Growth Behavior of Au Sn and Ag Sn Compounds during Solid state Reactive Diffusion between Au Ag Alloys and Sn

(1)

Growth Behavior of Au–Sn and Ag–Sn Compounds

during Solid-state Reactive Diﬀusion between Au–Ag Alloys and Sn

Toshio Takenaka

1;*1

_{, Satoru Kano}

1;1

_{, Masanori Kajihara}

1;*2

_,

Noriharu Kurokawa

2

and Katsuhiko Sakamoto

2

1_{Department of Materials Science and Engineering, Tokyo Institute of Technology, Yokohama 226-8502, Japan}

2_{Tyco Electronics AMP Co., Ltd., Kawasaki 214-8533, Japan}

The kinetics of the solid-state reactive diffusion between binary Au–Ag alloys and Sn was experimentally examined using Sn/ Au0:75Ag0:25/Sn and Sn/Au0:5Ag0:5/Sn diffusion couples. The diffusion couples were prepared by a diffusion bonding technique and then

isothermally annealed at temperatures ofT¼393, 433 and 473 K for various times up to 1272 h in an oil bath with silicone oil. Under the present experimental conditions, AuSn4and AuSn2compound layers were observed after annealing. Furthermore, ﬁne particles of Ag3Sn were rather

uniformly distributed in the Au–Sn compound layers. The total thicknesslof the Au–Sn compound layers is expressed as a power function of the annealing timetas follows:l¼kðt=t0Þn, wheret0is unit time, 1 s. Here, the exponent takes values ofn¼0:34{0:40. The mean interdistancerof

the Ag3Sn particles is also described as a power function oft:r¼krðt=t0Þp, wherep¼0:28{0:43. Assuming that the interdistancervaries in

proportion to the grain size of the Au–Ag compound during annealing, the rate-controlling process of the reactive diﬀusion was estimated. If the grain boundary diﬀusion across the Au–Sn compound layers is the only rate-controlling process, the values ofncalculated from the equation

n¼ ð1pÞ=2become smaller than the experimental values ofn¼0:34{0:40. Consequently, both the volume diffusion and the grain boundary diffusion should contribute to the rate-controlling process of the reactive diffusion.

(Received April 11, 2005; Accepted June 21, 2005; Published August 15, 2005)

Keywords: diﬀusion bonding, intermetallic compounds, bulk diﬀusion, solder, gold–silver–tin system

1. Introduction

In electronic industry, Sn-base solder alloys are widely used to interconnect Cu-base conductor alloys. However, Cu–Sn compounds are formed at the interface between the conductor and solder alloys due to soldering and then grow continuously during energization heating under usual service

conditions.1–9)_{Since such compounds are brittle and possess}

high electrical resistivities, their growth deteriorates the electrical and mechanical properties of the interconnection. Most of Cu-base conductor alloys are plated with Au to improve the corrosion resistance. When the Au-plated conductor alloy is in contact with the Sn-base solder alloy mechanically, the ductility and the electrical conductivity of the conductor alloy at the mechanical contact considerably degenerate owing to usual energization heating. Such degeneration is ascribable to the formation of Au–Sn compounds at the mechanical contact due to the reactive

diﬀusion between Au and Sn at solid-state temperatures.10–12)

The solid-state reactive diﬀusion was experimentally

studied by the present authors for the binary Au–Sn,10–12)

Ag–Sn13)_{and Cu–Sn}14)_{systems. In those experiments, Sn/}

Au/Sn, Sn/Ag/Sn and Sn/Cu/Sn diﬀusion couples with sandwich construction were prepared by a diﬀusion bonding technique and then annealed at various temperatures in an oil

bath. In the case of the Au–Sn system, AuSn4, AuSn2 and

AuSn compound layers were observed to form at the Au/Sn interface in the diﬀusion couple at annealing temperatures of

