°C, since exposure to higher temperatures will cause degradation of the organics in the circuit board. Typically, the solders used to attach bare power die to substrates have melting points in the range 250– 310°C, such as Sn–5Sb and Pb–10Sn. However, environmental issues require using alloys other than those containing Pb, and it appears that eventually Sb will also become environmentally unfavorable. Therefore, it has become necessary to start evaluating solder–backmetal reactions using alternative Sn-based solders. Also, for processes where Si die are soldered to organic substrates it is desirable to use a solder with a melting point below 250°C such as the eutectic Sn–Ag, Sn–Cu, or Sn–Ag–Cu solders. There have been some studies of the reactions between thin film metallizations containing Ni as the solderable layer and different solder materials including Sn–40Pb [1–3], pure Sn [2, 4], Sn–3.5Ag [3], and Sn–5Sb [3]. Also, many studies [2, 5–9] have been conducted regarding the reactions between Sn based solders and bulk or electroplated Ni.

1359-6454/01/$20.00  2001 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 6 4 5 4 ( 0 1 ) 0 0 1 8 7 - 2

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GHOSH: REACTIONS OF Ti/Ni/Ag METALLIZATIONS

Using “soft” solder requires a solderable metallization to be present on the back of the Si die. However, soft solders are known to react with various metallization schemes very rapidly in the liquid state and much slowly in the solid state. A consequence of the interfacial reaction is the change in solder chemistry and microstructure of the solder joints which may have significant bearing on its mechanical properties. An example of die backside metallizations is evaporated Ti/Ni/Ag. Here, the Ag-layer preserves the solderability of the underlying Ni-layer by limiting the oxidation at reflow temperature. In the absence of the Ag-layer, the solderability of Ni is rather poor. The Ni-layer serves as the solderable surface to which the joint is made. Ideally it should be thick enough to prevent complete consumption to form Ni–Sn intermetallic during reflow and the lifetime of a device at the service temperature. The Ti-layer acts as an adhesion layer between the Ni-layer and the Si die. A schematic cross section of a diode solder joint, employing the Ti/Ni/Ag metallization scheme, is shown in Fig. 1. It is important to note that the metallization schemes (on the die side and the substrate side) along with the Sn–Cu–Ag solder constitute a seven-component system. If the kinetics of interdiffusion is appreciable during processing and in service, the microstructural evolution in such solder joints can be quite complex. Furthermore, due to multilayer

Fig. 1. Schematic diagram showing the cross section of a diode/solder joint.

arrangement the microstructural evolution is expected to be strongly time dependent due to the possibility of sequential phase formation. This work reports the results of a systematic study of dissolution and interfacial reactions between Sn–3.0Ag–0.7Cu (mass%) solder and the thin-film Ti/Ni/Ag metallizations on the die side. In our study, the die can be either a diode or a metal-oxide-semiconductor fieldeffect transistor (MOSFET). This work was performed with the following objectives: (i) to model the dissolution kinetics of the Ag-layer in liquid solder, (ii) to characterize the interfacial reactions between the Ni-layer and the solder during the reflow process, and (iii) to investigate the microstructural dynamics and the interdiffusion processes involving the Ni- and Ti-layer, and Sn and Au during solid state aging of solder joints.

2. EXPERIMENTAL PROCEDURE

The diodes and the MOSFETs had backside metallizations that were deposited by vacuum evaporation. The diodes had Ti/Ni/Ag as the backmetal, with the Ti being in contact with the Si die, and the MOSFETs had Al/Ti/Ni/Ag as the backmetal, with the Al being in contact with the Si die. The diode backmetal layer thicknesses were 0.15, 0.25, and 2 µm for the Ti-, Ni-, and Ag-layer, respectively. The MOSFET backmetal layer thicknesses were about 0.15, 1, and 0.6 µm for the Ti-, Ni-, and Ag-layer, respectively. The solder was in the form of 75 µm thick preforms and had a nominal composition of Sn–3.0Ag–0.7Cu. The length and width of the preforms were matched to each of the diode and MOSFET. The diodes and MOSFETs were soldered to a substrate that had an electroless Ni(P) and immersion Au finish with thicknesses of 4 and 0.1 µm, respectively. The nominal P-content in the electroless Ni was about 8 mass%. All the diode and MOSFET samples were soldered to the substrates in a N2/H2 atmosphere using a reflow process. The solder has a liquidus of about 220°C, and it stays liquid for about 8 min during the reflow process. The peak temperature of the reflow process is about 265°C. The as-reflowed joints were subsequently aged at 125°C for 200 h and 200°C for 20 and 200 h. The reflowed and aged samples were cut using a diamond saw and polished. Microstructural characterization was carried out using a HITACHI S-4500 scanning electron microscope (SEM) equipped with a cold field-emission gun, a PGT energy dispersive X-ray (EDX) detector, and the IMIX software/database (PGT) for composition analysis. The SEM was operated at 20 kV. The quantitative EDX technique is applied to characterize the interfacial phases when their sizes are sufficiently large; otherwise, X-ray mapping technique is used to establish a qualitative understanding of the interdiffusion processes.

GHOSH: REACTIONS OF Ti/Ni/Ag METALLIZATIONS 3. RESULTS

3.1. As-deposited Ti/Ni/Ag metallizations Figure 2(a) shows the SEM micrograph of asdeposited metal layers on the backside of a diode. The backmetal layer thicknesses were determined to be 0.15, 0.25 and 2.1 µm for the Ti-, Ni-, and Aglayer, respectively. Figure 2(b) shows the SEM micrograph of the as-deposited metal layers on the backside of a MOSFET. As seen, the Ti-layer on top is very uniform and it is about 0.14 µm, the Ni-layer is also uniform and it is about 1.1 µm, and the outer Ag-layer is about 0.6 µm and somewhat non-uniform in thickness. 3.2. Diode metallization/solder interfacial reaction Figure 3(a) shows the joint between the diode backside metallization and the solder. The thickness of the solder is about 55 µm. After reflow the bulk solder microstructure is fairly uniform; however, occasionally a few large Ag3Sn dendrites emanating from both sides of the solder joints is also observed. Figure 3(b) shows the microstructure near the die/solder interface. There are three important features to be noted in Fig. 3(b). First, the Ag backmetal layer has dissolved completely in the solder during reflow process. The second feature of interest is that there are at least three morphologies of the intermetallic compound (IMC): (i) small whiskers, (ii) equiaxed scallops, and (iii) faceted scallops. The third feature of interest in Fig. 3(b) is that the Ni-layer has been completely consumed during the reflow process. As a result, in some areas the liquid solder comes in contact with the Ti-layer. These areas are shown (marked X), as an example, in Fig. 3(c). There are also differences in the compositions of the intermetallics near the diode/solder interface. The results of quantitative EDX analysis, using the spot mode of the beam, are listed in Table 1. Figure 3(b) shows two chemically distinct types of intermetallics, IMC-I and IMC-II. The IMC-I particles are several

