Improved Predictions of Lead Free Solder Joint ... - IEEE Xplore

Improved Predictions of Lead Free Solder Joint Reliability that Include Aging Effects Mohammad Motalab, Zijie Cai, Jeffrey C. Suhling, Jiawei Zhang, John L. Evans, Michael J. Bozack, Pradeep Lall Center for Advanced Vehicle Electronics Auburn University Auburn, AL 36849 Phone: +1-334-844-3332 FAX: +1-334-844-3307 E-Mail: [email protected]

978-1-4673-1965-2/12/$31.00 ©2012 IEEE

Introduction The microstructure, mechanical response, and failure behavior of lead free solder joints in electronic assemblies are constantly evolving when exposed to isothermal aging and/or thermal cycling environments. In our prior work on aging effects published at recent ECTC conferences [1-6], we have demonstrated that the observed material behavior variations of Sn-Ag-Cu (SAC) lead free solders during room temperature aging (25 C) and elevated temperature aging (50, 75, 100, 125, and 150 C) were unexpectedly large. The measured stress-strain data for SAC105, SAC205, SAC305, and SAC405 solders demonstrated large reductions (up to 50%) in stiffness, yield stress, ultimate strength, and strain to failure during the first 6 months of aging after reflow solidification. For example, Figure 1 illustrates the evolution of the stressstrain curve of SAC305 (95.5Sn-3.0Ag-0.5Cu) lead free solder subjected to up to two months aging at 100 C, and Figure 2 shows the corresponding 40% degradation of the Ultimate Tensile Strength (UTS) with aging time [4].

513

50

SAC305 RF

45

T = 25 oC

Stress, σ (MPa)

40 35

Increased Aging

30 25 20

Aging Conditions

15

As Reflowed 100 oC, 5 Days 100 oC, 10 Days 100 oC, 20 Days 100 oC, 30 Days 100 oC, 45 Days 100 oC, 60 Days

10 5 0 0.000

0.005

0.010

0.015

0.020

Strain, ε

50

SAC 305, RF T = 25 oC

45 40 35

UTS (MPa)

Abstract It has been demonstrated that isothermal aging leads to large reductions (up to 50%) in several key material properties for lead free solders including stiffness (modulus), yield stress, ultimate strength, and strain to failure. In addition, even more dramatic evolution has been observed in the creep response of aged solders, where up to 10,000X increases have been observed in the steady state (secondary) creep strain rate (creep compliance). Such degradations in the stiffness, strength, and creep compliance of the solder material are expected to be universally detrimental to reliability of solder joints in electronic assemblies. Traditional finite element based predictions for solder joint reliability during thermal cycling accelerated life testing are based on solder constitutive equations (e.g. Anand viscoplastic model) and failure models (e.g. energy dissipation per cycle models) that do not evolve with material aging. Thus, there will be significant errors in the calculations with lead free SAC alloys that illustrate dramatic aging phenomena. In our current research, we are developing new reliability prediction procedures that utilize constitutive relations and failure criteria that incorporate aging effects, and then validating the new approaches through correlation with thermal cycling accelerated life testing experimental data. In this paper, we report on the first step of that development, namely the establishment of a revised set of Anand viscoplastic stress-strain relations for solder that include material parameters that evolve with the thermal history of the solder material. The effects of aging on the nine Anand model parameters have been examined by performing stressstrain tests on SAC305 samples that were aged for various durations (0-6 months) at a temperature of 100 C. For each aging time, stress-strain data were measured at three strain rates (0.001, 0.0001, and 0.00001 1/sec) and five temperatures (25, 50, 75, 100, and 125 C). Using the measured stress-strain data, the Anand model material parameters have been determined for various aging conditions. Mathematical expressions were then developed to model the evolution of the Anand model parameter with aging time. Our results show that 2 of the 9 constants remain essentially constant during aging, while the other 6 show large changes (30-70%) with up to 6 months of aging at 100 C. Preliminary finite element simulations have also shown that the use of the modified Anand model leads to a strong dependence of the calculated plastic work dissipated per cycle on the aging conditions prior to thermal cycling.

30 25 20 15 10 5 0 0

10

20

30

40

50

60

Aging Time (Days)

Figure 1 - Evolution of the Stress-Strain Curve of SAC305 Solder with Aging at 100 C and Corresponding Degradation of the Ultimate Tensile Strength [4]

Even more dramatic evolution has been observed in the creep response of aged lead free solders, where up to 100X increases were found in the steady state (secondary) creep strain rate (creep compliance) of SAC solders that were simply aged at room temperature [1]. For elevated temperature aging at 125 C [2-4], the creep strain rate was observed to change even more dramatically (up to 10,000X increase for SAC105). For example, Figure 2 illustrates the evolution of the creep response of SAC305 lead free solder subjected to up to six months aging at 100 C, and Figure 2 shows the corresponding 325% increase (degradation) of the secondary creep strain rate with aging time [4]. 0.08

conditions (1000 hours at 150 C) prior to thermal cycling accelerated life testing.

SAC 305, RF o

T = 25 C

σ = 15 MPa

Strain, ε

0.06

0.04

Aging Conditions As Reflowed o 100 C, 0.5 Months o 100 C, 1 Month o 100 C, 2 Months o 100 C, 3 Months o 100 C, 4 Months o 100 C, 5 Months o 100 C, 6 Months

0.02

Figure 3 - Life Reduction in SAC305 BGA Assemblies Subjected to Aging Prior to Thermal Cycling [7]

0.00 0

2000

4000

6000

8000

We have found similar results in our study on the effects of aging on thermal cycling reliability of lead free BGA assemblies. In this ongoing investigation, PBGA daisy chain test assemblies are being subjected to up to 2 years of aging (25, 55, 85, and 125 C), followed by thermal cycling (-40 to 125 C and -40 to 85 C) to failure. The test vehicle (see Figure 4) includes four sizes of BGA components. The details of the BGA configurations are tabulated in Figure 5, and the testing includes components with SAC305, SAC105, and 63Sn-37Pb solder balls. The test matrix also includes several test board surface finishes including Im-Ag, Im-Sn, HASL Sn-Pb, and ENEPIG.

Time, t (sec)

10-1

SAC305, RF T = 25 oC

10-2

σ =15 MPa

Strain Rate (sec-1)

10-3 10-4 10-5 10-6 10-7 10-8 10-9 10-10 0

1

2

3

4

5

6

Aging Time (months)

Figure 2 - Evolution of the Creep Response of SAC305 Solder with Aging at 100 C and Corresponding Degradation of the Secondary Creep Rate [4] The degradations of the stiffness, strength, and creep compliance with aging shown in Figures 1 and 2 are expected to be universally detrimental to reliability of solder joints in lead free assemblies. This has been demonstrated explicitly in recent investigation of Lee and coworkers [7], where aging has been shown to degrade the Thermal Cycling Reliability (TCR) of lead free Plastic Ball Grid Array (PBGA) assemblies subjected to Accelerated Life Testing (ALT). For example, the Weibull failure rate plot in Figure 3 illustrates the degradations of the solder joint fatigue life of 13 mm lead free BGA components (SAC305, 432 balls, 0.4 mm pitch) that occurred with aging at either 100 C or 150 C prior to thermal cycling from 0 to 100 C (10 minute ramps and dwells). The amount of life degradation was found to be dependent on the surface finish of the PCB substrates, with 44% degradation observed for ENIG surface finish and 20% degradation observed for OSP surface finish under the most severe aging

Figure 4 - Assembled BGA Reliability Test Vehicle Body Size (mm) 19 x 19 15 x 15 10 x 10 5x5

Die Size (mm) 12.0 x 12.0 12.7 x 12.7 5.0 x 5.0 3.2 x 3.2

Ball Count 288 208 360 97

Pitch (mm) 0.8 0.8 0.4 0.4

Ball Alignment Perimeter Perimeter Perimeter Full Array

Figure 5 - Table of BGA Components in Aging Test Matrix We currently have results for aging up to 6 months prior to thermal cycling. For all component sizes and lead free solder

514

Figure 6 - Life Reduction in SAC305 BGA Assemblies Subjected to Aging Prior to Thermal Cycling

Figure 7 - Life Reduction in SAC105 BGA Assemblies Subjected to Aging Prior to Thermal Cycling

19mm BGA - Solder Joint Reliability 5000 Aging Conditions

Characteristic Life η (Cycles)

alloys, the solder joint thermal cycling reliabilities of the BGA components were severely reduced by prior aging. For example, Weibull failure rate plots are shown in Figures 5 and 6 for 19 mm BGA components with SAC305 and SAC105 solder balls, respectively. These results are for Im-Ag PCB surface finish and thermal cycling from -40 to 125 C. Clear degradations in life were observed to occur for aged components relative to non-aged components, and the amount of degradation was exacerbated with higher aging temperatures. Using the 63.2% Weibull characteristic life ( η ) as a failure metric, the reliability was observed to decrease by 37% (SAC305) and 53% (SAC105) for the 19 mm BGA components subjected to 6 months aging at 125 C prior to thermal cycling. Figure 8 contains a plot illustrating the decreases in characteristic life experienced by the 19 mm BGA components when exposed to various aging conditions prior to thermal cycling. The effects of aging for the components with Sn-Pb solder balls were much less than those exhibited by the components with SAC lead free solder balls.