T ¼393{473K. The total thickness of the Au–Sn compound

layers is mathematically expressed as a power function of the annealing time, and the exponent of the power function takes

values of 0.48, 0.42 and 0.36 at T ¼393, 433 and 473 K,

respectively.11,12)If the reactive diffusion is controlled by the volume diffusion of the constituent elements in each phase, the exponent is equal to 0.5. On the contrary, the grain boundary diffusion across the compound layer will govern the reactive diffusion at low temperatures where the volume diffusion is frozen out. When the reactive diffusion is purely controlled by the grain boundary diffusion and grain growth takes place in the compound layer according to the parabolic

law, the exponent becomes 0.25.15)_{Here, the parabolic law}

means that the grain size of the compound layer is propor-tional to the square root of the annealing time. In the Au–Sn

system, the exponent is equal to 0.36 at T ¼473K and

increases with decreasing annealing temperature. At

T ¼393K, it becomes close to 0.5. The value of 0.36 yields

that the grain boundary diﬀusion contributes to the rate-controlling process and the grain growth occurs at a certain

rate atT ¼473K. However, atT¼393K, the grain growth

will decelerate, though the contribution of the grain boundary diffusion becomes more conspicuous. When the grain growth is very stagnant, the volume fraction of grain boundaries with a finite thickness remains almost constant, and hence the effective cross-section for the grain boundary diffusion scarcely varies during annealing. In such a case, the exponent becomes nearly equal to 0.5, even if the reactive diffusion is purely controlled by the grain boundary diffusion. This is the

reason why the exponent is smaller than 0.5 atT¼473and

433 K but close to 0.5 at T ¼393K in the Au–Sn

system.11,12)_{Such temperature dependence of the exponent}

was observed also for the Ag–Sn system,13)_{but the reverse}

temperature dependence was recognized for the Cu–Sn system.14)

Binary Au–Ag alloys are used as corrosion-resistant conductor materials in electronic industry. In the binary

Au–Ag system,16)the complete solid solution phase with the

face-centered cubic (f.c.c.) structure appears at a wide *1_{Graduate Student, Tokyo Institute of Technology}

*2_{Corresponding author, E-mail: [email protected]}

(2)

temperature range. If the Au–Ag conductor alloy is mechan-ically contacted with the Sn-base solder alloy and then heated at solid-state temperatures under energization conditions, Au–Sn and Ag–Sn compounds can be formed at the mechanical contact. Such formation may also cause degen-eration of the electrical and mechanical properties of the conductor alloy. However, experimental information on the coinstantaneous formation of the Au–Sn and Ag–Sn com-pounds under such conditions is limited. Recently, the reactive diﬀusion between Sn and a binary Au–Ag alloy was

experimentally observed by the present authors.17) In that

experiment, a Au–25 at %Ag alloy was sandwiched between

pure Sn, and then annealed atT ¼433K for various times in

the oil bath. Due to annealing, the AuSn4 and AuSn2

compound layers are produced at the interface in the Sn/ (Au–Ag)/Sn diﬀusion couple. Furthermore, ﬁne particles of

Ag3Sn are distributed rather uniformly in the Au–Sn

compound layers. In order to examine the kinetics of the coinstantaneous growth of the Au–Sn and Ag–Sn compounds under energization heating conditions, the solid-state reactive diffusion between Au–Ag alloys and Sn was observed more extensively in the present study. Sn/(Au–Ag)/Sn diffusion couples were prepared by the diffusion bonding technique using pure Sn and binary Au–25 at %Ag and Au–50 at %Ag

alloys and then annealed at temperatures between T ¼393

and 473 K. The layer growth of the Au–Sn compounds was observed metallographically. The observation was carried out also for the grain growth of the Ag–Sn compound. On the basis of the observations, the rate-controlling process of the reactive diﬀusion will be discussed.

2. Experimental

Binary Au–Ag alloys with Ag concentrations of 25 and 50 at % were prepared as 25 g button ingots by argon arc melting from pure Au and Ag with purity of 99.99%. Plate

specimens with a size of 10mm5mm2mm were cut

from the ingot and cold rolled to a thickness of 0.1 mm. Sheet

specimens with a dimension of 20mm7mm0:1mm

were cut from the plate specimen and then chemically polished in an etchant composed of 20 vol % of hydrochloric acid, 10 vol % of nitric acid and 70 vol % of distilled water. The chemically polished sheet specimens were separately annealed in evacuated silica capsules at 1223 K for 2 h, followed by air cooling without breaking the capsules. The annealed sheet specimens were again chemically polished in the etchant mentioned above.

