1

Anisotropic thermal expansion of Ni3Sn4, Ag3Sn, Cu3Sn,

Cu6Sn5 and βSn

J.W. Xian1, G. Zeng1,2, S.A. Belyakov1, Q.Gu3, K. Nogita2, C.M. Gourlay1

1 Department of Materials, Imperial College, London. SW7 2AZ. UK 2 Nihon Superior Centre for the Manufacture of Electronic Materials (NS CMEM), School of Mechanical and

Mining Engineering, The University of Queensland, Brisbane, QLD 4072, Australia 3 Powder Diffraction Beamline, The Australian Synchrotron, Clayton, VIC 3168, Australia

Abstract

The directional coefficient of thermal expansion (CTE) of intermetallics in electronic

interconnections is a key thermophysical property that is required for microstructure-

level modelling of solder joint reliability. Here, CTE ellipsoids are measured for key

solder intermetallics using synchrotron x-ray diffraction (XRD). The role of the crystal

structure used for refinement on the CTE shape and temperature dependence is

investigated. The results are used to discuss the Sn-IMC orientation relationships

(ORs) that minimise the in-plane CTE mismatch on IMC growth facets, which are

measured with electron backscatter diffraction (EBSD) in solder joints on Cu and Ni

substrates. The CTE mismatch in fully-intermetallic joints is discussed, and the

relationship between the directional CTE of monoclinic and hexagonal polymorphs of

Cu6Sn5 is explored.

Keywords: A. intermetallics; B. anisotropy; C. joining (soldering); D. interfaces; F.

diffraction (X-ray), electron backscatter diffraction;

Contact Details

* Corresponding author

jingwei.xian@imperial.ac.uk

Tel: +447724714613

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1. Introduction

Thermo-mechanical fatigue is a common failure mechanism in Pb-free solder joints

[1-3]. One important factor is the mismatch in coefficient of thermal expansion (CTE)

which results in stress cycling during Joule heating and subsequent cooling. In

solder joints, there is CTE mismatch between surface mount components and the

circuit board, between the different phases in the joint, and at grain boundaries within

a polycrystalline phase due to the anisotropic CTE of non-cubic phases [3].

In many Pb-free solder joints (e.g. ball grid arrays (BGAs)), the majority of the joint is

Sn phase. Tetragonal Sn is well-known to exhibit strongly anisotropic thermal

expansion, with CTE along [001] approximately twice the CTE along [100]=[010] [4-

11]. During the thermal cycling of polycrystalline Sn, this CTE anisotropy leads to

plastic deformation concentrated near grain boundaries where there is CTE

mismatch and the expansion is constrained [12, 13]. In the more complex situation of

BGA joints, CTE mismatch-induced cracking near the chip-side solder-substrate

interface is a widespread failure mode and occurs by a combination of creep,

recovery and recrystallization [3, 14-17].

Additionally, Sn-based intermetallic compounds (IMCs) are present in solder joints,

both as an interfacial layer(s) between the metallic substrate and solder and also as

IMC particles within the Sn matrix of the bulk solder. These IMCs play an important

role in thermo-mechanical fatigue in addition to the Sn phase [18] and, with the

continuous miniaturisation of solder joints, IMCs are occupying an increasing

proportion of joints. In the case of micro-bumps or transient liquid phase soldering,

the joint often consists entirely of intermetallic phase(s). Depending on the

approach, this is often Ni3Sn4 [19] , a Cu6Sn5-Cu3Sn mixture [20] or Ag3Sn [21].

3

Thermal cycling is a potentially larger reliability concern in fully-intermetallic joints

because they often experience larger temperature changes as they can operate at

higher temperature than joints containing Sn phase [19]. Thus, the CTE of

intermetallics in solder joints is a key thermophysical property that needs to be

measured.

Past reports on the CTE of intermetallics relevant to soldering have only measured

the mean CTE (usually as the linear CTE) [22-24] and, therefore, the directional CTE

is not known for most solder intermetallics. However, intermetallics such as Ni3Sn4,

Ag3Sn, Cu3Sn and Cu6Sn5 are non-cubic and will be anisotropic. The current lack of

directional CTE data is an obstacle to (i) the design of optimum IMC microstructures

for fully-intermetallic joints and (ii) the development of microstructure-level models of

thermal cycling response in BGA and flip-chip joints. For the second example, it will

be necessary to include the eutectic IMC particles, the large primary IMCs and the

IMC layer between the solder and substrate in addition to the Sn grains. Thus, the

directional CTE data (i.e. the CTE as a function of IMC crystal orientation and

temperature) are required for each IMC in a solder joint.

In this paper, we first use synchrotron powder XRD to measure the directional CTE

of Ni3Sn4, Ag3Sn, Cu3Sn, Cu6Sn5 and compare these with the directional CTE of

βSn. We next explore the influence of the hexagonal to monoclinic phase

transformation on the CTE of Cu6Sn5, and then combine the CTE data with

measurements of the facets of the IMCs in solder joints to explore the in-plane CTE

mismatch at IMC-Sn interfaces.

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2. Methods

2.1 IMC powder preparation

Ni3Sn4 powder was produced from a near-eutectic Sn-0.16wt%Ni ingot. Previous

work has shown that solidification of Sn-0.16Ni leads to the formation of a

metastable Sn-NiSn4 eutectic [25, 26] and, therefore, a post-solidification heat

treatment of 225°C (~7K below the eutectic temperature) for 168 hours was used to

ensure full transformation to stable Ni3Sn4. The βSn matrix was then selectively

dissolved in a solution of 5% NaOH and 3.5% orthonitrophenol in distilled H2O at

~60C and the released Ni3Sn4 particles were then washed in ethanol.

Ag3Sn powder was produced from a near-eutectic Sn-3.5wt%Ag ingot that was given

a heat treatment of 150°C for 54 hrs before the βSn matrix was selectively dissolved

and the released Ag3Sn particles were washed in ethanol.

Cu3Sn was studied as a mixed Cu3Sn-Cu6Sn5 powder, prepared from a cast Sn-

30wt%Cu ingot. The βSn matrix was then selectively dissolved and the remaining

intermetallic phases were washed in ethanol and crushed into powder in an agate

mortar.

Cu6Sn5 powder was produced by the method given in [27]. Note that Cu6Sn5

undergoes a hexagonal monoclinic transformation at ~186°C and the hexagonal

polymorph can be stabilised by doping with elements such as Ni, Zn and Au [27, 28].

For comparison with binary Cu6Sn5, a hexagonal stabilised (Cu,Ni)6(Sn,Zn)5 solid

solution powder was prepared using the method given in [27, 28].

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βSn powder was produced by taking 99.99% purity Sn from a previous study [11],

pulverising it in an agate mortar and then transforming it back to Sn by holding at

80°C for 150 hrs in a Pyrex ampoule.