No Aging 6 Months at 25 C 6 Months at 50 C 6 Months at 85 C 6 Months at 125 C

4000

3000

2000

1000

0 SAC305

SAC105

SnPb

Solder Alloy

Figure 8 - Effects of Aging on Characteristic Life (19 mm BGA, Im-Ag Surface Finish) Smetana, et al. [8] have performed an extensive study on the effects of prior isothermal preconditioning (aging) on the thermal cycling lifetime for a variety of components. Similar to the investigations discussed above, it was observed that prior aging reduced the thermal cycling characteristic life of SAC BGA assemblies subjected to 0 to 100 C cycling. It was also found that changes occurred in the Weibull slope, suggesting other failure modes were created by aging. They also found that prior aging increased the thermal cycling reliability of certain components (e.g. 2512 chip resistors and certain QFNs). Similar results of improved reliability with aging were found for components subjected to a smaller thermal cycling range of 20 to 80 C. This led them to conclude that aging does not universally reduce solder joint fatigue life. Gradual aging also occurs during thermal cycling tests due the high temperature dwells at the top of each thermal cycle. Several recent studies [9-13] have demonstrated that there is a strong dwell time effect on thermal cycling reliability for lead free electronics, with longer dwell times leading to reductions in the thermal cycling life. Due to the strong influence of aging on the thermal cycling reliability of lead free solder assemblies, it is critical that aging effects be included in any reliability prediction methodology. This includes incorporation of the thermal history of the lead free solder joints such as thermal preconditioning (aging) before thermal cycling, as well as the gradual aging of the solders that occur during the thermal cycling process. Traditional finite element based predictions for solder joint reliability during thermal cycling accelerated life testing are based on solder constitutive equations (e.g. Anand viscoplastic model) and failure models (e.g. energy dissipation per cycle models) that do not evolve with material aging. Thus, there will be significant errors in the calculations with lead free SAC alloys that illustrate dramatic aging phenomena. In our current research, we are developing new reliability prediction procedures that utilize constitutive relations and failure criteria that incorporate aging effects, and then validating the new approaches through correlation with

515

thermal cycling accelerated life testing experimental data. In this paper, we report on the first step of that development, namely the establishment of a revised set of Anand viscoplastic stress-strain relations for solder that include material parameters that evolve with the thermal history of the solder material. The effects of aging on the nine Anand model parameters have been examined by performing stressstrain tests on SAC305 samples that were aged for various durations (0-6 months) at a temperature of 100 C. For each aging time, stress-strain data were measured at three strain rates (.001, .0001, and .00001 1/sec) and five temperatures (25, 50, 75, 100, and 125 C). The theoretical equations for the uniaxial stress-strain response of solder at constant strain rate have been established from the Anand viscoplastic model, and a nonlinear regression based procedure has been developed for extracting the Anand model constants from the experimental stress-strain data. Using the developed procedure and solder stress-strain data, the Anand model material parameters have been determined for the various aging conditions. Mathematical expressions were then developed to model the evolution of the Anand model parameter with aging time. The developed Anand constitutive equations for solder with aging effects have been incorporated into standard finite element codes (ANSYS and ABAQUS). We have then performed finite element simulations to model the solder joint deformations of several different PBGA components attached to FR-4 printed circuit boards that were subjected to thermal cycling. Calculations were made for non-aged PBGA assemblies, as well as for assemblies that had been aged at constant temperature for various times before being subjected to thermal cycling. The finite element reliability predictions show significant increases in the calculated plastic work dissipated per cycle for assemblies that had been pre-aged prior to thermal cycling.

material parameters of the Anand constitutive model. They showed that using temperature dependent values of the nine constants in the model gave better matching with the experimental results. Mysore and coworkers [18] conducted double lap shear tests on Sn3.0Ag0.5Cu solder alloy and used the results to fit the materials constants in the Anand model. They reported there were significant differences in results obtained with bulk samples and those found with solder joint specimens. A modified Anand Constitutive model was proposed by Chen, et al. [19] that involved using temperature dependent values of one of the model parameters (ho). Amagai, et al. [20] have established values for the Anand model constants for Sn3.5Ag0.75Cu and SAC105 (Snl.0Ag0.5Cu) lead free solders. In their work, one of the nine required constants was ignored (so), and only 8 were specified. Kim, et al. [21] presented values for all 9 constants for SAC105 lead free solder. A modified Anand model was presented by Bai, et al. [22] for SAC305 (Sn3.0Ag0.5Cu) and Sn3.5Ag0.7Cu lead free solders. Their approach employed temperature and strain rate dependent values of for one of the model parameters (ho). The Anand model has also been widely used in the finite element simulation of solder interconnection in electronic components [23-26]. Primary Equations of Anand Model (1D) The Anand model uses a scalar internal variable s to represent the isotropic resistance to plastic flow offered by the internal state of the material. It unifies the creep and rateindependent plastic behavior of the solder by making use of a stress equation, a flow equation, and an evolution equation. The model needs no explicit yield condition and no loading/unloading criterion. For the one-dimensional case (uniaxial loading), the stress equation is given by (1)

σ = cs; c < 1 Anand Viscoplastic Constitutive Model Introduction Anand, et al. [14-15] proposed a popular set of viscoplastic constitutive equations for rate-dependent deformation of metals at high temperatures (e.g. in excess of a homologous temperature of 0.5Tm). Although it was originally aimed at hotworking of high strength aluminum and other structural metals, the so-called Anand model has been adopted successfully to represent isotropic materials such as microelectronic solders (SnPb and lead free) with small elastic deformations and large viscoplastic deformations. A large number of researchers have used the Anand model for electronic packaging applications. For example, Che, et al. [16] have demonstrated four different constitutive models for the Sn-3.8Ag-0.7Cu solder alloy including elastic-plastic, elastic-creep, elastic plastic with creep, and the viscoplastic Anand model. They showed that the Anand model was consistent with fatigue life predictions for lead free solders. Pei, et al. [17] performed monotonic tensile tests at a wide range of different temperatures and strain rates with two types of lead free solders (Sn3.5Ag and Sn3.8Ag0.7Cu) to get the

where s is the internal valuable and c is a function of strain rate and temperature expressed as ⎧⎡ ε& ⎛⎜ Q ⎞⎟ 1 ⎪ p c = c(ε& p , T) = sinh −1 ⎨⎢ e ⎝ RT ⎠ ξ ⎪⎩⎢⎣ A

⎤ ⎥ ⎥⎦

m

⎫ ⎪ ⎬ ⎪⎭

(2)

where ε& p is the inelastic (plastic) strain rate, T is the absolute temperature, ξ is the multiplier of stress, A is the preexponential factor, Q is the activation energy, R is the universal gas constant, and m is the strain rate sensitivity. Substituting eq. (2) into eq (1), the stress equation can be expressed as:

516

⎧⎡ ⎛ Q ⎞⎤ ⎜ ⎟ s −1 ⎪⎢ ε& p ⎝ RT ⎠ ⎥ σ = sinh ⎨ e ⎢ ⎥ ξ ⎪⎢ A ⎦⎥ ⎩⎣

m⎫

⎪ ⎬ ⎪ ⎭

(3)

Rearranging eq.(3) and solving for the strain rate yields the flow equation of the Anand model:

ε& p

1 ⎛ Q ⎞ −⎜ ⎟⎡ m σ ⎤ ⎞ ⎛ RT = A e ⎝ ⎠ sinh ξ

⎢ ⎣

(4)

