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Reinforcements at nanometer length scale and the electrical resistivity of lead-free solders
Journal of Alloys and Compounds 478 (2009) 458–461
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Reinforcements at nanometer length scale and the electrical resistivity of lead-free solders P. Babaghorbani, S.M.L. Nai, M. Gupta ∗ Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore
a r t i c l e
i n f o
Article history: Received 19 September 2008 Received in revised form 12 November 2008 Accepted 13 November 2008 Available online 27 November 2008 Keywords: Lead-free solder Nanocomposite Electrical resistivity Mechanical properties
a b s t r a c t In this study, the influence of a wide range of reinforcements (SnO2 , Cu, Y2 O3 , ZrO2 + 8 mol.% Y2 O3 and TiB2 ) on the electrical resistivity of Sn–3.5Ag and Sn–3.5Ag–0.7Cu solders was investigated. The electrical resistivity test was conducted on the bulk samples of composite solders at ambient temperature. Results revealed that electrical resistivities of composites containing nanometer length scale reinforcement is not compromised for the optimal amount of reinforcement required to realize best tensile properties. This behavior was not displayed by composite containing micron size particles. The results of this study are expected to pave the way to develop lead-free nanocomposites especially for the industry using solid-state bonding technique. © 2008 Elsevier B.V. All rights reserved.
1. Introduction In the electronic industry, the most commonly interconnected materials are tin–lead alloys. Tin–lead alloys have a relatively low melting point and can be produced at a low cost, in comparison with other tin-based alloys with similar properties. However, lead-free solder materials are the subject of extensive studies due to the concerns and legislations pertaining to human health and environment over the use of toxic lead [1–7]. Moreover, through the years, as micro-/nano-systems technologies are advancing, the size of electrical components is shrinking leading to an increase in the number of input/output terminals. As a result, the small positional shifts in the joints would result in failures like open circuits, shorts or other mechanical or electrical faults. Composite solders, as an interconnect material, have been developed and applied in aerospace, automobile, and electronic industries, because of their excellent mechanical, electrical, and thermal performances [2,5,6,8]. Among the proposed candidates of lead-free alloys, Sn–3.5Ag is one of the most promising alloys to replace Pb–Sn solder because of its excellent mechanical properties and improved high temperature resistance when compared to Pb–Sn solder [2–4,9–13]. Sn–Ag–Cu is another lead-free alloy used widely because: (i) it has a better thermo-mechanical property when compared to those of conventional Sn–Pb solder [14,15] and (ii) it is a promising solder
∗ Corresponding author. Tel.: +65 6516 6358; fax: +65 6779 1459. E-mail address: [email protected] (M. Gupta). 0925-8388/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2008.11.074
in automotive and avionics applications where solder joints are subjected to temperatures up to 150 ◦ C [16,17]. In view of the abovementioned characteristics of Sn–3.5Ag and Sn–Ag–Cu, these two lead-free solder alloys were chosen as the matrix material in the present study. Since powder metallurgy (PM) technique offers some unique advantages such as near-net shaping, greater materials utilization and a more refined microstructure [7], it is used as one of the most common processing approaches to produce high-performance metallic materials for various applications. This synthesis method was used to develop composite solders in the present study. In our early studies, Sn–3.5Ag solder reinforced with nano-size Cu and SnO2 particles were developed using PM technique with a significant improvement of mechanical characteristics [18,19]. Moreover, Y2 O3 , ZrO2 + 8 mol.% Y2 O3 in nano-size and TiB2 in micron size were used to enhance the mechanical performance of Sn–3.5Ag–0.7Cu solder using PM approach [20–22]. Such composite solders are of relevance to current and futuristic applications particularly due to emergence of solid-state bonding techniques such as thermal compression, thermosonic, and ultrasonic bonding techniques [23–26]. Using these technologies, superior mechanical properties can be realized from the bonded area. While the use of reinforcement to enhance the mechanical properties of Sn–3.5Ag and Sn–Ag–Cu solders has been established, no work is reported to study the effect of near-equiaxed particulate reinforcement at the nanometer length scale on the electrical resistivity of solders. Electrical resistivity is one of the most important properties of metal matrix composites for electrical and electronic applications since if it is not controlled, undue heating may result during operation
P. Babaghorbani et al. / Journal of Alloys and Compounds 478 (2009) 458–461
459
Table 1 Average size and supplier of reinforcements used in this study. Matrix material Sn–3.5Ag
