Coarsening in BGA Solder Balls: Modeling and ... - Semantic Scholar

Cemal Basaran Associate Professor

Yujun Wen e-mail: [email protected] Ph.D. Candidate Electronic Packaging Laboratory, 212 Ketter Hall, University at Buffalo, State University of New York, Buffalo, NY 14260, USA

Coarsening in BGA Solder Balls: Modeling and Experimental Evaluation The reliability of solder joints in electronic packaging is becoming more important as the ball grid array (BGA) develops rapidly into the most popular packaging technology. Thermal fatigue of solder joints has been a reliability concern in the electronic packaging industry since the introduction of surface mount technology (SMT). Microstructural coarsening (phase growth) is considered to be closely related to thermomechanical fatigue failure. Many researchers proposed coarsening models for bulk scale metals. But these models have never been verified for micron-scale actual BGA solder balls. In the present study, three different phase growth models are investigated experimentally on BGA solder balls in a real-life electronic package. Model simulations obtained from three models were compared against test data. The best performing model was chosen for finite element fatigue reliability studies based on continuum damage mechanics. 关DOI: 10.1115/1.1602707兴

Introduction Thermal fatigue has been one of the most serious problems for solder joint reliability in electronic packaging. Many researchers have studied constitutive modeling and reliability of solder alloy under thermomechanical fatigue loading 共Solomon 关1兴, Solomon and Tolksdorf 关2兴, Dasgupta and Hu 关3兴, Wei and Chow 关4兴, Guo et al. 关5兴, Busso et al. 关6兴, Lau and Pao 关7兴, McDowell et al. 关8兴, Basaran and Chandaroy 关9–12兴, Basaran and Yan 关13兴, Basaran et al. 关14兴, Chandaroy and Basaran 关15兴, Basaran and Tang 关16兴, and Basaran et al. 关17,18兴兲. Morris, Jr. et al. 关19兴 pointed out that the thermal fatigue of Sn/Pb eutectic solder was characterized by microstructural coarsening in the fatigue failure region. Frear et al. 关20兴 theoretically studied the microstructural evolution of the solder and led to a suggestion that phase size is a damage parameter for evaluating thermal fatigue lifetime. Li and Muller 关21兴 studied the coarsening process in Pb/Sn solder from the extended diffusion equation of the phase-field model type that included classical Fickean diffusion and effects of surface tensions according to the Cahn-Hilliard formalism as well as diffusive morphology changes due to thermomechanical strains. However, it is still not very well understood how the microstructural coarsening relates to the thermal fatigue damage. Bangs and Beal 关22兴, Morris et al. 关19兴, Frear and Morris 关23兴, Wolverton 关24兴, and Tribula et al. 关25兴 have shown that during thermal fatigue of eutectic solders and some high Pb solders a coarsened band develops and that the fatigue failure initiates in this coarsened region. But it is not clear if failure initiates in the coarsened region because of coarsening or because coarsening leads to higher shear strength in a narrow band and as a result attracts higher stresses, which in turn lead to initiation of microcracks. It is very well known 关26兴 that as the phase size gets larger, the creep strain rate gets smaller due to the increased shear strength to viscoplastic flow. Kashyap and Murthy 关26兴 studied the influence of phase size on creep strain rate. They and many others have shown that there is a strong correlation between creep strain rate and phase size of Pb/Sn solder alloys. Wolverton 关24兴 observed that prior to failure the solder joints had bands of coarsened two-phase material parallel to the direction of the imposed shear. Zhao et al. 关27,28兴 have shown that as a result of coarsening Pb/Sn solder balls harden and the yield strength increases. Contributed by the Electronic and Photonic Packaging Division for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received Aug. 2002. Associate Editor: B. Michel.

