Abstract
The influence of nickel addition to tin substrate on microstructure, kinetics parameters as well as diffusion coefficients was studied on Cu/Sn diffusion couples. The results revealed that the presence of nickel did not affect the growth of Cu3Sn phase in comparison with that of the binary Cu/Sn diffusion couple. However, it substantially influenced the morphology and chemical composition of the (Cu1−xNix)6Sn5 phase, which grew with dual morphology and different chemical composition. The layer of the phase was poorer in nickel, whereas detached grains were richer in nickel concentration. The calculated kinetic parameters showed that the growth of the Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 phases was controlled by volume diffusion, but in the case of Ni-rich (Cu1−xNix)6Sn5 phase, the growth was controlled by a complex mechanism. The calculations of diffusion coefficients and activation energies of Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 phases revealed that the presence of nickel in the tin substrate did not affect the rate of formation/growth of those phases in comparison with the binary Cu/Sn diffusion couples.
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Introduction
The development of the basic knowledge in the field of phase transformations in the Cu–Ni–Sn ternary system considered as one of the most important in the soldering has an extra meaning for the implementation of new lead-free materials [1,2,3,4,5,6,7]. The intermetallic phases growing at the interface of under-bump metallization and solder strongly affect the electro-mechanical properties of the final product. Copper and nickel are the main components of the metallized layer [8,9,10,11], while tin is the key constituent of the lead-free solders. Therefore, the careful analysis of structural changes, supplemented with kinetics description of the process occurring during the interaction between Ni, Cu and Sn, is very important from the application point of view [12,13,14].
Previous studies have shown that even relatively small amount of Ni (up to 5 at.%) added to a copper substrate strongly affected the microstructure of the (Cu,Ni)/Sn reaction zone [15, 16]. In a classical Cu/Sn diffusion couple, the η[Cu6Sn5] phase formed first, and then the growth of ε[Cu3Sn] phase took place. The addition of even 1 at.% of Ni to Cu causes the appearance of (Cu1−xNix)6Sn5 phase together with ε[Cu3Sn]. Further addition of Ni (5 at.%) blocks the growth of ε[Cu3Sn] phase to such an extent that only (Cu1−xNix)6Sn5 is present in the reaction zone [15, 16]. Additionally, in the case of the (Cu,Ni)/Sn/(Cu,Ni) diffusion-soldered joints, the nickel addition to copper significantly affects the morphology of the (Cu1−xNix)6Sn5 phase, so that it does not grow as a continuous layer but it spreads in the form of many individual grains. Further annealing causes their agglomeration, and finally, they join together to create the layer [15]. Moreover, the nickel addition to copper leads to such a change in the diffusion mechanism that the phase transformations occurring in diffusion couples accelerate by about an order of magnitude [17]. However, the practical implementation of the nickel addition to copper may be challenging. Therefore, the present research is devoted to the study of the influence of nickel addition to tin on the diffusion phenomena and growth mechanism of the intermetallic phases at the Cu/(Sn,Ni) interface, being much more easy to apply in the production line. Although there are reports related to the nickel addition to lead-free solders such as SAC (SnAgCu) alloy, they are associated rather with the technological aspects [18].
Experimental
The (Sn,Ni) and Cu substrates used in the diffusion couple experiment were prepared using pure metals: Sn 99.998%, Ni 99.99% and Cu 99.99% (Alfa Aesar). The appropriate amounts of pure metals were melted in vacuum induction furnace (Leybold–Heraeus) under argon protective atmosphere (0.03 MPa) to obtain the (Sn,Ni)-based alloys with 1 at.% of Ni and Cu. Then, the cast alloys were cut into 3 mm thick pads. Before the diffusion couple experiment, the surfaces of the (Sn+1at.%Ni) and Cu substrates were ground with the paper of 2000 maximum gradation and then cleaned with acetone in an ultrasonic washer. The prepared pads were pressed, sealed in quartz ampoules and subjected to annealing at 200, 215 and 220 °C (473, 488 and 493 K) for 48, 120, 168 and 225 h followed by cooling with the furnace for an appropriate time interval.