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microns in length and about 2 µm wide, highly faceted, and most of them are detached from the reaction interface. The EDX results strongly suggest that the IMC-I particles are Ni3Sn4-type phase. Even though the overall composition of this phase is not a direct measure of the distribution of Cu atoms between Ni- and Sn-sublattices, we strongly believe that the Cu atoms reside primarily on the Ni sublattice. This may be explained in terms of experimental thermodynamic data that showed that Cu–Sn bonds are stronger than the Cu–Ni bonds. This causes a preferential partitioning of Cu atoms to the Ni-sublattice allowing for a minimum energy configuration by maximizing the number of Cu–Sn bonds [7, 8]. The IMC-II particles are about 1–2 µm in dimension, equiaxed, and closer to the reaction interface. As seen in Table 1, a substantial amount of Ni dissolves in IMC-II. Even though the stoichiometry could very well be described by Cu6Sn5, with Ni atoms residing on the Cu sublattice, it is uncertain whether IMC-II is Cu6Sn5 or a Cu–Ni–Sn ternary phase. Since the Culayer on the substrate side is completely buried under the Ni(P) layer [see Fig. 3(a)], virtually all the Cu found in the IMCs originates from the 0.7 mass% Cu in solder. The Ag-content in both types of IMCs was negligible. The dimension of the small whiskers, shown in Fig. 3(b) and (c), precludes the possibility of accurate composition analysis using the SEM/EDX technique. In Fig. 3(c), it is interesting to note the spalling of very small whiskers which are typically 0.2–0.5 µm in diameter. The reactive diffusion between Ni and liquid solder involves several processes including the grain boundary grooving of the intermetallic by the liquid solder. This along with the residual stress in thin films may have caused spalling of Ni3Sn4 at such small length scales. The important microstructural dynamics during solid state aging are (i) coarsening of dispersed (after reflow) IMCs, (ii) interfacial reaction involving the Ti-layer, and (iii) a segregation of Au from the substrate side. An interesting observation is that the

Fig. 2. SEM micrographs of as-deposited metallization scheme on the backside of (a) a diode, and (b) a MOSFET.

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GHOSH: REACTIONS OF Ti/Ni/Ag METALLIZATIONS

Fig. 3. SEM micrographs of as-reflowed diode/solder joint: (a) showing the microstructure of the solder, (b) two types of IMCs near the interface: (i) small whiskers and faceted scallops of (Ni, Cu)3Sn4 (IMC-I), and (ii) somewhat equiaxed Cu–Ni–Sn phase (IMC-II), and (c) solder in contact with the Ti-layer in the region marked X. Table 1. Composition of Ni3Sn4-type (IMC-I) and Cu–Ni–Sn (IMC-II) intermetallics in the diode solder joints as a function of heat treatment Treatment

As-relowed 125°C, 200 h 200°C, 20 h 200°C, 200 h

Composition of IMC-I (at.%)

Composition of IMC-II (at.%)

Cu

Ni

Sn

Cu

Ni

Sn

7.08±0.56 7.25±1.06 7.56±0.64 5.83±0.95

33.28±1.45 33.56±1.16 34.09±1.45 35.07±1.61

59.64±0.79 59.19±1.05 58.34±0.73 59.11±0.71

26.81±1.85 29.31±1.27 29.86±0.75 29.65±1.12

22.54±1.51 24.44±1.13 23.93±0.87 23.35±1.47

50.64±1.61 46.24±0.77 46.21±0.63 47.00±0.81

faceted scallops of IMC-I undergo coarsening along with the small whiskers. This suggests that the small whiskers are also Ni3Sn4 but they are too small for composition analysis by the SEM/EDX technique. Two types of interfacial reaction products, involving the Ti-layer, were observed during solid state aging. Figure 4(a) and (b) show the interfacial microstructures of diode solder joints after aging at 125°C for 200 h and at 200°C for 20 h, respectively. In these microstructures, even though the Ti-layer is completely shielded by the IMC-I grains, it is evident that the Ti-layer has reacted. However, the extent of reaction is rather non-uniform along the interface. Some

areas showed no reaction with the Ti-layer, while other areas such as area A in Fig. 4(a) and (b) show complete consumption of the Ti-layer in intermetallic formation. It is also obvious that the reaction starts at the Ti/solder interface and the reaction front moves towards the Ti/Si interface. X-ray mapping in the SEM showed the depletion of Ti and the presence of Sn in what used to be the Ti-layer. Therefore, the region marked A in Fig. 4(a) and (b) may correspond to a Ti–Sn intermetallic. The similarity of the microstructures in Fig. 4(a) and (b), with respect to the Tilayer, indicates that the fundamental interdiffusion mechanism leading to these microstructures is the

GHOSH: REACTIONS OF Ti/Ni/Ag METALLIZATIONS

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Fig. 4. Interfacial microstructures (SEM) after solid state aging of a diode/solder joint: (a) at 125°C for 200 h showing partial reaction of the Ti-layer, (b) at 200°C for 20 h showing showing partial reaction of the Tilayer, (c) at 200°C for 20 h (another region) showing the formation of a continuous layer of Au–Sn–Ti in contact with Sn and also the consumption of most of the Ti-layer, and (d) at 200°C for 200 h showing complete reaction of the Ti-layer and further growth of the Au–Sn–Ti layer relative to that in (c).

