[IEEE Multi-Physics simulation and Experiments in Microelectronics - Freiburg im Breisgau, Germany...

978-1-4244-2128-2/08/$25.00 C2008 IEEE9th. Int. Conf. on Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro-Electronics and Micro-Systems, EuroSimE 2008

1

Predictive Models for BGA and QFN Reliability Estimation

Juergen Wilde, Elena Zukowski Laboratory for Assembly and Packaging

Department of Microsystems Engineering University of Freiburg,

Georges-Koehler-Allee 103, 79110 Freiburg, Germany

Abstract The estimation of product reliability during the design

is one a key question in microelectronics. Lifetime is a function of such parameters as geometry, material properties and loads. These parameters have the tendency to vary from the designed ones. A probabilistic FE-simulation combined with statistical analysis is used in this work to create predictive models for the evaluation of inelastic strain amplitudes. Soldered joints are subjected to thermal-cycling conditions as a function of the different design parameters of BGA and QFN. The models include local and global models and can be used for the prediction of the reliability of BGAs and QFNs. In order to obtain statistical information on the effect of input parameters the analysis was carried out with parametric FE-models by multiple repetitions according to a three-factor Box-Behnken-design. Material properties (coefficient of thermal expansion), geometry (component size, substrate and chip pad diameters) and also load parameters (temperature range in thermal cycling) were used as random input variables for the deterministic model. The regression coefficients for evaluation of the influence of the independent variables and the cross-terms for BGAs and QFN were calculated. The developed quadratic regression models allow the reliability prediction with a precision almost comparable with complex finite element models. Thus results can be made available efficiently and this will allow user to understand the influences on the thermal-mechanical reliability. The model can be also used for the evaluation of the relative improvement of component design rather than the prediction of the absolute value of the lifetime.

1. Introduction Under the current rapid change of electronic

technology, the need to develop assemblies that are increasingly reliable is indispensable. FE analysis can be used to predict performance, lifetime, and reliability already in the design phase. For lifetime calculations, analytical models no longer play an essential role in the technology qualification phase.

Differences in the CTE of the assembly materials result in large stresses and strains during thermal cycling. This is the dominant mechanism leading to failure of soldered assemblies. It is important to predict not only thermal stresses and strains, but also to analyse how different design parameters influence the stress. Furthermore, it is necessary to determine which material

properties, geometry parameters and manufacturing process conditions are critical for reliability.

Recently some interesting statistical models to predict the thermal reliability of BGAs have been developed [1-3]. Reliability of soldered joints under temperature loads is critical not only for BGA but also for QFN (Quad Flat Non-leaded) packages, one of the most advanced package types. For complementing previous studies, which focused mostly on BGAs, this paper will compare the two packages types BGA and QFN. The objective of this study is the analysis of the influence of input parameters on solder joint life time, statistical determination of the sensitivity to these factors and development of predictive analytical models for both types.

2. FE-Models A reliability analysis has the following demands to

finite-element-modeling. Firstly, the model parameters must be parameterized, so that the geometry variation can be easyly simulated. Second, stochastic investigations are based on a large number of simulations. In order to reduce the total calculation time, the model must be fast.

To meet these requirements, the modular modeling concept was developed [4]. On the basis of this method a configurable FE-model was constructed, so that a parametric analysis could be performed with variable geometry and material properties without having to rebuild the model for each change. In order to not overload the model with excessive numbers of elements, solder interconnection meshes were simplified, except those from which the output parameters must be extracted. The capability to update finite elements models rapidly allows one to perform Monte Carlo simulations of assemblies with multiple random variables.

2.1 Geometric details For a probabilistic analysis, a quarter symmetry 3D

non-linear finite-elements models of both BGA and QFN packages were generated using a modular modeling method and thermo-mechanical finite-elements-analyses (FEA) were performed.

Despite of some geometric differences it is possible to allocate a number of parameters, which are characteristic for both packages. Among these are length of package & Si, thickness of the moulding compound cap & Si, die attachment adhesive etc. For a comparison of BGA and QFN packages, identical or comparable values of input parameters have been used (Table 1).