The obtained diffusion couples were subjected to detailed microstructure and chemical composition characterization using scanning electron microscope JEOL JSM 5510 LV equipped with an energy dispersive X-ray spectrometer (EDS), IXRF Model 500.
In order to perform the growth kinetics analysis and diffusion coefficient calculations, the thicknesses (Λ) of the intermetallic Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 phases, which were formed more or less as layers, were measured after different temperatures and times of annealing, using the specialized computer program—R-Tools, written in Borland Delphi 6.0 [19]. Its operation is based on the analysis of the imported image of the microstructure obtained in the scanning electron microscope. The interface between Ni-rich and Ni-poor variants of (Cu1−xNix)6Sn5 phase was indistinguishable during ordinary observations using backscattered electrons mode (BSE). Therefore, the thickness of Ni-poor (Cu1−xNix)6Sn5 phase variant was chosen based on the EDS line scans made across the reaction zone between the Cu and (Sn,Ni) substrates in many different places of the sample. Due to the irregular growth of the phases, at least 3 different photographs, taken at the same magnification, were used for the analysis. The average of 20 independent measurements of thickness was made for each image. The arithmetic average of the phase thicknesses and the standard deviations of measurements were calculated. The stereological analysis using the software ImageJ by Wayne Rasband 1.45 s from the National Institutes of Health, USA, was carried out in the case of the (Cu1−xNix)6Sn5 phase formed as irregular grains (Ni-rich variant) [17, 20], to obtain quantitative information about the phase area. Based on this analysis, the determination of the growth kinetics parameter for this variant of the (Cu1−xNix)6Sn5 phase was performed.
Results and discussion
Microstructure and chemical composition analysis
Studies of the microstructure and chemical composition of the Cu/(Sn+1at.%Ni) diffusion couples were performed for the samples annealed at 200, 215 and 220 °C (473, 488 and 493 K) for 48, 120, 168 and 225 h (2, 5, 7, 9.3 days), using scanning electron microscope (SEM). The examples of the SEM microstructures of the obtained cross sections of samples and the phase identifications are presented in Fig. 1.
The chemical composition analysis with SEM/EDS technique revealed the presence of three intermetallic phases (IMPs): Cu3Sn, (Cu1−xNix)6Sn5, (Ni1−xCux)3Sn4 (Fig. 1), due to the interdiffusion of elements across the interface. The (Ni1−xCux)3Sn4 phase appeared as a result of the copper diffusion into Ni3Sn4 grains dispersed in the (Sn+1at.%Ni) substrate. The Ni3Sn4 phase was present in the (Sn+1at.%Ni) pad before the experiment of diffusion couples (Fig. 2). The microstructure of Sn+1at.%Ni substrate is discussed in details in [21].
The appearance of Ni3Sn4 phase results directly from the Sn-Ni binary phase diagram [22]. The SEM/EDS analysis showed some fluctuations of the copper concentration in the (Ni1−xCux)3Sn4 phase depending on its distance from the Cu and (Sn+1at.%Ni) reaction zone. The grains located far from the interface contained on average: 3.1 ± 0.4 at.% of Cu, 39.4 ± 0.8 at.% of Ni, 57.5 ± 1.2 at.% of Sn and those located closer: 6.1 ± 1.0 at.% of Cu, 33.6 ± 1.3 at.% of Ni, 60.3 ± 1.2 at.% of Sn.
