### Inﬂuence of Ag on Kinetics of Solid-State Reactive Diﬀusion between Pd and Sn

### Taro Sakama

1### and Masanori Kajihara

2;*1_{Graduate School, Tokyo Institute of Technology, Yokohama 226-8502, Japan}

2_{Department of Materials Science and Engineering, Tokyo Institute of Technology, Yokohama 226-8502, Japan}

The inﬂuence of Ag on the kinetics of the solid-state reactive diﬀusion between Pd and Sn was experimentally examined using Sn/ (Pd–Ag)/Sn diﬀusion couples with a Ag concentration of 75 at% in the present study. The diﬀusion couples were isothermally annealed at temperatures of 433, 453 and 473 K for various periods up to 1365 h. During annealing, a compound layer dominantly consisting of polycrystalline PdSn4and Ag3Sn lamellae is formed at the (Pd–Ag)/Sn interface in the diﬀusion couple. The square of the thickness of the compound layer increases in proportion to the annealing time. This relationship is called the parabolic relationship. On the other hand, the interlamellar spacing in the compound layer is proportional to a power function of the annealing time, and thus grain growth occurs in the compound layer. The exponent of the power function is close to 1/3. The parabolic relationship of the layer growth and the occurrence of the grain growth guarantee that the growth of the compound layer is controlled by volume diﬀusion. The addition of Ag with 75 at% into Pd decreases the parabolic coeﬃcient by 93, 88 and 78% at 433, 453 and 473 K, respectively. Hence, Ag works as an eﬀective suppressant against the growth of the compound during the solid-state reactive diﬀusion between Pd and Sn. [doi:10.2320/matertrans.MRA2008292]

(Received August 25, 2008; Accepted November 14, 2008; Published January 8, 2009)

Keywords: diﬀusion bonding, reactive diﬀusion, intermetallic compounds, volume diﬀusion, solder, conductor

1. Introduction

Due to high electrical conductivity, Cu-base alloys are widely used as conductor materials in the electronics industry. If the Cu-base alloy is interconnected using a Sn-base solder, binary Cu–Sn compounds are formed at the interconnection owing to the reactive diﬀusion between the Cu-base alloy and the molten Sn-base solder during soldering and then gradually grow under usual energization heating conditions at solid-state temperatures. Since the Cu–Sn compounds are brittle and possess high electrical resistivities, their formation deteriorates the electrical and mechanical properties of the interconnection. The formation behavior of the Cu–Sn compounds has been experimentally studied by

many investigators.1–17) _{To suppress the formation of the}

Cu–Sn compounds, the Cu-base alloy is generally plated with a Ni layer. Such a Ni layer actually acts as an eﬀective barrier against the reactive diﬀusion between the Sn-base solder and

the Cu-base alloy.18–39) _{Unfortunately, however, Ni is not}

completely corrosion resistant. Thus, the Ni layer on the Cu-base alloy is usually plated with a Au or Pd layer to improve corrosion resistance. In such a multilayer Au/Ni/Cu or Pd/Ni/Cu conductor, reactive diﬀusion occurs at the interconnection between the Sn-base solder and the Au or Pd layer during solid-state energization heating unless the Au or Pd layer completely dissolves into the molten solder during soldering.

The solid-state reactive diﬀusion in the Au/Sn system was experimentally examined using Sn/Au/Sn diﬀusion couples

in previous studies.40–43) _{In these experiments, the }

diﬀu-sion couples were isothermally annealed at temperatures of

T ¼393{473K. Due to annealing, compound layers of AuSn4, AuSn2and AuSn are produced at the Au/Sn interface

in the diﬀusion couple. The total thickness of the compound layers is proportional to a power function of the annealing time. The exponent of the power function is 0.48, 0.42, 0.39

and 0.36 atT ¼393, 433, 453 and 473 K, respectively. The

exponent smaller than 0.5 means that both boundary and volume diﬀusion contributes to the growth of the compound layers and grain growth occurs in the compound layers.