Reinforcement
Average size
Supplier
SnO2
60–80 nm
Cu
50 nm
Nanostructured & Amorphous Materials, USA Argonide Corporation, USA
Y2 O3
32–36 nm
ZrO2 stabilized with 8 mol.% of Y2 O3
51–65 nm
TiB2
3–5 m
Sn–3.5Ag–0.7Cu
Nanostructured & Amorphous Materials, USA Nanostructured & Amorphous Materials, USA GE Advanced Ceramics, Japan
[8]. Accordingly, it is important to ensure that the electrical properties of the composite solders are not compromised at the expense of enhanced mechanical properties. This has been the prime motivation for this study which addresses the effects of type, size and amount of reinforcements on the electrical resistivity of lead-free solders. The outcome of this study will be catalytic in encouraging material scientists to develop new composite lead-free solders containing reinforcement at nanometer length scale. 2. Experimental procedures 2.1. Materials and processing of composites In this study, 96.5Sn–3.5Ag and 95.8Sn–3.5Ag–0.7Cu powder with a size range of 25–45 m (obtained from QualitekR , USA) were used as the matrix material. The characteristics of the reinforcements used in this study are shown in Table 1. Sn–3.5Ag–0.7Cu, Y2 O3 and ZrO2 stabilized with 8 mol.% Y2 O3 are designated as SAC, Y and ZY, respectively. Five different sets of composite materials were synthesized using the PM technique. The processing procedures of the composite solder involved blending the preweighed solder powder and reinforcements. Afterwards, the mixture was uniaxially compacted and then sintered. Since the solders are predominantly used in bar and wire forms which are produced using extrusion/wire drawing, the sintered billets were extruded and the microstructural characterization studies were conducted on the extruded samples using Scanning Electron Microscope (SEM) and Field Emission SEM (FESEM). 2.2. Electrical resistivity testing
x2
R= x1
V 2I
V I
(4)
3. Results and discussion The experimental results of electrical resistivity measurements for the solders reinforced with particles at the nanometer length scale are presented in Tables 2 and 3. The results revealed that the electrical resistivity of the bulk composite solders were comparable to that of the unreinforced Sn–Ag and Sn–Ag–Cu solders. It has been reported by other researchers that the electrical resistivity of composite material is affected by a combination of the following factors [8,31–34]: (i) the presence of reinforcement, (ii) the volume fraction of reinforcement, (iii) the reinforcement shape, (iv) the reinforcement size, and (v) the type of reinforcement and matrix. In accordance with the Matthiessen’s rule (see Eq. (5)), the total resistivity of a material is the sum of three components: (i) impurity (i ), (ii) thermal (t ), and (iii) deformation (d ) resistivity components [35]. (5)
Table 2 Results of electrical resistivity of monolithic Sn–3.5Ag and composite solders. Materialsa
Resistivity ( cm)
Sn–3.5Ag Sn–3.5Ag/0.5 SnO2 Sn–3.5Ag/0.7 SnO2 Sn–3.5Ag/1.0 SnO2
15.4 15.4 15.5 15.7
± ± ± ±
0.2 0.2 0.1 0.1
15.4 ± 0.1 15.6 ± 0.1 15.5 ± 0.2
Sn–3.5Ag/1.0 Cu Sn–3.5Ag/2.0 Cu Sn–3.5Ag/2.5 Cu All the reinforcements were added in volume percent.
(1)
x2 = dx = 4s 2(−x) 2x2
(2)
Table 3 Results of electrical resistivity of monolithic Sn–Ag–Cu and composite solders. Materialsa
Electrical resistivity ( cm)
SAC SAC/0.05 Y SAC/0.1 Y SAC/0.2 Y
13.2 13.0 13.2 13.3
x1
SAC/0.05 ZY SAC/0.1 ZY SAC/0.3 ZY
Due to the superposition of the current at the outer two tips, R=
= 2s
a
dx A
where A is the cross-sectional area of the sample, dx is the differential distance, and x is the distance from the outermost probe tip as shown in Fig. 1. By integrating between the inner probe tips where the voltage is measured, the resistance can be expressed as
and so, the bulk resistivity of the solder sample can be expressed as
total = i + t + d
The electrical resistivity () of bulk Sn–3.5Ag–0.7Cu, Sn–3.5Ag solder and the composite solder materials was measured at ambient temperature using a four-point probe setup. The samples used in this measurement were discs with an approximately 8 mm in thickness. A total of three samples were tested for each monolithic and composite system. The current used in this study was in the range of 100 mA to 1 A. This range of current is within the range of values (10 mA to 50 A) used and reported by other investigators for four-point probe testing [27–29]. The advantage of using the four-point probe method is the possibility to measure the samples resistance without any interference from the contact resistance at the probe contacts. A schematic of the four-point probe configuration used for the electrical resistivity measurements is shown in Fig. 1. In the present study, as the sample thickness (t) is much greater than the probe spacing (s), the following equations were used to calculate the samples electrical resistivity value [30]. The differential resistance (R) can be expressed as R =
Fig. 1. Schematic diagram showing the four-point probe configuration used for the electrical resistivity measurements.
