Absolute and Relative Fatigue Life Prediction ...

Absolute and Relative Fatigue Life Prediction Methodology for Virtual Qualification and Design Enhancement of Lead-free BGA Hun Shen Ng a,*, Tong Yan Tee a, Kim Yong Goh a, Jing-en Luan a, Tommi Reinikainen b, Esa Hussa b, Arni Kujala b a STMicroelectronics, 629 Lorong 4/6 Toa Payoh, Singapore 319521. * Phone: (65) 63897034 Fax: (65) 62598662 Email: [email protected] b

Nokia, Finland.

Abstract The semiconductor industry is driving toward lead-free solder due to environmental concern and legislation requirement. The industry has also concluded that SnAgCu solder alloy so far is the best lead-free alternative to SnPb solder. Therefore, most existing and new packages will have to be tested and qualified using lead-free solder. One of the critical concerns is board level solder joint reliability during thermal cycling test. In this paper, the methodology for an absolute life prediction is described for virtual qualification of packages. A good absolute fatigue life prediction requires an appropriate solder creep model and actual test data on packages. Two new sets of lead-free Anand’s constants for SnAgCu solder are introduced for creep models. These Anand’s creep models are compared with other lead-free and eutectic solder model and the relative design trend is similar. A fatigue corrective factor is introduced to integrate the different solder models together for convenient relative design enhancement with acceptable range of absolute life prediction. These fatigue corrective factors can also be used to compare different finite element modeling assumptions such as element size and solution time step. Subsequently, design analysis is performed to study the effects of 11 key package dimensions and material properties. It is found that the relative design trend for packages with lead-free and eutectic solder is similar. Therefore, the design guidelines established for the previous eutectic solder is still valid for lead-free solder.

European legislation has enforced semiconductor industry to remove lead from IC packages by July 2006. Therefore, all existing and new packages will have to be tested and qualified using lead-free solder. There are many lead-free alloys discussed in the literature, which includes SnAg, SnAgCu, SnBi, SnAgBi, and etc. However, the industry has concluded that SnAgCu is the most popular choice for properly designed lead-free packages. Thus, in-depth understanding on SnAgCu characteristic and material properties is necessary for better reliability of lead-free packages. However, Darveaux’s method with Anand’s model is not applicable for SnAgCu, due to lack of published creep properties (Anand’s constants). Here, two new sets of Anand’s constants are introduced for Sn2Ag0.4Cu and Sn4Ag0.5Cu / Sn3.4Ag0.8Cu. For the first time, Anand’s model for SnAgCu is available to the public with published constants for direct modeling input. The application of Darveaux’s method with Anand’s model is “revived” for lead-free BGA with SnAgCu solder. Years of modeling experience gained by many researchers on this popular modeling method for eutectic solder can now be extended for SnAgCu solder with this paper. There are different requirements for virtual package qualification and for design enhancement. Absolute life prediction is required for virtual package qualification (pass / fail) while relative comparison with reasonable range of life is sufficient for design enhancement. For any good absolute life prediction model, there must be good testing results and appropriate solder material creep models. However, there is a lack of consistent lead-free creep model and material properties presently. Moreover, most lead-free packages have good solder joint fatigue reliability. As such, absolute life prediction is not so crucial presently for solder joint fatigue as compared to drop test. Tee et al. [20, 22, 33] has performed an integrated study of drop and thermal cycling tests for both CSP (Chip Scale Package) and IPD (Integrated Passive Device) packages and found that lead-free solder will improve solder joint fatigue but give poor performance for drop test. Today, for handheld products, drop impact is critical and the design enhancement for drop test may result in poorer solder joint fatigue performance. Therefore, one day, the design margin between drop and thermal cycling tests will become narrower and solder joint fatigue will become critical again. The following sections will describe the fatigue life prediction methodology, followed by introducing a fatigue corrective factor to integrate the different solder creep models and modeling assumptions. The different design analysis on lead-free packages is also discussed.

1. Introduction Product manufacturers are usually concerned of board level solder joint reliability of BGAs during the thermal cycling tests. The typical thermal cycling condition required is -40°C to 125°C to ensure a reliable package performance under the extreme operating conditions. The required fatigue life varies among the customers. However, the process of thermal cycling test is timeconsuming and costly. Therefore, finite element modeling is widely used as an analysis tool for solder joint reliability [136], especially during the design stage of new package, due to the recent advances in high-speed computer and development of more sophisticated finite element models. There are many approaches used by researchers [36] in the modeling of fatigue life, e.g., stress-based, plastic/creep strain-based, energy-based, and damage accumulation-based. Darveaux methodology [34-35] is a common approach used in the fatigue modeling which applies both energy and damage accumulation-based theories. A life prediction accuracy of ±2x is generally considered adequate due to the complex nature of solder material’s creep behavior, and also uncertainty in the board level thermal cycling test. 0-7803-8906-9/05/$20.00 ©2005 IEEE 1282