As to the Pd/Sn system, the solid-state reactive diﬀusion was experimentally observed using Sn/Pd/Sn diﬀusion

couples in a previous study.44) The diﬀusion couples were

isothermally annealed atT¼433{473K in this experiment.

At the Pd/Sn interface in the diﬀusion couple, PdSn4, PdSn3

and PdSn2 layers are formed atT ¼433K, but only PdSn4

and PdSn3 layers are produced at T ¼453 and 473 K. In

this case, however, the square of the total thickness of the compound layers is proportional to the annealing time, though grain growth takes place in the compound layers. This relationship between the thickness and the annealing time is called the parabolic relationship. Consequently, the growth of the compound layers is controlled by volume diﬀusion. Thus, the rate-controlling process of reactive diﬀusion varies depending on the alloy system. Nevertheless, the overall growth rate of the compound layers is similar in the Pd/Sn and Au/Sn systems.

The eﬀect of Ag on the solid-state reactive diﬀusion in the Au/Sn system was experimentally examined in previous studies.45–47)In these experiments, Sn/(Au–Ag)/Sn diﬀusion couples with diﬀerent Ag concentrations were isothermally

annealed at T ¼393{473K. For Ag concentrations of 25–

63 at%, AuSn4and AuSn2layers dispersed with small Ag3Sn

particles are produced at the (Au–Ag)/Sn interface in the

diﬀusion couple due to annealing. On the other hand, AuSn4

and Ag3Sn layers are formed for Ag concentrations of 75–

87 at%. The overall growth rate of the compound layers is almost independent of the Ag concentration for 0–63 at%, but gradually decreases with increasing Ag concentration for 63–100 at%. Consequently, addition of Ag into Au up to 63 at% cannot suppress the growth of the compounds at the interconnection between the Sn-base solder and the multi-layer Au/Ni/Cu conductor during solid-state energization heating.

In contrast, the solid-state reactive diﬀusion in the
(Pd–Ag)/Sn system was experimentally observed using Sn/
*_{Corresponding author, E-mail: [email protected]}

parabolic coeﬃcient should decrease remarkably. Unfortu-nately, however, no reliable information is available for composition dependence of the parabolic coeﬃcient at such high Ag concentrations. In the present study, the inﬂuence of Ag on the solid-state reactive diﬀusion between Pd and Sn was experimentally examined using Sn/(Pd–Ag)/Sn diﬀu-sion couples with a Ag concentration of 75 at% in the temperature range of 433–473 K. The rate-controlling proc-ess of the reactive diﬀusion was discussed on the basis of the experimental result. Furthermore, simple diﬀusion models were used to account for the inﬂuence of Ag.

2. Experimental

A binary Pd–Ag alloy containing 75 at% of Ag was
prepared as a 25 g button ingot by argon arc melting from
pure Pd and Ag with purities of 99.9 and 99.99%,
respectively, in a manner similar to a previous study.48)_{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 consisting of 10 vol% of nitric acid, 20 vol% of hydrochloric acid and 70 vol% of distilled water. The chemically polished sheet specimens were separately annealed in evacuated silica capsules at 1173 K for 200 h, followed by air cooling without breaking the capsules. The annealed sheet specimens were again chemically polished in the etchant mentioned above.

Polycrystalline plate specimens of Sn with a size of

12mm5mm2mm 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 nitric acid, 20 vol% of hydrochloric acid and 60 vol% of

distilled water. The two surfaces with an area of 12mm

5mm of each Sn plate specimen were mechanically polished

on 800 emery paper. One of the two polished surfaces was again mechanically polished on 1000–4000 emery papers until a depth of 100mmand then ﬁnished using diamond with a diameter of 1mm.

scanning electron microscopy (SEM). Concentrations of Pd, Ag and Sn in each phase on the cross-section were measured by electron probe microanalysis (EPMA).