(3)
a
± ± ± ±
0.4 0.3 0.2 0.5
13.3 ± 0.2 13.0 ± 0.2 13.1 ± 0.4
All the reinforcements were added in volume percent.
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Table 4 Volume percentage of porosity in monolithic and nanocomposite solders. Materials
Porosity (%)
Sn–3.5Ag Sn–3.5Ag/0.5 SnO2 Sn–3.5Ag/0.7 SnO2 Sn–3.5Ag/1.0 SnO2
0.62 0.61 0.61 0.90
Sn–3.5Ag/1.0 Cu Sn–3.5Ag/2.0 Cu Sn–3.5Ag/2.5 Cu
1.05 0.61 0.61
Sn–3.5Ag–0.7Cu SAC/0.05 Y SAC/0.1 Y SAC/0.2 Y
0.13 0.34 0.88 1.01
SAC/0.05 ZY SAC/0.1 ZY SAC/0.3 ZY
0.23 0.66 0.78
These three components are the result of the disturbance of normal motions of electrons, which is primarily attributed to lattice scattering and impurity scattering. The presence of lattice imperfections reduces the mean free path of electron motion. This consequently leads to a reduction in electron mobility and hence an increase in the resistivity value. For composite solders, the total resistivity values are thus expected to increase due to the larger contributions of i and d when compared to that of monolithic solder samples. Furthermore, the size of the deformation region also affects the electrical resistivity of the material. The larger total volume fraction of the electron scattering centers, VT , will result in an increase in the material’s resistivity value; VT can be represented as follows [34]: VT = Vpz + Vr + Vp
(6)
where Vpz , Vr , and Vp represent the volume fraction of the plastic zone, the reinforcement, and the porosity, respectively. The plastic zone is characterized by a high density of dislocations. In this study, the resistivity results revealed that for all the composite solders reinforced with particles at the nanometer length scale, there was statistically insignificant change in the electrical resistivity value (see Tables 2 and 3). Recently, Nai et al. [36] also reported that there is no effect on the electrical resistivity of a solder reinforced with different amount of carbon nanotubes. This finding is consistent with the observations made in the current study. This can be attributed to the presence of low volume fraction of porosity (Vp ) in the composite solders (see Table 4). Since the porosity acts as nonconducting voids for the electron flow, the contribution of Vp to VT is limited (see Eq. (6)). Hence, the porosity effect on the electrical resistivity value will be restricted. In addition, the minimal change in the electrical resistivity can be attributed to the low amount of nano-size reinforcement (Vr ). Therefore, the contribution of Vr is also insignificant and this directly affects the volume fraction of the plastic zone (Vpz ). For a particulate reinforcement the volume fraction of the deformation region surrounding the reinforcement, Vpz , is expressed by [8] Vpz = (˛3 − 1)Vr
Fig. 2. Results of: (a) volume percentage of porosity and (b) electrical resistivity of monolithic Sn–Ag–Cu and SAC/TiB2 composite solders.
average resistivity value increased by approximately 30% with the addition of 7 volume percent of TiB2 particles into the Sn–Ag–Cu matrix. This can be attributed to: (i) high porosity level (see Fig. 2), (ii) addition of higher amount of reinforcement in micron size which led to the cluster-associated porosity (see Fig. 3) and (iii) presence of high volume percentage of TiB2 particles. With an increase in porosity level (∼1623%), the contribution of Vp in the case of Sn–Ag–Cu reinforced with micron-size TiB2 particles is considerable and this leads to an increase in electrical resistivity of the material (see Eq. (6)). Moreover, the maximum amount of micron-size TiB2 added to Sn–Ag–Cu was 7 volume percent which is approximately 2233% higher than the maximum amount of incorporated nano-size particles, SAC/0.3 ZY. Hence, in the case of SAC/7.0 TiB2 , presence of high volume fraction of reinforcement increased Vr and accordingly, Vpz value was increased in accordance to Eq. (7).
