The average drift velocity due to electromigration, as given by Huntigton and Grone [38] is
where J is the atom flux, C is the density of metal ions, B is the mobility, k is Boltzmann’s constant, T is the absolute temperature, eZ* is the effective charge of the ions, ρ is the metal resistivity, j is the electrical current density, Ea is the activation energy of diffusion, and D0 is the prefactor of diffusion constant. Equation (1) can be rewritten as
) Taking the logarithm of both sides of equation (2)
k
Therefore, by measuring solder drift velocity as a function of reciprocal temperature, the activation energy Ea and the product of diffusivity and effective charge number DZ* can be obtained.
Fiigure 4-8 shows the plot of ln(vT/j) as a function of the reciprocal temperature.
The activation energy (Ea) can be determined from the slope of the fitted line, and its value is 0.41eV in the temperature range of 80℃ to 120℃. However, the temperature in the solder needs to be calibrated due to the Joule heating effect, as shown in Figure 4-4.
The real temperatures in the solder were higher than the ambient ones, and the activation energy was calculated to be 0.45 eV using the real temperatures.
In addition, the product of diffusion diffusivity and effective charge number, DZ*,
1/T (K)
Figure 4-8: Plot of the ln vT/j as a function of reciprocal temperature. The activation energy of 0.41 eV was obtained from the slope of the fitted line.
0.00252 0.00259 0.00266 0.00273 0.00280 0.00287 -24.4
-24.2 -24.0 -23.8 -23.6 -23.4 -23.2 -23.0 -22.8
ln(vT/j)
0.41 eV
can be calculated from equation (3). Table I summarizes the product of the diffusivity and effective charge number, DZ*, and its average values are -1.8×10-10 cm2/sec at 80℃, -5.0×10-10 cm2/sec at 100℃, and -7.2×10-10 cm2/sec at 120℃. In order to estimate the value of Z*, the diffusivity data for pure Sn were adopted [49].
The average values of Z* were -27 at 80℃, -33 at 100℃, and -23 at 120℃, which are reasonable for solder materials.
Table 4-1: The product of diffusivity and effective charge number (DZ*) for various stressing conditions.
Temperature ( )℃ Current density (A/cm2) DZ* (cm2/sec)
80℃ 1.0×105 -2.26×10-10
80℃ 8.4×104 -1.72×10-10
80℃ 7.1×104 -1.61×10-10
Ave. : -1.86×10-10
100℃ 9.0×104 -6.88×10-10
100℃ 6.2×104 -5.35×10-10
100℃ 4.4×104 -2.80×10-10
Ave. : -5.01×10-10
120℃ 7.5×104 -1.03×10-9
120℃ 5.7×104 -1.03×10-9
120℃ 4.0×104 -8.12×10-10
120℃ 2.0×104 -3.37×10-10
Ave. : -7.26×10-10
D. Effect of microstructure on electromigration in eutectic SnAg3.8Cu0.7 solder stripes
It has been recognized that electromigration lifetime is strongly correlated to the microstructure of the metal lines. A number of studies have been carried out to investigated the effect of microstructure on electromigration life time [51]-[63]. By annealing the metal lines at elevated temperature to induce grain growth, the electromigration lifetime was found to increase until grain growth was constrained by the metal line thickness.
To investigate the effect of microstructure on electromigration in eutectic SnAg3.8Cu0.7 solder, as-prepared eutectic SnAg3.8Cu0.7 solder stripes were pre-annealed on the hotplate at 150℃ for 72 hours in the atmosphere. Afterwards, the pre-annealing samples were ground and polished and were stressed at various current densities and temperatures.
Figure 3-10 illustrates the cross-sectional TEM image of the specimen after heat treatment at 150℃ for 72 hours. It is found that the solder grains grew bigger. Layers of scallop-type Cu6Sn5 IMC formed at the interface between the solder and Ti layer.
Specifically, a thin (Ti, Sn, Cu) mixed layer formed beneath the Cu6Sn5 intermetallic compound, and the thickness is about 30 nm. The average thickness of the IMC was 1.42 µm. Through theoretical calculations, it was found that about 80% of the applied current would flow inside the solder, whereas about 19% of the current drifted along the IMC layer, and only about 1% stayed in the Ti layer.