2005 Electronic Components and Technology Conference

2. Absolute Fatigue Life Prediction Methodology The modeling methodology for thermal cycling fatigue life prediction is shown in Figure 1. This methodology has been applied successfully for life predictions and design enhancement of various advanced IC packages, mostly with eutectic solder by Tee et al. [1-33] in a series of 33 publications over the past six years, and now it is extended to lead-free BGA packages and modules with SnAgCu solder. The first step is to determine the failure criteria such as the first-failure life, mean life (50% failure rate) or characteristic life (63.2% failure rate) from the Weibull plot of the thermal cycling test data. The second step is to select the solder creep models such as the Anand’s model or the implicit creep models such as the hyperbolic sine function or the doublepower law function. Then the strain energy density (SED) accumulated per cycle can be calculated from finite element model. There are a few modeling assumptions to compute the fatigue life. Darveaux [34-35] proposed the computation of fatigue life using both the crack initiation and crack propagation life. One can also just use the crack initiation life or the crack propagation life as the dominant life prediction model, i.e. modified Darveaux’s method [14-15, 33]. The respective life correlation constants can then be computed by correlating the modeling and testing data using the least square method. The following sections will provide more details on the life prediction methodology.

failed when the resistance measured by the event detector is more than 300Ω. From the Weibull plot, there are three failure criteria that can be used for fatigue life correlation, i.e. the first failure, the mean life or the characteristic life. The mean life and the characteristic life should be preferred than the first failure as they are statistically more consistent and stable for accurate life prediction. However, some packages have very good thermal cycling solder joint reliability and therefore take a very long time (e.g. more than 2000 cycles) to start to fail. In such a case, the first failure may have to be used as the only failure criteria as extrapolation of mean life and characteristic life may be inaccurate due to limited failure data. This is especially so for lead-free BGAs which usually have 2-3 times better fatigue performance than BGA with eutectic solder and may take up to 3000 to 4000 cycles (3 to 4 months) to obtain the mean or characteristic life. However, one has to be careful to take the first failure as failure criteria as sometime early failures may be due to manufacturing or assembly issues rather than fatigue failures. Therefore, it is recommended to perform cross-section of the solder joints of the failed package to ensure that the failure mechanism is consistent with typical fatigue failures. For the two BGA packages tested, the first failure, the mean life and the characteristic life will all be used for the fatigue life correlation later. 99

2.1

Testing Data

Determine failure criteria:

90

• First failure, N1

80 70 60 50 40

• Mean life, N50

Solder Creep Model

Percent

• Characteristic life, N63.2 2.2

Select appropriate solder creep model: • Anand’s model (see Eq. 2-5 and Table 2) • Hyperbolic sine function (see Table 3)

2.3

Finite Element Model

30 20 10

• Double-power law function (see Table 3)

5

• Others

3

V a r ia b le B GCA 3 -1 (P b-free) B GCA -2 1 (P b-free)

2 2.4

Fatigue Life Correlation Constants

Determine failure criteria:

B GCA 5 -2 (E utectic)

1

• Crack initiation (see Eq. 6)

1 1000

10 10000

N orm alized L ife F ailure (C ycles) Datot a

• Crack propagation (see Eq. 7) • Crack initiation + Crack propagation (see Eq. 8) No

2.5

Figure 2. Weibull plot of lead-free BGA packages tested

Modeling-Testing Correlation satisfied?

Table 1. Details of lead-free BGA packages tested Yes

Successful lead-free solder life prediction model

Figure 1. Flow-chart for fatigue life modeling methodology 2.1. Testing Data For any good fatigue life prediction model, there must be good testing results with sufficient failure data for later correlation. Figure 2 shows the failure data plotted in Weibull chart for two lead-free TFBGA (Thin-profile Fine-pitch BGA) and VFBGA (Very-thin-profile Fine-pitch BGA) packages that have undergone board level thermal cycling test. The details of packages tested are described in Table 1. The packages are tested under temperature cycling test condition of –40 to 125°C. There are 30 units tested per package. Each unit is connected through daisy-chain to a channel in an event detector. The package is considered

Name

Pkg. Type

Pkg. Size (mm)

I/O

Pitch (mm)