Apart from the (Ni1−xCux)3Sn4 phase, the growth of two additional new intermetallic phases was observed, which were identified as (Cu1−xNix)6Sn5 and Cu3Sn. The (Cu1−xNix)6Sn5 phase formed with a dual morphology. From the (Sn+1at.%Ni) pad side, the grains of irregular shapes surrounded by the pure tin were observed, whereas the discontinuous layer of (Cu1−xNix)6Sn5 appeared closer to the center of the diffusion couple (Fig. 1). The EDS/SEM quantitative analysis clearly showed that dual morphology was accompanied by the fluctuation of the chemical composition of the (Cu1−xNix)6Sn5 phase. The layer of (Cu1−xNix)6Sn consisted of 48.5 ± 0.9 at.% Cu, 5.3 ± 0.3 at.% Ni and 46.2 ± 0.9 at.% Sn (called in the text as “Ni-poor”), while the large grains contained 35.0 ± 0.7 at.% Cu, 19.2 ± 0.8 at.% Ni and 45.8 ± 0.9 at.% Sn (referred to as “Ni-rich”). The differences in the morphology, chemical composition and localization of the (Cu1−xNix)6Sn5 phase were attributed to various mechanisms of its formation. The Ni-rich variant transformed from the Ni3Sn4 phase present in the initial (Sn,Ni) end member. On the other hand, the formation of the Ni-poor layer took place as a result of diffusion at the initial interface. The detailed description and explanation of the phenomena were presented in previous papers [21, 23]. The third phase, generated during annealing close to the copper substrate in the form of a continuous layer, was identified as Cu3Sn (74.5 ± 1.5 at.% of Cu, 0.2 ± 0.1 at.% of Ni and 25.3 ± 0.5 at.% of Sn) [21]. Such a complex microstructure of the reaction zone obtained in the Cu/(Sn,Ni) diffusion couples with 1 and 3 at.% of the nickel addition annealed at 160, 180 and 200 °C for various times up to 1139.5 h was also described by Nakayama et al. [24]. However, in comparison with the presented results, some differences in the chemical composition of the formed phases were found. Nakayama et al. [24] observed three intermetallic phases. The thin continuous layer of Cu3Sn phase was established close to the Cu pad. The next layer was identified as the Cu6Sn5 phase, without the nickel content. The Ni was detected only in single detached grains in the form of (Cu,Ni)6Sn5. The authors suggested that the different mechanisms of the Cu6Sn5 phase formation were the reason for the occurrence of dual morphology phenomena and fluctuations of the Ni concentration [24].
Growth kinetics of the intermetallic phases
The thickness of the Ni-poor (Cu1−xNix)6Sn5 and Cu3Sn phases was measured using the R-tools program based on the series of SEM micrographs [19].
The experimental results of the measured average thicknesses of Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 layers for different annealing times at temperatures 200, 215 and 220 °C are presented in Table 1 and Table 2.
The thickness of the growing phase/layer \( (\varLambda ) \) can be expressed as function of time (t)
where the value of the power n determines the mechanism controlling the kinetics of layer growth. For example, n = 0.5 means that the process is controlled by volume diffusion. Measured thicknesses of the layers Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 as function of time are presented in Figs. 3 and 4. The values of n for the Cu3Sn phase at temperatures 200, 215 and 220 °C calculated by the least square linear approximation method are 0.45 ± 0.08, 0.49 ± 0.02 and 0.48 ± 0.09. They indicate that the growth of Cu3Sn layer is controlled by volume diffusion for all studied temperatures.
The calculated values of n determined for Ni-poor (Cu1−xNix)6Sn5 layer were 0.49 ± 0.03, 0.43 ± 0.04 and 0.45 ± 0.05 for temperatures 200, 215 and 220 °C, respectively. Those data indicated that volume diffusion was a dominating growth mechanism at all temperatures.
Such a similar parabolic growth mechanism was reported by Tang et al. [25] and Yuan et al. [26] for the Cu3Sn and Cu6Sn5 phases formed in the Cu/Sn diffusion couples. Their results suggested that nickel addition to the Sn substrate did not influence the character of phases growth as significantly as the morphology.
In the case of the Ni-rich (Cu1−xNix)6Sn5 phase, the situation was even more complicated than it was mentioned above. The description of the phase growth which has a complex three-dimensional geometry may be expressed by the volume of Ni-rich (Cu1−xNix)6Sn5 phase in function of time. Unfortunately, only two-dimensional sections of these grains could be obtained from the experiments that had been carried out in the study. However, under some assumptions, useful information about the three-dimensional growth could be deduced from the two-dimensional measurements.
