Solder joint reliability based on creep strain energy density for SAC305 and doped SAC solders

Parallel to the development of new lead-free solders, electronic packaging has gone through a considerable evolution. A redistribution of layers allows the increase of functionality by increasing the number of inputs/outputsin the packagewhile reducing the size. The reliability of the package is strongly influenced by the reliability of the interconnects. During production and service life, there are thermal processes involved that may lead to thermal fatigue. In this work, a two-dimensional finite elementmodel of a Fan-Out Wafer Level Packaging (FO-WLP) was built, and simulations of thermal test cycles were carried out varying the solder interconnect material: SAC305, SACQ, SACR, orInnoLot. A thermal oscillating load from –40°C to 125°C was applied to the packaging for three hours.State of the art concerning solder joint reliability models based on creep behavior reveals the benefit of using energy-based parameters, as cycles to failure are inversely proportional to the average creep strain energy density.Based on theaverage creep strain energy density simulation results, the reliability of the package withdifferent solderswas compared.The qualitative results suggestthat SACQ has a significant advantage in the operational lifetime compared toSACR, InnoLot, and SAC305.

Currently, electronic equipment reliability is linked to performance and security [8]. Therefore, it is essential to understand reliability tests and mathematical models that can effectively predict the lifetime of materials. Regarding thermal cycling reliability tests, recent studies have proved the accuracy of Finite Element Analysis (FEA) on ICs simulations with lifetime prediction errors of less than 20% [9].Lead-free solder joint reliability is of great interest to accurately predict the service life of an electronic device.
In this work, a two-dimensional finite element model of a Fan-Out Wafer Level Packaging (FO-WLP) was built, and simulations of thermal test cycles were carried out varying the solder interconnect material: SAC305, SACQ, SACR, or InnoLot.State of the art concerning solder joint reliability models based on creep behavior reveals the benefit of using energy-based parameters. Based on the average creep strain energy density simulation results, the reliability of the package with different solders was compared. The qualitative results suggest that SACQ has a significant advantage in the operational lifetime compared to SACR, InnoLot, and SAC305.

Reliability and material models for solder joints
Reliability of ICs subjected to cycling thermal loads has been a core topic of research, with thermal fatigue analysis by predictions of the number of cycles to failure. Initially, Distance to Neutral Point (DNP) was identified as a key parameter; hence the farthest solder joint from the neutral point of the IC possesses a risk due to the highest thermo-mechanical loads and a geometry that limits the size of the packaging and number of I/Os [10]. However, the accuracy of the approach has been intensely discussed because electronic packaging layouts have been improved. Lau [11]reported that the DNP approach presents some limitations. For instance, DNP failure prediction has been proved to be valid for packaging without underfill; however, it has been incorrectly applied where underfillis used [12].
The state of the art of reliability models used for solder joint reliability is summarized in Table 1. The number of cycles before failure is related either to strain or energy type of parameters. Li et al. [13] successfully conducted a simulation to evaluate the thermal fatigue life of a SAC solder material. Creep strain and creep strain energy density were used for the lifetime prediction. From the results, creep strain energy density using hyperbolic-sine model approached more accurately to experimental data.
According to Norris et al. [14], constant was observed to be 2 for most of metals. Zubelewicz et al. [15] stressed that Coffin-Manson law does not fit experimental data for high strain rates. Recently, Clech [16] summarized researches that compare the Coffin-Manson model and critical Distance to Neutral Point (DNP).
Pang et al. [17] presented research where tables for , , and are listed. Additionally, they included a new approach that includes frequency dependency.
Syed [18] proposed employing the Monkman-Grant model to predict the number of cycles to failure based on accumulated creep strain and creep strain energy density per cycle. Using the Power-law and Hyperbolic-sine creep model, his founding demonstrates that both accumulated creep and energy density can effectively predict the lifetime of solder stacks. Although the Darveaux model was not available in commercial simulation programs, his approach was later corroborated to be more accurate than the Coffin-Manson model by Ramachandran et al. [19]. Table 1. Overview of solder joint reliability models.
(m/cycle), Crack growth rate per cycle.
(m), Critical length exposed to crack propagation. , Constants based on the element size of the solder.