426 Õ Vol. 125, SEPTEMBER 2003

The phase growth process that takes place in Pb/Sn solder alloys is due to two reasons. One is due to temperature and the second is due to strain. Callister 关29兴 states that after recrystallization is complete the strain-free phases will continue to grow if the metal specimen is stored at an elevated temperature. This phenomenon is called phase growth. As phases increase in size the total boundary area decreases, yielding an attendant reduction in the total energy, which is the driving force for phase growth. Phase growth occurs by migration of phase boundaries. Large phases grow at the expense of the small phases. Boundary motion is diffusion of atoms from one side of the boundary to the other side. Callister 关29兴 states that for many polycrystalline materials the phase diameter d varies with time t according to the following relationship, d n ⫺d n0 ⫽Kt,

(1)

where d is the phase diameter at time t, d 0 is the initial phase diameter, and K and n are time-independent constants. The value of n is generally equal to or greater than 2. Speight 关30兴 and Ardell 关31,32兴 proposed, independently, a phase boundary diffusion theory, which states that when the phase boundary diffusion is dominant the average phase size to the fourth power (d 4 ) increases proportional to time. Senkov and Myshlaev 关33兴 extended this theory to the phase growth process of superplastic alloys and validated the theory for Zn/Al eutectic alloy. They expressed the evolution of the average phase size d with time as follows, d 4 ⫺d 40 ⫽B

␦ ␥ ⍀C 0 D b RT

t,

(2)

where d 0 is the initial average phase size, B is the phase geometry parameter, ␦ is the phase boundary width, ␥ is the free energy per unit area of the phase boundary, ⍀ is the molar volume of the particle phase, C 0 is equilibrium solute concentration near the phase boundary, D b is the coefficient of solute diffusion in the phase boundary, R is the gas constant, T is the absolute temperature, and t is time. Sayama et al. 关34兴 applied the above-described phase boundary diffusion theory to Pb/Sn eutectic solder and derived the basic equations as follows. Differentiating Eq. 共2兲 with respect to time at constant temperature and including the temperature dependency of some properties in D b , Sayama et al. 关34兴 proposed the following equation,

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共 d 4 兲 ⬘ ⫽A 1 D b

(3)

where A 1 is constant and the prime denotes the derivative of the object in parentheses with respect to time. Applying the excess vacancy model of Clark and Arden 关35兴 to the phase boundary diffusion theory, Sayama et al. 关34兴 were able to add the influence of mechanical strain to the phase growth process. Using the excess vacancy model D b can be expressed as D b ⫽A 2 共 n t ⫹n c 兲 ,

(4)

where A 2 is a constant, n t is thermal equilibrium vacancy concentration, and n c is strain-induced vacancy concentration in the phase boundary. Assuming the production rate of n c is proportional to the equivalent creep strain rate ␧˙ c and the annihilation rate of n c is proportional to itself, then n˙ c ⫽A 3 ␧˙ c ⫺n c / ␶ c ,

(5)

where A 3 is a constant and ␶ c is the relaxation time of the vacancies. Under the condition of constant temperature and constant creep rate ␧˙ c , the solution of Eq. 共5兲 is given by

␶ c is of the order of 10⫺2 s at ambient temperature and is very small compared to the creep deformation time. Therefore, if creep deformation in the solder joint is the dominant deformation mode, then the phase growth can be expressed approximately by S t ⫽C 1 t,

S c ⫽C 2 ␧˙ c t.

(19)

Another Pb/Sn phase growth model was introduced by Frear et al. 关20兴. These authors introduced the phase size as a damage parameter and expressed the equivalent inelastic strain rate p˙ in as p˙ in⫽

冉冊冉冊

1⫺ ␮ Q f exp ⫺ 1⫺D RT

␭0 ␭

p

sinhm

冉

冊

1⫺ ␮ J2 , 1⫺D ␣ 共 c⫹c& 兲 (20)

where f, p, m, and Q are material parameters, R is the gas constant, T is the absolute temperature, ␭ is the current phase size, ␭ 0 is the initial phase size, J 2 is a second invariant of the stress difference, ␣ is a scalar function of the absolute temperature, and c and &c are state variables. Phase growth evolution is given by

(6)

␭⫽␭ 0 ⫹ 兵关 4.1⫻10⫺5 e ⫺11023/T ⫹15.6⫻10⫺8 e 3123/T p˙ in兴 t 其 0.256. (21)

where n c0 is the initial value of n c . Sayama et al. 关34兴 introduced the phase growth parameter S defined as

Wei and Chow 关4兴 provided the deformation hardening variable c and the other state variable &c for the Frear et al. phase coarsening model as

S⫽d 4 .

c˙ ⫽A 1 p˙ in⫺ 共 A 2 p˙ in⫹A 3 兲共 c⫺c 0 兲 2 ,

n c ⫽A 3 ␧˙ c 关 1⫺exp共 ⫺t/ ␶ c 兲兴 ⫹n c0 exp共 ⫺t/ ␶ c 兲 ,

(7)