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9th. Int. Conf. on Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro-Electronics and Micro-Systems, EuroSimE 2008

Fig. 1: Metallographic cross section of a BGA81, TopLine (top); a quarter symmetry FE-model

of BGA (bottom)

Fig.2 Metallographic cross section of a VQFN40, Infineon (top); a quarter symmetry FE-model

of QFN (bottom)

Table 1: Geometry parameters of BGA / QFN packages

Parameter BGA QFN

Moulding compound (X,Y), mm 6.5 6.2

Moulding compound (Z), mm 0.4 0.4

Si (X), mm 4.0 4.0

Si (Z), mm 0.25 0.25

Die attach adhesive (Z), mm 0.03 0.03

Interposer / Thermal pad (X,Y), mm 6.5 4.9

Interposer /Thermal pad (Z), mm 0.20 0.20

Printed circuit board (Z), mm 1.5 1.5

Solder mask (Z), mm 0.025 0.025

Pitch, mm 0.8 0.5

Solder mask opening radius /

QFN lead (XY), mm 0.15 0.550.25

PCB pad (radius) / (XY), mm 0.15 0.80.25

PCB pad (Z), mm 0.03 0.03

Ball radius, mm 0.225 -

Standoff, mm 0.35 0.06

2.2 Materials Model For the analysis the same materials (moulding

compound, solder mask and substrat) were used for both BGA and QFN packages.

Table 2: Material properties used in simulations for both BGA & QFN packages, (all data taken at 25C)

Material CTE, ppm/K Youngs

Modulus, GPa

Mold compound 14.7 18

Silicon 2.6 112

Die att. adhesive 48 5.9

FR4 (interposer) 15(X); 15(Y); 50(Z) 23

Cu 17 110

FR4 (PCB) 12(X); 12(Y); 45(Z) 23

Solder mask 70 3.8

The mechanical properties of solder alloys are non-

linear. For modelling the creep deformation of solder materials in FE-simulations, the well-known generalized Garofalo equation [5] was used. The inelastic strain rate is given as

[ ]

=

TCCC

dtd Ccr 4

21 exp)sinh( 3 (1)

is von-Mises stress.

The corresponding constants of steady-state creep deformation for Sn95.5Ag3.8Cu0.7 are listed in Table 3.

Table 3: Deformation constants for steady-state creep of SnAg3.8Cu0.7 alloy [6].

C1[1/s] C2 [1/MPa] C3 C4 [K] 2.78105 0.024 6.41 6500


3

3. Probabilistic simulation Under a deterministic approach it is assumed that the

values of geometry and material properties are fixed and variables are reduced to single values by means of statistical procedures like the average values. Such simplifications lead to an information loss by the transition from parameters of distributions to fixed values. In this case the results depend on the correctness of the input values at real conditions. In reality, these factors can not be represented by deterministic values, because materials and process parameters differ from their design values. This leads to a dispersion of the initial parameters, such as a design values (material, geometry) or boundary conditions (temperature). Material properties have an inherent variability and may differ from component to component.

Geometry can be reproduced only within tolerance ranges, depending on the used technology. The scatter of input parameters can cause large deviations in predicted values of lifetime and reliability. The variability of geometry and material properties leads to the stress-strain variation at the applied load. Therefore it is important to declare all initial parameters as distributions and to determine the sensitivity of the lifetime to every parameter variation. 3.1 Sensitivity analysis methods

From the spread of input parameters is possible to determine the sensitivity of the results to uncertainties in the dimensions or material properties due to fluctuations in the manufacturing process. The sensitivity can be calculated as the correlation coefficient between the input and the output parameters. Such correlations are an important result of stochastic analysis, and show which parameters have the greatest influence on the result.

At differential analysis (or direct method) sensitivity coefficient is based on the ratio of the change in output to change in the input parameter [7].

YX

XY i

ii

= . (2)

The ratio Xi / Y has been introduced in order to normalize the coefficient. Another method is the non-parametrical correlation test based on the rank-order correlation (Spearman test):

=

n

i

2i

n

i

2i

n

iii

S

)SS()RR(

)SS)(RR(r

(3)

where: Ri - rank of xi within the set of observations [x1,x2,..xn], Si - rank of yi within the set of [y1,y2,.yn],

RS , - average ranks of a Ri and Si respectively. Values of sensitivity rS span a range from +1 (perfect correlation), through 0 (no correlation), to -1 (perfect negative correlation).