⎜ ⎟⎥ ⎝ s ⎠⎦

The differential form of the evolution equation for the internal variable s is assumed to be of the form

include 9 material parameters (constants): A, ξ , Q/R, m in

)

eqs. (3, 4); and constants ho, a, so, s , and n in eq. (9). Theoretical Formulation for Uniaxial Stress-Strain Response The post yield uniaxial stress-strain relations predicted by the Anand model are obtained by substituting the expression for internal variable s from eq. (9) into the stress equation in eq. (3). The calculation results in:

s& = h (σ, s, T ) ε& p (5)

a ⎡ ⎛ s⎞ s ⎞⎤ ⎛ s& = ⎢h o ⎜1 − * ⎟ sign ⎜1 − * ⎟⎥ ε& p ; a > 1 ⎝ s ⎠⎦⎥ ⎣⎢ ⎝ s ⎠

σ=

where the term h (σ, s, T ) is associated with the dynamic hardening and recovery processes. Parameter ho is the hardening constant, a is the strain rate sensitivity of the hardening process, and the term s* is expressed as ⎡ & ⎛⎜ Q ⎞⎟ ⎤ εp * s = sˆ ⎢ e⎝ RT ⎠ ⎥ ⎥ ⎢A ⎥⎦ ⎢⎣

n

σ = σ (ε& p , ε p )

(6)

where sˆ is a coefficient, and n is the strain rate sensitivity of the saturation value of the deformation resistance. For s < s*, eq (5) can be rewritten as

⎧⎡ ε& ⎛⎜ Q ⎞⎟ ⎤ m ⎫ 1 ⎪ p ⎪ sinh −1 ⎨⎢ e⎝ RT ⎠ ⎥ ⎬ ξ ⎥⎦ ⎪ ⎪⎩⎢⎣ A ⎭

⎛ ⎡ ε& ⎛⎜ Q ⎞⎟ ⎤ n ⎜ p ⎝ RT ⎠ ⎥ − ⎜ sˆ ⎢ A e ⎦⎥ ⎜ ⎣⎢ ⎜ 1 (1− a) ⎜ ⎡⎛ n ⎤ 1− a ⎛ Q ⎞ ⎞ ⎜ ⎢⎜ ⎡ ε& p ⎜⎝ RT ⎟⎠ ⎤ ⎟ ⎥ + ⎥ − so ⎟ ⎜ ⎢⎜ sˆ ⎢ e ⎥ ⎟ ⎜ ⎢⎜⎝ ⎣⎢ A ⎦⎥ ⎥ ⎠ ⎜⎢ ⎥ n −a ⎫ ⎧ ⎜⎢ ⎥ ⎛ Q ⎞ ⎛ ⎞ ⎜ ⎢(a − 1)⎪ (h ) ⎜ sˆ ⎡⎢ ε& p e⎜⎝ RT ⎟⎠ ⎤⎥ ⎟ ⎪ ε ⎥ ⎨ o ⎜ ⎬ p⎥ ⎟ ⎜⎢ ⎜ ⎢⎣ A ⎥⎦ ⎟ ⎪ ⎪ ⎜⎢ ⎝ ⎠ ⎭ ⎦⎥ ⎩ ⎝⎣

⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠

(11)

For a uniaxial tensile test performed at fixed (constant) strain rate ε& p and constant temperature T, this expression represents highly nonlinear stress-strain behavior (power law type function) after yielding:

σ = σ (ε p )

(12)

a

s⎞ ⎛ ds = h o ⎜1 − * ⎟ dε p ⎝ s ⎠

(7)

and then integrated to yield

[(

s = s* − s* − s o

)

(1− a)

{

( )

+ (a − 1) (h o ) s *

−a

}ε ] p

1 1− a

(8)

where s(0) = so is the initial value of s at time t = 0. Substituting eq. (6) into eq. (8) yields the final version of the evolution equation for the internal variable s: n ⎡⎛ ⎤ ⎛ Q ⎞ ⎞ ⎟ ⎢⎜ ˆ ⎡ ε& p ⎜⎝ RT ⎟⎠ ⎤ ⎥ + − s e s ⎥ o⎟ ⎢⎜⎜ ⎢ A ⎥ ⎟ ⎦⎥ ⎢⎝ ⎣⎢ ⎥ ⎠ −⎢ ⎥ −a n ⎧ ⎢ ⎛ ⎡ ε& ⎛⎜ Q ⎞⎟ ⎤ ⎞ ⎫ ⎥ ⎢ (a − 1) ⎪⎨ (h ) ⎜ sˆ ⎢ p e ⎝ RT ⎠ ⎥ ⎟ ⎪⎬ ε ⎥ o ⎜ p ⎟ ⎢ ⎥ ⎜ ⎣⎢ A ⎪ ⎦⎥ ⎟⎠ ⎪ ⎥ ⎝ ⎢⎣ ⎩ ⎭ ⎦ (1− a)

⎡ ε& p ⎛⎜ Q ⎞⎟ ⎤ s = sˆ ⎢ e ⎝ RT ⎠ ⎥ ⎢⎣ A ⎥⎦

n

1 1− a

sˆ ⎡ ε& ⎜ ⎟ = ⎢ p e⎝ RT ⎠ ξ ⎢⎣ A ⎛ Q ⎞

UTS = σ ε

p →∞

n ⎧⎡ ε& ⎛⎜ Q ⎞⎟ ⎤ m ⎫ ⎤ ⎪ p * −1 ⎪ ⎥ sinh ⎨⎢ e ⎝ RT ⎠ ⎥ ⎬ ≡ σ ⎥⎦ ⎥⎦ ⎪ ⎪⎩⎢⎣ A ⎭

(13)

while the yield stress is given by the limit as ε p goes to 0:

σY = σ ε

(9)

p →0

⎧⎡ ε& ⎛⎜ Q ⎞⎟ ⎤ m ⎫ 1 ⎪ p −1 ⎪ = cs 0 = sinh ⎨⎢ e ⎝ RT ⎠ ⎥ ⎬ s 0 = c s 0 ≡ σ 0 ξ A ⎪⎩⎣⎢ ⎦⎥ ⎪⎭

(14)

Using the saturation stress ( σ* = UTS) relation in eq. (13), the post yield stress-strain response (power law) in eq. (11) can be rewritten as:

or

s = s(ε& p , ε p )

Anand model predictions for the yield stress ( σ Y ) and the Ultimate Tensile Strength (UTS = maximum/saturation stress) can be obtained by considering limiting cases of eq. (11). The UTS is given by the limit as ε p goes to ∞ :

(10)

The final equations in the Anand model (1D) are the stress equation in eq. (3), the flow equation in eq. (4), and the integrated evolution equation in eq. (9). These expressions

517

[(

σ = σ* − σ* − c s0

)

(1 − a )

+ ( a − 1)

{(ch

0

) (σ * )− a } ε p

]

1 /( 1− a )

(15)

Determination Procedure of the Model Parameters from the Stress Strain Data As discussed above, the nine parameters of the Anand ) model are A, ξ , Q/R, m, ho, a, so, s , and n. One method to obtain the values of these parameters for a specific material is to perform a series of stress-strain tests over a wide range of temperatures and strain rates [14-15]. From the measured data, the value of the saturation stress ( σ* = UTS) can be obtained for several strain rates and temperatures. In addition, the stress-strain ( σ, ε ) data for each temperature and strain rate can be recast as stress vs. plastic strain data ( σ, ε p ) by using

εp = ε −

σ E

(16)

where E is the initial elastic modulus of the material at the specific temperature and strain rate being considered. The Anand model parameters can be obtained by following procedure: 1.

2.

Determine the values of the parameters sˆ , ξ , A, Q/R, n and m in by non-linear regression (least squares) fitting of eq. (13) to the saturation stress vs. strain rate and temperature data. Determine the values of parameters so, ho, and a by non-linear regression (least squares) fitting of eq. (15) to the stress vs. plastic strain data at several strain rates and temperatures.

