Abstract
The past two decades have seen many approaches to solder fatigue and solder joint life published. This subject has proved difficult as various failure mechanisms are proposed and examined. While these theoretical bases are discussed, it often leaves the end developer in a difficult situation as to how to apply an accurate simulation approach to fatigue failure for a particular package. In this article, one approach is examined and used to evaluate a “typical” metal lid flip chip BGA (ball grid array) package under variation of a few key parameters via a 2-level DOE (Design of Experiment). The parameters examined in this article are the in-plane thermal expansion coefficient of the printed circuit board (PCB), the lid material, and the temperature range for the BGA environment. The DOE showed that all three individual parameters are statistically significant, as are interaction terms with packaging materials CTEs (coefficients of thermal expansion) and temperature cycle range, ΔT. Part 1 of this article described the background information, the simulation model, and the design of experiments. Part 2 presents the results of the simulations and discuss conclusions.
Background
Part 1 of this series [1] provided detailed background on the objectives and needs for thermal simulations to predict solder joint fatigue. It also described the Ball Grid Array (BGA) package that was modeled and design of experiments approach used in this study to demonstrate the simulation method. The BGA model included a 20mm silicon die, which was attached to the package substrate with flip chip solder bumps, and the substrate, which was lidded, that was attached the circuit board with solder balls. This article presents detailed information on the solder material models and the analysis results. Both articles in this series are based on material first presented in Reference [2].
Solder Material Models
The material models for the solder depend on what fatigue model is chosen to calculate the results. This paper follows the model type used in Syed et. al. [3].
The elastic-plastic portion of the Sn-2.5Ag bump behavior is modeled with a linear elastic component and then a plastic component. In the FEA code used here (Ansys 2022R2), the plasticity is modeled with a Multilinear Isotropic Hardening (MISO) model over various temperatures. The temperature dependence and higher stiffness of the solder at lower temperatures is shown in Figure 1.
As described in [3], the damage calculated for the flip chip bumps is best handled differently than the larger BGA solder balls typically evaluated in the literature. The steady state creep behavior is described by the hyperbolic sine (sinh)-based creep behavior shown in equation 1. However, the key difference between this and standard creep model that are often used (such as Garofalo) is the stress-based portioning of the damage calculation for both a low stress region and a high stress region. Hence the fatigue lifetime is calculated with equation 2.
In equation 2, Nf is the number of cycles to failure for the individual bump, SEDGBS and SEDMC are the accumulated strain energy densities (SED) for the for the low stress region, in which grain boundary sliding (GBS) and the high stress region, where matrix creep (MC) occurs. In matrix creep, cracks form within and through the grains. C1 and C2, which are used to weight each type of damage, are determined through experimental testing. Syed et. al. [3] reported values for Sn-2.3Ag of 0.00011 and 0.00028 for C1 and C2 respectively; this alloy was assumed close enough to the Sn-2.5Ag used in this study.
Computing the SEDs for the Sn-2.5Ag solder bumps requires examining the SED in the 5 μm slices in the top and bottom of each bump. That necessitates a proper creep model, and, for this work, the creep model was in the form of Combined Time Hardening, which differs from what is used for the solder balls (discussed next).
The solder ball lifetimes can be found with a somewhat simpler model. The solder used here is SAC305, and a correlation published by Syed [4] uses a creep energy density correlation to find the lifetime. As with the solder bumps, the solder is modeled in the FEA material model with a linear elastic section (temperature dependent as well), a plasticity MISO approach, and the sinh-based creep model (equation 1) with Garofalo constants. Figure 2 shows the plasticity plots (MISO) while Figure 3 shows the Garofalo constants used.
Like Reference [3], Reference [4] provides a correlation for solder lifetime for the solder balls relative to measured solder creep in cycling, in which the accumulated creep strain and dissipated creep strain energy are used. While low and high stress regions for damage accumulation are both addressed, for typical accelerated temperature ranges nearly all SnAgCu solder damage occurred in the high stress prediction [4]. Thus, total accumulated creep strain can be used for the solder ball lifetime (cycles to failure, Nf), as shown in Equation 3.
Analysis
With the background presented to this point, the BGA geometry and the various material properties were set up as a finite element model (FEM). Eight different analyses were run for the DOE matrix in Table 1, in which two levels were used for the printed circuit board (PCB) coefficient of thermal expansion (CTE), the lid CTE, and the amplitude of the thermal cycle temperature range relative to a low temperature of 20ºC were used. An additional analysis for run #1 was solved for a higher density mesh to examine mesh density effects.
| Run # | PCB CTE, ppm/K | Lid CTE, ppm/K | ΔT, °C |
|---|---|---|---|
| 1 | 13 | 17 | 50 |
| 2 | 13 | 10 | 20 |
| 3 | 9.5 | 10 | 50 |
| 4 | 13 | 17 | 20 |
| 5 | 9.5 | 17 | 20 |
| 6 | 9.5 | 10 | 20 |
| 7 | 13 | 10 | 50 |
| 8 | 9.5 | 17 | 50 |
Table 1: DOE factors and runs
The eight run analyses were conducted with a fairly coarse mesh, relative to that used in Reference [3]. The additional simulation run used a higher density mesh that was similar to that used in [3]. One goal was to determine whether the coarser mesh would be successful enough to be a useful tool for mapping out the experiment space when larger numbers of analyses are run. Figure 4, Figure 5, and Figure 6 show the coarser meshing used for the overall model, the solder bumps, and the solder balls, respectively.
