A thermal fatigue lifetime prediction model of ceramic ball grid array (CBGA) packages is proposed based on the Darveaux model. A finite element model of the CBGA packages is established, and the Anand model is used to describe the viscoplasticity of the CBGA solder. The average viscoplastic strain energy density increment ΔWave of the CBGA packages is obtained using a finite element simulation, and the influence of different structural parameters on the ΔWave is analyzed. A simplified analytical model of the ΔWave is established using the simulation data. The thermal fatigue lifetime of CBGA packages is obtained from a thermal cycling test. The Darveaux lifetime prediction model is modified based on the thermal fatigue lifetime obtained from the experiment and the corresponding ΔWave. A validation test is conducted to verify the accuracy of the thermal fatigue lifetime prediction model of the CBGA packages. This proposed model can be used in engineering to evaluate the lifetime of CBGA packages.
As electronic products have become smaller, lighter, and more reliable, ceramic ball grid array (CBGA) packaging has been increasingly used in electronic products. As a critical component of a stand-alone machine or a system, the failure of the CBGA device will cause the system to malfunction, resulting in high risks to product engineering. Therefore, the lifetime prediction of CBGA packages is essential to the reliability research of electronic products.
CBGA devices are high-density interconnect devices. In CBGA assembly, the device and the printed circuit board (PCB) are connected by soldering to form a component. The solder joints are prone to multiple failure modes during the assembly and subsequent testing under complicated loadings [
The Anand viscoplastic model is a common model to describe the constitutive relationships of solders, and the viscoplasticity of solder material in a thermal environment. It uses a single internal variable to describe the resistance of the internal state of the material to plastic flow. This model relates the deformation behavior of viscoplastic materials to the strain rate and temperature. Amagai et al. [
Many scholars have researched the reliability and lifetime prediction methods of solder joints. Che et al. [
Energy-based lifetime prediction models are also often used. Akay et al. [
Based on previous research, it can be noticed that the Darveaux model has a very effective application in the field of solder life prediction. Through the Darveaux model, the number of life cycles can be quickly obtained. However, the correlation coefficients of the Darveaux model vary greatly for different structural designs, structural parameters and material characteristics of the package. Therefore, for typical CBGA packages, modification of the Darveaux model is required.
A life prediction model of CBGA packages is established using a finite element model of a CBGA and the Anand constitutive model to characterize the viscoplasticity of the solder. The average viscoplastic strain energy increment ΔWave is obtained from the finite element simulation, and the influence of different structural parameters on ΔWave is analyzed. Multiple regression analysis is used to establish a simplified analytical model of ΔWave. A thermal cyclic test is conducted to modify the parameters of the Darveaux life prediction model. Experiments are conducted to determine the number of thermal fatigue life cycles of a typical CGBA. In addition, a validation test is carried out to verify the accuracy of the life prediction model of CBGA packages.
The Anand model [
The Anand model has two basic characteristics: (1) The model does not have a clear yield surface in the stress space; thus, there is no need to provide loading and unloading criteria during deformation. Plastic deformation can occur under all non-zero stress conditions. (2) The model uses the deformation resistance
The Anand constitutive model describes the relationship between the strain rate and temperature and the deformation behavior of viscoplastic materials, strain hardening, the historical effect of the strain rate, and the dynamic recovery of strain. Initially, the Anand model was primarily used to describe the thermal properties of high-strength aluminum and other structural metals. It is currently widely used to describe the viscoplastic behavior of solder.