Pure Sn plate specimens with a size of12mm5mm

2mm were prepared by cold rolling and spark erosion from a

commercial 1 kg rectangular ingot of pure Sn with purity of 99.99%. The cold-rolled plate specimens were separately annealed in evacuated silica capsules at 473 K for 2 h, followed by air cooling without breaking the capsules. The annealed Sn plate specimens were chemically polished in an etchant consisting of 20 vol % of hydrochloric acid, 20 vol % of nitric acid and 60 vol % of distilled water. The two

surfaces with an area of 12mm5mm of each Sn plate

specimen were mechanically polished on 1000 emery paper. One of the two polished surfaces was again mechanically

polished on 1500–4000 emery papers until a depth of 100mm

and then ﬁnished using diamond with a diameter of 1mm.

After chemical polishing, a Au–Ag sheet specimen was immediately sandwiched between the ﬁnished surfaces of two freshly prepared Sn plate specimens in methanol by a

technique used in previous studies.10–14)_{The Sn/(Au–Ag)/Sn}

couples were completely dried and then heat treated for

diﬀusion bonding in an oil bath with silicone oil atT ¼393,

433 and 473 K for 72, 24 and 6 h, respectively. After the heat

treatment, the diﬀusion couples were annealed atT ¼393,

433 and 473 K for various times up to 1200 h. The summation of the heat-treating and annealing times is hereafter merely called the annealing time. Cross-sections of the annealed diﬀusion couples were mechanically polished using diamond

with diameters of 15, 3 and 1mmand then ﬁnished with an

OP-S liquid by Struers Ltd. The microstructure of the cross-section was observed with a back-scattered electron image (BEI) by scanning electron microscopy (SEM). Concentra-tions of Au, Ag and Sn in each phase on the cross-section were measured by electron probe microanalysis (EPMA).

3. Results and Discussion

3.1 Microstructure

Typical BEI micrographs for the cross-section of the

Au0:5Ag0:5 diﬀusion couple annealed at T ¼433K for

t¼72h (2:59105s) are shown in Fig. 1. Here, t is the

annealing time. For simplicity, the type of diﬀusion couple is

denoted by the composition Auð1yÞAgyof the Au–Ag alloy

in the diﬀusion couple, whereyis the mol fraction of Ag. As

can be seen in Fig. 1(a), compound layers with slightly diﬀerent contrasts are observed to form at the (Au–Ag)/Sn interface. In such compound layers, ﬁne particles with the most dark contrast are distributed rather uniformly. In order to identify each phase, concentrations of Au, Ag and Sn were measured by EPMA. According to the measurements, the compound layer with a more dark contrast on the Sn specimen side is AuSn4, that with a less dark contrast on the

Au–Ag alloy side is AuSn2, and the ﬁne particle with the

most dark contrast in the AuSn4and AuSn2layers is Ag3Sn.

The solubility of Au in the Ag3Sn phase and those of Ag in

the AuSn4 and AuSn2 phases are less than 1 at %.

Further-more, ﬁne particles are spottily dispersed in the Sn specimen.

These particles are the AuSn4 phase precipitated during air

cooling after annealing.11,12)The Au–Ag compound layers in

the diﬀusion couple of Fig. 1(a) are magniﬁed in Fig. 1(b). Although no Ag3Sn particle is recognized in the region of the

AuSn4layer on the Sn specimen side, the mean grain size of

the Ag3Sn particles is almost equivalent in the AuSn4 and

AuSn2 layers.

As already mentioned in Introduction, the AuSn4, AuSn2

and AuSn layers are produced in the Au1Ag0diﬀusion couple

at T ¼393{473K.10–12) _{However, the AuSn layer was not}

clearly recognized in the Au0:75Ag0:25 and Au0:5Ag0:5

diﬀusion couples at the same temperatures. If we look at the micrograph in Fig. 1(b) carefully, we may ﬁnd that a very thin layer with a slightly dark contrast exists along the

interface between the AuSn2layer and the Au–Ag alloy. This

very thin layer may be the AuSn compound. Under the present annealing conditions, however, the AuSn layer does not grow to thicknesses enough to determine the composition

(3)

by EPMA accurately. On the other hand, in the Au0Ag1

diﬀusion couple, the Ag3Sn and layers are formed at

T ¼433{473K.13)_{However, only the Ag}

3Sn compound was

observed in the Au0:75Ag0:25 and Au0:5Ag0:5 diﬀusion

couples at T ¼393{473K. According to a recent phase

diagram in the ternary Au–Ag–Sn system,18)the Ag3Sn phase

is in equilibrium with the Sn, AuSn4, AuSn2, AuSn and

phases at T ¼479K. At this temperature, however, the

phase is not in equilibrium with the Sn, AuSn4 and AuSn2

phases. Such phase equilibria will be realized also at

T ¼393{473K. Consequently, the Ag3Sn phase appears in

the AuSn4 and AuSn2layers but not thephase.