The microstructurs of the as-prepared and the pre-annealed eutectic SnAg3.8Cu0.7
solder are respectively shown in figures 3-11(a) and (b). The samples were etched in the HCl + CH3OH (at the ration of 1:50) solution for one second to reveal the grain size.
Ag3Sn particles precipitated in the matrix and decorated the grain boundary in the as-reflowed sample. After pre-annealed at 150℃ for 72 hours, coarsening of Ag3Sn particles and growing of (Sn) grains occurred. Ag3Sn particles grew from initial sub-micron size to about 1 µm, and the number of particles reduced. The grain size grew from 1 µm to 7-10 µm after the annealing.
Figure 3-12 displays the average drift velocity of the pre-annealed stripes as a function of applied current density, showing a linear relationship for the three temperatures. By extrapolating the fitting line to the zero drift velocity, the threshold current density can be obtained. The estimated values are 4.6 × 104 A/cm2 at 80 °C, 3.9 × 104 A/cm2 at 100 °C, and 2.2 × 104 A/cm2 at 120 °C.
Figure 3-10 Cross-sectional TEM image of the solder Blech specimen after heat treatment at 150℃ for 72 hours.
Figure 3-11. Plan-view SEM images of eutectic SnAg3.8Cu0.7 solder (a) as-prepared, and (b) annealed.
(a)
(b)
Figure 3-12. Average drift velocity of the pre-annealed solder stripe as a function of applied current density. The threshold current densities were obtained by extrapolating the fitted lines to zero drift velocity.
4-3 Discussion
A. Threshold current density of SnAg3.8Cu0.7 solder stripes
To verify if these extrapolated values of threshold current density are correct or not, some specimens were stressed at current densities below the threshold current density.
Specimens were stressed at the current density of 3.5 × 104 A/cm2 at 80°C, 2.6 × 104 A/cm2 at100 °C, and 1 × 104 A/cm2 at100 °C for 72 hrs, and no detectable volume change was found.
Various stressing conditions have been investigated to study the electromigration behavior of SnAgCu bumps, and a large variety of conditions were reported to have caused damage in the bumps. Wu et al. conducted a MTTF experiment for SnAg4.0Cu0.5 bumps with thin-film under-bump metallization (UBM) of Al/Ni(V)/Cu, and found that the MTTF was 1454 hours for the bumps stressed by 5.0 × 103 A/cm2 at 153°C [45]. In addition, Choi et al. reported that the eutectic SnAgCu bumps with Al/Ni(V)/Cu UBM failed after the current stressing at 2.25 × 104 A/cm2 at 140 °C for 132 hours [42].
However, Lin et al. investigated the current carrying capability of eutectic SnAgCu bumps with 6 µm Ni under bump metallization, and found that there was no obvious electromigration damage in the bumps after the stressing by 2.55 × 104 A/cm2 at 150 °C for 2338 hours [46].
The above discrepancies may be due to the serious current crowding in the line-to-bump configuration of flip chip solder joints and also the Joule heating effect in the solder joints. Our previous simulation study on current density distribution showed that the joints with thin film Al/Ni(V)/Cu UBM had more serious current crowding effect
inside the solder bumps than that in the joints with thick UBM [50].
The current crowding ratio may be as high as 23 inside the solder for the joints with thin film Al/Ni(V)/Cu UBM, which means that the maximum current density near the solder close to the entrance point of Al trace is 23 times higher than the average value.
Thus the maximum current density in these solder bump may exceed 1.0 × 105 A/cm2. However, the current crowding ratio for the bumps with 6 µm electroless Ni UBM is about 11, leading to a higher current carrying capability by these bumps. On the other hand, Joule heating may increase the temperature of the solder bump, and the amount of temperature increase depends on the joint geometry, materials, and applied current.
Choi et al. found that the temperature increase due to Joule heating was between 38°C and 52°C.7 Therefore, the real stressing temperature was higher than 178°C for their bumps. Based on the above discussion, the threshold current density in the present work seems to be reasonable.