same for the two different aging conditions, with the interdiffusion kinetics being slower at the lower temperature. The other Ti-layer reaction occurred in areas where the IMC-I grains had spalled away from the die backmetal, exposing the Ti to the solder, as shown in Fig. 3(c). In this case, the reaction between the solder and the Ti-layer, during the aging at 200°C for 20 h, yielded a somewhat uniform and a thicker layer of intermetallic, as shown in Fig. 4(c). The EDX spectrum collected in the spot mode of the electron beam and X-ray mapping of this layer indicated that it is a Au–Sn–Ti compound. We also found that the amount of Cu and Ni varies from negligible to none. The exact composition of this layer could not be ascertained by the SEM/EDX technique due to relatively small thickness of this intermetallic layer, but the Aucontent was estimated to be about 12 mass%. It is worth pointing out that the origin of Au are: (i) the dissolved Au in liquid solder during reflow, and (ii) the migration of Au from the substrate side to the die side. However, we did not observed any Au-bearing intermetallic in the bulk solder. Figure 4(d) shows

further growth of the Au–Sn–Ti layer during prolonged aging at 200°C for 200 h causing complete consumption of the Ti-layer. It is interesting to note that the average thickness of the Au–Sn–Ti layer is about 0.75 µm, which is about five times thicker than the as-deposited Ti-layer. The compositions of the two other intermetallics, IMC-I and IMC-II, are listed in Table 1 as a function of aging treatment. It is seen that the composition of IMC-I is independent of heat treatment. However, after the aging treatment the IMC-II phase is further enriched with about 3 at.% Cu and depleted by about 3 at.% Sn. As mentioned before, it is uncertain whether the IMC-II particles are Cu6Sn5 or a Cu–Ni– Sn ternary phase. 3.3. MOSFET metallization/solder interfacial reaction Figure 5(a) shows the joint between the MOSFET backside metallization and the solder. The thickness of the solder is about 75 µm. After reflow the bulk solder microstructure is fairly uniform. Like the diode metallization/solder case, the Ag-layer dissolved

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GHOSH: REACTIONS OF Ti/Ni/Ag METALLIZATIONS

Fig. 5. SEM micrographs of as-reflowed MOSFET/solder joint: (a) showing the whole solder joint, (b) showing a large and isolated scallop of Ni3Sn4 (IMC-I), and (c) skeleton morphology of Ni3Sn4 (IMC-I) and also the non-uniform thickness of unconsumed Ni-layer.

completely in the liquid solder. As shown in Fig. 5(b), the presence of irregular shaped scallops near the MOSFET/solder interface may be noted. The composition of these relatively large and irregular scallops, labeled IMC-I is shown in Table 2. The results of quantitative EDX analysis show that these scallops are Ni3Sn4. The overall composition and the nature of Cu partitioning on the Ni sublattice are very similar to those observed in the case of diode/solder joints. Besides the isolated scallops, a three-dimensional skeleton-like microstructure, involving the intermetallic and solder, was also observed. An example of

this interfacial microstructure is shown in Fig. 5(c). The inner part of the skeleton microstructure consists of a continuous layer of IMC-I. The composition of this continuous layer was also identified as being Ni3Sn4 with the Cu atoms residing primarily on the Ni sublattice. Figure 5(c) also shows that the Ni-layer was not completely consumed during the reflow process. The average thickness of the unconsumed Nilayer is about 0.5 µm, but is rather non-uniform despite the fact that the as-deposited Ni-layer in the FET backside metallization was uniform in thickness. The important microstructural dynamics during

Table 2. Composition of isolated Ni3Sn4-type (IMC-I) scallops and the Ni3Sn4-type layer (IMC-I) in the MOSFET solder joints as a function of heat treatment Treatment

As-relowed 125°C, 200 h 200°C, 20 h 200°C, 200 h

Composition (in at.%) of isolated Ni3Sn4-type scallops (IMC-I) Cu

Ni

6.88±0.96 5.69±1.10 6.51±0.83 6.16±0.77

34.07±0.72 36.46±1.02 34.56±1.27 35.44±0.79

Sn 59.06±0.54 57.85±0.42 58.93±0.79 58.40±0.40

Composition (in at.%) of Ni3Sn4-type layer (IMC-I)

Cu

Ni

Sn

4.78±1.18 5.34±2.10 4.37±1.08 4.85±1.18

37.25±3.45 37.21±2.09 35.98±0.89 36.17±0.75

57.97±1.37 57.45±0.86 59.65±0.56 58.97±0.28

GHOSH: REACTIONS OF Ti/Ni/Ag METALLIZATIONS

solid state aging at 200°C are: (i) like the diode solder joints, Ni3Sn4 scallops coarsened from the asreflowed condition, (ii) the reactions between Ni and Sn resulted in significant growth of the Ni3Sn4 layer, (iii) like the as-reflowed MOSFET solder joint, the thickness of the Ni3Sn4 layer was non-uniform and at some places the original Ni-layer has been completely consumed, and (iv) at the areas where the Ni has been completely consumed due to the formation of Ni3Sn4, two continuous layers of intermetallics, Ni3Sn4 and Au–Sn–Ti, are observed during aging at 200°C. A non-uniformity of the unconsumed Ni-layer after reflow causes a non-uniformity of the interfacial microstructure during subsequent solid state aging. Figure 6(a) and (b) show the interfacial microstructures after aging at 200°C for 20 h. Figure 6(a) shows that in the presence of unconsumed Ni-layer, the Tilayer is protected from any interfacial reaction. As a result, the thickness of the Ti-layer is the same as that after vacuum evaporation. After the same aging treatment, we also find areas, an example is shown in Fig. 6(b), where the entire Ni-layer has been con-

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sumed to form Ni3Sn4 causing the formation of a Au– Sn–Ti layer. As a result, the thickness of the Ti-layer has decreased (on the average) by about 25%. These results show that the unconsumed Ni-layer acts as a good diffusion barrier for Au. Figure 6(c) shows coarsening of dispersed Ni3Sn4 scallops after aging at 200°C for 200 h. However, the dominant mechanism of coarsening is by physical coalescence, a process caused by anisotropic mass flow and the formation and growth of neck(s) between two or more particles. For example, scallops 1 and 2, and 3, 4 and 5 in Fig. 6(c) are undergoing coalescence. This phenomenon is commonly observed during liquid phase sintering process with very high volume fraction of the solid phase. Figure 6(d) shows the interfacial microstructure of the MOSFET/solder joint after aging at 200°C for 200 h. Here, the Ti-layer is completely consumed resulting in further growth of the Au–Sn–Ti intermetallic layer relative to that in Fig. 6(b). This microstructural observation is identical to that observed in the diode solder joint after the same aging treatment. Also, the

Fig. 6. Interfacial microstructures (SEM) after solid state aging of a MOSFET/solder joint: (a) at 200°C for 20 h showing the protection of the Ti-layer due to the presence of unconsumed Ni-layer, (b) another region in the same sample as in (a) showing the absence of a Ni-layer and partial consumption of the Ti-layer to form a continuous layer of Au–Sn–Ti, (c) at 200°C for 200 h showing coarsening of Ni3Sn4 scallops, and (d) at 200°C for 200 h showing complete reaction of the Ti-layer and further growth of the Au–Sn–Ti layer relative to that in (b).