(7)
where ˛ is the ratio of the size of the heterogeneous nucleation zone to that of the reinforcement. The ˛ value is dependent on the type of matrix and also the size, shape, and type of the reinforcement, but not on its volume fraction [37]. Further resistivity test was also conducted on SAC/TiB2 composite samples and the results are graphically represented in Fig. 2. With increasing incorporation of micron-size TiB2 particles beyond 1.5 volume percent, the average electrical resistivity value of the composite solders exhibited an increasing trend. Particularly, the
Fig. 3. Representative SEM micrograph showing the distribution of TiB2 particles and the presence of cluster-associated pores in SAC/7.0.
P. Babaghorbani et al. / Journal of Alloys and Compounds 478 (2009) 458–461 Table 5 Tensile properties of monolithic and composite solders [18–22]. Materials
0.2% YSa (MPa)
UTSb (MPa)
Total failure strain (%)
Sn–3.5Ag Sn–3.5Ag/0.5 SnO2 Sn–3.5Ag/0.7 SnO2 Sn–3.5Ag/1.0 SnO2
38 ± 1 40 ± 2 45 ± 1 40 ± 4
44 ± 1 47 ± 2 58 ± 2 44 ± 5
46 ± 1 35 ± 1 24 ± 1 21 ± 1
31 ± 2 58 ± 3 66 ± 3 22.45
34 ± 3 67 ± 4 76 ± 4 26.7
32 ± 5 28 ± 2 19 ± 3 24
Sn–3.5Ag–0.7Cu SAC/0.05 Y SAC/0.1 Y SAC/0.2 Y
31 ± 1 32 ± 3 33 ± 3 35 ± 3
35 ± 1 39 ± 3 38 ± 4 41 ± 4
47 ± 11 29 ± 0 27 ± 2 28 ± 3
SAC/0.05 ZY SAC/0.1 ZY SAC/0.3 ZY
33 ± 2 34 ± 1 38 ± 2
41 ± 4 40 ± 2 46 ± 2
29 ± 2 26 ± 1 26 ± 0
SAC/1.5 TiB2 SAC/3.0 TiB2 SAC/7.0 TiB2 Sn63/Pb37c
32 ± 1 39 ± 4 34 ± 5 27.23
38 ± 2 43 ± 5 38 ± 3 NA
27 ± 3 24 ± 2 16 ± 6 48
Sn–3.5Ag/1.0 Cu Sn–3.5Ag/2.0 Cu Sn–3.5Ag/2.5 Cu Sn–3.5Agc
a b c
YS: yield strength. UTS: ultimate tensile strength. Company catalogue provided by QualitekR , USA, 2006.
As shown in Table 5, a significant improvement in mechanical response of solder matrix materials was realized using metallic and ceramic reinforcements without compromising the electrical resistivity values. Exception was observed for Sn–Ag–Cu solder reinforced with micron-size TiB2 particles, whereby the resistivity value increased with the addition of amount of reinforcement (see Fig. 2). Hence, a threshold exists whereby addition of too much reinforcement will lead to degradation in the mechanical and electrical properties (see Table 5 and Fig. 2). As solders serve as electrical and mechanical interconnects, it is essential to ensure that mechanical and electrical properties of the solders are simultaneously enhanced and/or maintained but not compromised with the addition of reinforcements. An increase of 18% and 74% in 0.2% YS and 32% and 73% in UTS was realized in Sn–3.5/0.7 SnO2 and Sn–3.5Ag/2.5 Cu, respectively. In the case of Sn–Ag–Cu solder matrix, the best combination of mechanical properties was observed in SAC/0.3 ZY formulation (23% increase in 0.2% YS and 31% increase in UTS). Although total failure strain of composite solders decreased due to the presence of harder reinforcing phase serving as crack nucleation sites, it is worth mentioning that these values are still comparable to those of solder materials currently used in industry. 4. Conclusions The following conclusions can be made from this study: (a) Presence of reinforcements at the nanometer length scale, metallic or ceramic, does not affect the electrical resistivity of solder matrix.