B. Activation energy of eutectic SnAg3.8Cu0.7 solder stripes
The activation energy we measured by edge displacement technique was 0.45 eV, which was lower than the published value. Choi et al. measured the MTTF of eutectic SnAgCu solder joints, and they estimated the activation energy to be 0.8 eV by using Black’s equation [42]. It is speculated that the difference may be attributed to the smaller grain size of the solder in Blech specimens than in flip-chip solder joints. As shown in Figure 4-3(b), the grain size of the solder was only about 1 µm, which is smaller than that in the solder bumps. In addition, the stressing temperatures in this study ranged from 70%
to 77% of the absolute melting point of the eutectic SnAgCu solder. Therefore, the activation energy presented in this study is a combination of grain boundary and lattice diffusion. As a result, the contribution of grain boundary diffusion may be larger in our sample, resulting in a decrease in the activation energy for the solder film. The effect of grain boundary diffusion may have also affected the value of the estimate effect charge number which is smaller than what is expected in a bulk Sn sample.
C. Electromigration of Cu6Sn5 intermetallic compounds
Theoretically, a layer of Cu6Sn5 with 1.36 µm thick formed when the 0.4 µm Cu was entirely consumed during the reflow process. Our cross-sectional TEM results show that the average thickness of Cu6Sn5 was 1.42 µm, which almost matches the theoretical value.
Therefore, the Cu layer was almost consumed completely. In addition, the composition of the solder may not change much, since we applied a large amount of solder paste on the UBM during the reflow process, and then the excess solder was polished away, as described in the experimental section. Consequently, the composition of the SnAgCu is expected to remain close to the eutectic composition.
The Cu6Sn5 IMC exhibited a better electromigration resistance than the SnAg3.8Cu0.7
solder, since the IMC remained intact after electromigration test for most of the specimens, as shown in figure 4-5(b). However, for some specimens stressed at more stringent conditions, the IMC on the cathode end was also found to migrate away after the depletion of the solder. Figures 4-12 (a) and (b) demonstrate the microstructure evolution in the SnAg3.8Cu0.7 solder stripe before and after the stressing by 1.2
×105A/cm2 current density for 30 hours at 120℃, respectively. Both the SnAg3.8Cu0.7
solder and Cu6Sn5 IMC were migrated by electron flow on cathode side. In the meantime, Sn-Cu compounds were observed in the stripe after the current stressing. When the upper solder was depleted by the electron flow, the current density flowing in the remaining Cu6Sn5 IMC became higher. This was because the resistivity of the IMC (17.5 µΩ-cm) was lower than that of the Ti layer (43.1 µΩ-cm), and the thickness of the IMC was thicker than that of Ti layer. For the above stressing condition, it was estimated that the current density in the IMC layer after the complete depletion of the solder was about 1 × 105 A/cm2.Therefore, the Cu6Sn5 IMC may migrate under such high current density.
However, the electromigration study for the IMC needs to be investigated independently in order to measure the threshold current density.
30 µm
Figure 4-12: (a) Plan-view BSE SEM image of a SnAg3.8Cu0.7 solder stripe before current stressing. (b) Plan-view BSE SEM image of the stripe after stressing at 120℃
for 30 hours. The Cu6Sn5 IMC layer was also migrated after the current stressing.
(a) Residual flux
Si substrate
Solder stripe
30 µm
(b) Ti
Si substrate Sn-Cu IMC
e
30 µm
D. Effect of microstructure on electromigration in eutectic SnAg3.8Cu0.7 solder stripes
The drift velocities for the pre-annealed stripes were lower than those of the as-prepared stripes. It is obvious that the larger the grain size is, the less the total grain boundary area available for boundary diffusion, and therefore the drift velocity decreases.
The threshold current densities of the pre-annealing stripes were 3.9 × 104 A/cm2 at 100
°C, and 2.2 × 104 A/cm2 at 120 °C, which were lower than the values obtained by the as-prepared stripes: 3.2 × 104 A/cm2 at 100 °C, and 1.4 × 104 A/cm2 at 120 °C. However, the threshold current density doesn’t make obvious change when the test temperature was 80 . ℃ It is still not clear why the threshold current density at 80 did not change much. ℃ In the pre-annealed specimens, grain boundary and lattice diffusion have a different temperature dependence. Lattice diffusion is more sensitive to temperature change. Thus, as the temperature is raised, the rate of diffusion through the lattice increases more rapidly than the rate of diffusion along the boundaries. It is concluded that in the pre-annealed specimens the lattice diffusion dominates in specimens with a larger grain size at 120℃ and 100℃. Nevertheless, at 80℃ grain boundary diffusion dominates, leading the drift velocity doesn’t change obviously. To clarify the different temperature dependence, the sample was stressed under higher temperature. Figure 3-13 shows the plot of ln(vT/j) as a function of the reciprocal temperature of the pre-annealed stripes in the temperature range of 100℃ to 140℃. The activation energy (Ea) can be determined from the slope of the fitted line, and its value is 0.8eV. The activation energy corresponds to lattice diffusion value.