BGA-1

VFBGA

8x8

244

0.4

BGA-2

TFBGA

7x7

46

0. 5

Die Size (mm) 6x6x 0.17 3.7x3.7x 0.24

PWB Thk (mm) 1.0 1.0

2.2. Solder Creep Models The creep processes are expected to dominate the deformation kinetics as solder is above half of its melting point at room temperature and the loading rate is slow enough for creep deformations to occur. The melting temperature of eutectic solder is around 183°C and for SnAgCu solder is around 217°C. Therefore, an appropriate solder creep model is required for fatigue life prediction. Steady-state creep of solder can be expressed in the following form

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dε = C ss [sinh dt

 − Qa  exp    kT 

(ασ )]n

(1)

where dε /dt is the steady-state strain rate, k is Boltzmann’s constant, T is the absolute temperature, σ is the applied stress, Qa is the apparent activation energy, n is the stress exponent, α prescribes the stress level at which the power law dependence breaks down, and Css is a constant. The earlier version of ANSYS software (version 6 and earlier) does not have viscoplastic elements with implicit creep model as a standard option. Instead, it uses Anand’s constitutive model [37]. The use of Anand’s model is convenient since the user does not have to modify the source code. Anand’s model is broken down into a flow equation, and three evolution equations [38]: Flow Equation dε p dt

= A [sinh (ξσ / s )]

1/m

 − Q exp   kT

  

62Sn36Pb2Ag (near-eutectic) solder published by Darveaux [34-35] are listed in Table 2. The shear stress-strain data for Sn4Ag0.5Cu and Sn3.4Ag0.8Cu solder are very close, and can assume to share the same Anand’s constants. The steadystate creep data for Sn4Ag0.5Cu solder joints is shown in Figure 3. With the Anand’s constants for SnAgCu, the same solder creep model can now be conveniently used for fatigue analysis of lead-free solder as well as the eutectic solder by changing to the appropriate constants. There is no necessity to use different creep models for eutectic and lead-free solder. Thus, engineers and researchers can save significant amount of research and development time for lead-free fatigue model by using the same modeling methodology. Table 2.

(2)

Parameter

Evolution Equations

)

a

B B

 dε p   dt 

s B = 1− * s n  d ε p / dt   Q  s* = s ^  exp    A  kT   

The Anand’s constants provided by Darveaux [34-35] for 62Sn36Pb2Ag solder (close to 63Sn37Pb eutectic solder) have been widely used by researchers over the past 10 years for fatigue analysis of eutectic solder. Although there are many other creep models proposed, Darveaux’s method with Anand’s model is still the primary choice for many researchers and engineers, due to its popularity and ease of implementation. There are researchers who have characterized Anand’s constants for SnAgCu composition [39] but the values of constants were not published. Recently, for the first time, the Anand’s constants for SnAgCu compositions (Sn2Ag0.5Cu, Sn3.4Ag0.8Cu, Sn4Ag0.5Cu) have been characterized and published by Reinikainen et al. [40]. The above SnAgCu solder alloys have been tested to determine their deformation behavior in the temperature range of 23°C to 110°C and strain rates varying from 10-7 to 10-1 1/s. Typical observed temperature and deformation induced microstructural evolution phenomena include recrystallization, grain growth, and twinning. The deformation mechanisms of the alloys have been estimated based on the values of measured activation energies and stress exponents. The constant stress and constant strain-rate tests have been performed in a shear configuration, which enables a stress-state of nearly pure shear in the solder joint. In the intermediate stress regime, the deformation appears to occur by the slip mechanism, and the rate appears to be controlled by the dislocation climb process. The measured shear stress-strain data is utilized to determine the constants for the visco-plastic Anand’s constitutive model. The Anand’s constants for SnAgCu solder alloys characterized by Reinikainen et al. [40] and for

62Sn 36Pb 2Ag

6.6

1.3

12.41

8500

9000

9400

500

500

4e06

4.3

7.1

1.5

C5

m

0.16

0.3

0.303

C6

ho (MPa)

6100

5900

1379

C7

s^ (MPa)

28.7

39.4

13.79

C8

n

0.04

0.03

0.07

C9

a

1.3

1.4

1.3

C3

(5)

Sn4Ag 0.5Cu / Sn3.4Ag 0.8Cu

C4

C2

(4)

Sn2Ag 0.5Cu

So (MPa) Q/k (1/K) A (1/s) ξ

C1

(3)

Definitions Initial value of deformation resistance Activation energy / Boltzmann’s constant Pre-exponential factor Multiplier of stress Strain rate sensitivity of stress Hardening constant Coefficient for deformation resistance saturation value Strain rate sensitivity of saturation (deformation resistance) value Strain rate sensitivity of hardening

Steady-state Creep Rate of Sn4Ag0.5Cu Solder 1.E-01 Steady-State Creep Rate (1/s)

 ds =  h o ( B dt 

Anand’s Constants for SnAgCu alloys [40] and eutectic solder [1-2]