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GHOSH: REACTIONS OF Ti/Ni/Ag METALLIZATIONS

average thickness of the Au–Sn–Ti intermetallic layer after aging at 200°C for 200 h is very similar in both the diode and MOSFET solder joints. Figure 7(a)–(d) show the X-ray maps collected from the area shown in Fig. 6(d). Two most important features regarding the distribution of Au and Ti are: (i) the Au content in the Ni3Sn4 (IMC-I) ahead of the Au–Sn–Ti layer is almost negligible, and (ii) redistribution of Ti over a larger distance compared to the original thickness of the Ti-layer. Also, the Cu and Ni contents in the Au–Sn–Ti layer are negligible. The same results were found in the samples aged at 200°C for 20 h. The compositions of Ni3Sn4 scallops and the Ni3Sn4 continuous layer were determined by EDX analysis in the SEM, and the results are listed in Table 2 as a function of aging treatment. They differ slightly with respect to the Cu and Ni content, with the scallops having about 2 at.% more Cu than the layer. However, for a given morphology the composition is independent of aging treatment.

Fig. 8. Calculated Ag–Sn phase diagram showing the equilibrium (solid lines) and metastable (dotted lines) phase boundaries involving the liquid, f.c.c. and (Sn) phases.

4. DISCUSSION

4.1. Modeling the dissolution kinetics of Ag in molten solder Bader [10] reported a rapid dissolution of Ag in liquid solder. In our experiments, it is important to note that the complete dissolution of the Ag-layer may be rationalized based on a thermodynamic argument. Figure 8 shows the calculated stable (solid) and metastable (dotted) phase boundaries of the Ag–Sn system. In the reflow process, the peak temperature

reaches up to 265°C. A simple calculation shows that the dissolution of the 2 µm thick Ag-layer in a 60 µm thick solder in the case of diode joint and the dissolution of 0.6 µm thick Ag-layer in the case of MOSFET joint increase the Ag content of solder from 3 mass% to about 5.8 and 3.7 mass%, respectively. These are below the solubility limit (with respect to Ag3Sn) of 6.9 mass% at 265°C. Therefore, the experimental observations are consistent with equilibrium phase diagram.

Fig. 7. X-ray maps of (a) Au, (b) Ni, (c) Sn, and (d) Ti from the area shown in Fig. 6(d).

GHOSH: REACTIONS OF Ti/Ni/Ag METALLIZATIONS

In the following, we describe the modeling of dissolution kinetics of the Ag-layer in liquid solder. To study the dissolution kinetics, we have applied a modern computational thermodynamics and kinetics approach using Thermo-Calc [11] and DICTRA [12] software systems. While the Thermo-Calc computes thermodynamic equilibrium between phases in multicomponent systems, DICTRA solves one-dimensional diffusion equations in a volume-fixed frame of reference involving multiple phases in multicomponent systems. To simulate a moving boundary problem using DICTRA, it is necessary to have both thermodynamic and mobility parameters of the relevant phases. 4.2. Theoretical background The temporal profile of the diffusing specie k is given by the Fick’s first law in the mass conservation form ∂Ck = ⫺div(Jk) ∂t

(1)

approach, the composition dependence of both Qk and ⌽k is expressed by a Redlich–Kister polynomial [13, 14]. 4.3. Thermodynamic data The thermodynamic parameters for the liquid and f.c.c. (face centered cube) solid solution of the Ag– Sn and Cu–Sn systems have been assessed as a part of our ongoing research [15]. The thermodynamic data for the Ag–Cu system are taken from Hayes et al [16]. The excess thermodynamic parameters for liquid and f.c.c. solution phases are listed in Appendix A. 4.4. Mobility data The composition dependence of Mk in equation (4) is defined by that of the ⌬G∗k . An important source of information in evaluating ⌬G∗k is the tracer diffusivity data. Based on the assumption that the correlation effects are negligible, the tracer diffusivity of k (Dk*) is related to its mobility by means of Einstein’s relation Dk∗ = RTMk.

where Ck is the concentration in moles per volume, and div denotes the divergence operator. The diffusional flux of the specie k (Jk) in a multicomponent system is given by the Fick–Onsager law

冘

n⫺1

Jk = ⫺

DnkjⵜCj

(2)

j=1

Dnij are the chemical or reduced diffusion coefficients. The summation is performed over (n⫺1) independent concentration as the dependent nth component may be taken as the solvent. For a substitutional solution phase Dnij is given by Dnkj =

冘

(dik⫺xk)xkMk

i

冉

∂mi ∂mi ⫺ ∂xj ∂xn

冊

冉 冊

1 ⫺⌬G∗k exp RT RT

(5)

In the liquid solder, the ⌬G∗k for Ag, Cu, and Sn are modeled as = xAg⌬G∗(liq⫺Ag) + xCu⌬G∗(liq⫺Cu) (6a) ⌬G∗(liq) Ag Ag Ag ∗(liq⫺Sn) Cu) + xAgxCu⌬G∗(liq⫺Ag, + xSn⌬GAg Ag ⌬G∗(liq) = xAg⌬G∗(liq⫺Ag) Cu Cu + xCu⌬G∗(liq⫺Cu) + xSn⌬G∗(liq⫺Sn) Cu Cu

(6b)

⌬G∗(liq) = xAg⌬G∗(liq⫺Ag) Sn Sn + xSn⌬G∗(liq⫺Sn) . + xCu⌬G∗(liq⫺Cu) Sn Sn

(6c)