Figure 3-13. Plot of the ln vT/j as a function of reciprocal temperature. The activation energy of 0.8 eV was obtained from the slope of the fitted line.
4-4 Conclusions
The SnAg3.8Cu0.7 Blech test specimens have been successfully fabricated to investigate the electromigration behavior under various current densities in the temperature range of 80 to 120C°. We used AFM to measure drift velocity and analyzed the electromigration behavior of the Pb-free solder. The threshold current densities were measured to be 4.3 × 104 A/cm2 at 80 °C, 3.2 × 104 A/cm2 at 100 °C, and 1.4 × 104 A/cm2 at 120 °C. The measured activation energy was 0.45eV for the temperature ranges from 80 to 120℃. The measured product of diffusivity and effective charge number, DZ*, was -1.8×10-10 cm2/sec at 80℃, -5.0×10-10 cm2/sec at 100℃, and -7.2×10-10 cm2/sec at 120℃.
In the pre-annealing specimens, grain boundary and lattice diffusion have a different temperature dependence range from 80℃ to 140℃. The threshold current densities were measured to be 4.6 × 104 A/cm2 at 80 °C, 3.9 × 104 A/cm2 at 100 °C, and 2.2 × 104 A/cm2 at 120 °C. The measured activation energy was 0.8eV for the temperature ranges from 100 to 140℃.
Chapter 5: Summary and Future work 5-1 Summary
Electromigration in the eutectic SnAg3.8Cu0.7 solder has been respectively investigated in solder Blech structure and flip chip solder joint in this dissertation.
The electromigration-induced failures in SnAg3.8Cu0.7 solder joints on Ti/Cr-Cu/Cu has been investigated under current density of 1 × 104 A/cm2 and 2 × 104 A/cm2 at 100℃
and 150℃. The bumps failed at chip/cathode side. Cracks occurred along the solder and UBM interface, which led to the open failure of the bump. The current crowding effect played an important role on the failure. However, the electron flow does not cause apparent damage at the board side because of a much lower current density there than that in the chip side.
The SnAg3.8Cu0.7 Blech test specimens have been successfully fabricated to investigate the electromigration behavior under various current densities in the temperature range of 80 to 120C°. We used AFM to measure drift velocity and analyzed the electromigration behavior of the Pb-free solder. The threshold current densities were measured to be 4.3 × 104 A/cm2 at 80 °C, 3.2 × 104 A/cm2 at 100 °C, and 1.4 × 104 A/cm2 at 120 °C. The measured activation energy was 0.45eV for the temperature ranges from 80 to 120℃. The measured product of diffusivity and effective charge number, DZ*, was -1.8×10-10 cm2/sec at 80℃, -5.0×10-10 cm2/sec at 100℃, and -7.2×10-10 cm2/sec at 120℃.
In the pre-annealing specimens, grain boundary and lattice diffusion have a different temperature dependence range from 80℃ to 140℃. The threshold current densities were measured to be 4.6 × 104 A/cm2 at 80 °C, 3.9 × 104 A/cm2 at 100 °C, and 2.2 × 104 A/cm2
at 120 °C. The measured activation energy was 0.8eV for the temperature ranges from 100 to 140℃.
5-2 Future work
Electromigration behavior in the eutectic SnAg3.8Cu0.7 solder stripes was investigated in the vicinity of the device operation temperature of 100 °C by using the edge displacement technique. This edge displacement technique samples are highly reproducible and easy to measure the relevant parameters for electromigration of the solder, such as drift velocity, threshold current density, activation energy, as well as the product of diffusivity and effective charge number (DZ*). Therefore, it is feasible to systematically study a series of different kinds of solders such as high Pb solder, and Sn-based solders with variety of alloy elements.
Furthermore, in our previous study Ni UBM could be able to alleviate the crowding effect compared with Cu UBM [50]. In the prospective study, it would be interesting to study the electromigration behavior with Ni UBM in our Blech specimen.
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