In the Anand model, the deformation resistance is proportional to the equivalent stress:
where c is the material parameter, which is expressed as:
where
The flow equation of the viscoplastic Anand model adopts the hyperbolic creep law, which is described as:
The evolution equation for the internal variable s is:
where
where
where
Accordingly:
By integrating the above
where
The stress-strain relationship can be calculated using
where
where
where
The Darveaux life prediction model [
The Darveaux life prediction model divides the crack propagation into two parts. In the first part, the model predicts the number of cycles during which cracks are initiated. The predicted number of cycles in this part is given by:
where
In the second part, the model uses fracture mechanics to predict the growth rate of the crack and deduce the number of cycles required for the crack to expand and lead to the complete failure of the area. The predicted number of cycles in this part is given by:
where
Finally, the two parts are combined to obtain the number of cycles required for component destruction.
where
In addition, in Darveaux’s energy-based life prediction model, the coefficients
The flowchart of the life prediction methodology for CBGA packages is shown in
At present, CBGA packages are widely used in the aerospace field due to their high-density array and ease of assembly. The structural parameters and the material properties of the CBGA packages are determined to establish the finite element model. CBGA packages typically consist of three layers. From top to bottom, the first layer is the chip, the second layer contains the solder balls and solder, and the third layer is the substrate. The structural parameters include the size of the device, the diameter of the solder ball, the pitch of the solder joint, the standoff height of the solder, and other parameters. The typical CBGA structure is shown in
The simulation uses the typical structural parameter values used in a CBGA shown in
During the thermal cycle, the solder joints will creep. The Anand viscoplastic constitutive model is used to simulate the creep behavior of the solder joints. The 63Sn37Pb Anand model parameters are listed in
Parameter name | Parameter value |
---|---|
Pitch/mm | 0.8, 1.0, 1.27 |
Diameter/mm | 0.47/0.42/0.38, 0.64/0.56/0.49, 0.85/0.78/0.72 |
Size | 16 × 16, 18 × 18, 20 × 20, 22 × 22, 24 × 24 |
Standoff Height/mm | 0.07 |
Material name | Density (kg/mm3) | CTE (K−1) | Young’s modulus (MPa) | Poisson's ratio | |||
---|---|---|---|---|---|---|---|
63Sn37Pb | 8.4e−6 | 2.47e−5 | 30800 | 0.35 | |||
Ceramic | 3.6e−6 | 7.8e−6 | 380000 | 0.25 | |||
FR-4 | 2.27e−6 | X-direction | 1.6 e−5 | X direction | 27924 | XY direction | 0.11 |
Y-direction | 1.6 e−5 | Y direction | 27924 | YX direction | 0.39 | ||
Z-direction | 8.4 e−5 | Z direction | 12204 | XZ direction | 0.39 |
Parameters | Values |
---|---|
Constant |
26 |
Constant |
5797 |
Coefficient of deformation resistance saturation value s’ (MPa) | 83.12 |
Strain-hardening parameter |
92148 |
Stress factor |
10 |
Strain-rate sensitivity index |
0.256 |
Strain-rate sensitivity |
0.043 |
Strain-hardening parameter |
1.24 |
Initial value of internal variable |
37.9 |
The environmental parameters of the test are based on the temperature profile in the thermal cyclic test described in the ESCC-Q-70-08a standard. The temperature range is −55°C~100°C. The initial temperature is set to room temperature (22°C). The temperature change rate does not exceed 10° C/min. The maximum temperature is maintained for 15 min, and each cycle lasts 1 h. The temperature profile is shown in
In the simulation, the model has the same temperature conditions as in the thermal cyclic test profile. Since the CBGA package is centrally symmetric, it is only necessary to establish its 1/4 finite element model, and symmetric boundary conditions are used. The bottom of the model is fixed. After setting the boundary conditions of the displacement constraints shown in
The simulation is performed with different structural parameter values to predict the lifetime of the structure. The Darveaux model is used, and ΔWave is obtained from the simulation. The average viscoplastic strain energy density Wave(n) of the previous n cycles is derived by
The simulation results indicate that the maximum stress and plastic strain occur at the corners. Hence, failure is more likely at the corners, as shown in
The ΔWave values for different solder ball diameters are shown in
The values of ΔWave for different solder standoff heights are shown in
The ΔWave values for different package sizes are shown in
In addition, the pitch of the solder ball should also be considered. However, the range of the solder ball diameter depends on the pitch in practical applications. Thus, it is meaningless to determine the effect of the pitch of solder ball in the simulation.