2.2 XRD measurements

Powders were placed into 0.3mm capillaries and tested on the Powder Diffraction

beamline at the Australian Synchrotron at 30-305C using a Cyberstar hot-air blower.

High resolution X-ray powder diffraction data were collected using a Mythen-II

detector with a 15 keV beam (wavelength 0.8265Å) in the 2 range 10-80 at

ambient pressure. Once the desired temperature was reached, the sample was held

isothermally for ten minutes for data collection. A Si standard (NIST640C,

a=5.43119Å, Fd-3m, median particle size 4.9 µm) or LaB6 standard (NIST660b, a=

4.15689Å, Pm-3m, particle size ~2-40 µm) was measured at room temperature for

wavelength calibration.

2.3 CTE determination

Rietveld Refinement was performed in TOPAS 4.2 (Bruker-AXS, Germany). The

model structures that were refined were taken from the following references: Ni3Sn4

[29], Ag3Sn [30], mS44-’Cu6Sn5 [31], Cu6Sn5 [32, 33], oS80-Cu3Sn [34] and Sn

[35].

2θ zero error was determined from a standard 0.3 mm capillary of Si/LaB6 standard

sample for each beamtime. Instrument configuration functions were refined based on

standard sample patterns and they were the same and fixed across all XRD

6

patterns. Peak shapes of XRD patterns were described using the Fundamental

Parameters (FP) approach and the background, sample displacement corrections

[36] and scale factors were refined independently for each pattern.

Since the approach in this work is to use the sets of temperature dependent d-

spacings to calculate thermal expansion, Pawley fitting can be used to find a set of

I(hkl) at each temperature instead of performing a full Rietveld refinement at each

temperature. Pawley fitting was used for Cu3Sn and Cu6Sn5 in this work to find dhkl

vs. T without the need for a full refinement at every temperature of the complex

superstructures (mS44-Cu6Sn5 and oS80-Cu3Sn). Rietveld refinement was used to

find dhkl vs. T for all other phases. Furthermore, the XRD data for Cu3Sn were

Pawley fit twice, first assuming the oS80-Cu3Sn superstructure [34] and then

assuming the oP8-Cu3Sn structure [37] from which the superstructure is derived, to

explore the influence of the fitting structure on the resulting CTE data.

The conversion of vectors from crystal coordinates to Cartesian coordinates is

defined here such that the Z-axis is parallel to c and the X-axis is in the a-c plane for

all phases. The resulting conversion matrix A is given in Eq.1:

[𝑋𝑌𝑍] = [

𝐴11 𝐴12 00 𝐴22 0

𝐴31 𝐴32 𝐴33

] ∙ [𝑢𝑣𝑤

] Eq.1

where 𝐴×[𝑢𝑣𝑤] is the basis transformation, while (𝐴−1)𝑇×(ℎ𝑘𝑙) is the reciprocal

transformation which is equivalent to 𝐴×[ℎ𝑘𝑙]𝑝𝑙𝑎𝑛𝑒 𝑛𝑜𝑟𝑚𝑎𝑙. The components of matrix

A are given in Supplementary Information Part 1.

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All 𝑑ℎ𝑘𝑙 data with 2θ smaller than 80 were used for the analysis. The change in each

𝑑ℎ𝑘𝑙 with temperature was expressed as a 2nd order polynomial function (Eq. 2),

which gave least squares R2 >0.999 for all phases.

𝑑ℎ𝑘𝑙 = 𝐶0 + 𝐶1𝑇 + 𝐶2𝑇2 Eq.2

The value of 𝐶 coefficients were determined by linear regression techniques. The

CTE, 𝛼ℎ𝑘𝑙, along each hkl plane normal was then obtained by Eq.3:

𝛼ℎ𝑘𝑙 =1

𝑑ℎ𝑘𝑙

𝑑(𝑑ℎ𝑘𝑙)

𝑑𝑇=

𝐶1+2𝐶2𝑇

𝐶0+𝐶1𝑇+𝐶2𝑇2 Eq.3

For all planes in the XRD spectrum, values of 𝛼ℎ𝑘𝑙 along corresponding plane

normals facilitate the derivation of a CTE tensor. The relationship between 𝛼ℎ𝑘𝑙

values, XYZ Cartesian directions (derived from hkl plane normals) and the CTE

tensor (𝛼𝑖𝑗 components) is given by Eq.4 [38]:

[

𝛼ℎ𝑘𝑙1

⋮⋮

𝛼ℎ𝑘𝑙𝑛

] = [

𝑋12 𝑌1

2 𝑍12 𝑋1𝑌1 𝑌1𝑍1 𝑋1𝑍1

⋮⋮

𝑋𝑛2 𝑌𝑛

2 𝑍𝑛2 𝑋𝑛𝑌𝑛 𝑌𝑛𝑍𝑛 𝑋𝑛𝑍𝑛

] ∙

[ 𝛼11

𝛼22

𝛼33

2𝛼12

2𝛼23

2𝛼13]

Eq.4

For monoclinic crystals (the lowest symmetry considered here), 𝛼ℎ𝑘𝑙 data for at least

four planes are required to find the independent 𝛼𝑖𝑗 components (𝛼12 and 𝛼23 are

zero here), while the higher symmetry crystals need data for fewer planes. In this

work, there is 𝛼ℎ𝑘𝑙 data from numerous planes, which leads to an over-determined

system of linear equations for the CTE tensor that was solved in Matlab using matrix

left division. Notice that 𝛼11, 𝛼22, 𝛼33 are along the CTE crystallographic basis

vectors 𝑂𝐴 ,𝑂𝐵 ,𝑂𝐶 respectively.

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Eigenvalues (denoted E1, E2, E3 here) and eigenvectors of the CTE tensor were

then calculated from the 𝛼𝑖𝑗 components. The eigenvalues were used to plot 3D

thermal expansion ellipsoids as described in ref. [38, 39], in which the CTE 𝛼𝑟 along

any radius vector of a unit sphere (x’,y’,z’) is given as:

𝛼𝑟 = 𝐸1𝑥′𝑥′ + 𝐸2𝑦′𝑦′ + 𝐸3𝑧′𝑧′ Eq.5

The Cartesian coordinates of the end point of the radius vector 𝛼𝑟 are then given by:

𝑥 = 𝛼𝑟𝑥′, 𝑦 = 𝛼𝑟𝑦

′, 𝑧 = 𝛼𝑟𝑧′ Eq.6

These (x,y,z) points together form the surface of the thermal expansion ellipsoid.