3.2 Growth behavior of intermetallic layer

As mentioned earlier, the AuSn4 and AuSn2 layers are

observed in the BEI micrograph of the cross-section like

Fig. 1. Thus, from the BEI micrograph, the total thicknessl

of the Au–Sn compound layers was evaluated at each annealing time as follows:

l¼A=w: ð1Þ

Here,wandAare the total length parallel to the interface and the total area of the Au–Sn compound layers, respectively, on

the cross-section. The results atT ¼393, 433 and 473 K are

plotted as open triangles, squares and circles, respectively, in Fig. 2. In this ﬁgure, the ordinate indicates the logarithm of

the thicknessl, and the abscissa shows the logarithm of the

annealing timet. Figures 2(a) and (b) indicate the results for the Au0:75Ag0:25 and Au0:5Ag0:5 diﬀusion couples,

respec-tively. For convenience sake, the layer consisting of the

AuSn4 and AuSn2 compounds is hereafter called the

intermetallic layer. As can be seen in Fig. 2, the thicknessl

of the intermetallic layer monotonically increases with

increasing annealing time t. The plotted points at each

temperature are located well on a straight line. This means

that the thicknessl is mathematically expressed as a power

function of the annealing timetby the equation

l¼kðt=t0Þn: ð2Þ

Here,t0 is unit time, 1 s. It is adopted to make the ratiot=t0

dimensionless. The proportionality coeﬃcientkhas the same

dimension as the thickness l, but the exponent n is

dimensionless. From the plotted points in Fig. 2, the values

Fig. 1 Back-scattered electron images of cross-section for the Au0:5Ag0:5

diﬀusion couple annealed at 433 K for 72 h (2:59105_s).

Fig. 2 The thicknesslof the intermetallic layer versus the annealing timet

at temperatures of 393, 433 and 473 K for the (a) Au0:75Ag0:25 and (b)

Au0:5Ag0:5diﬀusion couples. Straight lines indicate the calculations from

[image:3.595.318.532.72.475.2] [image:3.595.48.291.73.444.2]

(4)

ofkandnwere determined by the least-squares method. The

determination gives k¼1:5107_{m and}_n_¼_0:40_at _T_¼

393K, k¼6:2107_{m and} _n_¼_0:36 _at _T_¼₄₃₃_{K and}

k¼8:4107_{m and}_n_¼_0:40_at_T _¼₄₇₃_{K for the Au}

0:75

-Ag0:25diﬀusion couple, andk¼2:0107m andn¼0:36

atT¼393K,k¼3:1107_{m and}_n_¼_0:40_at_T_¼₄₃₃_K

and k¼2:0106_{m and} _n_¼_0:34 _at _T _¼₄₇₃_{K for the}

Au0:5Ag0:5 diﬀusion couple. Using these values ofkandn,

the thicknesslwas calculated as a function of the annealing

timetfrom eq. (2). The results atT¼393, 433 and 473 K are shown as dotted, dashed and solid lines, respectively, in Fig. 2.

As already mentioned in Introduction, the solid-state reactive diﬀusion was experimentally studied by the present

authors for the binary Au–Sn10–12) and Ag–Sn13) systems

using the Au1Ag0and Au0Ag1diﬀusion couples,

respective-ly. The AuSn4, AuSn2 and AuSn layers are formed in the

Au1Ag0diﬀusion couple at T¼393{473K, and the Ag3Sn

andlayers are produced in the Au0Ag1diﬀusion couple at

T ¼433{473K. The experimental results of the total

thick-nesslversus the annealing timetfor the Au1Ag0and Au0Ag1

diﬀusion couples are shown as open circles and rhombuses, respectively, in Fig. 3. Also in this ﬁgure, the ordinate