(3)

where dik is the Kroneker delta, xk is the mole fraction and mi is the chemical potential of element i. The composition dependent atomic mobility Mk is given by Mk =

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(4)

where R is the universal gas constant, T is the temperature, and ⌬G∗k (⬅Qk⫺RT⌽k) is a composition dependent property of the specie k. It is worthwhile to point out that ⌬G∗k contains both the diffusion activation enthalpy (Qk) and the logarithm of the frequency factor (⬅⌽k). In the spirit of CALPHAD

The available experimental data for self and impurity diffusivities in liquid [17–29] are summarized in , ⌬G∗(liq⫺Cu) , and Table 3. The parameters ⌬G∗(liq⫺Ag) Ag Cu ∗(liq⫺Sn) represent the self-diffusivities of liquid Ag ⌬GSn [17, 18], Cu [19], and Sn, respectively. The para∗(liq⫺Sn) is evaluated from the available meter ⌬GSn experimental data in the temperature range of 525– and 925 K [20–22]. The parameters ⌬G∗(liq⫺Sn) Ag ∗(liq⫺Sn) represent tracer diffusivities of Ag and Cu ⌬GCu in liquid Sn, and they are adopted from the work of repMa and Swalin [24]. The parameter ⌬G∗(liq⫺Cu) Ag resenting the tracer diffusivity of Ag in liquid Cu is evaluated based on the experimental data, in the temperature range of 1416–1584 K, reported by Yamamura and Ejima [25] and Niwa et al [27]. The pararepresenting the tracer diffusivity of meter ⌬G∗(liq⫺Ag) Cu Cu liquid Ag is adopted from the work of Yamamura represents and Ejima [25]. The parameter ⌬G∗(liq⫺Ag) Sn

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GHOSH: REACTIONS OF Ti/Ni/Ag METALLIZATIONS

Table 3. The diffusivities [D = D0 exp(⫺Q/RT)] in liquid Ag, Cu and Sn, where R ( = 8.314 J mol⫺1 K⫺1) is the universal gas constant and T is the temperature in K

Self-diffusivity Ag Cu Sn

Impurity diffusivity Cu in Ag Sn in Ag Ag in Cu

Sn in Cu Ag in Sn Cu in Sn a

D0 (m2 s⫺1)

Q (J mol⫺1)

Reference

7.1×10⫺8 5.8×10⫺8 1.46×10⫺7 1.39×10⫺7 3.24×10⫺8 2.44×10⫺8

34116 32065 40646 16744 11586 10725

[17] [18]a [19]a [20] [21] [22, 23]

1.22×10⫺7 4.4×10⫺8 1.93×10⫺7 3.78×10⫺8 6.10×10⫺8 2.25×10⫺7 2.60×10⫺7 2.5×10⫺8 1.8×10⫺7

41860 25240 46926 31812 35581 52325 17580 12474 17580

[25]a [26]a [27] [28] [25] Assumed in this study [24]a [29] [24]a

Used in this study.

the tracer diffusivity of Sn in liquid Ag is taken from the work of Leak and Swalin [26]. The tracer diffusivity of Sn in liquid Cu is not known. Ejima and Yamamura [28] reported the tracer diffusivity of Sb in liquid Cu. Here, we have assumed that is same as that for Sb in liquid Cu. The ⌬G∗(liq⫺Cu) Sn Cu) , in equation 6(a), interaction parameter ⌬G∗(Liq⫺Ag, Ag is evaluated from the tracer diffusivity of Ag in a liquid Cu–14.6 at.% Ag alloy [27]. Based on the available experimental data, the ⌬G∗k for Ag, Cu, and Sn in the f.c.c. phase are modeled as = xAg⌬G∗(Ag:Va) + xCu⌬G∗(Cu:Va) (7a) ⌬G∗(f.c.c.) Ag Ag Ag ∗(Sn:Va) Sn:Va) + xSn⌬GAg + xAgxSn⌬G∗(Ag, Ag ⌬G∗(f.c.c.) = xAg⌬G∗(Ag:Va) Cu Cu + xSn⌬G∗(Sn:Va) + xCu⌬G∗(Cu:Va) Cu Cu

(7b)

⌬G∗(f.c.c.) = xAg⌬G∗(Ag:Va) + xCu⌬G∗(Cu:Va) (7c) Sn Sn Sn ∗(Sn:Va) ∗(Cu, Sn:Va) + xCuxSn⌬GSn . + xSn⌬GSn and ⌬G∗(Cu:Va) represent The parameters ⌬G∗(Ag:Va) Ag Cu self-diffusivities of Ag and Cu. Figures 9 and 10 show the available experimental data on the self-diffusivities of Ag [30–46] and Cu [47–60] as a function of temperature, respectively. Except few, generally there is a good agreement between various studies. Figure 11 show the tracer diffusivities of Ag in Cu [61, 62] and that of Cu in Ag [63–66] as a function and of temperature. The parameters ⌬G∗(Cu:Va) Ag are evaluated for these data. Similarly, Fig. ⌬G∗(Ag:Va) Cu 12 show the tracer diffusivities of Sn in Ag [67–69] and in Cu [70–74]. Using these data we have evaluand ⌬G∗(Cu:Va) . The ated the parameters ⌬G∗(Ag:Va) Sn Sn Sn:Va) and interaction parameters ⌬G∗(Ag, Ag Sn:Va) are evaluated from the tracer diffusivi⌬G∗(Cu, Sn

Fig. 9. The temperature dependence of self-diffusivity of Ag. Solid line is the model calculation.

ties of Ag in f.c.c. Ag–Sn solid solutions [75–77] and the interdiffusivity data in f.c.c. Cu–Sn solid solutions [78], respectively. represents the self-diffuThe parameter ⌬G∗(Sn:Va) Sn sivity of Sn in its hypothetical f.c.c. structure. This parameter is adopted from our previous modeling of mobilities of Pb, Sn, In and Au in f.c.c. solid solutions and ⌬G∗(Sn:Va) rep[79]. The parameters ⌬G∗(Sn:Va) Ag Cu resent tracer diffusivities of Ag and Cu in a hypothetical f.c.c. lattice of Sn. Since such experimental data can not be obtained, we have assumed that and ⌬G∗(Sn:Va) are the same as that of ⌬G∗(Sn:Va) Ag Cu ∗(Sn:Va) . The assessed ⌬G∗k parameters in liquid and ⌬GSn f.c.c. phases, based on equations (4)–(7), are listed in Appendix A. 4.5. Results of simulation Like many phase transformations, the dissolution process of a solid phase in a liquid phase represents

GHOSH: REACTIONS OF Ti/Ni/Ag METALLIZATIONS

Fig. 10. The temperature dependence of self-diffusivity of Cu. Solid line is the model calculation.