2.4 Solder joint fabrication and IMC characterisation

Sn-0.7Cu, Sn-3.5Ag and Sn-4Ag-0.5Cu alloy (wt%) were prepared by mixing

99.9%Sn with Sn-10%Cu and/or Sn-99%Ag. The mixture was melted at 450C,

solidified in a graphite crucible, rolled and punched into discs, and remelted on a hot

plate at 300C to produce 500 m solder balls using surface tension. The resulting

solder balls were then reflowed on different substrates with a ROL-1 tacky flux to

make Sn-0.7Cu/Cu, Sn-4Ag-0.5Cu/Cu and Sn-3.5Ag/Ni joints. The joints were then

given a final reflow by heating at 0.16 K/s to 250C and cooling at 0.33 K/s in a

Mettler Toledo DSC1.

Cu6Sn5, Ag3Sn and Ni3Sn4 single crystals were extracted from the joints by selective

etching of Sn using a solution of 5% NaOH and 3.5% orthonitrophenal in distilled

water. A Zeiss Auriga field emission gun SEM equipped with a Bruker e-FlashHR

electron backscatter diffraction (EBSD) detector was used for IMC characterization.

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Primary intermetallic crystals were extracted and laid flat on an SEM stub to identify

the major facets with EBSD. Intermetallic interfacial layers were studied directly by

EBSD.

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3. Results

3.1 Rietveld refinement

Figure 1 shows the full pattern Rietveld refinement of Ni3Sn4 at 30C in the 2 range

10-80, where the red spectrum is the Ni3Sn4 model structure from [29] refined to the

experimental blue spectrum. The difference plot is shown in grey and lower blue

vertical bars align with the corresponding difference peaks. In the magnified insert, it

is clear that the refined and measured profiles vary only in the magnitudes of peaks,

reflecting the goodness of refinement and accuracy of lattice parameters. Full pattern

Rietveld refinements of the other phases are shown in the Supplementary

Information (SI-Figures 1-4) and Table 1 summarises the resulting crystallographic

parameters and weighted-profile R-factors, Rwp, near room temperature.

Figure 1. Full pattern Rietveld refinement and difference plot of Ni3Sn4. (Figures for

other phases are shown in SI-Figures 1-4).

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Table 1. Crystallographic parameters and weighted-profile R-factor, Rwp, from the Rietveld refinements of six solder phases. Difference plots are shown in Figure 1 and SI-Figures 1-4.

Phase Pearson

symbol Space group Cell parameters

T

[C]

Volume

[Å3]

Density

gcm-3 R

wp Refined

from Ni

3Sn

4 mS14 C12/m1 a=12.1997

b=4.0606 c=5.2221

β=105.2531

30 249.5795 8.724 5.76 [29]

Ag3Sn oP8 Pmmn a=4.7831

b=6.0004 c=5.1664

30 148.2761 9.907 6.05 [30]

η-Cu6Sn

5 hP4 P6

3/mmc a=4.2225

c= 5.1172

200 79.0145 8.194 8.58 [32,33]

η'-Cu6Sn

5 mS44 C12/c1 a=11.0311

b=7.2851 c=9.8295

β=98.8245

25 780.5735 8.319 7.26 [31]

Cu3Sn oS80 Cmcm a=5.5264

b=47.7886 c=4.3278

30 1142.960 9.026 5.77 [34]

βSn tI4 l41/amd a=5.8314

c=3.1817 30 108.1932 7.288 7.30 [35]

For phases with multiple proposed crystallographies in the literature (i.e. Ag3Sn and

Cu3Sn), the data in Table 1 is for the structure that could be best refined to our XRD

data. In the case of Ag3Sn, three model structures [30, 40, 41] were used for

Rietveld refinement and that of Rossi et al. [30] was confirmed: for example, the

(022) peak shown in SI-Figure 1 could not be satisfactorily fit by the other structures.

Note, in Table 1, that hexagonal hP4-Cu6Sn5 data are given at 200C because this

phase is only stable at >186C [31, 32, 42].

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3.2 Ni3Sn4 CTE

The Ni3Sn4 lattice parameters and cell volume data at 30~250C are given in Figure

2 with second order polynomial fits. Table 2 lists the fitting coefficients. R2>0.9999 for

a,b,c and V, and >0.999 for β.

Figure 2. Ni3Sn4 lattice parameters as a function of temperature. Error bars are

standard deviations from Rietveld refinement of PXRD data. A second order

polynomial fit is applied to each. Fit results are given in Table 2. (Equivalent Figures

for other phases are shown in SI-Figures 5-8).

Table 2. Ni3Sn

4 lattice parameters and cell volume versus temperature, fit to 𝑎 =

𝐶0 + 𝐶1𝑇 + 𝐶2𝑇2 in Å and C.

C0 C1

C2 R

2 a [Å] 12.195 1.64E-04 9.21E-08 0.99993 b [Å] 4.059 5.45E-05 1.62E-08 0.99994 c [Å] 5.220 6.69E-05 1.72E-08 0.99993 ° 105.255 -4.12E-05 -2.57E-07 0.99966 V [Å3

] 249.276 9.92E-03 4.28E-06 0.99992

Figure 3 shows the thermal expansion behaviour of Ni3Sn4. Note that the axis limits

of plots are fixed throughout Figures 3-7 for comparison of all phases. Figure 3(a)

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compares the measured mean CTE (solid line) with literature values [22, 29, 43]

(symbols). Furuseth’s data [29] has been reanalysed by digitizing their original unit

cell-temperature plot and ignoring data above 350C due to an abrupt increase

above 350C. It can be seen that the slope of the mean CTE in this work is near-

parallel to all literature values and is within ~5% of the past data. Figure 3(b) shows

the CTE eigenvalues (E1, E2 and E3) of the directional CTE as a function of

temperature calculated by the tensor method; it can be seen that Ni3Sn4 expands

anisotropically and the CTE anisotropy increases with increasing temperature. In

Figure 3(c), the CTE shape of Ni3Sn4 in the (010) plane at 110C is visualised based

on two methods; the solid line has been calculated by the tensor method [39] and the

‘x’ symbols have been calculated from changes in individual d-spacings (dhkl) at

100C and 120C. All d-spacings with plane normal in (010) are included. Error bars

are given in the a and c directions, which come from standard deviations of refined

lattice parameters. It can be seen that the CTE shapes obtained by the two methods

are very similar and the result from the tensor method is within the error of the

individual d-spacing method, showing the validity of the experimental approach. In

Figure 3(d), the CTE ellipsoid at 180C is plotted in a Cartesian coordinate frame

with red (x-y-z) axes and the monoclinic unit cell axes (a-b-c) are oriented following

the definition in Eq.1. This can be understood by observing the red axes and the blue

unit cell wireframe, where z is parallel to 𝑂𝐶 and x is in the front 𝑂𝐴 ,𝑂𝐶 plane.

Comparing Figure 3(c-d) shows that the general CTE shape is maintained from 110

to 180C. Notice that, as Ni3Sn4 is monoclinic, only one crystallographic basis vector,

𝑂𝐵 , is an eigenvector (corresponding to E2), whereas E1 is ~5.2 off [203] and E3 is

~0.3 off [107].