461
(b) Presence of reinforcement at micron length scale (TiB2 ) affects the electrical resistivity of the solder matrix adversely. (c) Electrical resistivities of composites containing nanometer length scale reinforcement is not compromised for the optimal amount of reinforcement required to realize best tensile properties. This behavior was not displayed by solder composite containing micron size particles. Acknowledgments The authors gratefully acknowledge the support received from the Minerals, Metals and Materials Technology Centre (M3TC) of the National University of Singapore under Ref. C-534-000-003-414. Authors also wish to acknowledge Agency for Science, Technology and Research (A*STAR) for providing research scholarship. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]
[28] [29] [30] [31] [32] [33] [34] [35] [36] [37]
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Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Reinforcements at nanometer length scale and the electrical resistivity of lead-free solders P. Babaghorbani, S.M.L. Nai, M. Gupta ∗ Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore
a r t i c l e
i n f o
Article history: Received 19 September 2008 Received in revised form 12 November 2008 Accepted 13 November 2008 Available online 27 November 2008 Keywords: Lead-free solder Nanocomposite Electrical resistivity Mechanical properties
a b s t r a c t In this study, the influence of a wide range of reinforcements (SnO2 , Cu, Y2 O3 , ZrO2 + 8 mol.% Y2 O3 and TiB2 ) on the electrical resistivity of Sn–3.5Ag and Sn–3.5Ag–0.7Cu solders was investigated. The electrical resistivity test was conducted on the bulk samples of composite solders at ambient temperature. Results revealed that electrical resistivities of composites containing nanometer length scale reinforcement is not compromised for the optimal amount of reinforcement required to realize best tensile properties. This behavior was not displayed by composite containing micron size particles. The results of this study are expected to pave the way to develop lead-free nanocomposites especially for the industry using solid-state bonding technique. © 2008 Elsevier B.V. All rights reserved.
1. Introduction In the electronic industry, the most commonly interconnected materials are tin–lead alloys. Tin–lead alloys have a relatively low melting point and can be produced at a low cost, in comparison with other tin-based alloys with similar properties. However, lead-free solder materials are the subject of extensive studies due to the concerns and legislations pertaining to human health and environment over the use of toxic lead [1–7]. Moreover, through the years, as micro-/nano-systems technologies are advancing, the size of electrical components is shrinking leading to an increase in the number of input/output terminals. As a result, the small positional shifts in the joints would result in failures like open circuits, shorts or other mechanical or electrical faults. Composite solders, as an interconnect material, have been developed and applied in aerospace, automobile, and electronic industries, because of their excellent mechanical, electrical, and thermal performances [2,5,6,8]. Among the proposed candidates of lead-free alloys, Sn–3.5Ag is one of the most promising alloys to replace Pb–Sn solder because of its excellent mechanical properties and improved high temperature resistance when compared to Pb–Sn solder [2–4,9–13]. Sn–Ag–Cu is another lead-free alloy used widely because: (i) it has a better thermo-mechanical property when compared to those of conventional Sn–Pb solder [14,15] and (ii) it is a promising solder
∗ Corresponding author. Tel.: +65 6516 6358; fax: +65 6779 1459. E-mail address: [email protected] (M. Gupta). 0925-8388/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2008.11.074
in automotive and avionics applications where solder joints are subjected to temperatures up to 150 ◦ C [16,17]. In view of the abovementioned characteristics of Sn–3.5Ag and Sn–Ag–Cu, these two lead-free solder alloys were chosen as the matrix material in the present study. Since powder metallurgy (PM) technique offers some unique advantages such as near-net shaping, greater materials utilization and a more refined microstructure [7], it is used as one of the most common processing approaches to produce high-performance metallic materials for various applications. This synthesis method was used to develop composite solders in the present study. In our early studies, Sn–3.5Ag solder reinforced with nano-size Cu and SnO2 particles were developed using PM technique with a significant improvement of mechanical characteristics [18,19]. Moreover, Y2 O3 , ZrO2 + 8 mol.% Y2 O3 in nano-size and TiB2 in micron size were used to enhance the mechanical performance of Sn–3.5Ag–0.7Cu solder using PM approach [20–22]. Such composite solders are of relevance to current and futuristic applications particularly due to emergence of solid-state bonding techniques such as thermal compression, thermosonic, and ultrasonic bonding techniques [23–26]. Using these technologies, superior mechanical properties can be realized from the bonded area. While the use of reinforcement to enhance the mechanical properties of Sn–3.5Ag and Sn–Ag–Cu solders has been established, no work is reported to study the effect of near-equiaxed particulate reinforcement at the nanometer length scale on the electrical resistivity of solders. Electrical resistivity is one of the most important properties of metal matrix composites for electrical and electronic applications since if it is not controlled, undue heating may result during operation