2619

Fig. 12. The temperature dependence of tracer diffusivity of Sn in Ag and Cu. Solid line is the model calculation.

imposing an additional constraint on the conditions of local thermodynamic equilibrium. At steady state, the moving velocity of the interface calculated using each solute has the same value. Then, for the Ag– Cu–Sn system the interface compositions (or the tieline) can be calculated by solving the following nonlinear differential equation when the concentration of Sn is taken as the dependent variable xa xa JxL JxL Ag⫺JAg Cu⫺JCu = . xa xa CxL CxL Ag⫺CAg Cu⫺CCu

Fig. 11. The temperature dependence of tracer diffusivity of Ag in Cu, and that of Cu in Ag. Solid line is the model calculation.

a moving boundary problem. For an n-component system, the moving velocity of the interface (Jx) is given by the flux balance equation Jx =

xa JxL i ⫺Ji xL Ci ⫺Cxa i

i = 1, 2, …, n⫺1

(8)

where, CixL, Cxa i are the concentrations of the element i in liquid (L) and f.c.c. (a) at the phase interface, xa are the corresponding fluxes, and so on. and JxL i , Ji In a ternary system, the interface compositions of two phases in equilibrium with each other is given by one of the tie-lines between two phases. At a constant temperature and pressure, the two-phase equilibrium in a ternary system has one degree of freedom. Therefore, the interface compositions can be calculated by

(9)

Figure 13(a) and (b) show the simulated results of dissolution kinetics, with a planar solid/liquid interface, during continuous heating in the reflow process. In the simulation, time is counted from the moment solder reaches the liquidus temperature of 220°C during the reflow process. In other words, it is assumed that there is no interfacial reaction between the Aglayer and the solder during heating in the solid state. Due to a nonlinear heating rate, the temperature is approximated as a polynomial function (of degree two) of time. The initial configuration of the diffusion couple consists of a 2 µm thick Ag-layer (dotted vertical line) in contact with a 60 µm thick solder of uniform composition. The initial Ag-content in the solder is shown by a dotted horizontal line. The positions of the solid/liquid interface after 10, 100 and 205 s are shown by the horizontal arrows in Fig. 13(a). As the Ag-layer dissolves, the Ag-content of the solder increases and this is shown by the vertical arrows after 10, 100 and 205 s. Figure 13(b) shows the Ag concentration profile in solder after 0.1, 0.5, 1 and 10 s. The fundamental assumptions in this simulation is the local equilibrium between f.c.c. and liquid phases at the interface, and the absence of convective mass flow. To establish this local equilibrium,

2620

GHOSH: REACTIONS OF Ti/Ni/Ag METALLIZATIONS

early stage. We did not consider the Ag3Sn phase in the simulation due to the following reasons: (i) experimentally we did not observe a Ag3Sn layer at the interface; however, this does not preclude the possibility of formation of a Ag3Sn layer initially and then dissolve at a later stage, and (ii) the diffusivities in Ag3Sn are not known. Figure 14 shows the thickness of the Ag-layer as a function of time. As seen, the complete dissolution takes place in about 207 s while it takes about 360 s to reach the peak temperature of the reflow process. In diode and MOSFET solder joints, the complete dissolution of the Ag-layer causes an increase in the Agcontent from 3 mass% in the original solder to 5.8 mass% and 3.7 mass% after reflow, respectively. The measured Ag-contents in diode and MOSFET solder joints are found to be in good agreement with these values. 4.6. Phase stability and the interdiffusion mechanism for the growth of Au–Sn–Ti layer To rationalize the formation of Au–Sn–Ti layer during solid state aging, it is imperative to compare the relative thermodynamic stabilities of the possible phases. The Au–Sn–Ti layer may correspond to (i) a Au–Sn phase with some Ti dissolve in it, or (ii) a Ti– Au phase with some Sn dissolve in it, or (iii) a Ti– Sn phase with some Au dissolve in it, or (iv) a ternary phase. The Au–Sn phase diagram contains AuSn4, AuSn2 and AuSn intermetallics, and their heat of formation (⌬Hf) is well documented [80]. The Ti–Au phase diagram contains Ti3Au, TiAu, TiAu2 and TiAu4 intermetallics [81], and the Ti–Sn phase diagram contains Ti3Sn, Ti2Sn, Ti5Sn3, and Ti6Sn5 [81]. In the absence of experimental ⌬Hf of Ti–Au and Ti–

Fig. 13. Simulated dissolution kinetics of the Ag-layer (in the diode/solder joint) showing (a) the position of the Ag/solder interface (horizontal arrows) and the Ag-content in the liquid solder (vertical arrows) at 10, 100, and 205 s, and (b) the profile of Ag, on an expanded y-scale, in the liquid solder at 0.1, 0.5, 1 and 10 s.

a significant fraction of the Ag-layer is dissolved very rapidly followed by a slower dissolution kinetics. It is important to note that the diffusivity of Ag in liquid solder is very fast. A very rapid initial dissolution causes the concentration profile to exist only for few seconds, and after 10 s or more the solder composition becomes uniform. This is somewhat consistent, with the exception of few large Ag3Sn dendrites, with the observed uniform solder microstructures after reflow. As shown in Fig. 8, the solubility of Ag with respect to the f.c.c. solution phase in liquid Sn is higher than that with respect to Ag3Sn. This might account for an accelerated dissolution kinetics at the

Fig. 14. Simulated dissolution kinetics of the Ag-layer (in the diode/solder joint) showing the thickness of the Ag-layer as a function of time. The upper X-axis shows the temperature corresponding to the time in the lower X-axis.

