THERMAL CYCLING FATIGUE ANALYSIS OF SAC387 SOLDER JOINTS

Chandra Williams, Kok Ee Tan and John H. L. Pang*,

Nanyang Technological University, School of Mechanical & Aerospace Engineering,

Nanyang Avenue, Singapore 639798. *E-mail : mhlpang@ntu.edu.sg

ABSTRACT In this study, finite element analysis (FEA) was used to simulate a thermal cycling test result for a PBGA assembly with Sn-3.8Ag-0.7Cu solder joints subject to thermal cycling of –40oC to +125oC. The PBGA assembly was modeled using a 3D-quarter 1/8th octant model of the PBGA assembly. Two constitutive models for the SAC387 solder were investigated using the Anand Viscoplastic (AV) model and elastic-plastic-creep (EPC) model. Low cycle fatigue life prediction based on non-linear Plastic work (PLWK) and inelastic strain energy density (SED) were used to predict the thermal cycling fatigue life and compared to the test results. Volume averaging studies are needed to quantify the effect of the volume of elements selected on the non-linear Plastic work (PLWK) and inelastic strain energy density (SED), and fatigue life results KEY WORDS: Anand Model, Elastic Plastic Creep, Lead Free, Low cycle fatigue, PBGA, Solder joint fatigue, Strain Energy Density, Thermal Cycling

INTRODUCTION Thermal Cycling (TC) modeling of accelerated thermal cycling tests of soldered electronic assemblies require elastic plastic and creep properties of the solder material [1]. Solder materials subjected to thermal cycling test loading exhibit rate dependent plastic deformation behavior. A rate dependent viscoplastic deformation analysis model was proposed by Anand [2] and employed by Darveaux [3] for solder joint rate dependent deformation analysis of thermal cycling solder joint fatigue life prediction. Lead-free solder Sn-Ag-Cu (SAC) material properties for creep and low cycle fatigue behavior has been reported[4-8] and can be incorporated in finite element analysis and fatigue life prediction of SAC solder joint fatigue life subject to thermal cycling test condition. Cyclic strain in the solder material arises from thermal cycling induced deformations due to Coefficient of Thermal Expansion (CTE) mismatch in a package soldered onto the PCB, thus causing thermal fatigue failure in solder joints. In this study, the solder material constitutive model for Sn-3.8Ag-0.7Cu (SAC387) solder alloy was investigated for a PBGA assembly soldered on a PCB subject to thermal cycling test condition of -40oC to +125oC. The Elastic-Plastic-Creep (EPC) constitutive model and Anand Viscoplastic (AV)

constitutive model will be used in the FEA study and the effect of the constitutive model on fatigue life will be evaluated for different volume averaging segments of the non-linear Plastic work (PLWK) and inelastic strain energy density (SED) .

PBGA ASSEMBLY GEOMETRY A Plastic Ball Grid Array (PBGA) package is employed to assess the impact of using the AV and EPC constitutive models on solder joint reliability. The layout of the solder joint is presented in Figure 1 and the components of the package are presented in Figure 2. A coarse one-eighth model of the PBGA soldered assembly was modeled and a more detailed and finer mesh is employed in a sub-modeling approach for the critical solder joint. The PBGA assembly has 316 solder joints mounted on the FR4 PCB and was subjected to thermal cycling tests of –40oC to +125oC. The FEA simulation will locate the critical solder joint and the fatigue damage parameter either inelastic strain or inelastic energy will be used to calculate the low cycle fatigue life of the solder joint.

Figure 1 Geometry and Dimension of PBGA assembly

978-1-4244-5343-6/10/$26.00 ©2010 IEEE

Figure 2 PBGA assembly materials layout

THERMAL CYCLING LOADING The thermal cycling (TC) test profile has a cycle time of 60 minutes with 15 minutes dwell time at extreme temperature and 15 minutes ramp time. The solder joints were connected via daisy chains with in-situ resistance monitoring. Failure was recorded for a resistance value larger than 300 ohms. The Mean-Time-To-Failure (MTTF) for the soldered PBGA assemblies is 2741 cycles[8]. In the FEA model the stress- free condition is assumed to be at 25°C as shown in Figure 3. The temperature ramps up from 25°C to 125°C in 9 minutes and left to dwell for 15 minutes before ramping down to -40°C and left to dwell for 15 minutes. A total of three cycles was modeled under this TC profile.