The ΔWave results for different values of the structural parameters and mesh numbers obtained from the simulation are listed in
No. | Pitch/mm | Diameter/mm | Size/mm | Mesh number | ΔWave/MJ/m3 |
---|---|---|---|---|---|
1 | 1.27 | 0.85 | 30.48 | 293568 | 0.31897 |
2 | 1.27 | 0.78 | 30.48 | 227198 | 0.364487 |
3 | 1.27 | 0.72 | 30.48 | 179025 | 0.5348 |
4 | 1.27 | 0.85 | 27.94 | 246679 | 0.301893 |
5 | 1.27 | 0.78 | 27.94 | 190909 | 0.338698 |
6 | 1.27 | 0.72 | 27.94 | 150431 | 0.423149 |
7 | 1.27 | 0.85 | 25.4 | 203867 | 0.279362 |
8 | 1.27 | 0.78 | 25.4 | 157776 | 0.308169 |
9 | 1.27 | 0.72 | 25.4 | 124323 | 0.4377 |
10 | 1.27 | 0.85 | 22.86 | 165132 | 0.251078 |
11 | 1.27 | 0.78 | 22.86 | 127799 | 0.271908 |
12 | 1.27 | 0.72 | 22.86 | 100701 | 0.38176 |
13 | 1.27 | 0.85 | 20.32 | 130475 | 0.219764 |
14 | 1.27 | 0.78 | 20.32 | 100977 | 0.234838 |
15 | 1.27 | 0.72 | 20.32 | 79567 | 0.33075 |
16 | 1 | 0.64 | 30.48 | 203535 | 0.42191 |
17 | 1 | 0.56 | 30.48 | 137170 | 0.507009 |
18 | 1 | 0.49 | 30.48 | 92711 | 0.680472 |
19 | 1 | 0.64 | 27.94 | 171026 | 0.38491 |
20 | 1 | 0.56 | 27.94 | 115261 | 0.458203 |
21 | 1 | 0.49 | 27.94 | 77903 | 0.611384 |
22 | 1 | 0.64 | 25.4 | 141344 | 0.34389 |
23 | 1 | 0.56 | 25.4 | 95257 | 0.405 |
24 | 1 | 0.49 | 25.4 | 64383 | 0.537467 |
25 | 1 | 0.64 | 22.86 | 114489 | 0.29895 |
26 | 1 | 0.56 | 22.86 | 77158 | 0.346523 |
27 | 1 | 0.49 | 22.86 | 52150 | 0.457509 |
28 | 1 | 0.64 | 20.32 | 90460 | 0.25259 |
29 | 1 | 0.56 | 20.32 | 60965 | 0.285857 |
30 | 1 | 0.49 | 20.32 | 41205 | 0.378572 |
31 | 0.8 | 0.47 | 30.48 | 128292 | 0.46648 |
32 | 0.8 | 0.42 | 30.48 | 92658 | 0.497254 |
33 | 0.8 | 0.38 | 30.48 | 69629 | 0.632014 |
34 | 0.8 | 0.47 | 27.94 | 107801 | 0.41725 |
35 | 0.8 | 0.42 | 27.94 | 77858 | 0.44113 |
36 | 0.8 | 0.38 | 27.94 | 58508 | 0.561645 |
37 | 0.8 | 0.47 | 25.4 | 89092 | 0.36755 |
38 | 0.8 | 0.42 | 25.4 | 64346 | 0.385988 |
39 | 0.8 | 0.38 | 25.4 | 48354 | 0.492405 |
40 | 0.8 | 0.47 | 22.86 | 72164 | 0.31651 |
41 | 0.8 | 0.42 | 22.86 | 52120 | 0.328559 |
42 | 0.8 | 0.38 | 22.86 | 39167 | 0.42023 |
43 | 0.8 | 0.47 | 20.32 | 57019 | 0.26546 |
44 | 0.8 | 0.42 | 20.32 | 41181 | 0.272178 |
45 | 0.8 | 0.38 | 20.32 | 30946 | 0.348607 |
MATLAB is used to fit the simplified analytical model of ΔWave and perform multiple regression analysis for the prediction. Regression analysis provides a life prediction model with good generalization ability. The principle is to establish a prediction model that describes the distribution of the discrete sample points obtained from experiments or simulations. Commonly used regression algorithms include polynomial regression and linear regression. Multiple regression is used to predict the value and trend of the dependent variable using multiple independent variables. In addition, cross-validation is required to establish a life prediction model with a good fit and high predictability. Typically, the data are divided into a training set and a test set. In this study, the 45 sets of samples are divided into 40 sets of training data and 5 sets of test data.
