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Using FEM, cracking is correlated with average inelastic strain and strain energy density

Predictive models for fatigue life estimation of solder joints are empirical in nature and usually involve a relation between a certain damage parameter, for instance, strain energy density or inelastic strain to the experimentally measured characteristic life. The most common approach averages the damage parameter accumulated in the region of the solder joint with the highest likelihood of failure. A variety of such models exist for SnPb solder joints and to a lesser degree for Pb-free solder joints.^1-4,6,9 What has been missing from the picture is an intermediate set of data, which, although not necessary for all empirical models, may shed some light into the crack behavior of solder joints as a function of the imposed strain. Darveaux has provided an extensive range of data for SnPb-based alloys and for SnAg.¹⁰ This work focuses on crack growth rate measurements of SnAg4Cu0.5.

Test sample. The test sample was a 14 x 7 x 0.68 mm wafer-level chip scale package (WLCSP) device designed at IMEC. The footprint of the device consists of two 16 x 3 arrays (Figure 1). The die was a dummy DRAM memory die manufactured with IMEC's Thin Film technology. The structure consists of a 5 µm thick copper layer patterned to form a daisy chain when mounted on the PCB. BCB was used as a passivation layer and soldermask, and is opened over the pads to create soldermask-defined pads. The solder pad pitch is 0.8 mm and the opening is 0.25 mm. The device was bumped with 0.3 mm diameter solder spheres of SnAg4Cu0.5 composition from Umicore Corp. The bumping process involved applying tacky flux to the device pad followed by ball placement and solder reflow. The devices were then assembled onto a 1.6 mm thick FR-4 board with standard surface-mount processes of screen print, placement and reflow. The test board consists of 19 devices and can be monitored in-situ in the thermal cycling chamber.

Click here to see all tables and figures (1.8MB PDF file).

The final mount height of all samples was measured and the solder joint standoff estimated from these measurements. A few samples were cross-sectioned at various intervals for icrostructural evaluation and to measure the joint diameter. X-ray image analysis was performed on some samples and the joint diameter extracted from these images. On average, the joints were 205 µm tall with a standard deviation of 16 µm. Solder joint diameter was 317 µm with a standard deviation of 17 µm. These data sets were used as an input for the finite element modeling.

Test procedure. The board was subjected to thermal cycling and two units taken out at different intervals, depending on the cycling condition and the expected characteristic life based on previous experiments. The interval was approximately 1/6 of the estimated time to the last failure. Thermal cycling conditions are described in Table 1. The cycled device was then placed in a red dye (Steel Red Dye from Dykem). This dye has sufficiently low viscosity to penetrate the cracks that may have been generated in the joint due to thermal cycling. To aid dye flow, the sample is cleaned with acetone and dried completely by hot air. The dye was dropped onto one of the corners and permitted to fill the region under the device with capillary action along with an externally applied vacuum (to ensure complete removal of all air). The excess dye was then removed and the sample baked at 90°C for 6 hrs. to cure the dye. Once the dye was cured, the chip was removed from the assembly by means of a quick dip in liquid nitrogen and a gentle push on the edge. This ensures easy removal of the chip without damaging the solder joint shape (Figure 2).

Modeling. All the modeling work was performed with MSC Marc Finite Element software. Figure 3 shows the 3-D model.

All materials were assumed to be linear elastic in nature except the solder, for which we used the creep behavior model as described by Wiese et al.³ All simulations were performed with 3-D nonlinear elements. Syed evaluated the use of different solder creep models and found that most of these models lie within a narrow band.² It is further concluded that the models that use creep only (no plastic flow) can be used with a reasonable correlation to the experimental fatigue life.