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Figure 3. Ni3Sn4. (a) Measured mean CTE compared with literature values. (b) CTE

eigenvalues versus temperature. (c) (010) CTE at 110C. The solid line is calculated

by the tensor method and ‘x’s are calculated from changes in individual d-spacings

of all planes with normal in (010) at 100C and 120C. Error bars result from

standard deviations of refined lattice parameters. (d) CTE ellipsoid at 180C in the

Cartesian coordinate system (red axes), relative to the monoclinic unit cell (blue

wireframe).

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3.3 Ag3Sn CTE

The Ag3Sn lattice parameters and cell volume data in the range 30~250°C are

summarised in Table 3 and the data are plotted in SI-Figure 5. The R2>0.9999 is the

highest among the phases studied in this work.

Table 3. Ag3Sn lattice parameters and cell volume versus temperature, fit to 𝑎 =

𝐶0 + 𝐶1𝑇 + 𝐶2𝑇2 in Å and C. (Lattice parameters versus temperature plots are

shown in SI-Figure 5).

C0 C

1 C

2 R

2 a [Å] 4.780 8.58E-05 3.65E-08 0.99999 b [Å] 5.996 1.39E-04 1.43E-08 0.99990 c [Å] 5.164 9.05E-05 4.32E-08 0.99999 V [Å3

] 148.01 8.69E-03 2.93E-06 0.99998

Figure 4(a) shows the measured mean CTE of Ag3Sn. We found no past data (e.g.

linear CTE) for comparison with our mean CTE measurements, which is surprising

for an intermetallic in widespread industrial use. Figure 4(b) shows the CTE

eigenvalues versus temperature. Note that the magnitude of E2 and E3 are very

similar to each other at all temperatures and that Ag3Sn becomes more anisotropic

with decreasing temperature. In Figure 4(c), the Ag3Sn CTE shape in the (100) plane

at 110C is visualised based on the tensor method and on the individual d-spacings

method, which can be seen to be in good agreement. The full tensor ellipsoid at

180C and the unit cell orientation are plotted in Figure 4(d). When examining Figure

4(d), note that, as Ag3Sn is orthorhombic, the three crystallographic basis vectors

are the three eigenvectors of the CTE tensor.

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Figure 4. Ag3Sn. (a) Measured mean CTE. (b) CTE eigenvalues versus temperature.

(c) (100) CTE at 110C. Solid line = tensor method, symbols = changes in individual

d-spacings. Error bars result from standard deviations of refined lattice parameters.

(d) CTE ellipsoid at 180C in the Cartesian coordinate system (red axes), relative to

the orthorhombic unit cell (blue wireframe).

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3.4 Cu3Sn CTE

The Cu3Sn lattice parameters and cell volume data in the range 30~250°C are

summarised in Table 4 based on Pawley fitting of the oS80-Cu3Sn superstructure

(and the data are plotted in SI-Figure 6). The R2 values in Table 4 are slightly lower

than for the other phases but are still better than 0.999.

Table 4. Cu3Sn lattice parameters and cell volume versus temperature, fit to 𝑎 =

𝐶0 + 𝐶1𝑇 + 𝐶2𝑇2 in Å and C. (Lattice parameters versus temperature plots are

shown in SI-Figure 6).

C0 C1

C2 R

2 a [Å] 5.524 7.95E-05 9.45E-08 0.99911 b [Å] 47.765 8.12E-04 3.96E-07 0.99983 c [Å] 4.325 7.34E-05 1.66E-08 0.99970 V [Å

3] 1141.09 5.51E-02 3.49E-05 0.99994

Figure 5(a) shows that the measured mean CTE of oS8-Cu3Sn is within ~2% of the

values of linear CTE reported by Jiang et al. [22]. Figure 5(b) plots the CTE

eigenvalues versus temperature, showing that E1 of Cu3Sn is marginally higher than

E2 and E3 from 30-305C and E2 and E3 are interchanged at ~77°C. In Figure 5(b),

Cu3Sn has only weakly anisotropic CTE at all temperatures studied. Figure 5(c)

shows the CTE shape of (001) in Cu3Sn with both the tensor method and the

individual d-spacings method. The Cu3Sn (001) is chosen because it contains the

longest axis, b, and has the most individual d-spacing data to compare with the solid

line ellipse from the tensor method. It can be seen that the individual d-spacing data

are scattered significantly from the ellipse calculated by the tensor method, however,

the uncertainty is much lower when only high intensity (with normalised intensity

>1.5) peaks are considered as shown by the red symbols. Since the low intensity

18

peaks (with normalised intensity <1.5) are associated with the superstructure of

oS80-Cu3Sn and can be affected by the noise in the PXRD data, only peaks with

normalised intensity >1.5 were used for CTE determination.

Figure 5. Cu3Sn. (a) Measured mean CTE compared with literature values. (b) CTE

eigenvalues versus temperature. (c) (001) CTE at 110C. Solid line = tensor method,

‘x’s = changes in individual d-spacings where red symbols denote hkl peaks with a

high peak. Error bars result from standard deviations of refined lattice parameters.

(d) CTE ellipsoid at 180C in the Cartesian coordinate system (red axes), relative to

the orthorhombic unit cell (blue wireframe).

It was found that if the simpler oP8 [37] structure of Cu3Sn was used as the model

structure, the mean CTE is nearly unchanged but the directional CTE became much

more anisotropic. This shows how the derived CTE shape and temperature

dependence are sensitive to the model structure used for refinement in the PXRD

method and caution needs to be taken when selecting the model structure for the

analysis. The oS80 superstructure was used here because the small peaks (e.g. the

19

(2 20 0) peak shown in SI-Figure 2) in the PXRD data could only be fit well by this

superstructure and not by the simper oP8 structure, even though oP8 gave similarly

low rwp values.

20

3.5 Cu6Sn5 CTE

Cu6Sn5 has the added complexity of a monoclinic to hexagonal phase transformation

on heating. Figure 6(a) shows the mean CTE data of Cu6Sn5, where only a single

datapoint is shown for monoclinic ’Cu6Sn5 (blue symbol) at 100C and for

hexagonal Cu6Sn5 (red symbol) at 195C because the ’ phase transformation

leads to fewer usable measurements before and after the phase change. The

monoclinic ’Cu6Sn5 datapoint (blue symbol) is in good agreement with past work on

the linear CTE of Cu6Sn5 in Figure 6(a). The hexagonal Cu6Sn5 datapoint (red

symbol) is higher than the monoclinic data (extrapolated to the same temperature).

However, the hexagonal Cu6Sn5 datapoint is based on measurements at only two

temperatures and, therefore, should be treated with caution.