indicates the logarithm of l, and the abscissa shows the

logarithm of t. Figures 3(a) and (b) indicate the results at

T ¼433and 473 K, respectively. In this ﬁgure, the plotted

points in Figs. 2(a) and (b) are also represented as open squares and triangles, respectively. At each annealing time,

the thickness is almost equivalent among the Au1Ag0,

Au0:75Ag0:25 and Au0:5Ag0:5 diﬀusion couples but about

one order of magnitude greater for these diﬀusion couples

than for the Au0Ag1 diﬀusion couple. This means that the

growth rate of the Au–Sn intermetallic layer is rather insensitive to the composition of the Au–Ag alloy in the diﬀusion couple under the present experimental conditions. Consequently, it is concluded that the degeneration of the mechanical and electrical properties at the interface between the Au–Ag conductor and Sn-base solder alloys due to the formation of the Au–Sn compounds occurs at almost the same rate as the interface between pure Au and the Sn-base solder alloy under usual energization heating conditions.

The values of the exponentn atT¼393, 433 and 473 K

are plotted against the composition y as open triangles,

squares and circles, respectively, in Fig. 4. Here, the ordinate

and the abscissa indicate n and y, respectively. As can be

seen, nis close to 0.5 at y¼0 andT ¼393K. Except this

plotted point, however,ntakes values between 0.34 and 0.42.

As already mentioned in Introduction, the values ofnsmaller

than 0.5 are realized only by the combination of the occurrence of the grain growth and the contribution of the grain boundary diﬀusion to the rate-controlling process. The results in Fig. 4 indicate that such combination is practically actualized in most of the diﬀusion couples under the present annealing conditions.

Fig. 3 The thicknesslof the intermetallic layer versus the annealing timet. The results for the Au0:75Ag0:25and Au0:5Ag0:5diﬀusion couples in Fig. 2

are represented as open squares and triangles, respectively, at temperatures of (a) 433 and (b) 473 K. The corresponding results for the Au1Ag011,12)

and Au0Ag113)diﬀusion couples are shown as open circles and rhombuses,

respectively. Straight lines indicate the calculations from eq. (2).

Fig. 4 The exponentnversus the mol fractionyof Ag at temperatures of 393, 433 and 473 K.

[image:4.595.62.279.297.716.2] [image:4.595.318.535.546.757.2]

(5)

3.3 Grain growth in intermetallic layer

Under the present experimental conditions, ﬁne particles of Ag3Sn are rather uniformly distributed in the intermetallic

layer. Hence, the mean interdistancerof the Ag3Sn particles

in the intermetallic layer on the cross-section was evaluated by the equation

r¼ ða=cÞ0:5: ð3Þ

Here,ais the area of the intermetallic layer distributed with the Ag3Sn particles on the cross-section, andcis the number

of the Ag3Sn particles in the areaa. The results atT ¼393,

433 and 473 K are plotted as open triangles, squares and circles, respectively, in Fig. 5. In this ﬁgure, the ordinate

shows the logarithm of the interdistancer, and the abscissa

indicates the logarithm of the annealing timet. Figures 5(a)

and (b) show the results for the Au0:75Ag0:25 and Au0:5Ag0:5

diﬀusion couples, respectively. As can be seen, the

inter-distancermonotonically increases with increasing annealing

timet. If the interdistanceris mathematically described as a

power function of the annealing timetby the equation

r¼krðt=t0Þp; ð4Þ

the following values of the proportionality coeﬃcientkrand

the exponent pare obtained from the plotted points in Fig. 5

by the least-squares method: kr¼1:4108m and p¼

0:36atT ¼393K,kr¼1:3108m and p¼0:43atT ¼

433K andkr¼9:4108_{m and}_p_¼_0:33_at_T_¼₄₇₃_{K for}

the Au0:75Ag0:25diﬀusion couple; andkr ¼1:0108m and

p¼0:35atT ¼393K,kr¼3:4108_{m and} _p_¼_0:33_at

T ¼433K andkr¼1:6107_{m and}_p_¼_0:28_at_T_¼₄₇₃

K for the Au0:5Ag0:5diﬀusion couple. Using these values of

kr andp, the interdistancerwas calculated as a function of

the annealing timetfrom eq. (4). The results atT ¼393, 433 and 473 K are shown as dotted, dashed and solid lines, respectively, in Fig. 5.