GHOSH: REACTIONS OF Ti/Ni/Ag METALLIZATIONS

Sn intermetallics [81], we have accepted the calculated ⌬Hf based on a semi-empirical formalism proposed by Miedema and co-workers [82]. Figure 15 compares the relative stabilities of Au– Sn, Ti–Au, and Ti–Sn intermetallics by considering their heats of formation only, i.e. the entropy effect is neglected. It is seen that Ti–Au intermetallics are the most stable followed by Ti–Sn and Au–Sn. Since Au diffuses from the substrate side where there is AuSn4 during the entire aging treatment, the Au–Sn– Ti phase formed on the die side must be more stable than AuSn4. Furthermore, in the absence of Au diffusion we have observed the formation of Ti–Sn phase [Fig. 4(a) and (b)]. Therefore, based on our experimental observations in conjunction with the relative stabilities relevant binary intermetallics, we draw two conclusions. First, during solid state aging Ti reacts with Sn to form Ti–Sn intermetallic whose growth kinetics is governed by the diffusivity of Sn. Second, with the participation of Au in the interdiffusion process, Ti–Sn intermetallic transforms to a more stable Ti–Au intermetallic. This is merely a consequence of the relative kinetics of interdiffusion process where the phase selection criterion is governed by the local chemistry at a given time. It is also possible that the Au–Sn–Ti can form directly from the reaction between Au, Sn, and Ti as suggested in the micrographs shown in Figs 4(c), (d), 6(b) and (d). Since the Au–Sn–Ti phase diagrams are not known, it is not possible to make an assessment if the Au– Sn–Ti layer corresponds to a ternary phase. Based on our observation of microstructural dynamics of solder joints during solid state aging, Fig. 16 is the proposed schematic of interdiffusion processes during the growth of Au–Sn–Ti layer in the presence of a Ni3Sn4 layer. As mentioned in Section

Fig. 15. The heat of formation (⌬Hf) of Au–Sn, Ti–Au, and Ti– Sn intermetallics. The ⌬Hf of Au–Sn intermetallics represent experimental data, while those of Ti–Au and Ti–Sn intermetallics are the predicted values.

2621

3, in the presence of a Ni-layer we did not observe the formation of Au–Sn–Ti intermetallic. The Au–Sn–Ti layer forms and grows after complete consumption of the Ni-layer to form Ni3Sn4, and at this stage the growth kinetics of the Au–Sn–Ti layer is governed by the diffusion fluxes of Au (JAu) and Sn (JSn). In the presence of a Ni3Sn4 layer ahead of the Au–Sn– Ti layer [as in Fig. 6(b)], both these fluxes in Ni3Sn4 bk gb may have bulk (Jbk Au, JSn) and grain boundary (JAu, ) components. Since there is a limited supply of Jgb Sn Au and it is coming primarily from the substrate side, our assertion is that the diffusion of Au is the rate controlling step for the growth of Au–Sn–Ti layer. However, the Au-content in the Ni3Sn4 layer, ahead of the Au–Sn–Ti layer, is found to be negligible. Therefore, we postulate that the diffusion of Au in Ni3Sn4 by a grain boundary mechanism governs fairly rapid growth kinetics of the Au–Sn–Ti layer. This mechanism may be further justified based upon two more premises. First, the scallop morphology of Ni3Sn4 that forms during the reflow process and very fine size of the Ni3Sn4 grains, 0.2–0.5 µm in diameter as shown in Fig. 6(d), that form during solid-state aging. Second, the maximum aging temperature of 473 K represents a low (⬍0.5) homologous temperature, T/Tm, with Tm being taken as the peritectic temperature (1066 K) as a lower limit of the melting point of Ni3Sn4. All these factors are known to promote the grain boundary diffusion mechanism. 5. CONCLUSIONS

A results of an investigation of the dissolution and interfacial reactions between thin-film Ti/Ni/Ag metallization and the Sn–3.0Ag–0.7Cu solder are reported with the following conclusions: 1. In both diode/solder and MOSFET/solder joints, the Ag-layer dissolves during the reflow process. 2. We have simulated the kinetics of dissolution of the Ag-layer using the DICTRA software systems. With the exception of few large Ag3Sn dendrites, the observed uniform solder microstructure, after reflow, is consistent with the uniform Ag profile in liquid solder predicted by DICTRA simulation. Of course, the measured Ag-contents in solder after reflow agree very well with the values expected from mass balance. 3. Near the as-reflowed diode/solder interface three different morphologies of interfacial reaction products were found: small whiskers, highly faceted elongated scallops of Ni3Sn4 (IMC-I), and equiaxed scallops of Cu–Ni–Sn (IMC-II) intermetallics. At this time it is uncertain if IMC-II particles are Cu6Sn5 phase or a Cu–Ni–Sn ternary phase. 4. Near the as-reflowed MOSFET/solder interface, irregular shaped Ni3Sn4 scallops, and a skeleton of Ni3Sn4 and solder were observed. 5. After reflow the entire Ni-layer on the diode was

2622

GHOSH: REACTIONS OF Ti/Ni/Ag METALLIZATIONS

Fig. 16. Schematic interdiffusion mechanism during the growth of the Au–Sn–Ti layer in the presence of a Ni3Sn4 layer.

6.

7.

8.

9.

consumed to form Ni3Sn4. However, for the MOSFET, the thickness of the unconsumed Ni-layer was about 0.5 µm after the reflow process. During the solid state aging of diode solder joints, the primary microstructural dynamics are: (i) coarsening of IMC-I and IMC-II particles, (ii) diffusion of Au from the substrate towards the Si side, and (iii) interdiffusion of Au, Sn and Ti leading to the formation of a Au–Sn–Ti intermetallic layer. During the solid state aging of MOSFET solder joints, the primary microstructural dynamics are: (i) coarsening of Ni3Sn4 scallops and short whiskers, (ii) diffusion of Au from the substrate towards the Si side, (iii) interdiffusion of Ni and Sn leading to growth of the Ni3Sn4 layer, and (iv) interdiffusion of Au and Sn through the narrow solder channels between the Ni3Sn4 scallops leading to the formation of a Au–Sn–Ti intermetallic layer. It is possible to form Ti intermetallics at temperatures that actual electronic products will be exposed to during normal operation. The Sn–Ti intermetallic formed during aging is less stable compared to the Au–Sn–Ti intermetallic. We postulate that a grain boundary diffusion mechanism of Au through the Ni3Sn4 layer governs the growth kinetics of the Au–Sn–Ti layer.