More reliable hexagonal Cu6Sn5 data was obtained from stabilised hexagonal

(Cu,Ni)6(Sn,Zn)5, which has a hP4-Cu6Sn5 structure at all temperatures [28]. The

(Cu,Ni)6(Sn,Zn)5 lattice parameters and cell volume data in the temperature range

30~250°C are given in Table 5 and the data are shown in SI-Figure 7.

Table 5. Stabilised (Cu,Ni)6(Sn,Zn)

5 lattice parameters and cell volume versus

temperature, fit to 𝑎 = 𝐶0 + 𝐶1𝑇 + 𝐶2𝑇2 in Å and C. (Lattice parameters versus

temperature plots are shown in SI-Figure 7).

C0 C1

C2 R

2 a [Å] 4.195 7.50E-05 3.15E-08 0.99952

c [Å] 5.112 10.90E-05 3.58E-07 0.99989

V [Å3] 77.897 4.44E-03 1.83E-06 0.99971

Figure 6(a) compares the measured mean CTE (solid line) for (Cu,Ni)6(Sn,Zn)5 with

literature values on binary Cu6Sn5 (symbols) [22, 43]. (Cu,Ni)6(Sn,Zn)5 is ~8% higher

21

than past work on binary Cu6Sn5 and has a similar slope. Figure 6(b) shows the

(Cu,Ni)6(Sn,Zn)5 CTE eigenvalues versus temperature where E1 (=𝛼33), E2=E3 and

the anisotropy (E1/E3) remain similar at all temperatures. Figure 6(c)-(f) compare the

CTE ellipsoids of hexagonal (Cu,Ni)6(Sn,Zn)5 and monoclinic ’Cu6Sn5 in (c) and

(e) respectively, both in the (010) plane; and Figure 6(d) and (f) are 3D plots of the

CTE ellipsoids.

Note that the unit cell orientations are plotted relative to the Cartesian orientation for

both phases following the convention in section 2.3 and appear different when

viewed in this Cartesian frame. The link between the CTE of hexagonal and

monoclinic Cu6Sn5 is discussed in section 4.1.

22

Figure 6. Cu6Sn5. (a) Measured mean CTE of (Cu,Ni)6(Sn,Zn)5 compared with

literature values on Cu6Sn5. (b) CTE eigenvalues versus temperature. (c,e) (010)

CTE of Cu6Sn5 at 110C and ’Cu6Sn5 at 100C respectively. Solid line = tensor

method, ‘x’s = changes in individual d-spacings. Error bars result from standard

deviations of refined lattice parameters. (d,f) CTE ellipsoids of Cu6Sn5 at 180C and

’Cu6Sn5 at 100C in the Cartesian coordinate system (red axes), relative to crystal

axes.

23

3.6 βSn CTE

The CTE of Sn is included here to enable a comparison with the intermetallics. Fits

to the βSn lattice parameters and cell volume data in the range 30~250C are given

in Table 6 and the data are plotted in SI-Figure 8.

Table 6. Sn lattice parameters and cell volume versus temperature, fit to 𝑎 =𝐶0 + 𝐶1𝑇 + 𝐶2𝑇

2 in Å and C. (Lattice parameters versus temperature plots are shown in SI-Figure 8).

C0 C

1 C

2 R

2 a [Å] 5.829 8.29E-05 7.45E-08 0.99985 c [Å] 3.179 9.10E-05 9.25E-08 0.99995 V [Å3

] 107.994 6.16E-03 6.10E-06 0.99991

Figure 7(a) compares the measured mean CTE (solid line) with literature values

(symbols). The slope of the measured result is similar to most of the past data and is

within ~4% of the recommended values of Touloukian [44]. Note the outlying data of

Deshpande et al. [8] where the CTE is an increasing function of temperature as

opposed to the near-linear CTE vs T data of our and other researchers

measurements. The near-linear relationship results from a 2nd order polynomial fit

and the definition of 𝛼ℎ𝑘𝑙 in Eq.3, where the denominator is near-constant making

Eq.3 near-linear in T. Note that a 3rd order polynomial fit to the lattice parameters or

d-spacings would lead to a non-linear CTE curve versus temperature, i.e.

Deshpande data. However, for the shape of the data, there is no basis for fitting the

measured data to a 3rd order polynomial function and the near-linear CTE vs T data

of βSn is confirmed. Figure 7(b) shows the CTE eigenvalues versus temperature

where the ratio of E1/E3 is >2 and increases with increasing temperature. In Figure

7(c), the CTE shape of βSn in the (010) plane at 110C is plotted using the tensor

24

method and the individual d-spacings method. It can be seen that a ‘peanut’ shape is

obtained by the two methods. Note that, with the tensor method, a ‘peanut’ shape is

obtained whenever the CTE anisotropy (E1/E3) exceeds 1.5.

Figure 7. Sn. (a) Measured mean CTE compared with literature values. (b) CTE

eigenvalues versus temperature. (c) (010) CTE at 110C. The solid line is calculated

by the tensor method and ‘x’s are calculated from changes in individual d-spacings

of all planes with normal in (010) at 100C and 120C. Error bars result from

standard deviations of refined lattice parameters. (d) CTE ellipsoid at 180C in the

Cartesian coordinate system (red axes), relative to the tetragonal unit cell (blue

wireframe).

25

3.7 Recommended values for the directional CTE

Recommended values for the temperature and orientation dependent CTE of Ni3Sn4,

Ag3Sn, Cu3Sn, (Cu,Ni)6(Sn,Zn)5, ’Cu6Sn5 and Sn are given in Table 7 based on

the measurements and analysis in sections 3.2 to 3.6. The data are presented

following the equation 𝐴0 + 𝐴1𝑇, where 𝐴0 is the extrapolated CTE at 0C in K-1, 𝐴1 is

the slope and T is the temperature in C. Table 7 gives the eigenvectors in the

Cartesian form following the convention z||c and x in the a-c plane. Data for Cu6Sn5

are given for monoclinic ’Cu6Sn5 at 100C only, and hexagonal-stabilised Cu6Sn5

is given from 30-240C for (Cu,Ni)6(Sn,Zn)5 (i.e. doped with both Ni and Zn). When

using these data, note the multipliers are different for 𝐴0 (×10−6) and 𝐴1 (×10−9).

Table 8 lists the directions of E1, E2 and E3 with respect to the crystal axes.

Table 7. Summary of the CTE tensor components as a function of temperature. Data

are presented as 𝛼𝑖𝑗(𝑇) = 𝐴0 + 𝐴1×𝑇 where A is in units of strain and T is in C, so

that A0 is the extrapolated CTE component at 0C. Note the multipliers ( x10

-6 or

x10-9

). Data for monoclinic ’Cu6Sn

5 are given at 100C only.