Experimental Procedure

Test Matrix for Aging Experiments The effects of aging on the nine Anand model parameters have been examined by performing stress-strain tests on SAC305 samples that were aged for various durations (0-6 months) at a temperature of 100 C. The aging conditions included the baseline/reference state of no aging, as well as 6 different aging times including 1, 5, 20, 60, 120, and 180 days at 100 C. For each set of aging conditions, stress-strain experiments were performed at three strain rates (.001, .0001, and .00001 1/sec) and five temperatures (25, 50, 75, 100, and 125 C). Using the measured stress-strain data and procedure discussed above, the nine Anand model material parameters have been determined for each of the aging times. Uniaxial Test Sample Preparation Solder uniaxial samples are often fabricated by machining of bulk solder material, or by melting of solder paste in a mold. Use of a bulk solder bars is undesirable, because they will have significantly different microstructures than those present in the small solder joints used in microelectronics assembly. In addition, machining can develop residual stresses in the specimen, and heat generated during turning operations can cause localized microstructural changes on the exterior of the specimens. Reflow of solder paste in a mold

causes challenges with flux removal, minimization of voids, microstructure control, and extraction of the sample from the mold. In addition, many of the developed specimens have shapes that significantly deviate from being long slender rods. Thus, undesired non-uniaxial stress states will be produced during loading. Other investigators have attempted to extract constitutive properties of solders by direct shear or tensile loading or indenting of actual solder joints (e.g. flip chip solder bumps or BGA solder balls). While such approaches are attractive because the true solder microstructure is involved, the unavoidable non-uniform stress and strain states in the joint make the extraction of the correct mechanical properties and stress-strain curves from the recorded loaddisplacement data very challenging. Also it can be difficult to separate the various contributions to the observed behavior from the solder material and other materials in the assembly (bond pads, silicon die, PCB/substrate, etc.). In the current study, we have avoided many of the specimen preparation pitfalls identified above by a using a novel procedure where solder uniaxial test specimens are formed in high precision rectangular cross-section glass tubes using a vacuum suction process [1-6]. The tubes are first cooled by water quenching. They are then sent through a SMT reflow at a later time to re-melt the solder in the tubes and subject them to any desired temperature profile (i.e. same as actual solder joints). The solder is first melted in a quartz crucible using a pair of circular heating elements (see Figure 9). A thermocouple attached on the crucible and a temperature control module is used to direct the melting process. One end of the glass tube is inserted into the molten solder, and suction is applied to the other end via a rubber tube connected to the house vacuum system. The suction forces are controlled through a regulator on the vacuum line so that only a desired amount of solder is drawn into the tube. The specimens are then cooled to room temperature using a user-selected cooling profile.

Figure 9 - Specimen Preparation Hardware In this work, the glass tube solder samples were first water quenched. They were then sent through a reflow oven (9 zone Heller 1800EXL) to re-melt the solder in the tube and subject it to the desired temperature profile. Thermocouples are attached to the glass tubes and monitored continuously using a radio-frequency KIC temperature profiling system to ensure

518

that the samples are formed using the desired temperature profile (same as actual solder joints). Figure 10 illustrates the reflow temperature profile used in this work for SACN05 (N = 1, 2, 3, 4) solder specimens.

solidification temperature profile. Samples were inspected using a micro-focus x-ray system to detect flaws (e.g. notches and external indentations) and/or internal voids (non-visible). Figure 12 illustrates results for good and poor specimens. With proper experimental techniques, samples with no flaws and voids were generated.

Figure 10 - Solder Reflow Temperature Profiles for SAC (105/205/305/405)

Figure 12 - X-Ray Inspection of Solder Test Specimens (Good and Bad Samples)

Typical glass tube assemblies filled with solder and a final extracted specimen are shown in Figure 11. For some cooling rates and solder alloys, the final solidified solder samples can be easily pulled from the tubes due to the differential expansions that occur when cooling the low CTE glass tube and higher CTE solder alloy. Other options for more destructive sample removal involve breaking the glass or chemical etching of the glass. The final test specimen dimensions are governed by the useable length of the tube that can be filled with solder, and the cross-sectional dimensions of the hole running the length of the tube. In the current work, we formed uniaxial samples with nominal dimensions of 80 x 3 x 0.5 mm. A thickness of 0.5 mm was chosen because it matches the height of typical BGA solder balls. The specimens were stored in the aging oven immediately after the reflow process to eliminate possible room temperature aging effects.

Mechanical Testing System A MT-200 tension/torsion thermo-mechanical test system from Wisdom Technology, Inc., as shown in Figure 13, has been used to test the samples in this study. The system provides an axial displacement resolution of 0.1 micron and a rotation resolution of 0.001°. Testing can be performed in tension, shear, torsion, bending, and in combinations of these loadings, on small specimens such as thin films, solder joints, gold wire, fibers, etc. Cyclic (fatigue) testing can also be performed at frequencies up to 5 Hz. In addition, a universal 6-axis load cell was utilized to simultaneously monitor three forces and three moments/torques during sample mounting and testing. Environmental chambers added to the system allow samples to be tested over a temperature range of -185 to +300 °C.

(a) Within Glass Tubes

(b) After Extraction Figure 13 - MT-200 Testing System with Solder Sample

Figure 11 - Solder Uniaxial Test Specimens The described sample preparation procedure yielded repeatable samples with controlled cooling profile (i.e. microstructure), oxide free surface, and uniform dimensions. By extensively cross-sectioning several specimens, we have verified that the microstructure of any given sample is very consistent throughout the volume of the sample. In addition, we have established that our method of specimen preparation yields repeatable sample microstructures for a given

During uniaxial testing, forces and displacements were measured. The axial stress and axial strain were calculated from the applied force and measured cross-head displacement using

519

σ=

F A

ε=

ΔL δ = L L

(17)

Typical Test Data A typical recorded tensile stress strain curve for solder with labeled standard material properties is shown in Figure 14. The notation “E” is taken to be the effective elastic modulus, which is the initial slope of the stress-strain curve. Since solder is viscoplastic, this effective modulus will be rate dependent, and will approach the true elastic modulus as the testing strain rate approaches infinity. The yield stress σ Y (YS) is taken to be the standard .2% yield stress (upon unloading, the permanent strain is equal to ε = .002 ). Finally, the ultimate tensile strength σ u (UTS) is taken to be the maximum (saturation) stress realized in the stress-strain data. As shown in Figure 14, the solders tested in this work illustrated nearly perfect elastic-plastic behavior (with the exception of a small transition region connecting the elastic and plastic regions). As the strain level becomes extremely high and failure is imminent, extensive localized necking takes place. These visible reductions in cross-sectional area lead to non-uniform stress-states in the specimen and drops in the applied loading near the end of the stress-strain curve. σu Stress

σY

E .002

Strain

Figure 14 - Typical Solder Stress-Strain Curve and Material Properties Stress-Strain Data Processing Although, several different empirical models can be used to represent the observed stress-strain data for solder, we have chosen to use a four parameter hyperbolic tangent model

σ = C1 tanh( C 2 ε) + C 3 tanh( C 4 ε)

(18)

where C1, C2, C3, C4 are material constants to be determined through regression fitting of the model to experimental data. The initial (zero strain) effective elastic modulus E can be calculated from the model constants as

E = σ ′ ( 0 ) = C1 C 2 + C 3 C 4

(19)

Figure 15 illustrates a typical set of 10 solder stress strain curves measured under similar environmental and aging conditions, and the corresponding fit of eq. 18 to the data. The excellent representation provided by the empirical model suggests that it indeed provides a mathematical description of

a suitable “average” stress-strain curve for a set of experimental curves measured under fixed test conditions. 30 25

Stress, σ (MPa)

where σ is the uniaxial stress, ε is the uniaxial strain, F is the measured uniaxial force, A is the original cross-sectional area, δ is the measured crosshead displacement, and L is the specimen gage length (initial length between the grips). The gage length chosen in this study was 60 mm.

20 15 10 5 0 0.000

0.005

0.010

0.015

0.020

0.025

0.030

Strain, ε

Figure 15 - Solder Stress-Strain Curves and Empirical Model Tensile Testing Results for SAC305 Solder

Stress-Strain Data for Various Temperatures and Strain Rates Uniaxial tensile testing of SAC305 lead free solder has been performed for specimens subjected to 7 different sets of aging conditions prior to testing: 0, 1, 5, 20, 60, 120, and 180 days of aging at 100 C. For each aging time, stress-strain data were measured at three strain rates (.001, .0001, and .00001 1/sec) and five temperatures (25, 50, 75, 100, and 125 C). For example, Figures 16(a), 16(b), 16(c) illustrates typical stressstrain curves for SAC305 with no aging (0 days aging) prior to testing (samples were tested immediately after reflow and cooling) for strain rates of 0.001, 0.0001, and 0.00001, respectively. In each plot, the 5 colored curves are the stressstrain results for temperatures of T = 25, 50, 75, 100, and 125 C. Each curve is the “average” stress-strain curve representing the fit of eq. (18) to the 10 recorded raw stressstrain curves for a given set of temperature, strain rate, and aging conditions. For example, the top (black) curve in each plot is the average stress-strain curve at room temperature (25 o C), and the bottom (red) curve in each plot is the average stress-strain curve at 125 oC. Analogous results for the other aging conditions are shown in Figures 17-22. It is observed in each graph in Figures 16-22 that the effective elastic modulus, yield stress (YS), and ultimate tensile strength (UTS) all decrease monotonically with temperature as expected. These decreases have been found to be nearly linear with the testing temperature for all aging conditions as illustrated in Figure 23. By comparing the analogous results for the same temperature and aging conditions, but different strain rates, it has also been observed that as the strain rate decreases, the effective elastic modulus, yield stress (YS), and ultimate tensile strength (UTS) all decrease.