The measurement of assemblies indicates a variation in the solder joint standoff, hence simulations were performed for three different standoff heights (170, 205 and 240 µm) to establish a range of inelastic strain energy densities and strains accumulated in the critical region of the joint. Figure 3 shows the region from which the inelastic strain accumulated has been extracted. The mesh density for this region has been also varied with element thicknesses of 25, 12.5 and 8.3 µm by changing the number of layers in the damage volume. The region of the solder joint to a distance of 25 µm from the solder pad is used as the damage volume. More details regarding the setting up of the FE Model with MSC Marc for similar devices are described by Vandevelde et al.⁶

Results

Table 2 lists the crack growth rates measured for the outer 12 joints in each quarter of the device (Figure 4). Based on data collected from the samples at specific intervals for the different cycling conditions (a total of 2000 joints were examined: 8 joints per strain condition x 5 cycle intervals x 12 imposed strain values per temp. profile x 3 thermal profiles), the measured data for crack growth rates were plotted against the estimated inelastic strain and strain energy density values (for simulations using the mean standoff and two layers of elements in the damage region). The crack growth rates are measured by fitting a linear trend between the measured area and the number of cycles the sample was subjected to. The linear fit consistently gives the best R2 (>0.85) value of all the possible fits. The slope of this line is the crack growth rate. This rate is estimated for each different strain condition.

To measure the crack area on the device pad, image analysis software UTSCSA Image Tools is used. This software marks out an area of the image and counts the number of pixels. The pixel count is calibrated against images of samples of known lengths taken at the same magnification as that of the images of cracked area. Figure 5 shows a representative image of the cracked solder joints.

Discussion of the crack area of the solder joint specifically refers to the projected area of the actual cracked area onto two dimensions. All measurements in this paper refer to this 2-D projected area and not the true crack area (Figure 5). True crack surface is a very complex 3-D surface and as such difficult to measure. Darveaux has published the relations between inelastic strain/strain energy density as function of crack length. ^9,10 An idealized crack area based on this crack length measurement is used to estimate the crack area and relations between strain/strain energy density and crack have also been established. Darveaux also distinguishes between the primary and secondary crack growth rates. In our work, we focused on measuring the total crack area and have not separated the primary and secondary cracks. We believe that this approach is valid as both the primary and secondary cracks grow during the different parts of the thermal cycle and at the end this total crack area will be correlated to the accumulated inelastic strain energy density/ strain within a single cycle.

Each joint is at a different distance from the neutral point and has a different strain imposed per cycle on it. During cycling, the cracking of each joint is governed by the damage induced, which is a function of the strain imposed. Thus, if we can estimate the strain imposed on each joint and measure the crack growth rate for each corresponding joint, we will then have a larger data set for a wider range of strain ranges/strain energy densities accumulated in the joints per cycle. This is precisely what has been done in this work. The device has quarter symmetry and thus there are 24 joints with different strains imposed on them. By measuring the crack growth rates in all the joints, we can theoretically obtain the correlation for a wide range of strains.

However, this approach implicitly assumes that the strain each joint experiences remains constant throughout the duration of test. In reality, with every temperature excursion, the crack in the joints grows and the change in assembly stiffness results in continual strain redistribution. When one or more joints fail completely, this redistribution increases the strain on the remaining joints by as much as 40%, depending on the proximity to the failed joints and the distance to neutral point. In this study, the measurement was done only to the point where a few outer joints fail and hence we estimate (based of FE simulations of subsequent joint failures) that the imposed strain change lies in the range of 10 to 15%.

For inner joints, the total duration of testing may occupy only 10% of the expected fatigue life of these joints. Given the high standard deviation, especially for the lower crack areas, it can be concluded that fitting a line for these data points and extrapolating it outwards has the potential for giving erroneous results. In the data presented here, we have not used the measurements for the joints whose total cracked area at the last measurement is less than 30% of the total solder pad area. This reduces the number of usable joints to half. Figure 6 shows a representative plot of the crack growth data for a few joints from the three cycling conditions.

Variation in measurements. Figure 7 plots the normalized standard deviation vs. the measured crack area of the solder joints. The standard deviation is in the range of 0.8 to 1 for the smaller crack areas and decreases with the increasing crack area. This has also been observed by Darveaux for SnPb alloy.¹⁰ In general, beyond the crack area of 50% of the total area, the standard deviation drops to 0.2 to 0.3. While this is a rather high value in general, it reflects the reality in a typical assembly. Causes for this variation are numerous but we believe the three main reasons in these particular assemblies are:

Variation in standoff. As reported, the average standoff of the solder joint is 205 µm with a normalized standard deviation of 0.06. This translates to an estimated normalized deviation of 0.15 to 0.2 in the estimation of the strain and strain energy density values.

