Chapter 2 Influence of Cu column UBMs on current crowding and Joule heating
3.1 Introduction
3.3.2 Theoretical analysis on flux divergence at the IMC/solder interface
To explain the failure mode transition, we develop a model to calculate the EM flux and chemical potential flux of Sn at the IMC/solder interface. Figure 3-3 illustrates schematic drawing of the solder joint subject to a downward electron flow.
JSn in Sn stands for the downward EM flux of Sn atoms in the solder, while JSn in IMC represents the upward chemical potential flux of Sn atoms in the IMCs against the electron wind force. Considering the flux divergence at the interface of the solder and
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the IMC, when the downward Sn flux leaving the interface is larger, voids will form at the interface. Nevertheless, when the upward Sn flux is larger, the interfacial IMC will grow and no voids will form at the interface. In the following, we will calculate the two fluxes quantitatively using the available data in literature. Electromigration flux, JEM is typically expressed as [63]
current density. In solder near the IMC, Sn will migrate toward the substrate side by the electron wind force. The Sn EM flux is
j
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potential fluxes. The Sn chemical potential flux is
t
The IMC growth rate constants for Ni3Sn4 IMC in a Sn-Ag-Ni system are 0.0088 and 0.1178 µm/h0.5 at 125 °C and 175 °C, respectively [66]. In addition, the IMC growth rate constant for Cu6Sn5 IMC in a Sn-Cu-Ni system is 0.2232 µm/h0.5 at 150 °C [67].
With these parameters, we can plot the downward Sn EM flux and the upward Sn chemical flux as a function of time. Figure 3-4(a) shows the curves for the Sn EM and chemical potential fluxes stressed by 1.15 × 104 A/cm2 at 125 °C as a function of time.
Electromigration flux driven by a given current density at a constant temperature is independent of time, so it appears a horizontal line in the plot as a function of time.
However, chemical potential flux at a constant temperature is inverse proportional to the square root of time as described in Eq. (3-5), so the curve behaves like a hyperbolic curve in the plot. The Sn EM flux is always larger than the chemical potential flux in the 474.7 h stressing time, which agrees well with the void formation failure mode as shown in Figure 3-2(a).
On the contrary, chemical potential force may increase as the temperature increases because the metallurgical reaction rate is higher at high temperatures. Figure
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3-4(b) shows the curves for the Sn EM and chemical potential fluxes stressed by 5.3 × 103 A/cm2 at 175 °C as a function of time. The chemical potential flux represents the sum of the two upward Sn fluxes to form Ni3Sn4 and (Cu,Ni)6Sn5 IMCs. As shown in 3-2(b). From the mention above, the theoretic calculation successfully explains the experimental results.
It is noteworthy that some Sn atoms refill to the cathode side against electron wind force may be attributed to back stress of EM [68,69]. The Cu, Ni, and Sn atoms migrated to the substrate side because of electron wind force. However, the solder joints were confined by the underfill, and there were no hillocks or extrusion on the substrate side to release the compressive stress on the substrate side. At the same time,
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a tensile stress was developed on the chip side due to the deficiency of Cu, Ni, and Sn atoms. Therefore, a stress gradient was built up across the solder joints, which triggered the migration of Sn atoms to the original location of UBMs. On the other hand, the EM behaviors at the IMC/solder interface may be also affected by the Sn grain orientations [70]. When the electron flow direction is along the c-axis of Sn crystals, rapid depletion of the UBM dominates the EM behavior due to the fast diffusion of Cu and Ni atoms. However, so far, there is no available way to control the Sn grain orientation in a solder bump, and it deserves more study.
3.4 Summary
In summary, we investigated the EM failure mechanisms in SnAg solder joints with 5-μm-Cu/3-μm-Ni UBM at various stressing conditions. It was found that both the void formation and the UBM consumption failure mechanisms occurred at the stressing conditions without a TM driving force confirmed by IR microscopy. By considering the flux divergence at the IMC/solder interface, we proposed a model to calculate the Sn EM fluxes as well as the chemical potential fluxes. When the Sn EM flux is larger, void formation at the interface was responsible for the failure. However, UBM dissolution and IMC formation dominated the failure mechanism when the Sn chemical potential flux toward the cathode side exceeded. This model successfully
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explains the experimental results.
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Figure 3-1 Cross-sectional schematic structure of (a) the electromigration tests layout design and Kelvin bump probe structure for measuring bump resistance and (b) the solder joint configuration used in this study.
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Figure 3-2 Cross-sectional SEM image showing the microstructure of the solder joint after current stressing by (a) 1.15 × 104 A/cm2 at 133.2 °C for 474.7 h and (b) 5.3 × 103 A/cm2 at 175.3 °C for 83.2 h.
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Figure 3-3 Schematic drawing of a solder joint subject to a downward electron flow.
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Figure 3-4 The calculated curves for the Sn EM and chemical potential fluxes stressed by (a) 1.15 × 104 A/cm2 at 125 °C and (b) 5.3 × 103 A/cm2 at 175 °C as a function of time.
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