520

50

50

0 Days Aging at 100 oC

ε& = 0.001

40

Stress, σ (MPa)

Stress, σ (MPa)

40

30

20 25 oC 50 oC 75 oC o 100 C 125 oC

10

0 0.000

0.005

0.010

30

20 o 25 C o 50 C 75 oC 100 oC o 125 C

10

0.015

0 0.000

0.020

0.005

Strain, ε (a) ε& = 0.001 50


ε& = 0.0001

0.015

0.020

1 Day Aging at 100 oC

ε& = 0.0001 40

Stress, σ (MPa)

40

Stress, σ (MPa)

0.010

Strain, ε (a) ε& = 0.001

50

30

20 o

25 C 50 oC

10

75 oC

0 0.000

o 100 C o 125 C 0.005

0.010

0.015

30

20

0 0.000

0.020

25 oC 50 oC 75 oC 100 oC 125 oC

10

0.005

0.010

50

50


ε& = 0.00001

0.015

0.020

Strain, ε (b) ε& = 0.0001

Strain, ε (b) ε& = 0.0001


ε& = 0.00001 40

Stress, σ (MPa)

40

Stress, σ (MPa)


ε& = 0.001

30

20 o 25 C o 50 C o 75 C o 100 C o 125 C

10

0 0.000

0.005

0.010

0.015

25 oC o 50 C o 75 C 100 oC o 125 C

30

20

10

0 0.000

0.020

0.005

0.010

0.015

Strain, ε (c) ε& = 0.00001

Strain, ε (c) ε& = 0.00001

Figure 16 - Stress-Strain Curves for SAC305 with No Aging

Figure 17 - Stress-Strain Curves for SAC305 for 1 Day Aging at 100 oC

521

0.020

50

40

Stress, σ (MPa)

30

20

10

0 0.000

0.005

0.010

0.015


ε& = 0.001

25 oC 50 oC 75 oC 100 oC 125 oC

40

Stress, σ (MPa)

50


ε& = 0.001

25 oC 50 oC o 75 C 100 oC 125 oC

30

20

10

0 0.000

0.020

0.005

0.010

Strain, ε (a) ε& = 0.001 50

50

40 o

25 C o 50 C o 75 C o 100 C 125 oC

30

Stress, σ (MPa)

Stress, σ (MPa)


ε& = 0.0001

40

20

10

o

25 C 50 oC o 75 C 100 oC o 125 C

30

20

10

0 0.000

0.005

0.010

0.015

0 0.000

0.020

0.005

50

0.015

0.020

50


ε& = 0.00001

0.010

Strain, ε (b) ε& = 0.0001

Strain, ε (b) ε& = 0.0001


ε& = 0.00001

40

40

Stress, σ (MPa)

Stress, σ (MPa)

0.020

(a) ε& = 0.001 5 Days Aging at 100 oC

ε& = 0.0001

0.015

Strain, ε

o

25 C 50 oC 75 oC o 100 C o 125 C

30

20

10

0 0.000

0.005

0.010

0.015

25 oC 50 oC 75 oC 125 oC 25 oC

30

20

10

0 0.000

0.020

0.005

0.010

0.015

Strain, ε

Strain, ε (c) ε& = 0.00001

(c) ε& = 0.00001

Figure 18 - Stress-Strain Curves for SAC305 for 5 Days Aging at 100 oC


522

0.020

50

50

40

40 o

25 C 50 oC o 75 C 100 oC 125 oC

30

Stress, σ (MPa)

Stress, σ (MPa)


ε& = 0.001


ε& = 0.001

20

25 oC 50 oC 75 oC 100 oC 125 oC

30

20

10

10

0 0.000

0.005

0.010

0.015

0 0.000

0.020

0.005

0.010

50

50

40

Stress, σ (MPa)

Stress, σ (MPa)


ε& = 0.0001


40 o

25 C 50 oC 75 oC o 100 C o 125 C

30

20

25 oC o 50 C 75 oC o 100 C 125 oC

30

20

10

10

0 0.000

0.005

0.010

0.015

0 0.000

0.020

0.005

0.010

0.015

0.020

Strain, ε (b) ε& = 0.0001

Strain, ε (b) ε& = 0.0001 50

50


ε& = 0.00001


ε& = 0.00001

40

Stress, σ (MPa)

40

Stress, σ (MPa)

0.020

Strain, ε (a) ε& = 0.001

Strain, ε (a) ε& = 0.001

ε& = 0.0001

0.015

25 oC 50 oC o 75 C o 100 C o 125 C

30

20

o 25 C o 50 C 75 oC o 100 C o 125 C

30

20

10

10

0 0.000

0.005

0.010

0.015

0 0.000

0.020

Strain, ε

0.005

0.010

0.015

Strain, ε

(c) ε& = 0.00001

(c) ε& = 0.00001



523

0.020

50

Elaatic Modulus, E (GPa)

40

Stress, σ (MPa)

50


ε& = 0.001

o

25 C o 50 C 75 oC 100 oC o 125 C

30

20

10

0 0.000

0.005

0.010

0.015

ε& = 0.001 SAC 305, RF

40

30

o 0 Day, 100 C Aging o 1 Day, 100 C Aging o 5 Days, 100 C Aging o 20 Days, 100 C Aging o 60 Days, 100 C Aging o 120 Days, 100 C Aging o 180 Days, 100 C Aging

20

10

0

0.020

0

20

80

100

140

o 0 Day, 100 C Aging

ε& = 0.001


ε& = 0.0001

120

(a) Elastic Modulus 50

50

Col 72 vs Col 73

o 5 Days, 100 C Aging o 20 Days, 100 C Aging o 60 Days, 100 C Aging o 120 Days, 100 C Aging o 180 Days, 100 C Aging

SAC 305, RF

40

40 o

30

UTS (MPa)

25 C o 50 C o 75 C o 100 C o 125 C

20

10

30

20

10

0 0.000

0.005

0.010

0.015

0

0.020

0

20

40

Strain, ε (b) ε& = 0.0001 50

Yield Stress, σ (MPa)

40

20

Y

25 oC 50 oC o 75 C 100 oC o 125 C

30

10

0 0.000

0.005

0.010

80

100

Temperature (oC)

ε& = 0.001


ε& = 0.00001

60

120

140

(b) UTS

50

Stress, σ (MPa)

60

Temperature (oC)

Strain, ε (a) ε& = 0.001

Stress, σ (MPa)

40

0.015

o 0 Day, 100 C Aging o 1 Day, 100 C Aging o 5 Days, 100 C Aging o 20 Days, 100 C Aging o 60 Days, 100 C Aging o 120 Days, 100 C Aging o 180 Days, 100 C Aging

SAC 305, RF

40

30

20

10

0

0.020

0

Strain, ε (c) ε& = 0.00001

20

40

60

80

100

Temperature (oC)

120

140

(c) Yield Stress Figure 23 - Variation of SAC 305 Material Properties with Temperature (Aging for 0-6 Months)


524

Effects of Aging on the Stress-Strain Curves The effects of aging on the stress-strain response of SAC305 can be directly observed by regrouping of the various curves in Figures 16-22, so that each graph is at a constant testing temperature instead of a constant aging time. For example, Figure 24 illustrates the effects of aging for the 5 different testing temperatures (T = 25, 50, 75, 100, and 125 C) and a strain rate of 0.001. Similar results were obtained for the other two strain rates. The various colored curves in each graph represent the data for different aging times. In particular, the black top curve in each graph is for no aging (0 days aging) prior to tensile testing, and the red bottom curve in each graph is for 180 days aging at 100 C prior to testing. The results in Figure 24(a) for testing at T = 25 (room temperature) are similar to those published previously by the authors for SAC alloys tested at room temperature [1-6]. The results in Figures 24(b), 24(c), 24(d), and 24(e) for testing at T = 50, 75, 100, and 125 C, respectively, represent the first extensive set of published data on the effects of aging on the elevated temperature stress-strain response of lead-free solders. As expected, aging also causes large degradations in the elevated temperature mechanical behavior of SAC solders, with large degradations in the material properties (elastic modulus, yield stress, and UTS). The changes in UTS (maximum/saturation stress) with aging are especially evident from each of the 5 plots in Figure 24. Referring back to Figure 23, it can be seen that the majority of the changes in the material properties at each temperature occur during the first 20 days of aging, with slower degradations occurring from 20 to 180 days of aging.