According to the energy law description of the fatigue life of surface solder joints in the IPC-SM-785 standard, the potential cyclic fatigue damage is related to the structural parameters and the thermal profile. Here we use multiple nonlinear regression to fit and normalize the data as follows:
where ΔWave is the average viscoplastic strain energy density increment.
Common CBGA packages were selected for testing. The samples had different sizes, different diameters, and different solder ball pitches. CBGA575 is a large CBGA. Its structure is sensitive, and it is prone to failure. The structural parameters of the CBGA packages used in the test are listed in
No. | Array | Pitch/mm | Diameter/mm | Size of package/mm |
---|---|---|---|---|
1 | 26 × 26 | 1.27 | 0.76 | 33.02 |
2 | 24 × 24 | 1.27 | 0.76 | 30.48 |
3 | 22 × 22 | 1.27 | 0.76 | 27.94 |
4 | 18 × 18 | 1.27 | 0.76 | 22.86 |
5 | 16 × 16 | 1.27 | 0.76 | 20.32 |
6 | 21 × 21 | 1 | 0.65 | 21 |
7 | 15 × 15 | 1 | 0.65 | 15 |
8 | 14 × 14 | 1 | 0.65 | 14 |
9 | 27 × 27 | 0.8 | 0.5 | 13.5 |
10 | 24 × 24 | 0.8 | 0.5 | 12 |
11 | 21 × 21 | 0.8 | 0.5 | 10.5 |
In the thermal cyclic test, a common failure monitoring method is the daisy chain monitoring system and crack length monitoring. The daisy chain system is a real-time monitoring method that determines the failure by monitoring the change in the resistance value. When any solder joint in a link cracks and fails, the resistance value of the entire link changes. The daisy chain verification system has the advantages of full coverage and straightforward analysis. The coverage rate of the solder joints tested by this method is 100%. Therefore, the daisy chain monitoring system was used as a failure monitoring method in the test to obtain the lifetime of the CBGA package sample under thermal cyclic conditions. The test equipment is shown in
The thermal cyclic test profile shown in
During the thermal cycle test, we detect the fluctuation of the resistance of the daisy chain in real-time to evaluate the solder joint cracking of the assembly structure.