3.2 Parameter sensitivity analysis The sensitivity of the reliability (creep strain

amplitude) to component geometry and material proper-ties under temperature cycling has been investigated and the following parameters have been examined: component size, chip size, solder joint geometry, pitch, pad size, global CTE mismatch between a component and PCB.

In the simulation all random input variables are independent and uniformly distributed. All distributions have standard deviations of 10% of model values. Passive temperature shock cycles were simulated in the range from -40C to 125C. In this work a constant creep strain cr was reached already after two simulated temperature cycles.

The effect of each input parameter can be estimated from probabilistic sensitivity diagrams and from scatter plots. For Monte Carlo simulations sensitivities were calculated by means of the differential correlation coefficients as well as the rank-order correlation coefficients between the input variables and output parameters.

a_XY

_FR

X_S

I

Z_P

AD

E_C

U

ST_

OFF

a_C

U

E_F

R

E_S

O

E_K

L

Z_IN

T / D

iePa

d

TMIN

Z_SI

a_Z_

FR

Z_FR

A_S

M

Z_SM

a_KL

Z_KL

Z_M

O

a_M

O

E_S

M

E_M

O

TMA

X

a_S

O

PIT

CH

-0,4

-0,3

-0,2

-0,1

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

X Axis Title

BGA QFN

Fig.3 Rank-order sensitivity coefficients of creep strain amplitude to various input parameters of BGA and QFN

a_XY

_FR

X_S

I

Z_P

AD

E_C

U

ST_

OFF

a_C

U

E_FR

E_S

O

E_K

L

Z_IN

T / D

ieP

ad

TMIN

Z_S

I

a_Z_

FR

Z_FR

A_S

M

Z_S

M

a_K

L

Z_K

L

Z_M

O

a_M

O

E_S

M

E_M

O

TMA

X

a_S

O

PIT

CH

-0.0006

-0.0004

-0.0002

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

BGA QFN

Fig.4 Differential sensitivity coefficients of creep strain amplitude to input parameter of BGA and QFN

The input parameters could be divided into two

groups, namely those having a significant influence on the

4


output parameter and those being insignificant. The simulation was made for N=100 parameter sets. The Spearman rank order significance coefficient is 0.165 at 5 % significance level.

Results of sensitivity analyses are used to identify critical parameters, which affect the reliability of solder joint and can be included in a global model as input parameters. The diagram shows that despite some difference both packages show identical sensitivity of the creep strain amplitude cr to input parameter. So significant parameters are the CTEs of substrate and moulding compound, Si chip size, stand off, substrate and moulding cap thickness, as well as cycling test temperature. 4. Design of experiments

Predictive models were developed to evaluate the inelastic strain amplitude in the solder joints subjected to thermal-cycling conditions as a function of the different design parameters of BGA and QFN. These models include local models and global models.

At first, input and response parameter must be chosen for test planning. In order to reduce the number of parameters only parameters that have a significant effect on response were applied.

In the present study, the BoxBehnken experimental design is used. It is an independent quadratic design requiring three levels (high, low, and intermediate) for each factor. This design is suitable for construction of a second-order polynomial model, using a small number of experimental runs. Considering all the linear, quadratic, and interaction terms, the quadratic response model can be described as:

ji

N

1jij

N

1i

N

1iii0 xxbxbbY

===

++= (4)

where bo is a constant, bi - the linear effect of the input factor xi, bij- the interaction effect between the input factor xi and xj . The quadratic effect of input factor xi - bii is special case of bij [8].

The advantages of multivariate approach to developing of an analytical model are reductions in the number of experiments and consequently - of the simulation time. Furthermore, with such approach interaction effects between parameters can be investigated, which are not possible with a univariate approach. Basically the analysis involves follow major steps:

selection of input and response parameter; performing the statistically designed experiments; estimation of the coefficients in a mathematical

model; validation of the model by comparison of simu-

lated output values and calculated theoretical ones, checking the accuracy of the model.

4.1 Generation of a global predictive model The four most important parameters, which can affect

the reliability of solder joint, were included in a global model as input parameters: materials properties: DA corresponds to the global

CTE mismatch between a component and board in ppm / K,

accelerated temperature tests: DT is the temperature difference in the temperature cycle, in C,

size of the Si die: LSI/L is die to component size ratio, size of the components: L edge length of the

component in mm.