Figure 3 Thermal Cycling (TC) profile

PBGA ASSEMBLY MATERIAL PROPERTES In this study, two solder constitutive models were used for comparison, namely the Anand Viscoplastic (AV) model and Elastic-Plastic-Creep (EPC) model. The inelastic Plastic Work (���) and inelastic Strain Energy Density (SED) output from the finite element result were used as a fatigue damage parameter in a low cycle fatigue life prediction model for SAC387 solder. Different volume averaging segments based

on whole top layer, outer two rings and outermost rings were used in fatigue life prediction for comparison. The material properties of the components in the PBGA are presented in Table 1. The temperature dependent material properties are presented separately in Table 2. Table 1 Material properties for PBGA used in the FEA model

Materials Modulus (GPa)

Poisson’s Ratio

CTE (ppm/°C)

Solder Table 2 0.35 24.5 Copper 155.17 0.34 Table 2

FR4 PCB

in plane (x,z): 20 out-of-plane(y): 9.8

x,z: 0.28 y: 0.11

x,z: 18 Y: 50

BT Substrate

x,z: 26 y: 11

x,z: 0.39 y: 0.11

x,z: 15 y: 52

Die Table 2 0.278 Table 2 Adhesive 7.38 0.3 52

Mold 16 0.25 15

Table 2 Temperature dependent material properties used Temperature -40°C 25°C 50°C 125°C

Solder modulus 54.43 41.73 36.84 22.19 Copper CTE 15.3 16.4 16.7 17.3 Die modulus 192.1 191 190.6 190

CTE 1.5 2.6 2.8 3.1

CONSTITUTIVE MODELS FOR SAC387 SOLDER For the EPC model the solder was modeled as an elastic-plastic-creep material with temperature dependent Young modulus and yield stress. Elastic, bilinear kinematic hardening plastic behavior of solder was used. The temperature dependent yield stress of Sn-3.8Ag-0.7Cu (SAC387) solder is

v ]:gi en by [5-6 �� � � �� �� � �������� � ������ � �����������

(1) The creep behavior of solder is modeled using hyperbolic sine creep equation s ssed in Eq. (2): a expre

�� � !" #$

%&'() *+ ,

#-./

exp *�01$- (2) The equation is then re-written into Eq. (3) in the format for implicit creep mod S en byel in ANSY giv :

�� � !"2&'()�!���345exp *�46$

- (3) Elastic Plastic Creep model can be realized in ANSYS by combining bilinear kinematic hardening plasticity and implicit creep. Table 3 shows the four constants !", !�, !�, !7 for SAC387 solder. Table 3 Material constants creep m el for C soldeof

!" od!�

SA!�

r !7Solder Type

Sn-3.8Ag-0.7Cu 3200 0.037 51 6524.7

Mold Compound

Die Adhesive

BT Substrate

Copper pad Solder

FR4-PCB

�50

0

50

100

150

0 540 1440 2340 3240 3600

Tempe

rature�(°C)

Time�(s)

The Anand model is a rate dependent plasticity model and the basic features are firstly, this model needs no explicit yield condition and no loading/unloading criterion and the plastic strain is assumed to take place at all non-zero stress levels. Secondly, the model employs a single scalar internal variable, the deformation resistance 8 , to represent the average isotropic resistance to plastic flow. It has a flow equation, and three evolution eq atu ions:

Flow equation: ��� � 9 %&'() *:;< -." =>

exp *�01$- (4) Evolution equations:

8� � ?@A�BCB�D EBEBF ��� (5)

C � � <<G (6)

8G � 8 ^ %H�IJ exp * 01$-

where ��� is the effective plastic strain rate,�� is the effective true stress (MPa), 8 is the deformation resistance (MPa), K is the activation energy, L is Boltzmann’s constant, 9 is the pre-exponential factor, M is the stress multiplier, N is the strain rate sensitivity of stress, @A is the hardening constant (MPa), 8 is the coefficient for deformation resistance saturation value (MPa), O is the strain rate sensitivity of saturation value, and + is strain rate sensitivity of hardening.

./

(7)

^

The Anand Viscoplastic (AV) model is incorporated in the ANSYS program. The material constants were curve-fitted to creep and constant strain rate tensile test data for SAC387 results [6] and are shown in Table 4.

Ta8A ����

b n isc plas Mo nst nts fo SAC38l AK e 4PQ

�R�

an V9

�8�"�

d oM

ticN

del Co@A

�����

a9

r

8

7 ^ O

37.1 6656 65.92 8 0.346 @A 1.29 80.8 O

FATIGUE ANALYSIS AND VOLUME AVERAGING The energy-based low cycle fatigue model by Pang et al [6] was used for solder fatigue life prediction using the inelastic energy parameters obtained from an AV and EPC model analyses respectively. The inelastic energy low model is given by, cycle fatigue

ST/��� � 9 (8)

where O and 9 are material constant. For SAC387 tested at �UV and 0.001 Hz, O equals to 0.897 and 9 is 311.7 ���. Fatigue life prediction of solder joint are depends on plastic work density estimation.