Temperature

T=-40°C T=0°C T=25°C T=60°C T=95°C T=125°C

1.E-02 1.E-03 1.E-04 1.E-05 1.E-06 1.E-07 10

Stre ss (M Pa)

100

Figure 3. Steady-state creep of Sn4Ag0.5Cu solder joints There are also other numerous constitutive equations for creep deformations for SnAgCu compositions that have been published by different researchers over the years. For e.g., Schubert et al. [41] proposed the use of hyperbolic sine function to represent the creep data while Wiese et al. [42] represented steady-state creep behavior using double power law model. The above constitutive equations and their respective parameters, converted to tensile stress-strain rate

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the top solder interface thickness is critical and should be fixed for all design analysis. The choice of different modeling assumptions depends on requirements of package/board geometry complexity, solution time, and accuracy of results. 0

T em p eratu re = 25 C

1.E -02 1.E -03

(1/s)

Steady-State Creep Rate

1.E -01

1.E -04 Sc hubert Model (SnA gCu)

1.E -05

W ies e Model (Sn4A g0.5Cu) A nand Model (Sn2A g0.5Cu)

1.E -06

A nand Model (Sn4A g0.5Cu) A nand Model (62Sn36Pb2A g)

1.E -07

1

100

1000

0

Temperature = 60 C

1.E-02 1.E-03 1.E-04 Schubert Model (SnA gCu)

1.E-05

Wiese Model (Sn4Ag0.5Cu) A nand Model (Sn2A g0.5Cu)

1.E-06

A nand Model (Sn4A g0.5Cu) A nand Model (62Sn36Pb2Ag)

1.E-07

1

10

Stress (MPa)

100

1000

0

Temperature = 125 C

3

1.E-01

ε& = 4 × 10 −7 exp

Steady-State Creep Rate (1/s)

Sn4Ag0.5Cu (Wiese [42])

S tre ss (M P a)

1.E-01

Table 3. Constitutive relations for SnAgCu solder Lead-free Creep Laws Solder Alloys  − 3223  σ     T (°K )  1 MPa 

10

Steady-State Creep Rate (1/s)

format, are shown in Table 3. The constitutive models, including the Anand’s models for SnAgCu and eutectic solder are plotted in Figure 4 for various temperatures. There is some scattering of results for different lead-free constitutive models. The differences may be due to different SnAgCu solder composition tested and also solders tested at different strain rate for different solder creep models. Figure 4 also shows that at lower stress level, the predicted steady-state creep rate for SnAgCu solder is lower than for SnPb solder and vice versa at higher stress. Therefore, SnAgCu is generally more creep resistant than eutectic solder for most testing conditions of BGAs except for very high stress values. This is generally true for TFBGA and VFBGA packages that have been tested in which lead-free packages are two times better than packages with eutectic solder (see Figure 2). For the subsequent fatigue life correlation, the Anand’s model for Sn4Ag0.5Cu will be used as the default solder creep model. The other solder creep constitutive models can be related to this Anand’s model by using a fatigue corrective factor which will be introduced in Section 3. Absolute life prediction is less meaningful when variations of creep data by different researchers are large. Relative design trend is more meaningful with an acceptable range of absolute life predicted. The BGA packages with lead-free solder have larger design margin than those with eutectic solder, and thus, less demanding for accurate life prediction.

1.E-02 1.E-03

12

 − 7348  σ    + 1× 10 −12 exp  T (°K )  1 MPa 

1.E-04 Schubert Model (SnAgCu)

1.E-05

Sn3.8Ag0.7Cu  − 6500  Sn3.5Ag0.75Cu  ε& = 277984[sinh(0.02447σ )]6.41 exp Sn3.5Ag0.5Cu  T (°K )  Castin (Schubert [41]) Finite Element Model There are many finite element modeling assumptions that should be considered to compute the modeling results. Some of the major considerations are listed below: Geometry model Solder geometry model Elastic material model Solution control The overall package and board geometry model usually can be established using full 3-D model, quarter model, 1/8 model or sliced model [35]. The solder geometry model may apply global/local model, submodel or detailed global model. The elastic material properties of the packaging materials such as the mold compound, die attach, substrate and the PWB are also important. There are also different solution control and element sizes for the model. The element size of

Wiese Model (Sn4Ag0.5Cu) Anand Model (Sn2Ag0.5Cu)

1.E-06

Anand Model (Sn4Ag0.5Cu) Anand Model (62Sn36Pb2Ag)

1.E-07

1

10

Stress (MPa)

