Fit of Additional Data to First Order Creep Model

Kim et al.'s Data and Effect of Cooling Rate

Figure 30: Fit of first-order SAC model (solid line) to Kim et al.'s data for "Rapidly Cooled" specimens.

Since the first-order SAC creep model given by equation (38) is essentially empirical, it is important to bounce the model against additional, independent test data with the goal of identifying limitations of the model. Figures 29 and 30 show how the model compares to data gathered by Kim et al. (2001) for Sn-3.5Ag-0.7Cu, Sn-3.0Ag-0.5Cu and Sn-3.9Ag-0.6Cu tensile specimens. The specimens were either Slowly Cooled (SC) or Rapidly Cooled (RC) with cooling rates of 0.012°C/sec and 8.3°C/sec, respectively. The cooling rates were quoted as average values in the temperature range 230°C to 180°C. As pointed out by Kim et al., "RC is equivalent to the cooling speed for soldering in practical conditions in industry". The raw data, obtained from constant rate stress / strain tests conducted at room temperature, is given in Table B.3. The reader is referred to Kim et al.'s paper for further details on the experimental conditions and the authors' discussion on creep strength versus alloy composition and microstructure. Note also that specimens that were Moderately Cooled (MC) - at a rate of 0.43°C/sec from 230°C to 180°C - showed similar microstructures and UTS results as for the RC specimens.

Figures 29 and 30 show that the data for RC specimens fit the SAC creep model well. In Figure 8, the RC data falls within or very close to the model correlation band. Figure 30 shows that the RC data falls on either side of the centerline of the SAC model (shown as a solid line) and that the effect of alloy composition is rather small (compared to other effects), in the range 12% to 25%. The solid line in Figure 30 was obtained by back-solving equation (39) for stress at a given strain rate.

On the other hand, Figure 29 shows that the data for the SC specimens falls outside the correlation band of the SAC model. The offset in terms of creep rate is a factor of 100 times. This is shown by the solid line going through the SC data points which is set a factor of 100 times above the centerline of the SAC model. In terms of stress, and as pointed out by Kim et al., the strength of SC specimens is about 50% that of RC specimens.

Clearly, there is a strong effect of cooling conditions which is explained by Kim et al. in terms of the microstructure. Cooling rates were not reported quantitatively in the Kariya et al., Neu et al., Schubert / Wiese et al. publications. However, Kariya et al. indicated that their specimens were cooled rapidly ("water-quenched"). Thus, it seems appropriate that the SAC first order creep model agrees with the RC data but does not agree with the SC data of Kim et al.

NCMS Compression Creep Data

Figure 31: Fit of NCMS Sn-4.7Ag-1.7Cu compression creep data to the first-order SAC creep model.

Results of creep compression tests at 20°C, 75°C and 125°C for the NCMS-studied Sn-4.7Ag-1.7Cu alloy (NCMS, 1998) are plotted in Figure 31. Test specimens were short cylinders of dimensions: 0.4" in diameter by 0.8" in height. Interestingly, the specimens were cooled rapidly since, according to the NCMS report, molten solder was poured into a casting "mold that was chilled". The compression creep tests were run in load control mode.

The NCMS data falls within or close to the lower bound of the correlation band of the SAC creep model. Although the NCMS alloy has higher Ag and Cu contents and the SAC creep model is based on tensile creep data, the model seems to apply, at least to a first-order, to compression creep. However, the fact that the data is slightly to the right of the tensile master-curve and seems to follow a trendline with different slopes, suggests that the SAC alloy may also be an uneven material (similar to Sn-3.5Ag solder). Additional compression data would be needed to better characterize the compressive versus tensile response of SAC solders.

The Kim et al.'s creep data for the SAC specimens that were rapidly cooled is also shown on the same plot (Figure 31) to illustrate that the two datasets provide for first-order validation of the creep model at different stress levels: above 35 MPa for the Kim et al.'s "RC" data, below 35-50 MPa for the NCMS data.

Flip Chip Solder Joint Shear Data

Figure 32: Flip-chip solder joint shear model versus master-curve of bulk SAC tensile creep model.

Wiese et al., 2001, tested flip-chip solder joints of composition Sn-3.8Ag-0.7Cu in shear at 5°C, 25°C and 50°C. Their data (shown in Figure 20 and 23 in Wiese et al., 2001) was fit to the following power-law model:

where Q = 67.9 kJ/mole is the activation energy of the SAC creep model. Data points that are shown for equation (41) are calculated at temperatures of 5°C, 50°C and 50°C and in the stress range of the original test data obtained by Wiese et al.

Clearly, the flip-chip creep model and the master-curve of the tensile SAC creep model follow different trends. A similar difference between creep in shear and in tension was pointed out by Wiese et al., 2001. There are several possible reasons for this, although it is not clear how these differences can be resolved:

• Significant differences in micro-structures and dispersion of chip metallization elements or
  intermetallics in the flip-chip joints, the effects of which are not captured in the SAC creep model.
• Equation (40) was obtained by fitting shear creep data that were converted to tensile data using the uniaxial stress and strain transformations: = 3 and = /3. The latter are based on the application of a multi-axial Von-Mises yield criterion. This widely-used criterion is for materials with time-independent plastic flow and, in general, has not been verified under creep conditions. The applicability of the Von-Mises criterion to SAC solders has not been demonstrated either and may be questionable as in the case of Sn3.5Ag.
• The shear creep data derived by Wiese et al. converts shear forces and displacement rates into average shear stresses and shear strain rates assuming a uniform shear distribution in the minimum section of hour-glass shaped flip-chip joints. While this is a first-order engineering approach at handling the force-displacement rate data, it may be an over-simplifying assumption because of the complexity of shear strain distributions in solder joints.

A similar discrepancy between creep in shear and in tension has been reported by Darveaux et al., 1995, for Sn-Pb and Sn-3.5Ag solders.