Acknowledgements—Financial support from the National Science Foundation (DMR-9813919) and Motorola is gratefully acknowledged.

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73. Sen, S. K., Butt, M. B. and Barua, A. K., Phys. Stat. Solidi (a), 1975, 32, 345. 74. Krautheim, G., Neidhardt, A., Reinhold, U. and Zehe, A., Phys. Lett. A, 1979, 72, 181. 75. Gas, P. and Bernardini, J., Scripta metall., 1978, 12, 367. 76. Hehenkamp, Th. and Faupel, F., Acta metall., 1983, 31, 691. 77. Koehler, U., Neuhaus, P. and Herzig, C., Z. Metallkde, 1985, 76, 170. 78. Oikawa, H. and Hosoi, A., Scripta metall., 1975, 9, 823. 79. Ghosh, G. and Liu, Z. -K., J. Elect. Mater., 1998, 12, 1362. 80. R. Hultgren, P. D. Desai, D. T. Hawkins, M. Gleiser and K. K. Kelly (ed.), Selected Values of the Thermodynamics Properties of Alloys. ASM, Metals Park, OH 1973. 81. J. L. Murray (ed.), Phase Diagrams of Binary Titanium Alloys. ASM, Metals Park, OH 1987. 82. de Boer, F. R., Boom, R., Mattens, W. C. M., Miedema, A. R. and Niessen, A. K., Cohesion in Metals, Transition Metals Alloys. North Holland, Amsterdam, 1988.

APPENDIX A THE THERMODYNAMIC AND KINETIC PARAMETERS USED TO SIMULATE THE DISSOLUTION KINETICS OF AG IN THE MOLTEN SOLDER.

A.1. Excess thermodynamic parameters of the liquid and f.c.c. phases are listed in the format of the Thermo-calc software systems. The excess molar Gibbs energy is expressed by the Redlich–Kister– Muggiannu formalism. All paremeters are in J/mol and T is in K. A.1.1. Liquid phase L(Liquid,Ag,Cu;0) = 17534.6⫺4.45479T L(Liquid,Ag,Cu;1) = 2251.3⫺2.6733T L(Liquid,Ag,Cu;2) = 492.7 L(Liquid,Ag,Sn;0) = ⫺4606.5⫺6.9074T L(Liquid,Ag,Sn;1) = ⫺14946.0 + 2.4906T L(Liquid,Ag,Sn;2) = ⫺5767.5⫺5.3881T L(Liquid,Ag,Sn;3) = ⫺7730.9 + 8.6062T L(Liquid,Cu,Sn;0) = ⫺7631.6⫺8.0029T L(Liquid,Cu,Sn;1) = ⫺24312.8 + 7.1059T L(Liquid,Cu,Sn;2) = ⫺10565.7⫺2.5826T A.1.2. F.c.c. Phase L(F.c.c.,Ag,Cu:Va;0) = 33819.1⫺8.1236T L(F.c.c.,Ag,Cu:Va;1) = ⫺5601.9 + 1.32997T L(F.c.c.,Ag,Sn:Va;0) = ⫺13835.2 + 26.14712T L(F.c.c.,Ag,Sn:Va;1) = ⫺10905.7⫺32.70238T L(F.c.c.,Cu,Sn:Va;0) = ⫺7673.6⫺3.6497T L(F.c.c.,Cu,Sn:Va;1) = ⫺17325.6 + 5.3921T

2624

GHOSH: REACTIONS OF Ti/Ni/Ag METALLIZATIONS

A.2. The mobilities of Ag, Cu and Sn in the liquid and f.c.c. phases. The ⌬G∗ contains an activation energy (in j/mol) and a frequency factor (in m2/S). R ( = 8.314 J mol⫺1 K⫺1) is the universal gas constantand T is the temperature in K.

= ⫺12111 + RT ln(3.73×10⫺6) ⌬G∗(liq⫺Sn) Sn A.2.2. F.c.c. Phase Mobility of Ag:

A.2.1. Liquid phase

= ⫺175892 + RT ln(1.306×10⫺5) ⌬G∗(Ag:Va) Ag Mobility of Ag:

⌬G∗(Cu:Va) = ⫺191533 + RT ln(4.66×10⫺5) Ag

= ⫺32065 + RT ln(5.8×10⫺8) ⌬G∗(liq⫺Ag) Ag

⌬G∗(Sn:Va) = ⫺139800 + RT ln(1.354×10⫺1) Ag

⌬G∗(liq⫺Cu) = ⫺36936 + RT ln(7.23×10⫺6) Ag

Sn:Va) ⌬G∗(Ag, = 168588⫺35.952T Ag

⌬G∗(liq⫺Sn) = ⫺17580 + RT ln(2.6×10⫺7) Ag Cu) ⌬G∗(Liq⫺Ag, = 51551 Ag

= ⫺179012 + RT ln(2.693×10⫺5) ⌬G∗(Ag:Va) Cu ⌬G∗(Cu:Va) = ⫺205872 + RT ln(4.889×10⫺5) Cu

Mobility of Cu: = ⫺41860 + RT ln(1.22×10⫺7) ⌬G∗(liq⫺Ag) Cu ⌬G∗(liq⫺Cu) = ⫺40646 + RT ln(1.46×10⫺7) Cu ∗(liq⫺Sn) ⌬GCu = ⫺17580 + RT ln(1.8×10⫺7)

⌬G

= ⫺25240 + RT ln(4.4×10 )

⌬G

= ⫺52325 + RT ln(2.25×10⫺7)

∗(liq⫺Cu) Sn

⌬G∗(Sn:Va) = ⫺139800 + RT ln(1.354×10⫺1) Cu Mobility of Sn: = ⫺162608 + RT ln(1.968×10⫺5) ⌬G∗(Ag:Va) Sn ⌬G∗(Cu:Va) = ⫺187945 + RT ln(8.758×10⫺5) Sn

Mobility of Sn: ∗(liq⫺Ag) Sn

Mobility of Cu:

⫺8

⌬G∗(Sn:Va) = ⫺139800 + RT ln(1.354×10⫺1) Sn Sn:Va) ⌬G∗(Cu, = 87560 Sn