The CBGA575 sample is used as an example to illustrate the mapping of the daisy chain resistance changes and the crack growth. The first cracked solder joint we monitored was the first daisy chain link, which was located at the corner. The daisy chain resistance changes with the thermal cycle time, as shown in
The fluctuation of the resistance of the daisy chain detected during the test indicates that the solder joints inside the assembly structure have cracked. The greater the fluctuation, the longer the cracks are between the solder joint and the component. When the high resistance state is reached for the first time, it indicates that the solder joint crack has penetrated, and the assembly structure has failed. As shown in
Package name | Crack length (diameter of pad)/mm |
---|---|
CBGA575 | 0.72 |
CBGA256 | 0.635 |
CBGA160 | 0.47 |
No. | Crack length/mm | Pitch/mm | Diameter/mm | Size of |
ΔWave/MJ/m3 | Failure cycles |
---|---|---|---|---|---|---|
1 | 0.72 | 1.27 | 0.76 | 33.02 | 0.497436 | 343 |
2 | 0.72 | 1.27 | 0.76 | 30.48 | 0.448924 | 399 |
3 | 0.72 | 1.27 | 0.76 | 27.94 | 0.401539 | 419 |
4 | 0.72 | 1.27 | 0.76 | 22.86 | 0.310457 | 542 |
5 | 0.72 | 1.27 | 0.76 | 20.32 | 0.266946 | 641 |
6 | 0.635 | 1 | 0.65 | 21 | 0.233802 | 723 |
7 | 0.635 | 1 | 0.65 | 15 | 0.151884 | 955 |
8 | 0.635 | 1 | 0.65 | 14 | 0.139027 | 1019 |
9 | 0.635 | 0.8 | 0.5 | 13.5 | 0.138506 | 1007 |
10 | 0.47 | 0.8 | 0.5 | 12 | 0.119094 | 1362 |
11 | 0.47 | 0.8 | 0.5 | 10.5 | 0.100356 | 1503 |
The length of the solder joint cracks and the number of failure cycles were obtained from tests, and the ΔWave values were calculated by
Darveaux coefficient | ||||
---|---|---|---|---|
Value | 1.74E4 | −0.9789 | 1.112E−05 | 0.8111 |
Therefore, the thermal fatigue life prediction model of the CBGA packages is proposed as follows:
where ΔWave is the average strain energy density increment,
This paper establishes an analytical model for life prediction of CBGA Packages. It can quickly solve the lifetime of CBGA.
The improved Darveaux model is obtained by substituting
We chose other CBGA575s of the same specification to verify the life prediction model. The example of daisy chain resistance change during the verification tests is shown in
Darveaux coefficient | ||||
---|---|---|---|---|
Value | 2.44E−7 | −7.90 | 8.82 | 1.86 |
The failure cycles of tests and the predicted failure cycles of the Darveaux model are listed in
No. | Crack length/mm | ΔWave/MJ/m3 | Failure cycles of tests | Predicted failure cycles | Error/% |
---|---|---|---|---|---|
1 | 0.72 | 0.332739 | 518 | 501 | 3.2 |
2 | 0.635 | 0.307439 | 539 | 526 | 2.4 |
3 | 0.47 | 0.125493 | 1213 | 1174 | 3.2 |
4 | 0.72 | 0.497436 | 319 | 343 | 7.5 |
The errors between the test results and the prediction results of the Darveaux model are also shown in the table. Three of the errors are below 5%, and the other one is below 10%. They reflect the good accuracy of this life prediction model.
Simulations and experiments were used to determine the thermal fatigue lifetime of CBGA packages. A simplified analytical model of the average viscoplastic strain energy density increment ΔWave was established, and the Darveaux life prediction model of CBGA packages was modified based on the test results. After determining the structural parameters and material properties of the CBGA packages, a finite element simulation was carried out, and the ΔWave data were obtained. Subsequently, the influence of the different structural parameters on ΔWave was analyzed. Multiple regression analysis was used to establish a simplified analytical model of ΔWave using simulation data. Then, a thermal cyclic test was conducted to obtain the thermal fatigue life cycle number of typical CGBAs. We monitored the changes in the resistance value in real-time to evaluate the cracking of the solder joints of the assembly structure. The test results provided information on the thermal fatigue lifetime of typical CBGA packages and were used as part of the input into the Darveaux life prediction model. Meanwhile, the corresponding ΔWave was calculated using the simplified analytical model of ΔWave. The Darveaux life prediction model of the CBGA packages was then modified using the number of life cycles and ΔWave. The accuracy of the life prediction model of the CBGA packages was determined using a validation test. The proposed life prediction model of the CBGA packages is accurate and can be used to calculate the lifetime of CBGA packages in practical engineering applications.
The authors thank Ye Wang and Hongyan Leng of Beihang University for their thoughtful discussions and suggestions on writing and experimenting in this study.