Volume averaging is very important to estimate plastic work density for a se d lume of ele ents using equation (9): lecte vo m

��� � W XIYZ �[YZ\ZW [YZ\Z

� W XI]Z �[]Z\ZW []Z\Z

(9)

FEA MODEL OF PBGA WITH 1/8th SYMMETRY

The boundary conditions along symmetry surfaces indicate that the Ux and Uy displacements are constrained (zero) at the diagonal of the octant model. The Ux displacement is constraint at the edge of the die to simulate symmetry conditions as shown in Figure 4. Similarly a node in the centre of the package has all degrees of freedoms (DOFs) constrained. This is to prevent rigid body motion of the package from occurring during thermal cycling simulation. Sub-modeling or the cut-boundary displacement method is employed. The cut boundary is the boundary of the sub-model, which represents a cut through the coarse global model taken from Figure 4. Displacements calculated on the cut boundary of the coarse global model are transferred as boundary conditions to the sub-model with much finer mesh as shown in Figure 5.

Figure 4 Boundary Conditions for Octant (1/8th) Model

Figure 5 Sub-model of critical solder joint with finer mesh

The accuracy of FEA modeling is related to the mesh density of the model. Finer mesh models leads to better accuracy. However, the setback of finer mesh models is that it requires more computational resources and time. In order to overcome the challenges, sub-modeling method is employed to simulate PBGA octant model. Firstly, PBGA octant model is modeled with coarse mesh density to reduce the number of element involved in the simulation as shown in Figure 6. After three cycles of temperature cycling, critical solder joint is to be identified in order to proceed to sub-modeling level. Two material constitutive models, EPC model and AV model are employed in Global Coarse Model. Sub-modeling method requires proper cut boundaries to be selected in order to perform interpolation from Global Model results. From Figure 7, it can be seen the location where solder joint failure will occur. Sub-model with finer mesh density will then be developed around the critical solder joint as shown in Figure 8.

Figure 6 Global model for PBGA assembly

Figure 7 Solder joint plastic work results (AV model)

Figure 8 Identification of cut boundaries of sub-model ANAND VISCOPLASTIC (AV) MODEL RESULTS To investigate the effect of volume averaging of the solder joint for the AV model, the top layer elements (1/20th solder height) of the solder joint are selected as shown in Figure 9 and initially three cases are considered. The three cases of volume averaging are the whole layer of solder elements, the two outer rings of solder elements, and the outermost ring of solder elements.

Figure 9 Solder joint element used in analysis

Figure 10 Plastic Work (PLWK) contour plot

The plastic work density contour plots of three cases are presented in Figure 11-13. From the three plots, it can be seen that the maximum Plastic Work parameter is present in all three cases and is volume averaged using equation (9). The fatigue life is calculated using equation (8) and presented in Table 5.

Figure 11 Plastic Work plot for whole layer of elements

Figure 12 Plastic Work plot for two outer ring of elements

Figure 13 Plastic Work plot for outermost ring of elements

Table 5 Plastic Work De d fatigue life results nsity anPlastic Work/ Volume

����� Volume Cases Fatigue Life (Cycles)

Whole top layer 0.1400 5395 Two outer rings 0.2093 3446 Outermost ring 0.2418 2933

The outermost ring gave a fatigue life of 2933 cycles compared to the experimental MTTF result of 2741 cycles. The Plastic Work Density distribution shown in Figure 11 suggest that further selection of fewer element nearer to the maximum Plastic Work value can give a higher Plastic Work/Volume averaging magnitude and hence a shorter fatigue life and this will be discussed in the next section. Volume averaging for smaller segments Further examinations by focusing the volume averaging of the solder joint at the maximum plastic work density location reveals the importance of volume averaging of the solder joint in fatigue life prediction. Three further cases were considered with smaller segments with 10 elements, 5 elements, and 1 element with the maximum plastic work density value. They are shown in Figures 14-18. The fatigue life is calculated using Equation (8) for the corresponding cases and presented in Table 6.

Figure 14 Location of maximum plastic work

Figure 15 Volume averaging of 5 elements

Figure 16 Plastic work plot for 5 elements

Figure 17 Volume averaging of 10 elements

Figure 18 Plastic work plot for 10 elements

The maximum plastic work density gives the lowest fatigue life prediction of solder joint out of the test cases. The reduction in volume averaging results in reduction of fatigue life prediction as shown in Table 6.