3. Results and Discussion

3.1 Microstructure

A typical micrograph of OM for the cross-section of the annealed diﬀusion couple is shown in Fig. 1. This ﬁgure indicates the micrograph for the diﬀusion couple annealed at

T ¼473K for t¼89h (320 ks). In Fig. 1, the upper and

lower regions are the Sn specimen and the Pd–Ag alloy, respectively. As can be seen, a compound layer with a thickness of about 75mmis formed at the interface between the Pd–Ag and Sn. A magniﬁed SEM micrograph of the

compound layer in the diﬀusion couple withT¼473K and

t¼92h (331 ks) is shown in Fig. 2. As can be seen, the

compound layer mainly consists of two polycrystalline lamellar phases with slightly dark and bright contrasts. The overall longitudinal direction of the lamellae is parallel to the initial (Pd–Ag)/Sn interface. According to the EPMA

measurement, the dark and bright phases are Ag3Sn and

PdSn4, respectively. The solubility of Pd in Ag3Sn and that of

Ag in PdSn4 are negligible. Rather small particles of Ag3Sn

[image:2.595.306.548.570.756.2]are also distributed in the matrix of PdSn4. Hereafter, the

compound layer with the Ag3SnþPdSn4 two-phase

micro-structure is merely called the intermetallic layer. This type of intermetallic layer was recognized in all the diﬀusion couples

annealed at T¼433{473K. The intermetallic layer grows

mainly towards the Sn.

The solid-state reactive diﬀusion in the Ag/Sn system was experimentally observed using Sn/Ag/Sn diﬀusion couples

in a previous study.45) In this experiment, the diﬀusion

couples were isothermally annealed at T ¼433{473K.

Owing to annealing, Ag3Sn and layers are formed at the

Ag/Sn interface in the diﬀusion couple. In the case of the

solid-state reactive diﬀusion in the Pd/Sn system,44) _{}

how-ever, PdSn4, PdSn3 and PdSn2 layers are produced at

T ¼433K, but only PdSn4 and PdSn3 layers are formed at

T ¼453{473K. On the other hand, during the solid-state
reactive diﬀusion in the (Pd–Ag)/Sn system with Ag
con-centrations of 25–50 at%,48)_{a PdSn}

4layer dispersed with ﬁne

Ag3Sn particles is dominantly formed atT ¼433{473K. For

a Ag concentration of 75 at%, however, Ag3Sn is mostly

lamellar and partially granular as shown in Fig. 2. Thus, in

the (Pd–Ag)/Sn system, the morphology of the Ag3Snþ

PdSn4 two-phase microstructure in the intermetallic layer

varies depending on the Ag concentration. In contrast, PdSn3,

PdSn2andwere not clearly recognized in the (Pd–Ag)/Sn

system with Ag concentrations of 25–75 at%.

3.2 Growth behavior of intermetallic layer

From cross-sectional OM micrographs like Fig. 1, the mean thicknesslof the intermetallic layer was evaluated by the equation

l¼A=w; ð1Þ

whereAandware the area and the length of the intermetallic layer, respectively, on the cross-section. At each annealing time,lwas calculated from eq. (1) using the total values ofA

andwfor various cross-sections. The results ofT ¼433, 453 and 473 K are shown as open rhombuses, squares and circles, respectively, in Fig. 3. In this ﬁgure, the ordinate and the

abscissa indicate the logarithms of the thickness l and the

annealing time t, respectively. As can be seen, the

thick-ness l monotonically increases with increasing annealing

timet, and the plotted points at each annealing temperature

are located well on a straight line. This means that l is

mathematically expressed as a power function oftas follows.

l¼kðt=t0Þn ð2Þ

Here,t0is unit time, 1 s. It is adopted to make the argument t=t0of the power function dimensionless. The proportionality

coeﬃcient k possesses the same dimension as l, and the

exponent n is dimensionless. From the plotted points in

Fig. 3,kandnwere estimated by the least-squares method.

The estimated values are shown in Fig. 3. Using these values of kandn,lwas calculated as a function oft from eq. (2).

The results of T ¼433, 453 and 473 K are indicated as

dotted, dashed and solid lines, respectively, in Fig. 3. At each annealing time, the thicknesslmonotonically increases with increasing annealing temperatureT.