P. Babaghorbani et al. / Journal of Alloys and Compounds 478 (2009) 458–461
459
Table 1 Average size and supplier of reinforcements used in this study. Matrix material Sn–3.5Ag
Reinforcement
Average size
Supplier
SnO2
60–80 nm
Cu
50 nm
Nanostructured & Amorphous Materials, USA Argonide Corporation, USA
Y2 O3
32–36 nm
ZrO2 stabilized with 8 mol.% of Y2 O3
51–65 nm
TiB2
3–5 m
Sn–3.5Ag–0.7Cu
Nanostructured & Amorphous Materials, USA Nanostructured & Amorphous Materials, USA GE Advanced Ceramics, Japan
[8]. Accordingly, it is important to ensure that the electrical properties of the composite solders are not compromised at the expense of enhanced mechanical properties. This has been the prime motivation for this study which addresses the effects of type, size and amount of reinforcements on the electrical resistivity of lead-free solders. The outcome of this study will be catalytic in encouraging material scientists to develop new composite lead-free solders containing reinforcement at nanometer length scale. 2. Experimental procedures 2.1. Materials and processing of composites In this study, 96.5Sn–3.5Ag and 95.8Sn–3.5Ag–0.7Cu powder with a size range of 25–45 m (obtained from QualitekR , USA) were used as the matrix material. The characteristics of the reinforcements used in this study are shown in Table 1. Sn–3.5Ag–0.7Cu, Y2 O3 and ZrO2 stabilized with 8 mol.% Y2 O3 are designated as SAC, Y and ZY, respectively. Five different sets of composite materials were synthesized using the PM technique. The processing procedures of the composite solder involved blending the preweighed solder powder and reinforcements. Afterwards, the mixture was uniaxially compacted and then sintered. Since the solders are predominantly used in bar and wire forms which are produced using extrusion/wire drawing, the sintered billets were extruded and the microstructural characterization studies were conducted on the extruded samples using Scanning Electron Microscope (SEM) and Field Emission SEM (FESEM). 2.2. Electrical resistivity testing
x2
R= x1
V 2I
V I
(4)
3. Results and discussion The experimental results of electrical resistivity measurements for the solders reinforced with particles at the nanometer length scale are presented in Tables 2 and 3. The results revealed that the electrical resistivity of the bulk composite solders were comparable to that of the unreinforced Sn–Ag and Sn–Ag–Cu solders. It has been reported by other researchers that the electrical resistivity of composite material is affected by a combination of the following factors [8,31–34]: (i) the presence of reinforcement, (ii) the volume fraction of reinforcement, (iii) the reinforcement shape, (iv) the reinforcement size, and (v) the type of reinforcement and matrix. In accordance with the Matthiessen’s rule (see Eq. (5)), the total resistivity of a material is the sum of three components: (i) impurity (i ), (ii) thermal (t ), and (iii) deformation (d ) resistivity components [35]. (5)
Table 2 Results of electrical resistivity of monolithic Sn–3.5Ag and composite solders. Materialsa
Resistivity ( cm)
Sn–3.5Ag Sn–3.5Ag/0.5 SnO2 Sn–3.5Ag/0.7 SnO2 Sn–3.5Ag/1.0 SnO2
15.4 15.4 15.5 15.7
± ± ± ±
0.2 0.2 0.1 0.1
15.4 ± 0.1 15.6 ± 0.1 15.5 ± 0.2
Sn–3.5Ag/1.0 Cu Sn–3.5Ag/2.0 Cu Sn–3.5Ag/2.5 Cu All the reinforcements were added in volume percent.
(1)
x2 = dx = 4s 2(−x) 2x2
(2)
Table 3 Results of electrical resistivity of monolithic Sn–Ag–Cu and composite solders. Materialsa
Electrical resistivity ( cm)
SAC SAC/0.05 Y SAC/0.1 Y SAC/0.2 Y
13.2 13.0 13.2 13.3
x1
SAC/0.05 ZY SAC/0.1 ZY SAC/0.3 ZY
Due to the superposition of the current at the outer two tips, R=
= 2s
a
dx A
where A is the cross-sectional area of the sample, dx is the differential distance, and x is the distance from the outermost probe tip as shown in Fig. 1. By integrating between the inner probe tips where the voltage is measured, the resistance can be expressed as
and so, the bulk resistivity of the solder sample can be expressed as
total = i + t + d
The electrical resistivity () of bulk Sn–3.5Ag–0.7Cu, Sn–3.5Ag solder and the composite solder materials was measured at ambient temperature using a four-point probe setup. The samples used in this measurement were discs with an approximately 8 mm in thickness. A total of three samples were tested for each monolithic and composite system. The current used in this study was in the range of 100 mA to 1 A. This range of current is within the range of values (10 mA to 50 A) used and reported by other investigators for four-point probe testing [27–29]. The advantage of using the four-point probe method is the possibility to measure the samples resistance without any interference from the contact resistance at the probe contacts. A schematic of the four-point probe configuration used for the electrical resistivity measurements is shown in Fig. 1. In the present study, as the sample thickness (t) is much greater than the probe spacing (s), the following equations were used to calculate the samples electrical resistivity value [30]. The differential resistance (R) can be expressed as R =
Fig. 1. Schematic diagram showing the four-point probe configuration used for the electrical resistivity measurements.