The total volume of grains is given by integral \( |V| = \int\limits_{0}^{H} {|V_{h} |dh} , \) where \( V_{h} \) is the cross section of a set \( V \) at height \( h. \) Hence, \( V \) represents the grain phase and \( |\,\,\,\,| \) denotes the volume or area of a given set (3D or 2D measure). Assuming that a distribution of grains is uniform, the approximation \( |V_{h} | \approx A_{0} \) can be used; hence, \( |V| = A_{0} H, \) where \( A_{0} \) is the area of grains in any representative cross section. Thus
In practice \( A_{0} \) is the average of several measurements along the phase boundary for one cross section. Such possibility results from the fact that probabilities of grain distribution in “vertical” and “horizontal” directions are assumed to be equal. This is a very important property because it allows omitting the necessity to cut out many cross sections \( V_{h} \) for different \( h. \)
Thus, provided that the distribution is uniform and relatively dense, the kinetics of volume growth can be obtained by 2D measurements.
The question of the mechanism of kinetic growth (reaction or diffusion control) can be answered by the following reasoning. It can be shown that for simple shapes (spheres, cubes, ellipsoids), the linear dimension of growing grain is proportional to \( \sqrt t \) if the process is diffusion controlled; hence, the area is proportional to \( t. \) More complicated shapes can locally be viewed as similar to plane or sphere, so we can extrapolate this criterion to the general case. Thus, if the 2D area of grains fraction is proportional to t, i.e., \( \% A(t) \sim t, \) the kinetics is diffusion controlled.
The changes of the Ni-rich (Cu1−xNix)6Sn5 phase area with time in the bilogarithmic scale for temperatures 215 and 220 °C are presented in Fig. 5.
Mathematical model of layers growth
Based on the results presented above, the mathematical model of intermetallic layer growth was proposed and the diffusion coefficients for the Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 phases were determined. The diffusion coefficient calculations for the layer of Ni-rich variant require additional studies and will be the subject of further work because of the complex morphology of the (Cu1−xNix)6Sn phase. Figure 6 presents schematic graph of layer growth in Cu/(Sn+1at.%Ni).
The model assumes that growth of layers is the result of the diffusion of Cu and Sn components in each layer:
where c 2 and c 3 and \( J^{2} \) and \( J^{3} \) are the concentrations and fluxes of Cu in the layers “2” and “3,” respectively, i.e., for layers Cu3Sn and (Cu1−xNix)6Sn5.
The movement of the boundaries Cu/Cu3Sn, Cu3Sn/(Cu1−xNix)6Sn5 and (Cu1−xNix)6Sn5/Sn is described by mass balance equations at the moving boundaries s 1 (t), s 2 (t) and s 3 (t), respectively—so-called Stefan boundary conditions [27, 28]:
where \( c^{j} (x,t),\;J^{j} (x,t) \)—concentration and flux of copper in the \( j \)-th layer at position \( x \) and for the time \( t \), \( c_{L}^{j} ,\;c_{R}^{j} \)—concentrations of copper in the \( j \)-th layer on the left and right boundary, \( s_{1} (t),\;s_{2} (t)\,{\text{and}}\;s_{3} (t) \)—positions of the Cu/Cu3Sn, Cu3Sn/(Cu1−xNix)6Sn5 and (Cu1−xNix)6Sn5/Sn boundaries at time \( t \).
In the case of two component system, the flux of copper in the \( j \)-th layer can be expressed by Fick’s formula [29]
where \( \tilde{D}^{j} \) is the interdiffusion coefficient in the \( j \)-th layer [30]. For compounds of narrow homogeneity range (so-called line compounds), one can assume that the concentration profile is linear and consequently Eq. (4) can be expressed as follows
where \( c_{L}^{j} ,\;c_{R}^{j} \) are concentrations of copper in the \( j \)-th layer on its left and right boundary; \( s_{j} (t) - s_{j - 1} (t) \) is the thickness of \( j \)-th layer at time t.