Sample selection. In the experimental procedure, two samples are taken out at fixed intervals during the cycling. The time from the first failure to last can occupy as much as 50% of the total fatigue life in the case of the WLCSP (due to the high strains). As samples are randomly chosen, there is a probability of choosing a sample which may well be at the end of its life or may be only halfway through its life. Incorporation of this variation in our crack growth model is unresolved at the moment but it is easy to see that this can give an additional variation in the crack area measurements.

Measurement accuracy. We estimate that although the analysis software permits pixel measurements and thus can potentially give a linear accuracy of ~5 µm, the area measurement accuracy is around 1000 sq. µm.

Crack growth rate analysis. The relation between the crack growth rate and the inelastic strain/strain energy density is typically described with a power law

dA/dN = C₁(e)n₁ (I)

dA/dN = C₂(DW)n₂ (II)

where dA/dN is the crack area growth rate expressed in mm², C₁, C₂ are constants, n₁, n₂ are exponents fitted to the data, e is the average accumulated inelastic strain in damage volume over a single cycle and DW is the accumulated inelastic strain energy density in damage volume over a single cycle.¹⁰ Figures 8 and 9 are the plots of the crack growth rate vs. inelastic strain and strain energy density respectively for the standoff height of 205 µm and for two layers of elements in the damage volume. Table 3 lists the constants for different element thicknesses/mesh densities used in the finite element simulations. In all cases, the exponent values lie in the range of 0.95 to 1.05 for strain energy density correlation and between 1.1 to 1.25 for strain correlation. The correlation factor (R²) for all the cases lies in the range of 0.85 to 0.9.

For devices with such high strain values, crack initiation occurs early on in the cycling. Zhang et al¹¹ have shown that for WLCSP devices, the crack initiation occupies a very small part of the total fatigue life. Time zero analysis of the devices does not show any initial cracking but if the crack growth rate plots are extrapolated backward, one can see that this initiation takes place within the first few cycles. Hence in this study, we have not provided any correlation for the number of cycles to crack initiation.

Microstructural evaluation. Thermally cycled samples were cross-sectioned and analyzed with the aid of polarized light. Figure 10 shows a cross-sectioned joint after 480 cycles of 0° to 100°C. Looking closely in the region of the fracture crack, the most striking feature is the average grain size. Significant recrystallization has taken place in the region around the crack and also in front of the crack tip (Figure 11). This recrystallized zone extends to a region of 25 to 30 µm from the die pad. The average grain size in the recrystallized zone is around 10 µm. This has also been observed by Henderson⁷ and Reinikainen.⁸ Figure 11 shows SEM images of a device cycled in -40 to 125°C for 100 thermal cycles. Note that this sample was not opened by dipping in liquid nitrogen but was simply sheared off, thus the images are representative of the actual fracture conditions. The fatigue crack zone is readily distinguishable with the recrystallized grains (Figure 12). Fatigue crack striations can also be seen on the individual grains (Figure 13). Henderson⁸ et al have explained this crack growth mechanism as a combination of recrystallization of the grains enhancing the grain boundary sliding resulting in intergranular fracture. This has also been reported in the literature for high strain loading conditions.¹² Intermetallic separation is seen in some fractured samples but these occurrences are random and form a small portion of the overall measurements.

Conclusions

We have attempted to measure the crack growth rate in SnAgCu solder alloy. We measured these data for a wide range of strains from a single device. These assemblies were subjected to three different thermal cycles.

• The crack growth data in the strain range of 0.02 to 0.1 (volume averaged) and a strain energy density range of 1 to 5 MPa has been presented here. Due to the variation in solder joint height in the assembly, these data have been correlated to a range of strain values with a probabilistic distribution.

• For a vast majority of the joints examined, the fatigue crack was ductile. In some instances intermetallic separation occurred, but their extent and frequency was low.

• The normalized standard deviation for measured crack area is high (0.8 to 1.0) for the lower crack areas, drops with increasing crack area and settles down to a value in the range of 0.2 to 0.3.

• Power law fitting with the inelastic strain and strain energy density provide a reasonable goodness of fit (R²~0.8 and higher). The estimated strain and strain energy density values for the joints depend on the solder material model used and also on the element mesh size. We have provided these correlations for a certain range of element sizes.