Crack Initiation Crack Growth
Energy Density Model ( ) For creep material models, either hyperbolic-sine law or Anand's type of models are often used. A more detailed list of creep-based material characterization experiments is summarized in Table 2. The authors who used the hyperbolic-sine model stressed the lack of articles reporting Anand's constants.

Simulation Methods
Finite Element Analysis (FEA) has been successfully applied for package reliability analysis [30]. According to Gokhale et al. [30], Computer-Aided Engineering (CAE) can predict failures with a 90% accuracy. An Integrated CircuitS-PBGA-N167 from the Texas Instrument [31]in an advanced Fan-Out Wafer Level Packagingwas used as the base for the 2-D finite element model.Half of the package was modeled. Boundary conditions on the left edge were applied for symmetry with constrained displacements in the x-direction. A vertical constrain was placed to the left bottom corner concerning the y-direction displacementsto ensure a unique mathematical solution (see Fig. 1).The IC comprises nine different materialsdetailed in Fig.  1.Corresponding material properties are listed in Table 3 for most constituents, except for the solders, which are shown in Table 4.   For solder materials, four types were selected in this study: SACQ, SACR, InnoLot, and SAC305. The chemical compositions of the solder alloys are shown in Table 5 for comparison. The visco-plastic mechanical model was employed for the solder behavior in the form of Anand's creep model [35]. Anand properties for each used solder are detailed in Table 4. An oscillating thermal load from -40°C to 125°Cwith tree cycles was used, with a ramp-up time of 15 minutes, a dwell time of 15 minutes, a cooling time of 15 minutes, and another dwell time of 15 minutes, altogether 3 hours.

Fig. 2.Thermal Load.
Multicriteria time stepping was selected for the load cases (3 load cases of 3600s each) with fine criteria conditions to assure a minimum of 100 steps per thermal cycle.

Results
Creep strain energy density (CSED) data was collected from the four simulation replicates. The bottom corner locations of each solder ball displayed a high CSED for all the scenarios. The location with the most critical value of CSED (see Fig. 3) was situated in the bottom right corner of the outer solder ball(the most distant point from the line of symmetry).
As the multi-criteria was utilized for time-stepping, each CSED vs. time curve presenteda different number of points: SAC305, 1808 points; SACQ, 4135points;InnoLot, 1669points; and SACR, 579points. The number of points was directly proportional to the simulation time that varied from nearlyone hour to over five hours. The CSED vs. time curves from the critical location (Fig. 3) of each replicate were summarized in Fig 4. It is worth noting that SACQ presents the lowest CSED accumulation among the different soldering materials and the highest expected resolution due to a large number of steps. Additionally, InnoLot and SAC305 curves display a similar behavior during the first two thermal cycles. Nevertheless, the approximation of the average of CSED only considers the CSED subtraction between the third and second thermal cycle (calculated in Table 6).

Fig. 4. Creep Strain Energy Density Comparison.
The aim of the comparison addresses creep-based reliability. From Table 1, Morrow's model was selected following the authors' trend in Table 2. Morrows's model requires the average creep strain energy density, ΔW av, as a key parameter of the number of cycles to failure calculation. According to Che and Pang [28], three thermal cycles are enough to obtain a stable plastic work density that approximates the average creep strain energy density. It can be computed by taking the values at the end of the third and second thermal cycle as detail in Eq. (1).
Calculation of average creep strain energy density (ΔW av ) [28]: (1) Where: , average creep strain energy density; rd C and nd C Creep strain energy density at the end of the third and second thermal cycle (TC), respectively.
The computed approximation of average CSED shows that SACQ presents the lowest value, whereas SAC305 displays the highest value (see Table 6).Based on Morrow'sreliability modelpresented in Table 1, the number of cycles to failure is inversely proportional to the average of CSED. Therefore, SACQ would resist the most extended working lifetime, followed by SACR, InnoLot,and SAC305. These results agree with a similar experimental comparison performed by Wei et al. [37] where SAC305 endured the least number of cycles to failurethan SACQ, SACR, and InnoLot, under stress-controlled conditions.

Conclusions
Reliability of an advanced electronic package is strongly influenced by the reliability of the interconnects. In this work, a two-dimensional finite element model of a Fan-Out Wafer