Ni3Sn4

30-250C βSn

30-230C Ag3Sn

30-255C Cu3Sn

30-305C (Cu,Ni)6(Sn,Zn)5

30-240C ’Cu6Sn5

100C A0

[10-6

] A1

[10-9

] A0

[10-6

] A1

[10-9

] A0

[10-6

] A1

[10-9

] A0

[10-6

] A1

[10-9

] A0

[10-6

] A1

[10-9

] [10

-6]

𝛼11 13.708 16.39 14.195 25.53 17.812 16.06 16.292 17.83 17.890 14.57 19.195 𝛼22 13.368 8.09 14.195 25.53 23.677 0.39 16.600 17.31 17.890 14.57 17.684 𝛼33 12.746 7.25 28.662 56.79 17.474 16.87 16.553 14.45 21.292 13.76 18.695 𝛼13 0.283 3.09 0 0 0 0 0 0 0 0 -0.700 𝐸1 13.784 17.34 𝛼33 𝛼33 𝛼22 𝛼22 𝛼22 𝛼22 𝛼33 𝛼33 19.688 𝐸2 13.368 8.09 𝛼11=22 𝛼11=22 𝛼11 𝛼11 𝛼33/11* 𝛼33/11* 𝛼11=22 𝛼11=22 18.202 𝐸3 12.669 6.31 𝛼11=22 𝛼11=22 𝛼33 𝛼33 𝛼11/33* 𝛼11/33* 𝛼11=22 𝛼11=22 17.684

𝛼𝑚𝑒𝑎𝑛 13.274 10.58 19.017 35.95 19.654 11.11 16.482 16.53 19.024 14.30 18.525 * E2 and E3 are interchanged at ~77.2°C as shown in Figure 5(b).

26

Table 8. Directions of CTE the eigenvectors with respect to the crystal axes.

Ni3Sn4 110C

βSn 30-230C

Ag3Sn 30-255C

Cu3Sn 30-90C & 90-305C

(Cu,Ni)6(Sn,Zn)5 30-240C

’Cu6Sn5 100C

E1 [203] ~5.2° [001] [010] [010] & [010] [0001] [201]~4.0°

E2 [010] [UV0] [100] [001] & [100] [uvt0] [102]~3.9°

E3 [107]~0.3° [VU0] [001] [100] & [001] [u1v1t10]† [010]

† u ∙ u1 + v ∙ v1 + t ∙ t1 = 0.

27

4. Discussion

4.1 CTE of Cu6Sn5 polymorphs

The typical cooling rate at the end of soldering is sufficient to retain Cu6Sn5 in the

hexagonal polymorph [45] and this metastable Cu6Sn5 can transform into

monoclinic ’Cu6Sn5 during Joule heating in service (the ‘nose’ of the T-T-T curve is

at ~150C [45]). Therefore, it is useful to consider (i) how the thermal expansion

differs in the hexagonal and monoclinic Cu6Sn5 phases and (ii) how the

transformation affects the expansion behaviour.

To compare the CTE of the two Cu6Sn5 polymorphs, we note that monoclinic

’Cu6Sn5 can be considered a superstructure-ordering of the hexagonal Cu6Sn5

phase [31] and, directions in one phase can be related to directions in the other by

the transformation matrix in Eq. 7:

[𝑢𝑣𝑤

]

𝜂′

= [0.2011 −1.006 0.4015

0 −0.5022 00.4021 −0.2010 −0.2007

] ∙ [𝑢𝑣𝑤

]

𝜂

Eq.7

Figure 8(a) is a plot of the hexagonal and monoclinic Cu6Sn5 CTE ellipsoids in the

(010) plane after the transformation matrix has been applied to make equivalent

crystallographic directions co-incident. The major CTE eigenvalue in hexagonal

Cu6Sn5 is in the [0001]Cu6Sn5 direction (Figure 6) which corresponds to

[201]’Cu6Sn5. The direction of the measured major CTE eigenvalue in monoclinic

’Cu6Sn5 is within 4.0° of [201]’Cu6Sn5. Indeed, the principal axes of the CTE tensor

have almost the same orientation when and ’ are oriented in this

crystallographically equivalent frame of reference, showing that there is near-

equivalence in the CTE anisotropy.

28

Figure 8. CTE and crystallographic similarities between Cu6Sn5 and ’Cu6Sn5. (a)

CTE of (0110)-stabilised and (010)’ with [0001] || [201] ’. (b) Expanded hexagonal

Cu6Sn5 supercell (1x1x4), with only 20% Cu2 sites (half-filled) presented for

comparison with ordered ’Cu6Sn5 structure in (c). (c) 2x2x2 supercell of ’Cu6Sn5,

dashed lines outlining a pseudo-hexagonal structure within which atoms are shown.

Note that (a) is the top view of (b-c). (d) Linear thermal expansion Δl/l of binary

Cu6Sn5.

The similar CTE anisotropy can be explained by examining the crystallographic

similarities between the phases in more detail. Figure 8 (b) shows an expanded

hexagonal Cu6Sn5 supercell (1x1x4). The common description of Cu6Sn5 [33, 46,

47] assigns all Cu2 sites a 20% occupancy but, in order to show the relationship with

the superstructure-ordered ’ phase, Figure 8(b) has filled only those Cu2hex sites

that correspond to the equivalent Cu sites of the monoclinic ’Cu6Sn5 phase (shaded

mixed blue -white). Figure 8(c) shows the equivalent atoms in monoclinic ’Cu6Sn5.

The large wireframe box is an expanded 2x2x2 supercell of monoclinic ’Cu6Sn5 to

show how the atoms are oriented relative to the monoclinic axes. Comparing Figure

8(b) and (c), it can be understood that the pseudo-hexagonal structure in ’ is slightly

29

distorted due to local contraction near the vacant Cu2hex sites in the parent

hexagonal phase and local expansion near the occupied Cu2hex sites. It can also be

seen that the two phases are very similar when considered in this way.

There is further complexity with Cu6Sn5 because dimensional changes occur during

heating/cooling due to both (i) thermal expansion and (ii) transformation expansion

during ’. To explore this, we compare the directional CTE results of and

’Cu6Sn5 in this study with linear CTE measurements (equivalent to mean CTE) from

dilatometry in a recent study by some of the authors [48]. Binary Cu6Sn5 dilatometry

results are plotted in Figure 8(d) using data from [48]. It can be seen that there is a

discontinuity in the expansion associated with the monoclinic hexagonal

transformation. This corresponds to a Δl/l0~0.1% linear expansion/contraction due to

the phase transformation which is equivalent to ~35°C of temperature change.