100

1000

Figure 4. Comparison of creep models for SnAgCu The finite element model for the BGA studied in this paper is shown in Figure 5. This is a quarter model with the global model uses coarser mesh to reduce computational time while the local model is only applied for diagonal solder joints. The local model uses much finer mesh and constraint equation is applied along the boundary between the global and local models to transfer the displacements. This global/local model approach was successfully applied in fatigue analysis of many CSPs [6, 14, 33]. For the BGA packages tested, the copper pad at package side is soldermask defined (SMD) while it is non-soldermask defined (NSMD) at PWB side. SED or plastic work results of a typical BGA using Anand’s model is shown in Figure 6. Volume averaging of the SED is performed at the top solder interface with a fixed thickness to reduce sensitivity to meshing and stress

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singularity. The critical solder with the highest SED is usually found to be below the die corner. This is also confirmed by testing results. The solder fails at the interface between the solder and copper pad on package side which correlates well with experimental results of failure analysis (see Figure 7). Global Model

Local Model MC

Substrate

Substrate

MC

SMD

PC B

Solder Ball

Cu Pad

Die

S. Mask

NSMD

Solder Ball

PCB

Crack propagation life : N = p

a K 3∆w K 4

(7)

: α w = No + N p

Fatigue life

(8)

a K3∆wK4 where K1 to K4 are life correlation constants, a is solder mask opening size, and αw is characteristic life at 63.2% failure rate. One an also assume fatigue life to be dominant by either crack initiation life or crack propagation life [14-15, 33] so that only two constants (either K1 & K2 or K3 & K4) are required to be computed. The least square fit method is applied to correlate both the modeling and testing fatigue lives to compute the appropriate life correlation constants by numerical iterations. = K1∆wK2 +

Normalized Fatigue Life (Cycles)

Figure 5. Global / local finite element model of BGA

7 3500 6 3000

First Failure

2500 5

Mean Life

4 2000

Char Life

1500 3 1000 2 1 500 0 0.07

0.09

0.11

0.13

0.15

0.17

0.19

0.21

Avg SED at Top Solder Interface (MPa) SED (MPa)

Figure 8. SED vs. experimental fatigue life

Figure 6. SED distribution of a typical lead-free BGA package Experimental Failure Analysis

Fatigue Modeling (SED)

Cu Pad Solder ball

2.5. Modeling-Testing Correlation Currently there are only two lead-free packages that have been tested to failures and therefore, the fatigue life modeling-testing correlation of the lead-free BGA packages is not plotted (perfect match with only two test data). The modeling-testing difference will be calculated in future when more testing data is available for lead-free BGA. Nevertheless, the above methodology has been successfully applied to BGAs with eutectic solder with modeling-testing correlation [14] within ±15%. Sample correlation plot is shown in Figure 9. FEA - TC Correlation for BGA Packages 10000

Solder crack and delamination

2.4. Fatigue Life Correlation Constants The SED calculated from modeling can be correlated with the first failure, mean life or characteristic life from testing data. Figure 8 shows the plot for the SED against the first failure, mean life and characteristic life for the two lead-free BGA packages tested. It is observed that the correlation curve follows the typical power law, i.e. higher SED leads to lower fatigue life. Darveaux [34-35] proposed the use of crack initiation life and crack propagation life to compute the fatigue life which is described below: (6) Crack initiation life : N o = K 1 ∆w K 2

FEA (Cycles)

Figure 7. Correlation on solder joint failure interface

+2x +15% -15% -2x

1000

100 100

1000 TC Fatigue Life (Cycles)

10000

Figure 9. Sample modeling-testing correlation plot A life prediction accuracy of ±50% is generally considered adequate due to the complex nature of solder material’s creep behavior, and also uncertainty in the board level thermal cycling test. The demand for absolute life prediction accuracy for lead-free solder is not as high as eutectic solder due to larger design margin. However, the situation will change