50

Stress, σ (MPa)

40

30

20

0 0.000

εε&& = 0.001 = 0.001

Stress, σ (MPa)

40

0 Day, 100 oC o 1 Day, 100 C 5 Days, 100 oC o 20 Days, 100 C 60 Days, 100 oC 120 Days, 100 oC 180 Days, 100 oC

T= 100 25 oo CC T=

30

20

10

0 0.000

0.005

0.010

0.015

0.020

Strain, ε

(d) T = 100 oC ε&ε&==0.001 0.001

40

Stress, σ (MPa)

Stress, σ (MPa)

0.020

50

25 ooC T= 25

0 Day, 100 oC 1 Day, 100 oC 5 Days, 100 oC 20 Days, 100 oC 60 Days, 100 oC 120 Days, 100 oC 180 Days, 100 oC

10

0.005

0.010

0.015

0 Day, 100 oC 1 Day, 100 oC 5 Days, 100 oC 20 Days, 100 oC 60 Days, 100 oC 120 Days, 100 oC o 180 Days, 100 C

30

20

0 0.000

0.020

0.005

0.010

0.015

0.020

Strain, ε

(e) T = 125 oC

(a) T = 25 oC

Figure 24 - Effects of Aging on the Stress-Strain Curves for SAC305 Solder ( ε& = .001)

50

ε&ε&==0.001 0.001

T= T= 50 25 ooCC

30

20


10

0.005

oo T= T= 25 125 C C

10

Strain, ε

Stress, σ (MPa)

0.015

50

20

0 0.000

0.010

(c) T = 75 oC

30

40

0.005

Strain, ε

0.001 ε& = 0.001

0 0.000

T= 25 75 oC

10

50

40


ε& = 0.001

0.010

Strain, ε

(b) T = 50 oC

0.015

0.020

Effects of Aging on the Anand Model Material Parameters The Anand model parameters for SAC305 lead free solder material have been determined for each aging time from the temperature and strain rate dependent stress-strain data in Figures 16-22. The curves in each Figure were first processed to extract saturation stress (UTS) vs. strain rate and temperature data for each aging time, as well as stress vs. plastic strain data at several strain rates and temperatures for each aging time. From the extracted data from each Figure, the nine Anand parameters were calculated for each aging time using eqs. (13, 15) and the nonlinear regression analysis

525

procedure discussed above. The results of these computations are tabulated in Figure 25. 10000

SAC 305 5 Days Aging





Anand Constant

Units

1

s0

MPa

21.0

13.5

8.0

6.0

5.9

5.8

2

Q/R

1/K

9320

9320

9320

9320

9320

9320

3

A

sec-1

3501

3960

4065

4095

4105

4110

4

ξ

4

4

4

4

4

4

5

m

0.25

0.21

0.19

0.18

0.18

0.18

6

ho

MPa

180000

135050

103218

89682

80825

77540

7

sˆ

MPa

30.2

26.0

22.8

22.3

22.0

21.9

8

n

0.0100

0.0030

0.0015

0.0011

0.0010

0.0098

9

a

1.78

1.98

2.01

2.03

2.04

2.05

9800

Q/R (1/K)

Constant Number


9600

9400

9200

9000 0

40

60

80

100

120

140

160

180

200

Aging Time (Days)

(b) Variation of Q/R with Aging Time

5000

Figure 25 - Anand Model Parameters for SAC305 Solder for Various Aging Times (0-6 Months) at 100 C -1

A (sec )

4500

The effects of aging on the Anand model parameters for SAC305 tabulated in Figure 25 can be better visualized by plotting the extracted model parameters vs. aging time. Such graphs are presented in Figure 26 for parameters so, Q/R, A, ξ , m, ho, sˆ , n, and a. The discrete parameter values in these Figures illustrate smooth variations with aging, and empirical mathematical models with linear and nonlinear terms have been able to accurately represent the variations of all of the Anand parameters with aging time. Parameters Q/R and ξ were found to be constant, and thus independent of aging. This is logical since Q is the activation energy of the SAC solder, which should be constant independent of aging. The other 7 parameters (so, A, m, ho, sˆ , n, and a) all exhibit rapid changes during the first 20 days of aging, and then slow variations for aging times between 20 and 180 days. This is similar to the variations of the material constants shown in Figures 1 and 2. The slow variations for longer aging times were found to be approximately linear with the aging time. The mathematical expressions for the aging time dependent empirical models used in Figure 26 are tabulated in Figure 27. In all cases, the models included constant and linear terms with aging time, along with a nonlinear functional term.

4000

3500

3000

2500 0

20

40

60

80

100

120

140

160

180

200

Aging Time (Days)

(c) Variation of A with Aging Time

5.0

4.5

ξ

4.0

3.5

3.0 0

20

40

60

80

100

120

140

160

180

200

Aging Time (Days)

(d) Variation of ξ With Aging Time

0.30

30

0.25

25

0.20

m

20

So (MPa)

20

15

0.15

10

0.10

5

0.05

0.00

0 0

20

40

60

80

100

120

140

160

180

0

200

20

40

60

80

100

120

140

160

180

Aging Time (Days)

Aging Time (Days)

(e) Variation of m with Aging Time

(a) Variation of so with Aging Time

526

200

200x103 180x103

Form of Empirical Fitting Equation

So, m, n, a

Parameter = C o + C1 t + C 2 e − C3t

A, sˆ

160x103

ho (MPa)

Anand Constant

140x103

ho

120x103 100x103

Q/R, ξ

80x103

C4

Parameter = C 0 + C1 t + C 2 (1 − e − C3 t ) C2 Parameter = C 0 + C1 t + C3 + e t

Parameter = Co

60x103 0

20

40

60

80

100

120

140

160

180

Figure 27 - Empirical Models for Variation of the Anand Model Parameters with Aging Time

200

Aging Time (Days)

(f) Variation of ho with Aging Time

Correlation of the Predictions of the Anand Model with the Experimental Stress-Strain Data Once the Anand constants are determined for each aging time, it is possible to predict the stress ( σ ) vs. plastic strain ( ε p ) curve at a particular set of temperature, strain rate, and

40

30

aging conditions using eq. (11). This result can be adjusted to a stress ( σ ) vs. total strain curve ( ε ) by adding the elastic strain to the plastic strain:

Sˆ (MPa) 20

10

ε =εe + εp

0 0

20

40

60

80

100

120

140

160

180

200

εe =

σ E

(20)

Aging Time (Days)

(g) Variation of sˆ with Aging Time

0.025

0.020

n

0.015

0.010

0.005

0.000

0

20

40

60

80

100

120

140

160

180

200

Aging Time (Days)

(h) Variation of n with Aging Time

2.4

a

2.2

2.0

1.8

1.6

0

20

40

60

80

100

120

140

160

180

200

Aging Time (Days)

(i) Variation of a with Aging Time Figure 26 - Variation of the Anand Model Parameters of SAC305 Solder with Aging Time

where E is the initial elastic modulus at the particular temperature, strain rate, and aging conditions Figure 28 illustrates the correlation between the model predictions and the experimental stress-strain curves for no aging. In this case, the Anand model constants from Figure 25 for 0 days aging were utilized. The experimental curves were those shown earlier in Figure 16. Good correlations are obtained, with the Anand model able to represent the stressstrain curves accurately over a wide range of temperatures and strain rates. Analogous comparisons for 20 days aging are shown in Figure 29. In this case, the Anand model constants from Figure 25 for 20 days aging were utilized, along with the experimental curves from Figure 19. Again, good correlations were obtained for all temperatures and strain rates. We have done similar comparisons for all of the other aging conditions (1, 5, 60, 120, and 180 days aging at 100 C). In all cases, the Anand model predictions match the experimental stress-strain curves well for all temperatures and strain rates. Example Finite Element Application of the Anand Model with Aging Effects The developed Anand constitutive equations for solder with aging effects have been incorporated into standard finite element codes (ANSYS and ABAQUS). We have then performed finite element simulations to model the solder joint deformations of several different PBGA components attached to FR-4 printed circuit boards that were subjected to both thermal aging and thermal cycling. Calculations have been made for non-aged PBGA assemblies, as well as for assemblies that had been aged at 100 C for various times before being subjected to thermal cycling.