Three thermal cycles were applied to the model with each cycle lasting 3000 seconds, as shown in Figure 7.
For each DOE run, it is important to check the base analysis results to verify that the solution is working properly. For these static structural analyses, the deformations should be assessed to ensure all elements deform in a reasonable manner. This can be a problem with thin or small elements, especially if contact elements are used between parts. Figure 8 shows a sample total deformation plot for run 8. All nine analyses passed these deformation checks.
The total strain (summation of elastic, plastic, and creep) for run #8 are shown for the solder bumps (Figure 9) and balls (Figure 10) for the maximum strain point in the third thermal cycle (7500s). As expected, highest strains occur where solder contacts a pad, at the top and bottom extremes of the solder.
Figure 11 shows the strain progressing through the three cycles, revealing that the total strain increases with each cycle of the solder balls. This increase in strain per cycle generally stabilizes between cycles 2 and 3.
To solve equations (2) and (3) for the solder bumps and balls, the terms used in those equations must be for the thin regions at the top and bottom sections, where the maximum strain occurs. Depending on the finite element software, this typically requires the use of a script to determine the strain energy for each element and summing it over those regions. As described in [1], the model included nine solder bumps and six solder balls, which each required separate scripts to account for the top and bottom sections, for a total of 30 scripts. Additionally, each element in the solder bumps was evaluated to determine whether the strain energy density was in the SEDGBS or SEDMC category, with results then partitioned and summed appropriately.
Tables 2 and 3 below show the predicted minimum solder life (fewest cycles to failure) for each run case, for both bumps and balls.
| DOE Run # | Bump # | Location | Nf |
|---|---|---|---|
| 1 | 3 | Top | 34,944 |
| 2 | 2 | Top | 10,380,100 |
| 3 | 2 | Top | 126,020 |
| 4 | 2 | Top | 24,196,400 |
| 5 | 2 | Top | 19,594,400 |
| 6 | 2 | Top | 8,945,040 |
| 7 | 3 | Top | 126,977 |
| 8 | 2 | Top | 198,963 |
Table 2: Minimum solder bump life
| DOE Run # | Ball # | Location | Nf |
|---|---|---|---|
| 1 | 6 | Bottom | 77,924 |
| 2 | 1 | Top | 7,896,440 |
| 3 | 5 | Bottom | 55,755 |
| 4 | 1 | Top | 7,906,040 |
| 5 | 5 | Bottom | 23,935,800 |
| 6 | 5 | Bottom | 23,417,300 |
| 7 | 5 | Bottom | 47,874 |
| 8 | 5 | Bottom | 55,992 |
Table 3: Minimum solder ball life
Analysis of Results
Initial assessment of the results shown in Table 2 and Table 3 shows the unsurprising result that components subjected to the smaller ΔT of 20ºC (runs 2, 4, 5, and 6) had the longest life for both the bumps and solder balls, due to the smaller strain resulting in a smaller SED. The results also showed that the first failure doesn’t always occur in the same place; the lower cycle life may occur in either the bumps or balls. For example, in run 1, the worst-case bump has half the life cycles of the worst-case ball, while in run 3, the worst-case ball had less than half the life of the worst-case bump.
Thus, the results indicate that the BGA design can favor one solder location (bump vs. ball) over the other for the same ΔT cycle swing. To better understand how one could modify a given BGA design to shift package life in a particular direction, the data were analyzed using Analysis of Variance (ANOVA). For brevity, this analysis is not shown here but is described in detail in Reference [2], with the key observations reported here.
Each ANOVA was conducted using the square root of Nf as the dependent variable in creating suitable transfer functions. This was done to account for the large differences of lifetimes at low vs. high ΔT. These analyses showed that the PCB CTE had very little impact on the life of the solder bumps. Similarly, the lid CTE affected the solder bumps far more than the balls, Therefore, one could “tune” a solder lifetime by tuning the parts closest to the desired solder region.
The ANOVA provided insight into the interactions that lead to the solder bumps having the minimum life in some conditions while the balls had the minimum life in others. While the choice of solder likely affects this, the combined DOE parameters also have an effect. In run 1, the bumps had the shortest lifetime while reducing the lid and PCB CTEs (in run 3) led to the balls failing before the bumps, but still having a longer minimum life than the run 1 configuration. Changing design factors may shift the shortest lifetime solder joint from one area to another (balls vs. bumps) as well as affect the overall lifetime of the mounted BGA.
As a side note, the lid CTE would have far more effect if it was attached to the substrate with an adhesive with greater stiffness. The model used a relatively soft silicone RTV adhesive that is more compliant than an epoxy or a solder. This is another variable to consider if the manufacturing process allows.