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3.1. Integration of Solder Creep Models Five solder creep models i.e. Anand’s models (eutectic, Sn2Ag0.5Cu, Sn4Ag0.5Cu), Schubert model (SnAgCu) and Wiese model (Sn4Ag0.5Cu) are applied for four different TFBGA packages as shown in Figure 10. It is observed that different solder creep models affect the absolute SED but the relative trend remains similar. The absolute SED obtained from different lead-free constitutive models vary for the same package. The difference may be due to the different SnAgCu composition used in various models and the solders were characterized at different strain rates. The SED obtained from eutectic solder is consistently larger than the various lead-free constitutive models. A higher SED implies a lower fatigue life, and therefore for TFBGA packages studied, eutectic solder has poorer solder joint reliability fatigue performance compared to lead-free solder. Figure 10 also shows that the relative trend for the various lead-free constitutive models is similar to eutectic solder for different packages. This implies that as long as all the packages are tested using the same solder material, any of the lead-free constitutive models or even eutectic solder constitutive model can be correlated with the testing results of lead-free BGA with acceptable accuracy. There have been a number of lead-free constitutive models published over the recent years. As discussed in the previous section, lead-free solder has much better solder joint fatigue performance than eutectic solder. Therefore, it is important to test lead-free packages longer to obtain more failures for mean life or characteristic life. Various solder constitutive models can be related to one another with fatigue corrective factors, fc (see Figure 11). The fatigue corrective factors can be computed using the least square fit method to correlate all the solder creep models for all the packages together with Anand’s model for Sn4Ag0.5Cu as the control case. With this corrective factor, the solder joint fatigue performance of lead-free packages can be modeled using any creep model according to the following modified equation, assuming crack initiation life dominant.

(9)

This equation can be in any form from Eqs. (6-8), depending on modeling-testing correlation. With fc, the life correlation constants (K1-K4) can be kept the same for different creep models or finite element assumptions (e.g. element size). Effect of Different Solder Creep Models 0.18

Anand's Model (Eutectic) Anand's Model (Sn2Ag0.5Cu) Anand's Model (Sn4Ag0.5Cu) Schubert Model (SnAgCu) Wiese Model (Sn4Ag0.5Cu)

0.17 SED (MPa)

3. Relative Fatigue Life Comparison Methodology The previous section describes the methodology of absolute fatigue life prediction. However in most engineering applications, relative design trends in terms of SED comparison with reasonable range of fatigue life are usually sufficient. This section will compare the different solder creep models and finite element assumptions to show that these factors only affect the absolute fatigue life, but not the relative design trend. The relative trend of fatigue performance is mainly affected by the stiffness and CTE mismatch between the package and PWB. A fatigue corrective factor, fc, will be introduced later to integrate together the various solder creep models as well as variations in finite element assumptions.

N = K1 ( f c ⋅ ∆w) K 2

0.16 0.15 0.14 0.13 0.12 TFBGA 8x8- TFBGA 5x5- TFBGA 6x6- TFBGA 6x6120 64 105 84

Figure 10. Effect of different solder creep models Effect of Different Solder Creep Models

SED (MPa)

when the fatigue performance is compromised to improve drop impact reliability which may have different design trends [20, 22, 33]. If the life prediction accuracy is not satisfactory, the various assumptions such as test data, solder creep model, finite element model and failure criteria should be reexamined, and the modeling steps in Section 2 will be updated with new modeling methodology.

0.17 0.16 0.16 0.15 0.15 0.14 0.14 0.13 0.13 0.12

Anand's Model (Eutectic) Anand's Model (Sn2Ag0.5Cu) Anand's Model (Sn4Ag0.5Cu) Schubert Model (SnAgCu) Wiese Model (Sn4Ag0.5Cu)

TFBGA 8x8- TFBGA 5x5- TFBGA 6x6- TFBGA 6x6120 64 105 84

Figure 11. Integrate different solder creep models using fatigue corrective factor The corrective factors, fc, for various solder creep models are shown in Table 4 (see Appendix) while Figure 12 shows the effect of fc on percentage difference in SED as well as fatigue lives (first failure, N1; mean life, N50; and characteristic life, N63.2) compared with Anand’s model for Sn4Ag0.5Cu. The raw data for Figure 12 is also listed in Table 4. It is clearly shown from Figure 12 that the fatigue corrective factor can provide great improvement in both the SED and absolute fatigue life prediction. It is interesting to note that with fc, the popular Anand’s model with eutectic solder can be applied to analyze lead-free BGA with only 9% difference in fatigue life (27% without fc) using the same lead-free life correlation constants. The fatigue life between eutectic and lead-free solder is more than 2 times difference if life correlation constants of eutectic solder are used. This corrective factor helps to extend the usefulness of Anand’s model for many years to come, by keeping the relative design trend, but improving on absolute fatigue life prediction.