(3)
a
± ± ± ±
0.4 0.3 0.2 0.5
13.3 ± 0.2 13.0 ± 0.2 13.1 ± 0.4
All the reinforcements were added in volume percent.
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Table 4 Volume percentage of porosity in monolithic and nanocomposite solders. Materials
Porosity (%)
Sn–3.5Ag Sn–3.5Ag/0.5 SnO2 Sn–3.5Ag/0.7 SnO2 Sn–3.5Ag/1.0 SnO2
0.62 0.61 0.61 0.90
Sn–3.5Ag/1.0 Cu Sn–3.5Ag/2.0 Cu Sn–3.5Ag/2.5 Cu
1.05 0.61 0.61
Sn–3.5Ag–0.7Cu SAC/0.05 Y SAC/0.1 Y SAC/0.2 Y
0.13 0.34 0.88 1.01
SAC/0.05 ZY SAC/0.1 ZY SAC/0.3 ZY
0.23 0.66 0.78
These three components are the result of the disturbance of normal motions of electrons, which is primarily attributed to lattice scattering and impurity scattering. The presence of lattice imperfections reduces the mean free path of electron motion. This consequently leads to a reduction in electron mobility and hence an increase in the resistivity value. For composite solders, the total resistivity values are thus expected to increase due to the larger contributions of i and d when compared to that of monolithic solder samples. Furthermore, the size of the deformation region also affects the electrical resistivity of the material. The larger total volume fraction of the electron scattering centers, VT , will result in an increase in the material’s resistivity value; VT can be represented as follows [34]: VT = Vpz + Vr + Vp
(6)
where Vpz , Vr , and Vp represent the volume fraction of the plastic zone, the reinforcement, and the porosity, respectively. The plastic zone is characterized by a high density of dislocations. In this study, the resistivity results revealed that for all the composite solders reinforced with particles at the nanometer length scale, there was statistically insignificant change in the electrical resistivity value (see Tables 2 and 3). Recently, Nai et al. [36] also reported that there is no effect on the electrical resistivity of a solder reinforced with different amount of carbon nanotubes. This finding is consistent with the observations made in the current study. This can be attributed to the presence of low volume fraction of porosity (Vp ) in the composite solders (see Table 4). Since the porosity acts as nonconducting voids for the electron flow, the contribution of Vp to VT is limited (see Eq. (6)). Hence, the porosity effect on the electrical resistivity value will be restricted. In addition, the minimal change in the electrical resistivity can be attributed to the low amount of nano-size reinforcement (Vr ). Therefore, the contribution of Vr is also insignificant and this directly affects the volume fraction of the plastic zone (Vpz ). For a particulate reinforcement the volume fraction of the deformation region surrounding the reinforcement, Vpz , is expressed by [8] Vpz = (˛3 − 1)Vr
Fig. 2. Results of: (a) volume percentage of porosity and (b) electrical resistivity of monolithic Sn–Ag–Cu and SAC/TiB2 composite solders.
average resistivity value increased by approximately 30% with the addition of 7 volume percent of TiB2 particles into the Sn–Ag–Cu matrix. This can be attributed to: (i) high porosity level (see Fig. 2), (ii) addition of higher amount of reinforcement in micron size which led to the cluster-associated porosity (see Fig. 3) and (iii) presence of high volume percentage of TiB2 particles. With an increase in porosity level (∼1623%), the contribution of Vp in the case of Sn–Ag–Cu reinforced with micron-size TiB2 particles is considerable and this leads to an increase in electrical resistivity of the material (see Eq. (6)). Moreover, the maximum amount of micron-size TiB2 added to Sn–Ag–Cu was 7 volume percent which is approximately 2233% higher than the maximum amount of incorporated nano-size particles, SAC/0.3 ZY. Hence, in the case of SAC/7.0 TiB2 , presence of high volume fraction of reinforcement increased Vr and accordingly, Vpz value was increased in accordance to Eq. (7).