Assuming negligible solubility of tin in copper in layer “1” and constant copper concentration in layer “4” it can be assumed:
Consequently, Eq. (3) takes the following form
Introducing the notations:
Equation (8) can be written as follows:
From (10), the equations describing velocities of the boundaries can be obtained:
Subtracting Eqs. (11):
and introducing further notations:
Equation (12) takes the form:
Equation (14) with the initial condition—i.e., thicknesses of layers \( X, \, Y \) at time zero, defines the following Cauchy problem [31] for a system of two ordinary differential equations (ODEs):
Solving numerically problem (15) gives layer thicknesses \( X(t){\text{ and }}Y(t) \) as function of time.
Determination of diffusion coefficients for the layers of Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 phases
A numerical solution of problem (15) is a function of (unknown) interdiffusion coefficients, \( \tilde{D}^{2} ,\;\tilde{D}^{3} \) in layers “2” and “3,” respectively:
These diffusion coefficients can be determined by solution of the suitable inverse problem, but additional information is necessary, in this case, the measured layer thicknesses at several times. Denoting as:
the measured thicknesses of layers Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 at times \( t_{1} , \ldots ,t_{N} , \) the following function can be defined:
which is a “distance” between measured and calculated (from the model) thicknesses of layers “2” and “3” at times \( t_{1} , \ldots ,t_{N} . \)
In order to determine diffusion coefficients, function (18) has to be minimized and values of \( \tilde{D}^{2} ,\tilde{D}^{3} \) which minimize goal function (18) are looked for:
The calculations for the system Cu/(Sn + 1at.% Ni) were performed for temperatures 200, 215 and 220 °C using the following data (see notations in Fig. 6):
-
1.
\( c_{L}^{1} = c_{R}^{1} = 1\;{\text{mol}}/{\text{mol}} \)
-
2.
\( c_{L}^{2} = 0.76\;{\text{mol}}/{\text{mol}} \)
-
3.
\( c_{R}^{2} = 0.747\;{\text{mol}}/{\text{mol}} \)
-
4.
\( c_{L}^{3} = 0.56\;{\text{mol}}/{\text{mol}} \)
-
5.
\( c_{L}^{3} = 0.545\;{\text{mol}}/{\text{mol}} \)
-
6.
\( c_{L}^{4} = c_{R}^{4} = 0\;{\text{mol}}/{\text{mol}} \)
-
7.
\( X(0) = 1 \cdot 10^{ - 9} \,{\text{m}},\quad Y(0) = 1 \cdot 10^{ - 9} \,{\text{m}} \)
Based on the formulated above inverse problem (18)–(19), the diffusion coefficients for layers Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 for the system Cu/(Sn+1at.%Ni) and temperatures 200, 215 and 220 °C were calculated and are presented in Table 3.
Figures 7, 8 and 9 show comparison of calculated evolution of layer thickness (for diffusion coefficients from Table 3) with experimentally measured average thicknesses of Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 layers for various annealing times at 200, 215 and 220 °C. As it can been seen, a very good agreement was achieved.
Calculated layer thicknesses (for diffusion coefficients from Table 3)—lines and experimentally measured average thicknesses of Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 layers (dots) for selected times for temperature 200 °C
Calculated layer thicknesses (for diffusion coefficients from Table 3)—lines and experimentally measured average thicknesses of Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 layers (dots) for selected times for temperature 215 °C
Calculated layer thicknesses (for diffusion coefficients from Table 3)—(lines) and experimentally measured average thicknesses of Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 layers (dots) for selected times for temperature 220 °C
The calculated diffusion coefficients (solution of the inverse problem for Cu/(Sn+1at.%Ni) diffusion couples) for layers Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 are compared in Tables 4 and 5 with literature data accessible for the Cu/Sn system.