Additionally, noting that the linear CTE is the gradient of a Δl/l0 vs T plot, it can be

seen that the linear CTE of monoclinic and hexagonal Cu6Sn5 are similar. That is to

say, other than a discontinuity due to the phase transformation, the linear CTE is

little affected by whether the phase is monoclinic or hexagonal. This result has

similarities to order-disorder transformations in some intermetallics. For example, in

CuAu FCC and Cu3Au FCC, the expansion discontinuity at the order-disorder

transition is Δl/l0~0.1% and the CTE is not significantly affected by ordering [49]. In

the case of Cu6Sn5 there is limited information on the nature of the ’

transformation [42, 45]. However, from the crystallographic differences between the

two phases in Figure 8 it can be seen that the transformation involves the ordering of

Cu atoms on the 20%-occupied Cu2hex sites and only a slight distortion in other atom

positions. Such relatively small differences in structure explain why there are only

minor differences in mean CTE (or linear CTE) between the ’ and polymorphs of

30

Cu6Sn5 (Figure 6(a) and Figure 8(d)) and why the CTE anisotropy is similar when the

two phases are considered in a crystallographically equivalent orientation (Figure

8(a)).

31

4.2 CTE mismatch in fully-intermetallic joints

Figure 9(a) shows the CTE anisotropy (E1/E3) and maximum CTE mismatch (E1-

E3) for single phases and between pairs of phases at 100C based on the data in

Table 7. Note that stable equilibrium interfaces do not exist for βSn-Cu3Sn (i.e. there

is no tie line between the phases) but the interface is still compared for

completeness. For single phases, Figure 9(a) shows that IMCs have significantly

smaller maximum CTE mismatch (E1-E3<5×10−6) and anisotropy (E1/E3<1.3) than

βSn, indicating that all four IMCs have significantly less anisotropic CTE than βSn. It

can also be seen that Cu3Sn has near isotropic CTE. Thus, transient liquid phase

soldered joints or microbumps consisting solely of Cu3Sn may offer a route to

improved thermal fatigue resistance. Of mixtures of IMCs, Figure 9 shows that a

Cu3Sn-Cu6Sn5 mixture has the smallest maximum CTE mismatch which would give

some advantages to mixed Cu3Sn-Cu6Sn5 joints.

Figure 9. (a) The maximum CTE mismatch (blue axis) and CTE anisotropy of each

phase (red axis) at 100C. (Cu,Ni)6(Sn,Zn)5 is hexagonal-stabilised -phase. *

32

indicates the interface does not exist in equilibrium. (b)The maximum CTE mismatch

of single phases (solid line) and interphases (dashed lines) at various temperatures.

’Cu6Sn5 data is only available at 100C and omitted in (b) for clarity.

The temperature dependence of the maximum CTE mismatch is summarised in

Figure 9(b), where single data points of ’Cu6Sn5 are omitted for clarity. Figure 9(b)

shows that the maximum CTE mismatch of Sn-Sn or Sn-IMC is always

higher/worse (>11x10-6 K-1) than that of the intermetallics, and the maximum

mismatch increases with temperature. The temperature dependence for mixtures of

IMCs is variable but the overall mismatch is generally low (<7x10-6 K-1) and do not

increase significantly with temperature. From the varied temperature dependence,

Figure 9(b) stresses the importance of using the anisotropic and temperature

dependent CTE data, since the mismatch could either increase or decrease with

temperature depending on the combination of phases which is not accessible from

mean CTE measurements.

33

4.3 CTE mismatch at Sn-IMC interfaces

Among all pairs of phases, the largest maximum CTE mismatch is for βSn-Ni3Sn4

which occurs when ([001]βSn||[107]Ni3Sn4=E1βSn-E3Ni3Sn4). Note that this is larger than

E1-E3 of the single phase βSn, because E3Ni3Sn4 is smaller than E3βSn (Table 7).

Figure 9 also shows that the maximum CTE mismatch of any βSn-IMCs interface

(E1βSn-E3IMC) is approximately as severe as the maximum mismatch for βSn-βSn

grain boundaries. Furthermore, for any βSn-IMC interface with E1βSn not parallel to

E3IMC, the maximum CTE mismatch decreases only marginally as E3IMC rotates

away from E1βSn || E3IMC because E1βSn is significantly larger than all three

eigenvalues of each IMC (Table 7).

The sum of the total CTE mismatch between two phases is constant no matter how

they are orientated, which means the total stress induced by CTE mismatch at any

interface is not a function of orientation. However, since the shear stress acting on

the interface is more deleterious than the normal stress [50], the minimum mismatch-

induced damage is expected when the in-plane CTE mismatch is minimised. We

next consider the in-plane CTE mismatch at IMC-Sn interfaces in solder joints and

the orientation relationships that would minimise the in-plane mismatch.

Cu6Sn5 and Ni3Sn4 commonly grow as reaction layers on Cu and Ni substrates

respectively [51, 52], and large intermetallics can form as primary solidification

phases (i.e. by crystal growth prior to Sn nucleation) such as the large Ag3Sn plates

and Cu6Sn5 rods in BGA joints [53-55]. Under BGA soldering conditions the IMCs

typically grow as faceted crystals [54, 56]. The growth facets on Cu6Sn5, Ag3Sn and

Ni3Sn4 are identified in Figure 10 and their captions based on EBSD analysis of IMC

34

crystals in common solder-substrate combinations. In Figure 10 note that the IMCs

have been rotated to have a facet near-parallel with the SEM stub and that the facet

plane normal is indicated by the red triangles in the pole figures. It can be seen that

the faceted growth mechanisms result in Cu6Sn5 scallops in the reaction layer with

{10-10} facets (Figure 10(d)), Cu6Sn5 primary hexagonal rods bounded by {10-10}

facets (Figure 10(b)), Ag3Sn plates with (001) as the major facet (Figure 10(f)), and

irregular Ni3Sn4 rods with (100), (001) and (-201) facets (Figure 10(i) and SI-Figure

9). Although preferred nucleation orientation relationship (ORs) can form between

these IMCs and Sn (e.g. [57]), most IMC-Sn interfaces in solder joints are random

because Sn nucleates elsewhere and the interfaces form when Sn grows into the

IMC during solidification [58]. However, since the large IMCs have reproducible

facets, the IMC plane at the IMC-Sn interface is reproducible and the in-plane CTE

mismatch depends only on the relative Sn orientation. It is therefore worth exploring

optimum ORs at these IMC-Sn interfaces on large IMC facets.

35

Figure 10. Facets of primary (a-c) Cu6Sn5, (e-g) Ag3Sn and (h-k) Ni3Sn4. (a,e,h) in

partially etched solder joints of Sn-0.7Cu/Cu, Sn-4Ag-0.5Cu/Cu and Sn-3.5Ag/Ni.

(b,f,i) primary intermetallics with one facet near-parallel with a SEM stub. (c,g,k) pole

figures showing Cu6Sn5 rod has {1010} facets, Ag3Sn blade has one main (001)

facet and Ni3Sn4 rod has {201} facet plus {100} and {001} facets as marked on (j)

and confirmed by SI-Figure 9. (d) Facet determination of Cu6Sn5 layer using FIB

tomography coupled with EBSD using methods in [57].

In the case of Cu6Sn5, the IMC plane at the IMC-Sn interface, {10-10}, is the plane

containing both the minimum (E3) and maximum (E1) CTE eigenvectors in Cu6Sn5.