3.3 Rate-controlling process

As mentioned earlier, the solid-state reactive diﬀusion in
the (Pd–Ag)/Sn system was experimentally examined using
Sn/(Pd–Ag)/Sn diﬀusion couples with Ag concentrations of
0,44)_{25, 50}48)_{and 100}45)_{at% in previous studies. Hereafter,}

the concentration of Ag in the Pd–Ag alloy of the diﬀusion

couple is described with the mol fraction y of Ag. The

experimental values of n for T ¼433, 453 and 473 K are

plotted againstyas open circles with error bars in Fig. 4(a),

(b) and (c), respectively. As can be seen, n is close to

0.5 for y¼0{0:75 but slightly smaller than 0.5 for y¼1. If the growth of the intermetallic layer is controlled by volume diﬀusion,nis equal to 0.5.49–56)In contrast, boundary diﬀusion may govern the layer growth at low tempera-tures where volume diﬀusion is frozen out. When the layer growth is purely controlled by boundary diﬀusion across the intermetallic layer and grain growth occurs in the interme-tallic layer according to a parabolic law,nbecomes equal to

Fig. 2 Cross-sectional SEM micrograph of compound layer in diﬀusion couple annealed at 473 K for 92 h.

[image:3.595.313.542.70.293.2] [image:3.595.49.290.71.264.2]0.25.57)_{Here, the parabolic law means that the grain size is}

proportional to the square root of the annealing time.

How-ever, n is also equal to 0.5 even for the layer growth

con-trolled by boundary diﬀusion unless grain growth occurs.58)

Experimental results of many alloy systems in previous
studies59–71)_{indicate that the reactive diﬀusion is not }

neces-sarily controlled by volume diﬀusion. Consequently, in the case ofn¼0:5, there are two possibilities for the rate-con-trolling process. In such a case, the rate-conrate-con-trolling process cannot be conclusively determined only from the value ofn.

3.4 Grain growth in intermetallic layer

To estimate the rate-controlling process for the layer growth, the occurrence of grain growth in the intermetallic

layer should be conﬁrmed experimentally. As shown in Fig. 2, PdSn4and Ag3Sn mostly construct the lamellar

two-phase microstructure, and Ag3Sn is partially distributed as

small particles in the matrix of PdSn4. For the Ag3Sn

lamellae, the mean interlamellar spacing d was measured

from cross-sectional SEM micrographs like Fig. 2. Since the overall longitudinal direction of the lamellae is almost parallel to the initial (Pd–Ag)/Sn interface and thus normal to

the cross-section, d almost corresponds to the mean of the

three-dimensional interlamellar spacing. Furthermore, the

mean grain sizes of the polycrystalline PdSn4 and Ag3Sn

lamellae may be proportional tod. The results ofy¼0:75for

T ¼433, 453 and 473 K are shown as open rhombuses,

squares and circles, respectively, in Fig. 5. In this ﬁgure, the

[image:4.595.60.538.70.571.2]ordinate and the abscissa indicate the logarithms ofdandt, respectively. As can be seen,dmonotonically increases with

increasing value of t. This means that grain growth surely

takes place in the intermetallic layer. The plotted points at each annealing temperature lie well on a straight line. Thus,d

is expressed as a power function of t by the following

equation of the same formula as eq. (2).

d¼kdðt=t0Þp ð3Þ

From the plotted points in Fig. 5, the proportionality

coeﬃcient kd and the exponent p were estimated by the

least-squares method. In this ﬁgure, dotted, dashed and solid

lines show the results of T¼433, 453 and 473 K,

respec-tively. As can be seen, these lines are nearly parallel to one

another. At each annealing time,dis smaller forT¼433K

than forT¼453{473K but similar inT ¼453{473K.