Substituting Eqs. 共4兲 and 共6兲 into Eq. 共3兲 and then defining some constants provide S˙ ⫽S˙ t ⫹S˙ c ,

(8)

S˙ t ⫽C 1 ,

(9)

S˙ c ⫽C 2 ␧˙ c 关 1⫺exp共 ⫺t/ ␶ c 兲兴 ⫹S˙ c0 exp共 ⫺t/ ␶ c 兲 ,

(10)

where S˙ t is the thermal equilibrium growth rate, S˙ c is the straininduced growth rate, S˙ c0 is the initial value of S˙ c , ␶ c is the relaxation time of vacancies, ␧˙ c is the equivalent creep strain rate, and C 1 and C 2 are phase growth material properties with temperature dependency. In the computational simulation of the phase growth process, temperature and S˙ c are assumed to be constant in any arbitrary time increment ⌬t of the creep deformation analysis. The phase growth parameter increment ⌬S, which corresponds to ⌬t, is calculated by the following equations, ⌬S⫽⌬S t ⫹⌬S c ,

(11)

⌬S t ⫽C 1 ⌬t,

(12)

⌬S c ⫽C 2 ␧˙ c 关 ⌬t⫺ ␶ c 兵 1⫺exp共 ⫺⌬t/ ␶ c 兲其兴 ⫹S˙ c0 ␶ c 兵 1⫺exp共 ⫺⌬t/ ␶ c 兲其 .

(13)

The growth process is simulated by calculating ⌬S and adding up successively for each time step. Based on the microstructural observation of the thermal equilibrium phase growth process, Sayama et al. 关34兴 estimated C 1 and C 2 for eutectic Pb/Sn solder as C 1 ⫽1.96⫻104 exp共 ⫺6.03⫻103 /T 兲 ,

(14)

C 2 ⫽5.91⫻10 exp共 5.99⫻10 /T 兲 .

(15)

2

2

In our tests, we found C 1 and C 2 to be C 1 ⫽2.16⫻104 exp共 ⫺6.33⫻103 /T 兲 ,

(16)

C 2 ⫽6.51⫻10 exp共 6.29⫻10 /T 兲 .

(17)

2

2

Frear et al. 关20兴 estimated ␶ c as

␶ c ⫽5.2⫻10⫺14 exp共 7.9⫻103 /T 兲 . Journal of Electronic Packaging

(18)

&c ⫽A 7

冉冊 ␭0 ␭

(22)

A8

,

(23)

where c 0 , A 1 , A 2 , A 3 , A 7 , and A 8 are material parameters. Corresponding to our own test results the modified coefficients we found are ␭⫽␭ 0 ⫹ 兵关 2.9⫻10⫺3 e ⫺11023/T ⫹7.8⫻10⫺6 e 3123/T p˙ in兴 t 其 0.256, (24) where t is time 共in seconds兲, p˙ in is the equivalent inelastic strain rate, T is the absolute temperature 共in kelvin兲, ␭ 0 is the initial phase size, and ␭ is the current phase size under thermal cyclic loading. Lifshitz and Slyozov 关36兴 provided another phase growth model based on diffusive atomic flux. The physical process of microstructural coarsening with the release of excess energy in twophase alloys is associated with the high dissolution of fine phase particles with a high surface-to-volume ratio. The process is postulated to be similar to the theoretically well-studied and accepted growth model of second-phase particles in a matrix 共Hillert 关37兴 and Martin and Doherty 关38兴兲. The presence of a concentration gradient results in diffusive atomic flux that leads to the shrinkage of fine particles and to the growth of coarse particles. Theoretical analysis of the particle growth process induced by volume diffusion results in the following relationship 关36兴 between the average particle radius and time, r 3 ⫺r 30 ⫽B 1