(7)
where ˛ is the ratio of the size of the heterogeneous nucleation zone to that of the reinforcement. The ˛ value is dependent on the type of matrix and also the size, shape, and type of the reinforcement, but not on its volume fraction [37]. Further resistivity test was also conducted on SAC/TiB2 composite samples and the results are graphically represented in Fig. 2. With increasing incorporation of micron-size TiB2 particles beyond 1.5 volume percent, the average electrical resistivity value of the composite solders exhibited an increasing trend. Particularly, the
Fig. 3. Representative SEM micrograph showing the distribution of TiB2 particles and the presence of cluster-associated pores in SAC/7.0.
P. Babaghorbani et al. / Journal of Alloys and Compounds 478 (2009) 458–461 Table 5 Tensile properties of monolithic and composite solders [18–22]. Materials
0.2% YSa (MPa)
UTSb (MPa)
Total failure strain (%)
Sn–3.5Ag Sn–3.5Ag/0.5 SnO2 Sn–3.5Ag/0.7 SnO2 Sn–3.5Ag/1.0 SnO2
38 ± 1 40 ± 2 45 ± 1 40 ± 4
44 ± 1 47 ± 2 58 ± 2 44 ± 5
46 ± 1 35 ± 1 24 ± 1 21 ± 1
31 ± 2 58 ± 3 66 ± 3 22.45
34 ± 3 67 ± 4 76 ± 4 26.7
32 ± 5 28 ± 2 19 ± 3 24
Sn–3.5Ag–0.7Cu SAC/0.05 Y SAC/0.1 Y SAC/0.2 Y
31 ± 1 32 ± 3 33 ± 3 35 ± 3
35 ± 1 39 ± 3 38 ± 4 41 ± 4
47 ± 11 29 ± 0 27 ± 2 28 ± 3
SAC/0.05 ZY SAC/0.1 ZY SAC/0.3 ZY
33 ± 2 34 ± 1 38 ± 2
41 ± 4 40 ± 2 46 ± 2
29 ± 2 26 ± 1 26 ± 0
SAC/1.5 TiB2 SAC/3.0 TiB2 SAC/7.0 TiB2 Sn63/Pb37c
32 ± 1 39 ± 4 34 ± 5 27.23
38 ± 2 43 ± 5 38 ± 3 NA
27 ± 3 24 ± 2 16 ± 6 48
Sn–3.5Ag/1.0 Cu Sn–3.5Ag/2.0 Cu Sn–3.5Ag/2.5 Cu Sn–3.5Agc
a b c
YS: yield strength. UTS: ultimate tensile strength. Company catalogue provided by QualitekR , USA, 2006.
As shown in Table 5, a significant improvement in mechanical response of solder matrix materials was realized using metallic and ceramic reinforcements without compromising the electrical resistivity values. Exception was observed for Sn–Ag–Cu solder reinforced with micron-size TiB2 particles, whereby the resistivity value increased with the addition of amount of reinforcement (see Fig. 2). Hence, a threshold exists whereby addition of too much reinforcement will lead to degradation in the mechanical and electrical properties (see Table 5 and Fig. 2). As solders serve as electrical and mechanical interconnects, it is essential to ensure that mechanical and electrical properties of the solders are simultaneously enhanced and/or maintained but not compromised with the addition of reinforcements. An increase of 18% and 74% in 0.2% YS and 32% and 73% in UTS was realized in Sn–3.5/0.7 SnO2 and Sn–3.5Ag/2.5 Cu, respectively. In the case of Sn–Ag–Cu solder matrix, the best combination of mechanical properties was observed in SAC/0.3 ZY formulation (23% increase in 0.2% YS and 31% increase in UTS). Although total failure strain of composite solders decreased due to the presence of harder reinforcing phase serving as crack nucleation sites, it is worth mentioning that these values are still comparable to those of solder materials currently used in industry. 4. Conclusions The following conclusions can be made from this study: (a) Presence of reinforcements at the nanometer length scale, metallic or ceramic, does not affect the electrical resistivity of solder matrix.
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(b) Presence of reinforcement at micron length scale (TiB2 ) affects the electrical resistivity of the solder matrix adversely. (c) Electrical resistivities of composites containing nanometer length scale reinforcement is not compromised for the optimal amount of reinforcement required to realize best tensile properties. This behavior was not displayed by solder composite containing micron size particles. Acknowledgments The authors gratefully acknowledge the support received from the Minerals, Metals and Materials Technology Centre (M3TC) of the National University of Singapore under Ref. C-534-000-003-414. Authors also wish to acknowledge Agency for Science, Technology and Research (A*STAR) for providing research scholarship. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]
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