527

50

50


ε& = 0.001

40

Stress, σ (MPa)

40

Stress, σ (MPa)


ε& = 0.001

30

20

o

25 C, Experiment o 50 C, Experiment o 75 C, Experiment o 100 C, Experiment o 125 C, Experiment o 25 C, Model Prediction o 50 C, Model Prediction o 75 C, Model Prediction o 100 C, Model Prediction o 125 C, Model Prediction

10

0 0.000

0.005

0.010

0.015

30

20

10

0 0.000

0.020

0.005

0.010


ε& = 0.0001


ε& = 0.0001 40

Stress, σ (MPa)

40

Stress, σ (MPa)

0.020

50

50

30

20 25 oC, Model Prediction o 50 C, Model Prediction 75 oC, Model Prediction o 100 C, Model Prediction 125 oC, Model Prediction

o

25 C, Experiment 50 oC, Experiment 75 oC, Experiment 100 oC, Experiment o 125 C, Experiment

10

0 0.000

0.005

0.010

0.015

30

20

10

0 0.000

0.020

0.005

0.010

0.015

0.020

Strain, ε (b) ε& = 0.0001

Strain, ε & (b) ε = 0.0001 50

50

40

Stress, σ (MPa)

40

30

20

25 oC, Experiment 50 oC, Experiment o 75 C, Experiment o 100 C, Experiment o 125 C, Experiment

10

0 0.000


ε& = 0.00001


ε& = 0.00001

Stress, σ (MPa)

0.015

Strain, ε (a) ε& = 0.001

Strain, ε (a) ε& = 0.001

0.005

0.010

o

25 C, Model Prediction 50 oC, Model Prediction o 75 C, Model Prediction 100 oC, Model Prediction o 125 C, Model Prediction

0.015

20

10

0 0.000

0.020

Strain, ε (c) ε& = 0.00001

Figure 28 - Correlation of the Anand Model Predictions with Experimental Stress-Strain Data for No Aging

30

0.005

0.010

0.015

0.020

Strain, ε (c) ε& = 0.00001

Figure 29 - Correlation of the Anand Model Predictions with Experimental Stress-Strain Data for 20 Days Aging

528

For example, Figure 30 illustrates a 3D slice finite element mesh (half model) for a 676 I/O PBGA component examined in one set of analyses. For the specified loading, this configuration was subjected to thermal cycling from 0 to 100 C as shown in Figure 31 (8 minute ramps and 10 minute dwells). The solder balls were taken to be SAC305 lead free alloy, and the Anand model with aging dependent material parameters was utilized as the solder constitutive model. The other materials in the assembly (FR4 PCB, silicon chip, BT laminate, epoxy overmold) were modeled as linear elastic with temperature dependent properties.

initial configuration of the assembly before cycling was assumed to be the “stress free” state of the assembly. The critical solder ball in this PBGA configuration was the fourth from the center (under the die shadow). The volume averaged inelastic energy dissipation ΔW =PLWK (plastic work) accumulated per cycle is often taken to be the metric for damage accumulation and failure of solder joints. We have calculated this quantity for the three rows of elements at the top of the critical solder ball. Figure 32 shows the calculated PLWK accumulation as a function of time for the first 3 thermal cycles for the various aging conditions considered prior to cycling. As expected, it was found that longer aging times prior to cycling resulted in additional energy dissipation (and thus more damage accumulation) in the solder joints. After a few cycles, the amount of energy dissipated per cycle becomes constant (steady state), and Figure 33 shows the dependence of the steady state PLWK accumulated per cycle with the duration of aging prior to the beginning of cycling. For the most extreme aging conditions (6 months at 100 C), a 25% increase occured in the energy dissipated per cycle, suggesting an acceleration of damage accumulation and a reduction in the final fatigue life of the solder joint. 1.2

3 Cycles 1.0

PLWK (MPa)

0.8

Figure 30 - 3D Slide Finite Element Model of 676 PBGA

Temperature (oC)

120

Third Cycle

0.6

0.4

100

0.2

80

0.0

o 0 Day Aging at 100 C o 1 Day Aging at 100 C o 5 Days Aging at 100 C o 20 Days Aging at 100 C o 60 Days Aging at 100 C o 120 Days Aging at 100 C o 180 Days Aging at 100 C

Second Cycle First Cycle

0

1000

2000

3000

60

4000

5000

6000

7000

Time (Sec)

40

Figure 32 - Energy Dissipation During Thermal Cycling for Different Durations of Aging Prior to Cycling

20 0

0.40

0

20

40

60

80

100

120

140

160

180

Aging at 100 oC

200 0.35

Time (min)

Figure 31 - Thermal Cycle (0 to 100 C, 10 Minute Dwells) ΔWavg

The analysis of the solder stresses, strains, and deformations during thermal cycling was performed assuming different durations of aging at 100 C prior to the beginning of thermal cycling. To match the material characterization tests presented earlier, the aging conditions were taken to be 1, 5, 20, 60, 120, and 180 days at 100 C prior to the initiation of cycling. For the different aging times, finite element simulations of the thermal cycling were performed using the various sets of Anand parameters given in Figure 25. The

529

0.30

0.25

0.20 0

20

40

60

80

100

120

140

160

180

200

Aging time (Days)

Figure 33 - Energy Dissipation per Cycle for Different Durations of Aging Prior to Cycling

The calculations and discussion above are based on the assumption that the aging of the assemblies occurs as thermal preconditioning before thermal cycling. Aging also occurs gradually during the thermal cycling process due to the exposure of the assemblies to the high temperature dwell in each thermal cycle. We have also analyzed the case of gradual in-situ aging of the PBGA assembly during thermal cycling. In this case, no aging was assumed to have occurred prior to thermal cycling. The aging state of the assembly (and thus the Anand model constants) were allowed to evolve during the cycling due to the exposures at the high temperature dwells. Figure 34 illustrates the calculated evolution of the energy dissipation per cycle as a function of the number of thermal cycles. The PLWK and damage accumulation increases as cycling progresses due to use of the modified Anand model with aging effects. This again suggests an acceleration of damage accumulation and a reduction in the final fatigue life of the solder joint. Using the standard Anand model with constant material parameters, the energy dissipation per cycle remains constant during the entire cycling exposure. 0.40

Aging at 100 oC

0.35

ΔWavg

0.30

The theoretical equations for the uniaxial stress-strain response of solder at constant strain rate have been established from the Anand viscoplastic model, and a nonlinear regression based procedure has been developed for extracting the Anand model constants from the experimental stress-strain data. Using the developed procedure and solder stress-strain data, the Anand model material parameters have been determined for the various aging conditions. Mathematical expressions were then developed to model the evolution of each Anand model parameter with aging time. As expected, the material properties and Anand model parameters evolved (degraded) dramatically during first few 20 days of aging, and then the degradation becomes linear for longer aging times. The developed Anand constitutive equations for solder with aging effects have been incorporated into standard finite element codes (ANSYS and ABAQUS). We have then performed finite element simulations to model the solder joint deformations of an example PBGA assembly subjected to thermal cycling. Calculations were made for non-aged PBGA assemblies, as well as for assemblies that had been aged at constant temperature for various times before being subjected to thermal cycling. The finite element reliability predictions show significant increases in the calculated plastic work dissipated per cycle for assemblies that had been pre-aged prior to thermal cycling. Thus, aging will result in an acceleration of damage accumulation and a reduction in the final fatigue life of the solder joint. In addition, in-situ aging also occurs during thermal cycling due to the exposures at the high temperature dwells. We have shown that such aging also leads to an acceleration of damage accumulation relative to non-aged components.

0.25

Acknowledgments This work was supported by the US Army and the NSF Center for Advanced Vehicle and Extreme Environment Electronics (CAVE3).