In order to study the combined effect of these factors, FE-simulations were performed for different combinations of these parameters using statistically designed experiments. The range of values for the input variables is given in Table 4. For these input parameters the low, middle and high levels of each variable were designated as 1, 0, and +1 respectively. A total of 25 simulation runs were necessary to estimate the coefficients of the model using multiple linear regressions.

Table 4: Input variables for BoxBehnken experimental design

Parameter Level -1 0 1

DA, ppm/K 10 5 0

T DT, C 135 165 195

Die size LSI/L 0.4 0.6 0.8

Size L, mm (BGA/QFN) 4.5/ 4.5 7.0/6.5 9.5/8.5

In order to determine the effect of global CTE mismatch (parameter DA) three different combinations of moulding compound and substrate materials properties (Table 5) were used according to the Box-Behnken design.

Table5: CTE and Youngs moduli of components and boards for BoxBehnken experimental design

-1 0 1

CTE of moulding compound, ppm/K 8 10 12

Youngs modulus of moulding compound, GPa 26 22 18

CTE of substrate, ppm/K 18 15 12

Youngs modulus of substrate, GPa 20 25 30


5

4.1.1 BGA modelling

Fig.5: Examples of BGA geometry with different I/O-numbers and die size ratio

The sensitivity is obtained by the Spearman

correlation coefficient between a random input variable and the response. According to the correlation coefficients the input parameters sensitivity has the following values.

Table 6: Sensitivity of creep strain amplitude to BGA input parameters

Parameter Sensitivity Normalized

DA 0.188 14.64%

T DT 0.298 23.21%

Die size LSI/L 0.031 2.43%

Size L 0.767 59.72%

L

DT

DA

Lsi/L

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Sensitivity

Fig.6: Sensitivity of creep strain amplitude to BGA input

parameters

The creep strain was mostly affected by package size, Fig.6. It was indicated that the creep strain amplitude increased and the BGA package reliability decreased with an increase in package size (parameter L). A similar trend was also observed for temperature difference DT and CTE mismatch DA. The die to component size ratio LSI/L is having least significant effect.

The output parameter cr was fitted using a quadratic regression model. Box-Cox transformation and the forward stepwise filtering technique were applied for the regression analysis. A confidence level of 90.0% was used to filter out insignificant terms of the regression equation. The second-order non-linear mathematical models have been developed to predict the influence of selected input parameters on creep strain amplitude. The mathematical model for four factors considered in the present case is:

10-2

SISI

SI

29cr

)L0.0062 +L0.122

-LL0.887-DT)L

L0.0076+(-0.00726

+DA)LL73139.02-DT319.982+(1614.495

+DA101.432-(2.997

=

These mathematical models can predict creep strain

amplitude cr. The number of cycles to failure can be calculated with a suitable fatigue model, for example

295.1crf )(5.4N

= [9]. The equation represents the quantitative effect of input parameters and their interactions on the response. The values of the mathematical models coefficients are related to the effect of these variables on the response. A value > 0 represents a positive contribution while one < 0 indicates a negative effect of this parameter.

0,00 0,01 0,02 0,03 0,04 0,05

0,01

0,02

0,03

0,04

0,05

c

r, m

odel

cr, simulation

Fig. 7: Predicted values vs. FE simulation for creep strain

amplitude cr for BGA

For a model validation the values of the input parameters were set into the equation to obtain the theoretical values of cr. These were compared with the

L = 9.5 mm

L = 7.0 mm

L = 4.5 mm

6


FE simulation values and both were found to be in reasonably close agreement. A coefficient of determination R2 value is 0.81 and adjusted coefficient of determination R2adj 0.88.

4.1.2 QFN modelling

The 25 simulation data sets of the same input

parameters as in the BGA case (see Table 4 and 5) were used to evaluate the sensitivity using the correlation coefficients between all random input variables and response.

DA

DT

Lsi/L

L

0,0 0,2 0,4 0,6 0,8 1,0Sensitivity

Fig. 8: Sensitivity of creep strain amplitude to QFN input

parameters

It should be noted that QFN life-time in contrast to BGA is strongly influenced by CTE mismatch between component and board DA (Fig 8). So the reliability of QFN decreases with increase of this parameter. At the same time all other parameters have roughly the same negative effect on the reliability. The reliability of QFN generally decreases with an increase in such parameters as temperature difference DT, die to component ratio LSI/L and component size L.