In both cases of Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 phases, a good agreement with literature data was obtained. The results confirm, once again, that in general the addition of the nickel into the tin does not affect significantly the diffusion processes associated with Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 phases in comparison with Cu3Sn and Cu6Sn5 formed in the binary Cu/Sn system.
The interdiffusion coefficients for layers Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 for Cu/(Sn+1at.%Ni) diffusion couples as function of temperature in the Arrhenius plot are presented in Fig. 10.
The activation energies for the layers Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 were determined to be 34 ± 9 and 33 ± 11 kJ mol−1 using the standard least square linear approximation. However, significant discrepancies of activation energies for Cu3Sn and Cu6Sn5 layers in the binary Cu/Sn system were found in the literature.
The presented results are in good agreement with those obtained by Onishi and Fujibuchi [32], in whose works the activation energy was 36.4 kJ mol−1 for Cu3Sn and 46.0 kJ mol−1 for Cu6Sn5 and those obtained by Kumar et al. [34] who reported 38.7 ± 7.5 and 47.3 ± 5.2 kJ mol−1, respectively. Quite different values of activation energies of interdiffusion for Cu3Sn and Cu6Sn5 were determined by Paul et al. [33], 73.8 and 81 kJ mol−1, respectively, whose values were two times higher. Also in the case of Tang et al. [25], the activation energy for Cu3Sn phase 90.4 kJ mol−1 was almost three times higher than the value obtained in this work, while the value of 41.4 kJ mol−1 for Cu6Sn5 appeared similar. A possible reason for those differences of the discussed results, according to Onishi and Fujibuchi [32], was probably the difference in the measured width of the phases.
Lack of significant differences in the activation energies of the intermetallic layer formation in the Cu/Sn and Cu/(Sn+1at.%Ni) systems suggests that nickel addition into the tin substrate does not affect the growth rate of Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 phases. The comparison of the microstructure of the reaction zone in the Cu/Sn and Cu/(Sn+1at.%Ni) diffusion couples, annealed under the same experimental conditions, is the confirmation of these results (Fig. 11). As it can be seen, the thickness of the phases is more or less the same in both systems. The obtained results clearly suggest that it is very important to which substrate (Cu or Sn) the nickel is added, especially in the case of the (Cu1−xNix)6Sn5. As was presented previously [17], the addition of Ni (5 at.%) into the Cu substrate strongly accelerated the growth of the (Cu1−xNix)6Sn5 phase blocking the formation/growth of Cu3Sn. Also Paul [16] observed that even 1 at.% of Ni addition into copper results in increase of the thickness of Cu6Sn5.
Conclusions
The presented results showed that the 1 at.% nickel addition into the tin substrate did not substantially affect the growth of Cu3Sn phase, while it strongly influenced the morphology and chemical composition of the (Cu1−xNix)6Sn5 phase. The latter phase occurred in two forms/variants—almost continuous layer and detached irregular grains. The fluctuation of the Ni concentration in the phase was also observed. The studies of the formation kinetics of the Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 phases indicated that the dominating growth mechanism was a volume diffusion process. In the case of the Ni-rich (Cu1−xNix)6Sn5 phase, the growth showed a complex mechanism of transport. The comparison of the diffusion coefficients as well as activation energies calculated for Cu3Sn and Ni-poor (Cu1−xNix)6Sn5 phases with literature data, revealed that the presence of the nickel in the tin substrate did not influence the rate of formation of those phases in comparison with the binary Cu/Sn diffusion couples.
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This work has been financially supported by the National Science Centre under Grant No. 2011/03/B/ST8/06158.
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Wierzbicka-Miernik, A., Miernik, K., Filipek, R. et al. Kinetics of intermetallic phase growth and determination of diffusion coefficients in solid–solid-state reaction between Cu and (Sn+1at.%Ni) pads. J Mater Sci 52, 10533–10544 (2017). https://doi.org/10.1007/s10853-017-1187-2
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DOI: https://doi.org/10.1007/s10853-017-1187-2