The values of p for the Au0:75Ag0:25 and Au0:5Ag0:5

diﬀusion couples are plotted against the annealing

temper-atureT as open circles and squares, respectively, in Fig. 6.

Here, the ordinate and the abscissa indicate p and T,

respectively. Recently, the solid-sate reactive diﬀusion

between Pd and Sn was experimentally studied at T ¼

433{473K using Sn/Pd/Sn diﬀusion couples by the present

authors.19) _{At the interface in the diﬀusion couple, PdSn}

4,

PdSn3 and PdSn2 layers were observed at T ¼433K, but

only PdSn4 and PdSn3 layers were recognized at T¼453

and 473 K. Unlike the Au–Sn intermetallic layer, however, grain boundaries were discerned clearly in the Pd–Sn

intermetallic layer. Thus, the mean grain size g of the Pd–

Sn intermetallic layer could be determined experimentally.

According to the experimental results, the grain size g is

expressed as a power function of the annealing time t:

g¼kgðt=t0Þp. The values of p for the Pd–Sn intermetallic

layer are shown as open rhombuses in Fig. 6. As can be seen,

pis much greater for the Au–Sn intermetallic layer than for

the Pd–Sn intermetallic layer. Although the relationship

between the interdistancerand the grain sizegis not known

for the Au–Sn intermetallic layer, r should be a monotone

Fig. 5 The interdistancerof the Ag3Sn particles versus the annealing time

tat temperatures of 393, 433 and 473 K for the (a) Au0:75Ag0:25and (b)

eq. (4).

Fig. 6 The exponent p versus the annealing temperature T for the Au0:75Ag0:25and Au0:5Ag0:5diﬀusion couples. The corresponding results

[image:5.595.61.275.326.736.2] [image:5.595.317.535.542.746.2]

(6)

increasing function of g. Therefore, the results in Fig. 6 imply that the grain growth occurs more remarkably in the Au–Sn intermetallic layer than in the Pd–Sn intermetallic layer.

3.4 Grain growth of Ag3Sn particle

Assuming that the shape of the Ag3Sn particle in the

intermetallic layer is the sphere with a constant diameter ofd,

we evaluate the mean size s of the Ag3Sn particle on the

cross-section by the equation

s¼2ðb=Þ0:5: ð5Þ

Here,bis the mean value for the area of each Ag3Sn particle

intersected by the cross-section. Furthermore, there exists the

following relationship between the mean size s and the

diameterd:

ðs=2Þ2d¼ ðd=2Þ34=3; ð6Þ

and hence we obtain the equation

d¼sð3=2Þ0:5: ð7Þ

The mean areab was determined from the BEI micrograph

like Fig. 1, and then the diameter d was estimated from

eqs. (5) and (7). The results atT ¼393, 433 and 473 K are

plotted as open triangles, squares and circles, respectively, in Fig. 7. In this ﬁgure, the ordinate and the abscissa show the logarithms ofd andt, respectively. Figure 7(a) indicates the results for the Au0:75Ag0:25 diﬀusion couple, and Fig. 7(b)

shows those for the Au0:5Ag0:5 diﬀusion couple. As can be

seen, the diameterdmonotonically increases with increasing

annealing timet. Whendis expressed as a power function of

tby the equation

d¼kdðt=t0Þm; ð8Þ

the following values ofkdandmare obtained from the plotted

points in Fig. 7 by the least-squares method: kd ¼6:9

109_{m and}_m_¼_0:35_at_T _¼₃₉₃_K,_kd _¼_2:9₁₀8_{m and}

m¼0:32atT ¼433K andkd ¼7:0108_{m and}_p_¼_0:30

at T ¼473K for the Au0:75Ag0:25 diﬀusion couple; and

kd¼1:0108_{m and}_m_¼_0:32_at_T _¼₃₉₃_K, _kd _¼_1:8

108m andm¼0:35at T¼433K andkd¼5:2108m

and m¼0:36 at T ¼473K for the Au0:5Ag0:5 diﬀusion

couple. Using these values ofkdandm,dwas calculated as a

function oft from eq. (8). The results atT¼393, 433 and

473 K are shown as dotted, dashed and solid lines, respec-tively, in Fig. 7.

The values of m for the Au0:75Ag0:25 and Au0:5Ag0:5

diﬀusion couples are plotted against the annealing

temper-atureT as open circles and squares, respectively, in Fig. 8.