Table 7: Sensitivity of creep strain amplitude to QFN input parameters


CTE DA 0.947 65.03%

T DT 0.200 13.76%

Die size LSI/L 0.158 10.84%

Size L 0.151 10.37%

The creep strain amplitude of QFN can be estimated by:

3,3322

SI

SI

28cr

)L0.001529-L0.0262+LL0.119

+LL0.1168-DTDA39.7839+DT0.0004

+DA104.1478+DA4348.0919+(0.0696

=

The predicted values from the mathematical model are plotted in Fig.9 for comparison to simulation data.

0,00 0,01 0,02 0,03 0,04 0,050,00

0,01

0,02

0,03

0,04

0,05

cr, m

odel

cr, simulation

Fig. 9: Predicted values vs. FE simulation for creep strain

amplitude cr for QFN The model provides a coefficient of determination R2 of 0.98 and an adjusted value of R2adj - 0.99. The predicted and observed creep strains were well correlated and showed good agreement. 4.2 Local geometry models 4.2.1 BGA local geometry model

Four parameters of ball geometry were included in the

FE-model as random input variables to analyse their effect on the BGA component reliability

Ball radius (RBALL) Ball height (STOFF) Pad radius on the substrate side (RS) Solder mask opening on the package side (RP)

Fig. 10: Local geometry input parameters of the BGA

RP

RBALL

RS


7

Table 8: Input variables for BoxBehnken experimental design


Ball height STOFF, mm 0.28 0.35 0.42

Solder mask opening on the package side RP , mm 0.12 0.15 0.18

Pad radius on the substrate side RS, mm 0.12 0.15 0.18

Ball radius RBALL, mm 0.18 0.225 0.27

Fig. 11: Examples of different BGA solder joint

geometries

Table 9: Sensitivity of creep strain amplitude to BGA local geometry


Ball height STOFF -0.209 14.01%

Solder mask opening on the package side RP -0.925 61.77%

Pad radius on the substrate side RS 0.125 8.37%

Ball radius RBALL 0.237 15.86%

The chart shows that the radius of solder mask opening on the component side RP and the radius of the solder joint RBALL are sensitive parameter for the solder joint reliability.

SToff

Rp

Rs

Rball

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4

Sensitivity

Fig. 12: Sensitivity of creep strain amplitude to BGA

solder joint geometry The quadratic model was used to explain the mathematical relationship between independent variables and dependent responses. The mathematical expression of the relationship of creep strain with variables like pad and solder mask opening radius, standoff as well as ball radius are shown below as a regression model:

1BALLpS

OFFBALLpcr

)RR2.1375R139.4

ST9.68R8.269R3.2324.127(+

+=

In order to fit the model better, a Box-Cox transformation was used for the regression analysis. The agreement between the calculated and simulated data sets was acceptable: the determination coefficient R2=0.93 and adjusted the R2adj=0.90.

0,00 0,01 0,02 0,03 0,040,00

0,01

0,02

0,03

0,04

cr, m

odel

cr, simulation

Fig. 13: Predicted values of creep strain amplitude cr in

BGA solder joint vs. FE simulation data

8


4.2.2 Local QFN geometry For comparison, we have investigated the geometry

parameters, which can have an influence on the QFN solder joint lifetime. Five parameters were used as random input variables for the analysis of the solder joint local geometry.

height of the solder joint STOFF pad length on the substrate side XS pad width on the substrate side YS pad length on the package side XP pad width on the package side YP

Fig. 14: Input parameters of the QFN model The parameters and their distributions were shown in the Table 10.