• Microstructural analysis eveals that the region under highest strain shows severe recrystallization. This recrystallization occurs ahead of the crack front. The damage volume used to extract data from the FE Models is taken to be the zone where recrystallization is seen, in the range of 25 to 30 µm.

The correlation data published here should be used with some caution because they are generated from a creep-only solder material model. Moreover, the strain ranges are on the higher end of typical applications and the validity of extrapolating this to lower strain values is unknown. Given the nature of the test device, loading the solder joints takes place in more or less pure shear condition. These data may be used for devices that operate in high strain ranges and with the use of appropriate damage volume. The damage volume chosen should be the recrystallization zone in the solder joint, as has been done in this work. In future, more measurements will be conducted on specially designed test vehicles and also for lower imposed strain values and the data presented here will be updated.

Acknowledgments

The authors would like to acknowledge the valuable assistance of Peter Ratchev and Nele Van Steenberge for the analysis of samples and Prof. Dr. Jozef Van Dyck for interesting discussions regarding statistical analysis. We would also like to acknowledge the support of the ALSHIRA Project sponsored by IWT Flanders, Belgium (imec.be/ALSHIRA), Olivier Hutin and Stefan Merlau of Umicore Corp. for providing SAC solder spheres and Alcatel Bell, Geel for assembly support.

References

1. R. Darveaux, K. Banerji, A Mawer and G. Dody, "Reliability of Plastic Ball Grid Array Assembly," Ball Grid Array Technology, McGraw-Hill, 1995.

2. A. Syed, "Accumulated Creep Strain and Energy Density Based Thermal Fatigue Life Prediction Models for SnAgCu Solder Joints," Electronic Components and Technology Conference, pp. 737-746, June 2004.

3. S. Wiese, et al, "Microstructural Dependendence of Constitutive Properties of Eutectic SnAg and SnAgCu Solders," Electronic Components and Technology Conference, pp. 197-206, May 2003.

4. A. Schubert, et al, "Fatigue Life Models of SnAgCu and SnPb Solder Joints Evaluated by Experiments and Simulations," Electronic Components and Technology Conference, pp. 603-610, May 2003.

5. Q. Zhang, et al, "Viscoplastic Constitutive Properties and Energy-Partioning Model of Pb-free Sn3.9AgCl.6Cu Solder Alloy," Electronic Components and Technology Conference, pp. 1862-1868, May 2003.

6. B. Vandevelde, M. Gonzalez, P. Limaye, P. Ratchev and E. Beyne, "Thermal Cycling Reliability of SnAgCu and SnPb Solder Joints: A Comparison for Several IC-Packages," EuroSimE 5th International Conference, pp. 565-570, May 2004.

7. D.W. Henderson, et al, "The Microstructure of Sn in Near-Eutectic SnAgCu Alloy Solder Joints and Its Role in Thermomechanical Fatigue," J. Mater. Res., vol. 19, pp.1608-1612, June 2004.

8. T.O. Reinikainen, et al "Deformation Characteristics and Microstructural Evolution of SnAgCu Solder Joints," EuroSIME 6th International Conference, May 2005.

9. R. Darveaux, "Effect of Simulation Methodology on Solder Joint Crack Growth Correlation," Electronic Components and Technology Conference, pp. 1048-1063, 2000.

10. R. Darveaux, "Crack Initiation and Growth in Surface Mount Solder Joints," ISHM International Symposium on Microelectronics, pp. 86-97, November 1993.

11. L. Zhang, R. Sitaraman, V. Patwardhan, L. Nguyen, N. Kelkar, "Solder Joint Reliability Model Vath Modified Darveaux's Equations for the Micro SMD Wafer Level-Chip Scale Package Family," Electronic Components and Technology Conference, pp. 572-577, May 2003.

12. A.R. Syed, "Thermal Fatigue Reliability Enhancement of Plastic Ball Grid Array (PBGA) Packages," Electronic Components and Technology Conference, pp. 1211-1216, May 1996.

This article was presented at SMTA International in September 2005 and is used with permission of the SMTA (smta.org).

Paresh Limaye is a researcher at IMEC (imec.be); paresh.limaye@imec.be. Bart Vandevelde is section leader and senior scientist at IMEC. Dirk Vandepitte and Bert Verlinden are professors of engineering at Katholieke Universiteit (kuleuven.ac.be).