Here, the ordinate and the abscissa indicate m and T,

respectively. As can be seen, m is close to 1/3 for all the

plotted points. Hence, at ﬁrst glance, the grain growth of the

Ag3Sn particle seems to take place according to the Ostwald

ripening.20)However, the total volume of the Ag3Sn particle

monotonically increases with increasing annealing time during the reactive diﬀusion. Consequently, the grain growth

of the Ag3Sn particle cannot be described with a simple

coarsening model. Nevertheless, the results in Fig. 8 imply

Fig. 7 The diameterdof the Ag3Sn particle versus the annealing timetat

temperatures of 393, 433 and 473 K for the (a) Au0:75Ag0:25 and (b)

eq. (8).

Fig. 8 The exponent m versus the annealing temperature T for the Au0:75Ag0:25and Au0:5Ag0:5diﬀusion couples.

[image:6.595.62.275.69.479.2] [image:6.595.316.535.70.274.2]

(7)

that a coarsening process similar to the Ostwald ripening works in the Au–Sn intermetallic layer.

3.5 Rate-controlling process

As already mentioned in Section 3.3, the relationship

between the grain sizegof the Au–Sn intermetallic layer and

the interdistance r of the Ag3Sn particle is not known.

However,rshould be a monotone increasing function ofg.

Assuming that r is proportional to g, the rate-controlling

process for the growth of the Au–Sn intermetallic layer was estimated. When the growth is purely controlled by the grain boundary diﬀusion across the intermetallic layer, the follow-ing relationship15)_{holds good between the exponents}_n_and_p_.

n¼ ð1pÞ=2 ð9Þ

The values ofncalculated from eq. (9) for the Au0:75Ag0:25

and Au0:5Ag0:5 diﬀusion couples are plotted against the

annealing temperature T as open circles and squares,

respectively, connected with dashed lines in Fig. 9. In this ﬁgure, open circles and squares connected with solid lines show the experimental values ofn for the Au0:75Ag0:25 and

Au0:5Ag0:5diﬀusion couples, respectively, in Fig. 4. As can

be seen in Fig. 9, most of the calculated values are smaller than the corresponding experimental values. This means that eq. (9) overestimates the contribution of the grain boundary diffusion to the rate-controlling process. Consequently, it is concluded that the growth of the Au–Sn intermetallic layer is controlled by both the volume diffusion and the grain boundary diffusion and the grain growth occurs at certain rates in the intermetallic layer.

4. Conclusions

The solid-state reactive diﬀusion between binary Au–Ag alloys and Sn was experimentally studied using the Sn/

Au0:75Ag0:25/Sn and Sn/Au0:5Ag0:5/Sn diﬀusion couples

prepared by the diﬀusion bonding technique. The diﬀusion couples were isothermally annealed at temperatures between

T ¼393 and 473 K for various times in the oil bath with

silicone oil. Due to annealing, the AuSn4 and AuSn2

compound layers are formed at the (Au–Ag)/Sn interface in the diﬀusion couple. Furthermore, the ﬁne particles of

Ag3Sn are rather uniformly distributed in the Au–Sn

compound layers. The total thickness l of the Au–Sn

compound layers monotonically increases with increasing annealing timetaccording to the equationl¼kðt=t0Þn, where

t0 is unit time, 1 s. For the Sn/Au0:75Ag0:25/Sn diﬀusion

couple,k¼1:5107_,_6:2₁₀7_and_8:4₁₀7_{m at}_T _¼

393, 433 and 473 K, respectively, and n¼0:40, 0.36 and

0.40 atT ¼393, 433 and 473 K, respectively. On the other

hand,k¼2:0107,3:1107 and2:0106m atT ¼

393, 433 and 473 K, respectively, and n¼0:36, 0.40 and

0.34 at T ¼393, 433 and 473 K, respectively, for the Sn/

Au0:5Ag0:5/Sn diﬀusion couple. The mean interdistancerof

the Ag3Sn particles in the Au–Sn compound layers is also

expressed as a power function oftas follows:r¼krðt=t0Þp.