The values of p for y¼0:75 are plotted against the

annealing temperature T as open circles in Fig. 6. In this

ﬁgure, the corresponding results of y¼0,44) 0.25 and

0.548)are also represented as open rhombuses, squares and

triangles, respectively. Fory¼1, however, each grain in the
intermetallic layer was not distinguished in a
metallograph-ical manner, and thus grain growth could not be conﬁrmed
experimentally.45)_{As can be seen in Fig. 6,}_{p}_{is greater than 0}

for y¼0{0:75. This means that grain growth occurs in the

intermetallic layer. Nevertheless, as shown in Fig. 4, n is

close to 0.5 fory¼0{0:75atT¼433{473K. Consequently, it is concluded that the solid-state reactive diﬀusion in the

(Pd–Ag)/Sn system withy¼0{0:75is controlled by volume

diﬀusion. However, pis smaller than 0.5, and thus the grain growth does not obey the parabolic law. In the case of

y¼0:75, p is close to 1/3 atT ¼433{473K. This implies that a mechanism similar to Ostwald ripening governs the grain growth and hence the interfacial energy between PdSn4

and Ag3Sn is the most important driving force of the grain

growth. On the other hand, fory¼0{0:5, pis smaller than

1/3 and gradually increases with increasing value of T.

Therefore, a diﬀerent mechanism of grain growth works for

y¼0{0:5.

3.5 Composition dependence of kinetics

For the reactive diﬀusion controlled by volume diﬀusion, the parabolic relationship holds between the thicknesslof the intermetallic layer and the annealing time t. The parabolic relationship is expressed by the following equation:

l2¼Kt: ð4Þ

Here, K is the parabolic coeﬃcient. The open symbols in

Fig. 3 are plotted again in Fig. 7. In this ﬁgure, however, the ordinate showsl, and the abscissa indicates the square root of

t. From the plotted points in Fig. 7,K was estimated by the least-squares method. Using the estimated values ofK,lwas

calculated as a function of t from eq. (4). The results of

T ¼433, 453 and 473 K are shown as dotted, dashed and

solid lines, respectively, in Fig. 7. Sincenis almost equal to 0.5 fory¼0:75atT ¼433{473K as indicated in Fig. 4, the open rhombuses, squares and circles are located well on the dotted, dashed and solid lines, respectively, in Fig. 7.

The mean and the standard error of K for y¼0:75 at

T ¼433{473K are listed in Table 1. In this table, the
corresponding results for y¼0,44) _{0.25, 0.5}48) _{and 1}45) _{at}

T ¼433{473K determined in previous studies are also

represented. As shown in Fig. 4, however, n is slightly

smaller than 0.5 for y¼1. This means that both boundary

and volume diﬀusion contributes to the growth of the intermetallic layer. Thus, eq. (4) may not be valid fory¼1. Nevertheless, to ﬁnd the composition dependence of the overall growth rate of the intermetallic layer, eq. (4) is still

convenient. The values ofKforT ¼433, 453 and 473 K in

Table 1 are plotted againstyas open rhombuses, squares and circles, respectively, with error bars in Fig. 8. As can be seen,

K monotonically decreases with increasing value of y. The

dependence ofKonyis more remarkable fory>0:5than for

y<0:5. Thus, addition of Ag withy>0:5 into Pd

consid-Fig. 5 The mean interlamellar spacingdversus the annealing timetat 433, 453 and 473 K shown as open rhombuses, squares and circles, respec-tively.

Fig. 6 The exponent pversus the annealing temperatureTfory¼0,44)

0.25, 0.548)_{and 0.75 shown as open rhombuses, squares, triangles and}

erably decelerates the growth of the intermetallic layer.