冋

册

␥ ⍀C 0 D v t, RT

(25)

where r is the average particle radius, r 0 is the initial radius of an average particle, D v is the coefficient of solute diffusion in the matrix, B 1 is a parameter related to the volume fraction of the particles, C 0 is the solute concentration in equilibrium with an infinitely large particle, ␥ is the interfacial free energy per unit area of the particle-matrix interface, and ⍀ is the molar volume of the particles. Hacke et al. 关39兴 studied coarsening behavior of Pb/Sn eutectic solder joints and experimentally observed that the solder microstructure coarsened in accordance with the cubic coarsening model. During thermal mechanical cycling between ⫺30°C and 130°C 共24 minute temperature cycles兲 the solder joints were observed to coarsen rapidly in regions with fine degenerate eutectic SEPTEMBER 2003, Vol. 125 Õ 427


Fig. 2 Cross section of the BGA package

Verification of Models

Fig. 1 Schematic of the specimen on the fixture

structure and the phase size increased 共mean linear intercept as per Ref. 关39兴兲 with the number of thermomechanical cycles. The phase growth was in accordance with the cubic coarsening model written in the following format: r 3 共 t 兲 ⫺r 30 共 t 兲 ⫽

冉

冊

c 1t ⌬H g exp ⫺ , T RT

(26)

where d is the mean phase diameter at time t, d 0 is the initial mean phase diameter, c 1 is a kinetic factor that depends on matrix composition 共in ␮m3 °K/h兲, ⌬H g is the activation energy for the volume diffusion of atoms, R is the gas constant, and T is the absolute temperature in kelvins. This model accounts for the effect of time and temperature on phase growth kinetics. However, it does not include the effects of stress, which is considered to be one of the primary factors for phase growth 共Arrowood et al. 关40兴 and Nabarro 关41兴兲. Upadhyayula 关42兴 modified the cubic coarsening model to include the mechanical stress effects as follows, r 3 共 t 兲 ⫺r 30 共 t 兲 ⫽

冉

c 1t ⌬H g exp ⫺ T RT

冊冋冉冊册 1⫹

⌬␶ c2

nc

,

(27)

where ⌬␶ is the stress range in MPa, R is the gas constant, ⌬H g ⫽94 kJ/mol, which is the activation energy for volume diffusion of atoms, the stress exponent n c ⫽1, the matrix composition constant, c 1 ⫽4.2⫻1015 ␮ m3 K/h, and the reference stress c 2 ⫽64.52 MPa.

In order to implement a phase growth model in a damage mechanics–based constitutive model we needed to validate these phase growth models for actual BGA solder joints. Some of the models discussed above were verified on bulk scale metal specimens 共not alloys兲 but not for an actual micron scale BGA solder joint. Bonda and Noyan 关43兴 have shown that specimen size can make a significant difference in mechanical properties of Pb/Sn solder alloys. Three different models presented in the preceding section were used to simulate the coarsening behavior of actual BGA solder joints under thermal cycles. Figure 2 shows the cross section of the package that was subjected to thermal cycling. The thermal cycling range varied from 0°C to 75°C with a period of 42 minutes 共see Fig. 3兲. The elastic material properties are given in Table 1. In order to verify the models discussed in the preceding section the BGA package shown in Fig. 2 was subjected to thermal cycling. There were 15 BGA packages that were subjected to thermal cycling and used for measuring phase growth. Results presented in this paper are for average values. In order to measure the phase size each solder joint in the package was polished to a high degree for SEM observation. SEM micrographs were taken for each solder joint in a row in the package and the phase size was measured. Due to the significantly heterogeneous structure and variable void ratio of solder joints in actual BGA packages, the measured results were averaged for all solder joints in the study. Hence the test data presented in this paper are the average values for all the solder joints that were tested during the course of this study. In order to perform computer simulations of the phase growth process using the models discussed above a strain rate function is needed. We introduce the creep strain rate model in Eq. 共28兲. This is a modified version of the Kashyap-Murthy 关26兴 eutectic Pb/Sn viscoplasticity model. The strain rate function was implemented in the ABAQUS general purpose finite element code using the userdefined material subroutine option in the software.

Experimental Procedure A high capacity Super AGREE environmental thermal chamber is used to control the environmental temperature. Manufactured by THERMOTRON 共SA-36CHV-30-30兲, this chamber has 5°C/ min to 30°C/min change rates, a temperature range of ⫺77°C to 177°C, and work space dimensions of 42 in.⫻42 in.⫻36 in. Temperature cycling can be programmed and run in automatic mode. The chart recorder records the temperature history for each test. Figure 1 shows the schematic of the thermal cyclic loading fixture. Packages were fixed on the fixture and put into the chamber. After a certain number of cycles the package was taken out of the thermal chamber and observed under scanning electron microscope 共SEM兲. SEM micrographs were taken for each solder joint in a row in the package and the phase size was measured with the mean linear intercept method.