For the Sn/Au0:75Ag0:25/Sn diﬀusion couple, kr¼1:4

108_{m and} _p_¼_0:36_at_T _¼₃₉₃_K,_kr_¼_1:3₁₀8_{m and}

p¼0:43atT¼433K, andkr¼9:4108_{m and}_p_¼_0:33

atT ¼473K. On the contrary,kr ¼1:0108_{m and} _p_¼

0:35atT ¼393K,kr¼3:4108_{m and} _p_¼_0:33_at_T _¼

433K, andkr¼1:6107_{m and}_p_¼_0:28_at_T _¼₄₇₃_{K for}

the Sn/Au0:5Ag0:5/Sn diﬀusion couple. If the interdistancer

is proportional to the grain sizegfor the Au–Sn compound

layers, the exponent p represents also the annealing time

dependence ofg. Assuming that the grain boundary diﬀusion

across the Au–Sn compound layers is the only

rate-control-ling process, the exponentn is estimated from the equation

n¼ ð1pÞ=2.15)_{However, most of the estimated values are}

smaller than the corresponding experimental values. This means that the reactive diffusion should be controlled by both the volume diffusion and the grain boundary diffusion.

Acknowledgements

The present study was supported by Tyco Electronics AMP Co., Ltd., Japan. The study was also partially supported by a Grant-in-Aid for Scientiﬁc Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

REFERENCES

1) L. Zakraysek: Welding Research Supplement Nov. (1972) 536–541. 2) K. N. Tu: Acta Metall.21(1973) 347–354.

3) H. N. Keller: IEEE Trans. Components, Hybrids, Manuf. Tech. CHMT-2 (1979) 180–195.

4) H. N. Keller and J. M. Morabito: Surf. Interface Anal.3(1981) 16–22. 5) J. O. G. Parent, D. D. L. Chung and I. M. Bernstein: J. Mater. Sci.23

(1988) 2564–2572.

6) A. J. Sunwoo, J. W. Morris, Jr. and G. K. Lucey, Jr.: Metall. Trans.23A

(1992) 1323–1332.

7) P. T. Vianco, P. F. Hlava and A. L. Kilgo: J. Electron. Mater.23(1994) 583–594.

8) D. R. Frear and P. T. Vianco: Metall. Trans.25A(1994) 1509–1523. 9) S. Choi, T. R. Bieler, J. P. Lucas and K. N. Subramanian: J. Electron.

Mater.28(1999) 1209–1215. Fig. 9 The exponentnversus the annealing temperatureT. The values ofn

for the Au0:75Ag0:25and Au0:5Ag0:5diﬀusion couples in Fig. 4 are plotted

[image:7.595.63.277.70.280.2]

(8)

10) M. Kajihara, T. Yamada, K. Miura, N. Kurokawa and K. Sakamoto: Netsushori43(2003) 297–298.

11) T. Yamada, K. Miura, M. Kajihara, N. Kurokawa and K. Sakamoto: J. Mater. Sci.39(2004) 2327–2334.

12) T. Yamada, K. Miura, M. Kajihara, N. Kurokawa and K. Sakamoto: Mater. Sci. Eng. A390(2005) 118–126.

13) K. Suzuki, S. Kano, M. Kajihara, N. Kurokawa and K. Sakamoto: Mater. Trans.46(2005) 969–973.

14) T. Takenaka, S. Kano, M. Kajihara, N. Kurokawa and K. Sakamoto: Mater. Sci. Eng. A396(2005) 115–123.

15) Y. L. Corcoran, A. H. King, N. de Lanerolle and B. Kim: J. Electron. Mater.19(1990) 1177–1183.

16) T. B. Massalski, H. Okamoto, P. R. Subramanian and L. Kacprzak: Binary Alloy Phase Diagram (ASM International, Materials Park, OH, 1990) vol. 1, p. 12.

17) S. Kano: Master Eng. Thesis, Tokyo Institute of Technology, 2003. 18) P. Villars, A. Prince and H. Okamoto: Handbook of Ternary Alloy

Phase Diagrams (ASM International, Materials Park, OH, 1995) vol. 3, p. 2170.

19) T. Takenaka, M. Kajihara, N. Kurokawa and K. Sakamoto: Mater. Sci. Eng. A, in press.

20) R. Wagner, R. Kampmann and P. W. Voorhees: in Phase Trans-formations in Materials, ed. G. Kostorz (Wiley-Vch Verlag GmbH, Weinheim, 2001), pp. 370–373.