According to Table 1, K is smaller by 93, 88 and 78%

for y¼0:75 than for y¼0 at T ¼433, 453 and 473 K,

respectively. Fory>0:6, however, the Pd–Ag alloy gradual-ly loses excellent corrosion resistance with increasing value ofy. Hence,y¼0:6is the upper limit of Ag concentration for the corrosion resistant Pd–Ag layer in the multilayer (Pd– Ag)/Ni/Cu conductor. Using the values ofKfory¼0:5and

0.75, we obtain interpolated values of K¼3:661015_{,}

1:371014_{and}_{6}_{:}_{08}_{}_{10}14_{m}2_{/s for}_{y}_{¼}_{0}_{:}_{6}_{at}_{T} _{¼}_{433}_{,}

453 and 473 K, respectively. Thus,Kis smaller by 72, 75 and 44% fory¼0:6than fory¼0atT ¼433, 453 and 473 K, respectively. Consequently, the deceleration eﬀect of Ag is

notable atT ¼433{453K but less remarkable atT ¼473K.

The logarithm ofKis plotted against the reciprocal ofTas

various open symbols for diﬀerent values ofyin Fig. 9. As

can be seen, the open symbols lie well on the corresponding straight lines. Hence, the dependence ofKonT is expressed by an Arrhenius equation as follows.

K¼K0expðQK=RTÞ ð5Þ

The pre-exponential factorK0and the activation enthalpyQK

were estimated from the plotted points in Fig. 9 by the

least-squares method. The estimated values of QK are plotted

against y as open circles in Fig. 10. As can be seen, QK

monotonically increases from 90.4 to 142 kJ/mol with

increasing Ag concentration from y¼0 to y¼0:75, but

decreases to 64.6 kJ/mol fory¼1.

The reactive diﬀusion controlled by volume diﬀusion was
theoretically analyzed using a mathematical model in a
previous study.49)_{In this analysis, a hypothetical binary alloy}

system composed of one intermetallic compound and two primary solid-solution phases was treated, and then the growth rate of the compound layer was evaluated for various semi-inﬁnite diﬀusion couples initially consisting of the two primary solid-solution phases. The analysis indicates that the most predominant parameters determining the growth rate are the diﬀusion coeﬃcient and the solubility range of the growing compound phase. However, the diﬀusion coeﬃ-cients and the solubility ranges of the primary solid solution phases also possess certain eﬀects on the growth rate. Hence, the mathematical model was also used to analyze numerically the relationship between the temperature dependence of the interdiﬀusion in each phase and the kinetics of the reactive

[image:6.595.55.286.70.293.2]Fig. 7 The results in Fig. 3 are plotted as the mean thicknessl of the compound layer versus the square root of the annealing timet.

Table 1 The meanMand the standard errorSEof the parabolic coeﬃcientKmeasured in m2_{/s for various values of the mol fraction}_{y}_{of}
Ag in the Sn/(Pd–Ag)/Sn diﬀusion couple and the annealing temperature T. The results of y¼0,44Þ _{0.25, 0.5}48Þ _{and 1}45Þ _{for}
T¼433{473K in previous studies are also represented.

y K

433 K 453 K 473 K

M SE M SE M SE

0 1:301014 _{1}_{:}_{43}_{}_{10}15 _{5}_{:}_{40}_{}_{10}14 _{2}_{:}_{81}_{}_{10}15 _{1}_{:}_{08}_{}_{10}13 _{1}_{:}_{84}_{}_{10}15
0.25 7:411015 _{5}_{:}_{00}_{}_{10}16 _{2}_{:}_{26}_{}_{10}14 _{1}_{:}_{55}_{}_{10}15 _{9}_{:}_{76}_{}_{10}14 _{2}_{:}_{29}_{}_{10}15
0.5 5:531015 _{5}_{:}_{21}_{}_{10}16 _{1}_{:}_{86}_{}_{10}14 _{1}_{:}_{68}_{}_{10}15 _{8}_{:}_{53}_{}_{10}14 _{2}_{:}_{23}_{}_{10}15
0.75 8:671016 _{4}_{:}_{36}_{}_{10}17 _{6}_{:}_{39}_{}_{10}15 _{4}_{:}_{35}_{}_{10}16 _{2}_{:}_{41}_{}_{10}14 _{9}_{:}_{11}_{}_{10}16
1 6:151017 _{6}_{:}_{79}_{}_{10}18 _{1}_{:}_{01}_{}_{10}16 _{8}_{:}_{78}_{}_{10}18 _{2}_{:}_{83}_{}_{10}16 _{2}_{:}_{42}_{}_{10}17

diﬀusion.50) In the numerical analysis, the temperature

dependence of the interdiﬀusion coeﬃcientDwas expressed

by an Arrhenius equation of

D¼D0expðQ=RTÞ; ð6Þ

and the following assumptions were adopted: (A) the molar volume, the solubility range and the pre-exponential factor