␧˙ i j ⫽

冉冊冉冊冉冊

AD 0 Eb b ␬T d

p

␴ E

n

exp ⫺

Q ⳵F , RT ⳵␴ i j

(28)

where the dimensionless constant A⫽4.5⫻102 , the frequency factor D 0 ⫽100 mm2 /s, the universal gas constant R ⫽8.314 J/K mol, B⫽3.2⫻10⫺7 mm for Pb/Sn alloy, the Boltz-

Table 1 Material properties

E (GPa) ␯ ␣ (10⫺6 /°C)

FR-4

Solder 共63Sn/37Pb兲

Polymer

17.4 0.35 16

14.7 0.32 24.7

11 0.25 48 Fig. 3 Temperature profile of thermal cycle loading




Fig. 4 „a… Initial state, the average phase size d 0 Ä3.017 ␮ m. „b… After 150 cycles, the average phase size d 150Ä4.645 ␮ m. „c… After 250 cycles, the average phase size d 250Ä5.096 ␮ m. „d… After 300 cycles, the average phase size d 300Ä5.231 ␮ m.

mann constant ␬ ⫽1.38⫻10⫺23 J/K, T is the temperature 共in kelvin兲, the activation energy Q⫽44.7 kJ/mol (T⬍408 K), 81.1 kJ/mol (T⬎408 K), the phase size exponent p⫽3.34, the stress exponent n⫽1.67, E is Young’s modulus of solder joints, d is the average phase size, and ␴ is the unbalanced shear stress.

model III, respectively. The curve for model I is closer to test data from 15 BGA packages compared with model II and model III. The actual phase size shows nonmonotonic convergence to saturation level; on the other hand, all models exhibit monotonic convergence. Figure 5 indicates that model I outperforms other models. Hence model I was chosen as the primary phase growth

Results and Discussion Figure 4共a兲 shows the initial SEM picture of a solder joint. The initial phase size is calculated as d 0 ⫽3.017 ␮ m. The SEM pictures for a solder joint after 150 cycles, 250 cycles, and 300 cycles are shown in Fig. 4共b兲, Fig. 4共c兲, and Fig. 4共d兲, respectively. It is easy to see that phase growth occurs and the corresponding phase size becomes d 150⫽4.645 ␮ m, d 250⫽5.096 ␮ m, and d 300 ⫽5.231 ␮ m respectively. The phase size versus the number of thermal cycles for three different models and test data are shown in Fig. 5. In Fig. 5 model I is the Sayama et al. model, model II is the Frear et al. model, and model III is the modified LifshitzSlyozov model. Phase size increases with thermal cycling for all three models. But the rate of growth is quite different. Model I increases rapidly at first, and finally slowly. Model II increases nearly linearly. Model III increases almost linearly, but the rate is very small compared with model II. By comparing the results for the three models and test data we see that after 300 cycles, phase size increases 73%, 55%, 68%, 27% for the test, model I, model II, Journal of Electronic Packaging

Fig. 5 Comparison of the phase size change between simulation and observation

SEPTEMBER 2003, Vol. 125 Õ 429


model for Pb/Sn fatigue reliability studies based on the damage mechanics approach. We believe that nonmonotonic convergence of the phase size for test data is due to the heterogeneous structure and nonuniformity of the solder joints in actual BGA packages.

Conclusions A comparison between computational simulations for three phase growth models and test data has been presented. Results indicate that the quadratic power phase growth model fits the test data best. This model is based on systematic microstructural observations and is derived from the excess vacancy model based on phase boundary diffusion theory. The microstructural evolution is characterized by the phase growth parameter S that is defined as the average phase size to the fourth power and increases proportional to time and equivalent creep strain rate. In the phase growth process the strain rate plays a very important role.

Acknowledgments This research project is partially sponsored by the Office of Naval Research Power Electronics Building Block Program under the supervision of 共the late兲 Dr. George Campisi and partially by the National Science Foundation CMS Division Surface Engineering and Material Design program under the supervision of Dr. Jorn Larsen-Basse.

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