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Effect of D ifferent FEA Assumptions

Effect of Fatigue Corrective Factor on SED and Fatigue Life 0.17

30% %% DSED ∆ SED

25%

SED (MPa)

(with fc)

20% % Diff

0.16

%% DSED (w ith fc) ∆ SED %% DN1 ∆ N1 %% DN1 (w ith fc) ∆N 1

15%

(with fc)

%% DN50 ∆ N50

10%

0.14 Control

%% DN50 ∆ N(w ith fc) 50

0.13

(with fc)

5%

0.12

%% DN63.2 ∆ N (w ith fc) 63.2

Anand's Model (Eutectic)

Anand's Model (Sn2Ag0.5Cu)

Schubert Model (SnAgCu)

Wiese Model (Sn4Ag0.5Cu)

TFBGA 8x8-120

(with fc)

Figure 12. Effect of fatigue corrective factors, fc, on SED and fatigue life Effect of Different FEA Assumptions 0.17 0.16 0.15 0.14 Control 0.13

Coarse Mesh Large Time Step

0.12 TFBGA 8x8-120

TFBGA 5x5-64

TFBGA 6x6-105

TFBGA 6x6-84

Figure 13. Effect of different FEA modeling assumptions

TFBGA 6x6-105

TFB GA 6x 6-84

4. Design Analysis of Lead-free BGA The previous section has shown that any good creep model should has similar relative design trend, but the corrective factor, fc, helps to provide an acceptable range of life prediction. The different design analyses are modeled for TFBGA package (BGA-2, see Table 1) with lead-free and eutectic solders (see Figure 15). The different design cases are described in Table 6. The design cases are varied one parameter at a time with respect to the control case (C0). It is seen that the relative trend for both lead-free and eutectic solders are similar. Therefore, the relative design guidelines gained previously from BGA packages with eutectic solder [14] can still be used for lead-free BGA packages under the same thermal cycling test condition of –40 to 125°C. Effect of Different Design Cases

0.20

Larger Time Step (2X) 1.02

0.15 SED (MPa)

fc

TFBGA 5x 5-64

Figure 14. Integration of different FEA modeling assumptions using fatigue corrective factor

Table 5 Fatigue corrective factors, fc, for finite element modeling assumption Coarse Mesh (2X) 0.95

Coarse M esh Large Tim e Step

%% DN63.2 ∆ N63.2

0%

SED (MPa)

0.15

3.2. Integration of Finite Element Model Assumptions Similar to the different solder creep model, the different finite element model assumptions such as element size and solution time step will only change the absolute SED but not the relative trend for different packages studied. Figure 13 shows the SED of four different packages using a coarser solder mesh (2X) and larger time step (2X). Therefore, these factors can also be integrated together using the fatigue corrective factor, fc, as described in Section 3.1. Figure 14 shows the integration of all these modeling assumption together using the corrective factors, fc, listed in Table 5. As shown in Figure 14, there is almost a perfect fit for all the four packages with different modeling assumption using fc. This is very useful as the life correlation constants (K1-K4) can be kept the same for different creep models or finite element assumptions (e.g. element size) by varying only the fatigue corrective factor, fc. Darveaux [35] has suggested different K1-K4 using different modeling assumptions such as geometry model (slice/quarter), element size, time step, ANSYS version or solder constitutive model. However with the corrective factor, fc, the life correction constants (K1-K4) can be kept constant for all these cases.

0.10 Eutectic

0.05

Pb-free

0.00 C0

C1

C2

C3

C4 C5 C6 C7 De sign Case s

C8

C9 C10 C11

Figure 15. Effect of different design analysis on SED Table 6. Design analysis cases

1288

No

Design Variations

1

Die size

2 3 4 5 6 7 8 9 10 11

Die Thickness Ball Standoff Max. Ball Diameter Solder Mask Opening Board Size Board Thickness Substrate Thickness MC Thickness MC Modulus MC CTE

Control

Values

3.7x3.7 mm

4.7x4.7 mm 0.375 mm 0.30 mm 0.40 mm 0.350 mm 20x20 mm 1.6 mm 0.30 mm 0.5 mm 25 GPa 11 ppm/°C