D0are constant and equivalent for all the phases; and (B) the

activation enthalpyQis equivalent for the solution phases but diﬀerent between the compound and the solution phase. According to the numerical analysis, eq. (5) is reliable enough to express the temperature dependence of experi-mental values ofKbut not completely exact. IfQis smaller for the compound than for the solution phases,QKis close to

Qof the compound. In this case, the temperature dependence

ofKcorresponds well with that ofDof the compound. Such a

relationship no longer holds unless Q is smaller for the

compound than for the solution phases. To examine whether

these conclusions are universally valid, assumption (B) was
eliminated in previous numerical analyses.51,52)_{Nevertheless,}

attention was focused on the relationship between the temperature dependency of the kinetics and those of the interdiﬀusion coeﬃcients of the constituent phases. As a consequence, assumption (A) still remained in these numer-ical analyses. Under such conditions, the validity of the

relationship between QK and Q could be conﬁrmed

con-clusively.51,52)_{As previously mentioned, however, the }

inter-metallic layer mainly consists of PdSn4 for y¼0, PdSn4

and Ag3Sn for y¼0:25{0:75, and Ag3Sn for y¼1. The

volume fraction of Ag3Sn in the intermetallic layer increases

with increasing value of y. The conclusions in previous

studies49–52)may not be necessarily valid for the growth of the intermetallic layer with such a two-phase microstructure.

Therefore, the dependence ofQK onyin Fig. 10 cannot be

interpreted in a straightforward manner.

3.6 Diﬀusion models

As shown in Figs. 8 and 9,Kdecreases by more than two

orders of magnitude with increasing value ofyfrom 0 to 1. In this section, simple diﬀusion models were used to explain quantitatively the dependence ofKony.

Cross-sectional microstructures of a hypothetical

interme-tallic layer composed of and phases are schematically

drawn in Fig. 11. Here, theandphases are the compounds

in the binary A–C and B–C systems, respectively, and the intermetallic layer possesses a uniform thickness of l. For simpliﬁcation, the following assumptions were adopted:

(a) the solubility range c of component C is equivalent

between theand phases; (b) the solubility is negligible

for components B and A in theandphases, respectively;

and (c) the diﬀusion coeﬃcient is independent of the

composition for theandphases. In Fig. 11, the interface

between the and phases is perpendicular to the

cross-section. On the other hand, the=interface is perpendicular to the intermetallic layer in Fig. 11(a), but parallel to that in Fig. 11(b). The models in Fig. 11(a) and (b) are hereafter

Fig. 9 The parabolic coeﬃcientKversus the annealing temperatureTfor

[image:7.595.56.285.67.290.2]y¼0{1.

[image:7.595.63.279.331.538.2]Fig. 10 The activation enthalpyQKversus the mol fractionyof Ag.

[image:7.595.323.527.549.748.2]J¼f1J1þf2J2: ð8cÞ

Here, J1 and J2 are the diﬀusional ﬂuxes of component C

across the and phases, respectively,D1 andD2 are the

interdiﬀusion coeﬃcients of theandphases, respectively,

and f1andf2are the volume fractions of theandphases,

respectively. The volume fraction fi is calculated by the

following equation.

fi¼

wi

w1þw2 ði¼1;2Þ ð9Þ

Here, w1 and w2 are the lengths of the and phases,

respectively, along the intermetallic layer. From eqs. (7) and (8), we obtain the relationship

D¼f1D1þf2D2: ð10Þ

On the other hand, the following relationships are valid for model II in Fig. 11(b):