Tabelle 10: Input variables for BoxBehnken experimental design


Height of the solder joint STOFF,mm 0.054 0.06 0.066

Pad length on the substrate side XS, mm 0.72 0.80 0.88

Pad width on the substrate side YS, mm 0.225 0.25 0.275

Pad length on the package side XP, mm 0.495 0.55 0.605

Pad width on the package side YP, mm 0.225 0.25 0.275

Fig 15: Examples of different QFN solder joint

geometries

Table 11: Sensitivity of creep strain amplitude to QFN local geometry

Parameter Sensitivity NormalizedPad width on the package side YP -0.668 36.01%

Height of the solder joint STOFF -0.438 23.62%

Pad width on the substrate side YS 0.316 17.02%

Pad length on the package side XP 0.314 16.94%

Pad length on the substrate side XS -0.119 6.40%

Yp

SToff

Ys

Xp

Xs

-0,8 -0,6 -0,4 -0,2 0,0 0,2 0,4Sensitivity

Fig 16 Sensitivity of creep strain amplitude to QFN solder joint geometry

For QFN the lifetime of the solder joints shows a positive sensitivity to an increasing width of the peripheral pads and standoff. The final mathematical equation is given below:

SPPOFF

2OFFPS

PSOFFcr

XX0.14XST2.52-ST17.35Y0.045-Y0.012

X0.038X0.078-ST0.88-0.072

++

++=

The predicted values were compared with the simulation values and were found to be in reasonable agreement. In this case, the values of determination coefficient R2 and R2adj are 0.80 and 0.77.

XP

XS YS

YP


9

0,008 0,010 0,012 0,0140,008

0,010

0,012

0,014

cr, m

odel

cr, simulation

Fig. 17: Predicted values of creep strain amplitude cr in

QFN solder joint vs. FE simulation data

5. Conclusions In this work some predictive models for the

assessment of creep strain amplitude as a function of different design parameters were developed. The sensitivity to various design parameters were analyzed and evaluated with regard to their influence. The regression coefficient for the representation of the effect of the independent variables, and the interaction coefficients were calculated for BGA and QFN.

These models can be used for a lifetime prediction with a significant reduction in the simulation time. The method is suited for the estimation of creep strain amplitude and a comparison of the performance of packages with varying geometric and material properties. It is sufficient to use quadratic equations, in order to calculate the lifetime for each set of input parameters. The developed models allow the reliability prediction with a precision comparable with FE models. So quick and inexpensive results can be made available to understand the impact of solder joint geometry, component size, material properties and temperature cycles on the thermo-mechanical reliability of the component solder joint.

The model can be used to evaluate the improvement instead of the prediction of the absolute value of the lifetime use. The developed models can be an effective tool for the component selection and its lifetime estimation particularly for users, which want to avoid costly simulations.

Acknowledgments The described investigations were funded by the

Federal Ministry of Economics and Labour BMWA under the AIF research program (AIF project number 13.821 N) and supported by the Research Association on Welding and Allied Processes of the German Welding Society DVS (DVS-No. 10.040). The authors are very grateful for this support.

References

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[2] Vandevelde, B.; Beyne, E.; Zhang K.; Caers, J.; Vandepitte, D.; Baelmans, M.: Parameterized modeling of thermomechanical reliability for CSP assemblies; Journal of Electronic Packaging; V.125, 2003, pp. 498-505

[3] Stoyanov, S.; Yannou, J. M.; Bailey , C.; Strusevich, N.: Reliability based design optimisation for system-in-package; Proc. Eurosime 2007, pp. 289-296.

[4] Zukowski, E., Deier, E., Wilde, J.: Correct modelling of geometry and materials properties in the thermo-mechanical finite-elements-simulation of chip scale packages; Proc. Eurosime 2005, pp. 545-552.

[5] ANSYS 11.0 Documentation

[6] Schubert, A., Dudek, R., Auerswald, E., Gollhardt, A., Michel, B., Reichl, H.: ''Fatigue life models of SnAgCu and SnPb solder joints evaluated by experiments and simulations,'' 53rd ECTC Conference Proc., 2003, pp. 603-610

[7] Hamby, D. M.: A review of techniques for parameter sensitivity analysis of environmental models, Environmental Monitoring and Assessment V.32: pp. 135-154, 1994.

[8] Helton, J.C., Iman, R.L. and Brown, J.B.: Sensitivity analysis of the asymptotic behavior of a model for the environmental movement of radionuclides, Ecol. Modelling. 28, (1985), pp. 243-278.

[9] Dudek, R., Rzepka, S., Dobritz, S., Doring, R., Keybig, K., Wiese, S., Michel, B.: Fatigue life prediction and analysis of wafer level packages with SnAgCu solder balls, Electronics System Integration Technology Conference, 2006, Vol. 2, pp. 903-911

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