0.235 mm 0.25 mm 0.30 mm 0.275 mm 10x10 mm 1.0 mm 0.22 mm 0.6 mm 20 GPa 8 ppm/°C


4.1 Effect of Die Size Bigger die size has shorter fatigue life, because the die edge is closer to the critical diagonal ball, resulting in more local CTE mismatch. The die also reduces the overall package CTE, leading to greater global CTE mismatch with the board, and more strain induced in the solder ball. 4.2 Effect of Die Thickness Die thickness has little effect on fatigue life. Thicker die has worse solder joint performance, because there is more local CTE mismatch between die and solder joint. Thicker die implies that the overall CTE of package is lower, resulting in more global CTE mismatch with the FR4 board. Thinner board is more compliant, and therefore, the strain induced in critical solder ball is lower. 4.3 Effect of Ball Standoff Higher ball standoff helps to increase the fatigue life. By changing the ball standoff from 0.25mm to 0.3mm, the fatigue life can be enhanced by 11%. The larger separation distance of solder helps to reduce the shear strain induced during thermal cycling. 4.4 Effect of Maximum Ball Diameter For the barrel-shape solder ball studied, bigger maximum ball diameter (with the same ball standoff and solder mask opening) has negative effect on fatigue life. This effect may be solder joint shape-dependent. The collapse of solder ball during reflow leads to larger maximum ball diameter and shorter ball standoff (combination of two negative effects studied), which weaken the fatigue life. 4.5 Effect of Solder Mask Opening For SMD pad design, size of solder mask opening determines the interfacial length of solder ball and upper copper pad. According to Eq. (7), a larger solder mask opening requires longer time for crack to propagate through the failure interface. This is a significant and practical design change. 4.6 Effect of Board Size The board size has little effect on fatigue life. In this fatigue modeling, smaller board size (3mm larger than package size) was assumed to reduce the computational time. Bigger board size will induce slightly larger global CTE mismatch with the package. 4.7 Effect of Board Thickness Thicker board has much lower fatigue life because the global CTE mismatch between package and board is increased. Thinner board is more compliant, and therefore, the strain induced in critical solder ball is reduced. It is important to use consistent board size and thickness in the thermal cycling test to minimize variations among packages of similar type. 4.8 Effect of Substrate Thickness Thicker substrate only slightly improves the fatigue life by increasing the overall package CTE, and reducing global CTE mismatch with the board. It implies that future substrate design can be thinner to reduce the cost, without significant negative effect on the fatigue life.

4.9 Effect of Mold Compound Thickness Sometimes thinner mold compound (MC) is desired to assemble thinner package. Here, thinner mold compound leads to slightly longer fatigue life. The CTE of mold compound used is close to the mean CTE of the package (die + substrate + mold compound), therefore the thickness of mold compound has little effect on the fatigue life. 4.10 Effect of Mold Compound Modulus Lower mold compound modulus helps to slightly increase the fatigue life because the material is less stiff, therefore induces lower stress to the neighboring materials. 4.11 Effect of Mold Compound CTE Higher mold compound CTE helps to increase the fatigue life, as it increases the mean package CTE, and reduces the CTE mismatch with PCB. Ideally, there should be an optimum mold compound CTE [15] which minimizes the global CTE mismatch between the package and the board. This requires more modeling trials of different CTE values, ranging from 8 to 30 ppm/°C, which will be reported in the future study. 5. Conclusions In this paper, the absolute life prediction methodology is described for virtual qualification of packages and relative prediction with acceptable absolute life is applied for design enhancement. The life prediction model uses the recently published Anand’s constants for SnAgCu solder which will help to revive the “out-dated” Anand’s model for applications in today’s lead-free BGA fatigue analysis. These Anand’s creep models are compared with other lead-free and eutectic solder creep models, and the relative design trend is similar. A fatigue corrective factor is introduced to integrate together the different solder creep models as well as different modeling assumptions such as different mesh size and time step for convenient relative design comparison with acceptable range of absolute life prediction. The fatigue corrective factor is found to greatly reduce the SED and fatigue life difference among the different solder creep models and provide almost perfect fit for different finite element modeling assumptions. Therefore, with this fatigue corrective factor, the fatigue life correction constants can be kept unchanged for any modeling variation. Subsequently, design analysis is performed to study the effects of 11 key parameters and in general, smaller die size, higher solder ball standoff, smaller maximum solder ball diameter, bigger solder mask opening, thinner board, higher mold compound CTE contribute to longer fatigue life. It is found that the relative trend for lead-free and eutectic packages is similar. Therefore, the previous know-how gained from the eutectic solder is still valid and applicable for lead-free solder, as long as the engineering analysis is not on variation in solder material. Acknowledgments The authors would like to thank Dr. Carlo Cognetti and Mr. Kho Chek Lim from STMicroelectronics’ Corporate Package Development (CPD) for the management support in this project.

1289


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Appendix Table 4. Effect of fatigue corrective factors, fc, on SED and fatigue life % ∆N1 Solder Creep % ∆SED fc % ∆SED % ∆N1 Models (with fc) (with fc) Anand’s 19.6 5.4 15.1 4.8 model 0.882 (Eutectic) Anand’s 3.6 1.5 3.2 1.3 model 0.978 (Sn2Ag0.5Cu) Anand’s model 1 (Sn4Ag0.5Cu) Schubert 12.8 4.5 10.4 3.9 model 0.926 (SnAgCu) Wiese model 13.0 4.1 10.6 3.6 0.921 (Sn4Ag0.5Cu)

1291

% ∆N50

% ∆N50 (with fc)

% ∆N63.2

% ∆N63.2 (with fc)

25.5

8.4

26.6

8.8

5.6

2.4

5.9

2.5

-

-

-

-

18.0

6.9

18.7

7.2

18.3

6.4

19.0

6.7