J1¼ D1 c1

l1 ; ð11aÞ

J2¼ D2c2

l2 ð11bÞ

and

J¼J1 ¼J2: ð11cÞ

Here, l1 and l2 are the thicknesses of the and phases,

respectively, and c1 and c2 are the concentration

dif-ferences of component C in the and phases along the

distancesl1andl2, respectively. The following relationships

hold for these parameters:

l¼l1þl2 ð12aÞ

and

c¼c1þc2: ð12bÞ

In model II, the volume fraction fi is calculated from the

thicknessliby the following equation.

fi¼

li

l1þl2 ¼ li

l ði¼1;2Þ ð13Þ

Consequently, eqs. (7) and (11)–(13) yield the relationship

D¼ D1D2

f1D2þf2D1

: ð14Þ

using the values of K for y¼0 and 1 in Fig. 8. In this

calculation, y stands for the relative mol fraction of Ag

between Ag and Pd in the intermetallic layer, andK1andK2

correspond to the values ofKfor the binary Pd–Sn and Ag–

Sn systems, respectively. Since the volume diﬀusion of Sn in the Pd–Ag alloy is frozen out and the solubilities of Ag

and Pd in Sn are negligible at T ¼433{473K, the mol

fractionyof Ag in the Pd–Ag alloy is equal to the relative mol fraction owing to mass conservation. The calculations by eqs. (15) and (16) are shown as bold and thin curves,

respectively, in Fig. 8. As can be seen, K is much smaller

for model II than for model I at intermediate values of y.

This means that the growth rate of the intermetallic layer is sensitive to the morphology of microstructure for the intermetallic layer even at the same value ofy. Aty¼0:75, like model II, the overall direction of the lamellar micro-structure is rather parallel to the intermetallic layer as shown in Figs. 1 and 2. Nevertheless, most of the open symbols lie

well on the bold curves at y¼0{1. Thus, the dependence

of K on y is satisfactorily explained by model I. On the

other hand, the open rhombus withT ¼433K andy¼0:75

is located on the lower side of the bold dotted curve. The lamellar microstructure of the intermetallic layer is rather

granularly coarse at T ¼453{473K as shown in Fig. 2,

but lamellarly ﬁne at T¼433K. Therefore, at T ¼433K,

the diﬀusion process of model II considerably contributes to the growth of the intermetallic layer withy¼0:75.

4. Conclusions

The solid-state reactive diﬀusion in the ternary (Pd–Ag)/ Sn system was experimentally observed using the sandwich Sn/(Pd–Ag)/Sn diﬀusion couples containing 75 at% of Ag. The diﬀusion couples were prepared by the diﬀusion bonding technique, and then isothermally annealed in the temperature range between 433 and 473 K for various times up to 1365 h in the oil bath with silicone oil. Under such

conditions, the compound layer with the PdSn4þAg3Sn

two-phase lamellar microstructure is formed at the (Pd–Ag)/ Sn interface in the diﬀusion couple. The overall longitudinal

direction of the PdSn4 and Ag3Sn lamellae is almost

a relationship is denominated the parabolic relationship. Furthermore, the interlamellar spacing increases in propor-tion to a power funcpropor-tion of the annealing time, and hence grain growth takes place in the compound layer. Conse-quently, the growth of the compound layer is governed by volume diﬀusion. Since the exponent of the power function is close to 1/3, a mechanism similar to Ostwald ripening may control the grain growth. The parabolic coeﬃcient for the ternary (Pd–Ag)/Sn system with a Ag concentration of 75 at% is 6.7, 11.8 and 22.4% of that for the binary Pd/Sn system at 433, 453 and 473 K, respectively. Thus, the growth of the compound during the solid-state reactive diﬀusion in the Pd/Sn system is considerably decelerated by the addition of Ag with 75 at% into Pd.

Acknowledgements

The authors are grateful to Messrs. K. Sakamoto and N. Kurokawa at Tyco Electronics AMP Co. Ltd., Japan for stimulating discussions. 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.

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