This was a simple 3 factor DOE; a study with more factors would likely identify other significant parameters that could be used to ‘tune’ a BGA design to meet a given use requirement. In addition to the lid adhesive that was mentioned, the substrate CTE is likely a significant contributor that can be adjusted. Since the substrate is between the solder balls and bumps, varying its CTE would likely introduce some interesting results. Reducing it would likely improve solder bump life while increasing it would likely help the solder ball life. A variation of this paper’s DOE would be to use a single ΔT value (no longer a factor) and add the substrate CTE, and use the shortest lifetime, bump or ball, as the output. This would likely produce an output model showing the best CTE choices for the substrate given the variations in the lid and PCB CTE values.
Higher mesh density results
Run 1 was meshed with a higher density to assess the mesh dependency of the model (and the suitability of using a lower quality mesh). The overall mesh was increased from 378,844 elements to 963,712 elements with significant refinements in and near the solder bumps and balls. Figure 12 and Figure 13 show the solder refinements to the bumps and balls respectively.
The key result of run 9 is the comparisons between the shortest lifetimes of the two solder regions relative to the coarser mesh used in run 1, as shown in Table 4. This table includes numbers along with the location for the lowest lifetime, in which the number indicates the bump or ball location.
| Solder | Coarse mesh | Refined mesh | ||
|---|---|---|---|---|
| Bump | 3, Top | 34944 | 3, Top | 32217 |
| Ball | 6, Bottom | 77924 | 1, Bottom | 81814 |
Table 4: Solder lifetime coarse vs refined mesh
The lifetime numbers are similar (< 10% difference), with the lowest lives occurring in the same bump but for different solder balls. Since the solder bump lifetime is lower with the refined mesh, one should use a refined mesh to derive final lifetime numbers. However, the coarse mesh is reasonably close and can be used in exploratory DOE calculations to arrive at designs more quickly (the author’s computer needed 2.3 hours to solve each coarse mesh problem, and 13 hours to solve the refined mesh).
Conclusions
Using a three-factor, two-level DOE of a typical BGA, a FEA model, which used previously demonstrated methods for determining solder ball and bump life (see [3] and [4]). was analyzed. This study found:
The balls and bumps are affected differently by the factors used in this analysis; this is affected by the distance from the solder location to the part (the longer the distance, the less the effect)
- Different factors can create the shortest life in either the bumps or the balls; the factor combinations in this model can cause either location to fail first
- Using these observations about the factor effects, it is possible that a BGA can be tuned for maximum solder life
- Other factors not evaluated in the DOE likely will have significant effects, and may need to be considered
- A coarse mesh is feasible for an exploratory DOE and acceptable results are possible, but a final design should have a refined mesh to improve lifetime calculations
Authors
James Petroski is the owner of Design by Analysis Technical Consulting LLC. He has worked in the area of electronics packaging for nearly 40 years and has a special focus on thermal and mechanical engineering of packages and electronic systems. His background includes equipment design for naval nuclear propulsion instrumentation and controls, NASA space flight experiments (with three shuttle flights of space hardware), computer systems/enclosures, handheld commercial and industrial products, graphite thermal materials and applications, LED lighting systems, and packaging of die and die/substrate systems. He received his Bachelor’s in Engineering Science and Mechanics from Georgia Institute of Technology (Georgia Tech) and an MS degree in Engineering Mechanics from Cleveland State University.
Andy Carrasco has worked in electronic circuit design and semiconductor packaging for 27 years. He worked the first half of his career in EDA developing custom IC package design tools. He co-founded nSentia in Japan to pioneer an acclaimed IC package visualization and assembly verification tool. Since 2012, he has consulted on numerous hardware development projects, specializing in complex advanced IC package substrates, with a particular focus on large body, high-speed, high-power, 2.5D devices, the last 5+ years at Cisco Silicon One. Throughout his career, he has focused attention on blending electronics engineering with mechanical modeling. He holds an undergraduate degree from Temple University Japan.
References
[1] J. Petroski and A. Carrasco, “Simulation of Solder Fatigue Effects on Typical BGA Package due to Material and Temperature Variations – Part 1”, Electronics Cooling Magazine, Winter 2024, pp. 9-12
[2] J. Petroski and A. Carrasco, “Simulation of Solder Fatigue Effects on Typical BGA Package due to Material and Temperature Variations”, 2024 40th Semiconductor Thermal Measurement, Modeling & Management Symposium (SEMI-THERM), San Jose, CA, USA, 2024, pp. 36-45.
[3] Syed, A., Sharon, G., & Darveaux, R. (2012, May). Factors affecting Pb-free flip chip bump reliability modeling for life prediction. In 2012 IEEE 62nd Electronic Components and Technology Conference (pp. 1715-1725). IEEE.
[4] Syed, A. (2004, June). Accumulated creep strain and energy density based thermal fatigue life prediction models for SnAgCu solder joints. In 2004 Proceedings. 54th electronic components and technology conference (IEEE Cat. No. 04CH37546) (Vol. 1, pp. 737-746). IEEE.