For Ag3Sn, the IMC plane at the IMC-Sn interface, (001), contains E2 and E1 but

36

since E2~E3 (Figure 4(b)), the Ag3Sn facet plane also effectively contains both the

minimum and maximum CTE eigenvectors. Thus, due to the growth facets of Cu6Sn5

and Ag3Sn, there is the possibility of the maximum in-plane CTE mismatches

occurring in the IMC-Sn interface (i.e. with E1Sn||E3IMC in the interfacial plane).

E1Sn||E3IMC interfaces are a reliability concern since E1Sn - E3IMC > 11x10-6 K-1 for

each IMC studied from 30-200C (Figure 9(b)) and can increase up to 25x10-6K-1 at

200C, and this is likely to be one reason that strain has been found to localise at the

interfaces between large Ag3Sn plates and Sn during thermal cycling [53].

The minimum in-plane CTE mismatch on the interface between Sn and the IMC

facets in Figure 10, occurs for the Sn orientation for which the two largest CTE

components in the ellipsoid cross-section of IMC facets are cancelled out as much

as possible by some Sn ellipsoid cross-section. Figure 11 shows the optimum OR

that minimises the in-plane CTE mismatch between Sn and the red (10-10) Cu6Sn5

facet. Figure 11(b-c) shows that when E1Sn is rotated by 60 around the x-axis, the

in-plane mismatch between the red Cu6Sn5 ellipsoid cross-section and the black Sn

ellipsoid cross-section come to a minimum. Note that, because the anisotropy E1/E3

of Sn (i.e. the peanut shape) changes significantly with temperature (e.g. Figure 7),

the rotation angle (the OR) depends on the temperature. For example, at 0C the

rotation angle is ~45.3. In addition, when in-plane CTE mismatch is minimised on

one (10-10) facet, other {10-10} facets (e.g. the green (1-100) facet in Figure 11(c))

have larger (worse) in-plane CTE mismatch. Therefore, the minimum in-plane

mismatch cannot be achieved on all Cu6Sn5 facets simultaneously.

37

Figure 11. (a) Cu6Sn5 CTE ellipsoid with coloured cross-sections representing {10-

10} macroscopic facets. (b) Optimum OR to minimise in-plane CTE mismatch

between Sn and the red (10-10) facet at 180oC is obtained by rotating E1Sn

around the x-axis by 60o. (c) The in-plane CTE mismatch between Sn and Cu6Sn5

facets (i.e. CTE ellipsoid cross-sections for the optimum OR), where the coloured

curves are cross-sections through the Cu6Sn5 ellipsoid, and black curves are through

the Sn ellipsoid.

To minimise the in-plane CTE mismatch on a Ni3Sn4 facet, E1 of Sn should always

be perpendicular to the facet. This is because the entire Ni3Sn4 ellipsoid is within that

of Sn and the optimum Sn CTE cross-section to cancel out a Ni3Sn4 cross section

should be the (001)Sn. Figure 12 shows the minimum in-plane mismatch on (-201)

as an example. Note that when (-201) is minimised, the CTE mismatch on the other

two facets (001) and (100) becomes much worse as shown in Figure 12 (c).

38

Figure 12. (a) Ni3Sn4 CTE ellipsoid highlighting the (001), (-201) and (001)

macroscopic facets. (b) Optimum OR to minimise in-plane CTE mismatch between

Sn and the red (-201) facet at 180oC is obtained by having E1Sn perpendicular to

(-201)Ni3Sn4. (c) The in-plane CTE mismatch (i.e. CTE ellipsoid cross-sections for the

optimum OR for (-201)), where the coloured curves are cross-sections through the

Ni3Sn4 ellipsoid, while black curves are through the Sn ellipsoid.

In the case of Ag3Sn plates, a similar analysis gave a minimum in-plane CTE

mismatch on the major facet (001) of Ag3Sn when E1Sn is ~34.2 off E1Ag3Sn at

0C. Since primary Ag3Sn form thin plates (Figure 10 (e) and (f)), this OR would

minimise the in-plane mismatch for the whole plate. However since, in practice, the

OR is near-random between Sn and primary intermetallics [57], it is preferable to

have no primary intermetallics to ensure that the worst in-plane mismatch with Sn

does not occur; and to encourage Cu6Sn5, Ag3Sn and Ni3Sn4 to grow as numerous,

small, closely-spaced eutectic particles where some benefit might be achievable

from CTE mismatch strengthening as is used in composite design [59].

39

5. Conclusions

CTE ellipsoids have been measured using synchrotron powder X-ray diffraction on

Ni3Sn4, Ag3Sn, Cu3Sn, Cu6Sn5, ’Cu6Sn5 and βSn over the range of temperatures

relevant to solder joint manufacturing and operation. The datasets in Table 7 and 8

are suitable to be used as inputs in reliability models and to guide the desired

textures and orientations in both fully-intermetallic joints and in BGA and flip-chip

scale joints.

Each of Ni3Sn4, Ag3Sn, Cu3Sn, and Cu6Sn5 has significantly less anisotropic CTE

than βSn, which is an advantage that could be exploited in fully-IMC joints. In

contrast, in joints containing Sn, the maximum CTE mismatch between Sn and

each of the intermetallic phases is large, and similar to the maximum CTE mismatch

at Sn-Sn grain boundaries. Additionally, the E1 of Sn (the CTE along the c-axis)

increases with temperature more rapidly than in any direction in the IMCs, further

increasing the maximum CTE mismatch at high temperature. This highlights the

importance of using temperature and orientation dependent CTE data in reliability

models.

The growth facets of Cu6Sn5 and Ag3Sn contain both the highest and the lowest CTE

direction in each crystal and, therefore, it is possible for the worst in-plane CTE

mismatch to occur at Sn-Cu6Sn5 and Sn-Ag3Sn interfaces. This is likely to be the

origin of strain localisation at the interfaces between primary intermetallics and Sn

during thermal cycling. While it is possible to minimise the in-plane CTE mismatch on

a particular facet of Ni3Sn4, Ag3Sn, or Cu6Sn5, there will always be a substantial CTE

mismatch on at least one facet.

40

There are only minor differences in the CTE of the monoclinic and hexagonal

polymorphs of Cu6Sn5 when the two phases are considered in a crystallographically

equivalent orientation. However, there is an additional transformation expansion of

magnitude equivalent to ~35C of temperature change. This can be avoided by

stabilising the hexagonal polymorph with additions such as Ni and Zn.

Acknowledgements

The authors are grateful for funding from Nihon Superior Co., Ltd., the UK EPSRC

(grant EP/M002241/1), and Australian synchrotron beamtimes: AS132/PD/5784 and

AS141/PD/7413. We also thank Prof. K.C. Mills for suggestions.

References

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