0.20 0

5000

10000

15000

20000

25000

30000

No. of cycles

Figure 34 - Evolution of the Energy Dissipation per Cycle During Thermal Cycling Due to Insitu Aging Summary and Conclusions In several recent investigations, isothermal aging has been shown to degrade the thermal cycling reliability of lead free PBGA assemblies subjected to accelerated life testing. In this paper, we have reported on the first step of developing new reliability prediction procedures that utilize constitutive relations and failure criteria that incorporate aging effects. A revised set of Anand viscoplastic stress-strain relations have been established for solder that include material parameters that evolve with the thermal history of the solder material. The effects of aging on the nine Anand model parameters have been examined by performing stress-strain tests on SAC305 samples that were aged for various durations (0-6 months) at a temperature of 100 C. For each aging time, stress-strain data were measured at three strain rates (.001, .0001, and .00001 1/sec) and five temperatures (25, 50, 75, 100, and 125 C). Variations of the mechanical properties (elastic modulus, yield stress, ultimate strength, etc.) were observed as a function of aging time.

References 1. Ma, H., Suhling, J. C., Lall P., Bozack, M. J., “Reliability of the Aging Lead-free Solder Joint,” Proceeding of the 56th Electronic Components and Technology Conference, San Diego, CA, pp. 849-864, 2006. 2. Ma, H., Suhling, J. C., Zhang, Y., Lall, P., and Bozack, M. J., “The Influence of Elevated Temperature Aging on Reliability of Lead Free Solder Joints,” Proceedings of the 57th IEEE Electronic Components and Technology Conference, pp. 653-668, Reno, NV, May 29-June 1, 2007. 3. Zhang, Y., Cai, Z., Suhling, J. C., Lall, P., and Bozack, M. J., “The Effects of Aging Temperature on SAC Solder Joint Material Behavior and Reliability,” Proceedings of the 58th IEEE Electronic Components and Technology Conference, pp. 99-112, Orlando, FL, May 27-30, 2008. 4. Zhang, Y., Cai, Z., Suhling, J. C., Lall, P., and Bozack, M. J., “The Effects of SAC Alloy Composition on Aging Resistance and Reliability,” Proceedings of the 59th IEEE Electronic Components and Technology Conference, pp. 370-389, San Diego, CA, May 27-29, 2009.

530

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

Cai, Z., Zhang, Y., Suhling, J.C., Lall, P., Johnson, R. W., Bozack, M. J., “Reduction of Lead Free Solder Aging Effects using Doped SAC Alloys,” Proceedings of the 60th Electronic Components and Technology Conference, pp. 1493-1511, Las Vegas, NV, 2010. Mustafa, M., Cai, Z., Suhling, J., Lall, P., "The Effects of Aging on the Cyclic Stress-Strain Behavior and Hysteresis Loop Evolution of Lead Free Solders," Proceedings of the 61st Electronic Components and Technology Conference, Orlando, FL, pp. 927-93, 2011. Lee, T. K., Ma, H., Liu, K. C., and Xue, J., “Impact of Isothermal Aging on Long-Term Reliability of Fine-Pitch Ball Grid Array Packages with Sn-Ag-Cu Solder Interconnects: Surface Finish Effects,” Journal of Electronic Materials, Vol. 39(12), pp. 2564-2573, 2010. Smetana, J., Coyle, R. Read, P., Popowich, R., Fleming, D., and Sack, T., “Variations in Thermal Cycling Response of Pb-Free Solder Due to Isothermal Preconditioning,” Proceedings of the 2011 SMTAI Conference, pp. 641-654, Fort Worth, TX, October 1720, 2011. Coyle, R., McCormick, H., Osenbach, J., Read, P., Popowich, R., Fleming, D., and Manock, J., “Pb-free Alloy Silver Content and Thermal Fatigue Reliability of a Large Plastic Ball Grid Array (PBGA) Package,” SMTA Journal, Vol. 24(1), pp. 27-33, 2011. Coyle, R., Osenbach, J., Read, P., McCormick, H., Fleming, D., Popowich, R., Reid, M., Punch, J., Collins, M., Kinyanjui, R., and Kummer, S., “Dwell Time, Microstructural Dependencies, and the Interpretation of Thermal Fatigue Test Data of SnPb and Pb-Free Solders,” Proceedings of the 2009 SMTAI Conference, pp. 384392, San Diego, CA, October 4-8, 2009. Borgesen, P., Al-Momani, E., and Meilunas, M., “Effect of Dwell Time on the Life of Lead Free BGA Joints in Thermal Cycling,” Proceedings of the 2009 SMTAI Conference, pp. 377-383, San Diego, CA, October 4-8, 2009. Coyle, R., Reid, M., Ryan, C., Popowich, R., Read, P., Fleming, D., Collins, M., Punch, J., and Chatterji, I., “The Influence of the Pb-free Solder Alloy Composition and Processing Parameters on Thermal Fatigue Performance of a Ceramic Chip Resistor,” Proceedings of the 59th IEEE Electronic Components and Technology Conference, pp. 423-430, San Diego, CA, May 27-29, 2009. Manock, J., Coyle, R., Vaccaro, B, McCormick, H., Popowich, R., Fleming, D., Read, P., Osenbach, J., and Gerlach, D., “Effect of Temperature Cycling Parameters on the Solder Joint Reliability of a Pb-Free PBGA Package,” SMTA Journal, Vol. 213, pp. 36-46, 2008. Anand, L., “Constitutive Equations for the RateDependent Deformation of Metals at Elevated Temperatures,” Journal of Engineering Materials and Technology, Vol. 104(1), pp. 12–17, 1982. Brown, S., Kim, K., and Anand, L., “An Internal Variable Constitutive Model for Hot Working of Metals,” International Journal of Plasticity, Vol. 5(2), pp. 95–130, 1989.

16. Che, F., Pang, H., Zhu, W., Sun, W., and Sun, A., “Modeling Constitutive Model Effect on Reliability of Lead-Free Solder Joints”, Proceedings of the 7th International Conference on Electronics Packaging Technology, pp. 1-6, 2006. 17. Pei, M., and Qu, J., “Constitutive Modeling of Lead-Free Solders,” Proceedings of the International Symposium on Advanced Packaging Materials, pp. 45-49, 2005. 18. Mysore, K., Subbarayan, G., Gupta, V., and Zhang, R., “Constitutive and Aging Behavior of Sn3.0Ag0.5Cu Solder Alloy”, IEEE Transactions, Electronics Packaging and Manufacturing, Vol. 32(4), pp. 221-232, 2009. 19. Chen, G., Chen, X., and Sakane, M., “Modified Anand Constitutive Model for Lead-Free Solder Sn-3.5Ag,” Proceedings of ITHERM 2004, Vol. 2, pp. 447-452, 2004. 20. Amagai, M., Watanabe, M., Omiya, M., Kishimoto, K., and Shibuya, T., “Mechanical Characterization of Sn-Ag Based Lead-Free Solders,” Microelectronics Reliability, Vol. 42(6), pp. 951-966, 2002. 21. Kim, Y., Noguchi, H., and Amagai, M., “Vibration Fatigue Reliability of BGA-IC Package With Pb-Free Solder and Pb-Sn Solder,” Proceedings of 53rd Electronic Components and Technology Conference, pp. 891-897, 2003. 22. Bai, N., Chen, X., and Gao, H., “Simulation of Uniaxial Tensile Properties for Lead-Free Solders with Modified Anand Model,” Materials and Design, Vol. 30, pp. 122128, 2009. 23. Wilde, J., Becker, K., Thoben, M., Blum, W., Jupitz, T., Wang, G., and Cheng, Z., “Rate Dependent Constitutive Relations Based on Anand Model for 92.5Pb5.0Sn2.5Ag Solder,” IEEE Transaction on Advanced Packaging, Vol. 23(3), pp. 408–414, 2000. 24. Wang, G., Cheng, Z., Becker, K., and Wilde, J., “Applying Anand model to Represent the Viscoplastic Deformation Behavior of Solder Alloys,” Journal of. Electronic. Packaging, Vol. 123, pp. 247–247, 2001. 25. Rodgers, B., Flood, B., Punch, J., and Waldron, F., “Determination of the Anand Viscoplasticity Model Constants for SnAgCu,” in Proceedings of InterPACK 2005, pp. 17-22, 2005. 26. Bhate, D., Chan, D., Subbarayan, G., Chiu, T., Gupta, V., and Edwards, D., “Constitutive Behavior of Sn3.8Ag0. 7Cu and Sn1.0Ag0.5Cu Alloys at Creep and Low Strain Rate Regimes,” IEEE Transactions on Components and Packaging Technology, Vol. 31(3), pp. 622–633, 2008.

531