Table 6 Plastic Work and fatigue life for AV model

Volume Cases Plastic

Work/Volume �����

Fatigue Life (Cycles)

10 elements 0.2468 2844 5 elements 0.3204 2143

1 element (with Maximum PLWK) 0.3746 1800

ELASTIC-PLASTIC-CREEP (EPC) MODEL RESULTS The EPC model results were volume-averaged in the same manner as the AV model cases in Table 5. The inelastic Strain Energy Density (SED) distribution for the three cases of volume averaging and the corresponding fatigue results are given in Table 7. The Creep SED and Plastic SED were calculated independently and added to give the total inelastic SED. Then Equation (8) was used to calculate the solder joint fatigue life.

Table 7 Inelastic SED and Solder Fatigue life

Test Case Creep SED �����

Plastic SED �����

Total Inelastic

SED �����

Fatigue Life

(Cycles)

Whole Top layer 0.139 0.0227 0.1617 4594

Two outer rings 0.175 0.0335 0.2085 3460

Outermost ring 0.2 0.0412 0.265 2649

The fatigue life prediction of the outermost ring cases for the AV and EPC model results are compared in Table 8. The EPC model results agree closer to the experimental results by predicting a shorter life of 2649 cycles compared to the AV model results with a fatigue life of 2933 cycles compared to the experimental test data of 2741 cycles. Both the EPC model and AV model results are within -3% and +7% of the MTTF results.

Table 8 Fatigue Results for EPC model and AV model Material Constitutive

Model Fatigue Life

(Cycles) %

Difference EPC model 2649 -3.35% AV model 2933 +7.00%

Note: Experiment MTTF = 2741 cycles Although the fatigue life predictions for both EPC and AV models are relatively close to the experimental MTTF data of 2741 cycles, the computational time taken for the EPC model is faster by a factor of 2X, than that of the AV model.

CONCLUSION Finite element analysis of SAC387 solder joints in a PBGA assembly was modeled using a 1/8th octant 3D model of the subject to thermal cycling loading of –40oC to +125oC. Two constitutive models for SAC387 solder were investigated using the AV and EPC constitutive models. The EPC and AV model results for the same volume averaging case for the outermost ring, gave good agreement in solder joint fatigue within a range of -3% and +7% compared to the MTTF results. For the AV model case, different volume averaging segments at the top layer of elements, outer two rings, outermost ring of elements, selected 10 elements, 5 elements and 1 element

show that the plastic work varies from 0.14 to 0.3746 MPa with corresponding fatigue life from 5395 to 1800 cycles. The sensitivity of volume averaging effect on the fatigue life should be handled with care in interpreting solder joint fatigue life prediction results.

REFERENCES [1] Darveaux, R., and Banerji, K., (1992), “Constitutive Relations for Tin-Based Solder Joints”, IEEE Transactions on Components, Hybrids and Manufacturing Technology, Vol.15, pp.1013-1024. [2] Anand, L., (1985), “Constitutive Equations for Hot-Working of Metals”, International Journal of Plasticity, Vol.1, pp.213-231. [3] Darveaux, R., (2000), “Effect of Simulation Methodology on Solder Joint Crack Growth Correlation”, Proceedings of 50th Electronic Components and Technology Conference, May 21-24, Las Vegas, pp.1048-1058. [4] Schubert, A., Dudek, R., Auerswald, E., et al., (2003), “Fatigue Life Models for SnAgCu and SnPb Solder Joints Evaluated by Experiments and Simulation”, Proceedings of 53rd Electronics Components and Technology Conference, New Orleans, pp.603-610. [5] Pang, H.L.J., Low, T.H., Xiong, B.S. et al., (2003), “Design for Reliability (DFR) Methodology for Electronic Packaging Assemblies”, Proceedings of 5th Electronic Packaging Technology Conference, December 10-12, Singapore, pp.470-478. [6] Pang, H.L.J., Xiong, B.S. and Low, T.H., (2004), “Creep and Fatigue Characterization of Lead Free 95.5Sn-3.8Ag-0.7Cu Solder”, Proceedings of 54th Electronic Components and Technology Conference, June 1-4, Las Vegas, pp.1333-1337. [7] Syed,A.(2004), “Accumulated Creep Strain and Energy Density Based Thermal Fatigue Life Prediction Effects in Eutectic Solder Alloy”, International Journal of Fatigue, 22, pp.217-228. [8] Che, F.X., and Pang, H.L.J., (2004), “Thermal Fatigue Reliability Analysis for PBGA with Sn-3.8Ag-0.7Cu Solder Joints”, Proceedings of 6th Electronics Packaging Technology Conference, December 8-10, Singapore, pp.787-792.