Comparative Sensitivity Analysis for µBGA and QFN Reliability

Jürgen Wilde, Elena Zukowski University of Freiburg,

Department of Microsystems Engineering Laboratory for Assembly and Packaging

Georges-Koehler-Allee 103, 79110 Freiburg, Germany

Abstract The estimation of product reliability during the design

is one of the key questions in microelectronics. The assembly lifetime is a function of such parameters as geometry, material properties and loads. All these influences exhibit systematic and stochastic variations. The effect of variability can be analysed by a probabilistic FE-simulation and statistical methods. This paper presents an approach for the prediction of thermal fatigue life of two CSP types, the µBGA and the QFN. Besides geometry parameters, also material properties and cycle temperatures are used as variable inputs. Based on a preliminary study the input parameters were defined as normal distributed. Sensitivities of the lifetime to the design parameters were computed and ranked after FE-simulations for both µBGA and QFN packages parameters had been performed. The fatigue life prediction of solder joints used in this work is based on a Coffin-Manson model and it was performed using the stress-strain data extracted from FE-simulations. As there exists a dependency on the solder deformation behaviour, the correct choice of the deformation model of lead-free solder alloys is an important aspect of this work. Summarising, in this work a probabilistic simulation method was developed to compute realistic failure distributions of two CSP types.

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 cycles. This is the dominant mechanism leading to failure of soldered assemblies. It is important to predict not only thermal stresses and strains within the system, but also to analyse how different design parameters influence the stress. Furthermore, it is necessary to determine which material properties, geometry parameters and manu-facturing process conditions are critical for reliability.

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 µBGA and VQFN. Here the solder fatigue life of the assemblies is predicted using the Coffin-Manson equation in combination with parametric FE-models.

2. FE-Model The investigation of design parameters like material

properties, or geometry was carried out using the parametric study approach. A configurable 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. The capability to update finite elements models rapidly allows one to perform Monte Carlo simulations of assemblies with multiple random variables. The existing parameterised deterministic model of µBGA and QFN [1] was extended to a probabilistic model by treating the geometry, dimensions and material properties as random variables.

2.1 Geometric Details A quarter symmetry 3D non-linear finite-elements

model was generated using a modular modelling method [1].

Fig.1 A quarter symmetry 3D FE-µBGA model

Fig.2 A quarter symmetry 3D FE-QFN model

Packages chosen for this study included a QFN and

µBGA packages with 0.5 mm and 0.8 mm pitch size respectively. The connection of the chip to the substrate is accomplished using 49 I/O in a 7×7 matrix for the µBGA and 40 I/O (8×12) in the case of QFN solder joints. Both packages were mounted to non-solder mask defined 1.5 mm thick FR4 board.

Figures 1-3 illustrate the constructed FE-models and provide a detailed view of the copper lands and the solder joint region.

Fig.3a Detailed view of the copper lands-solder joint region of a metallographic QFN cross-section

Fig.3b Detailed view of the copper lands-solder joint region of QFN model

2.2 Material Model Most of the materials properties were assumed to be

linear elastic.

Table 1. Material properties used in simulations, (all data taken at 25°C)

Material CTE, ppm/K E Modulus,

MPa

Silicon 2.6

Orthotropic

c11=165640

c12= 63940

c44= 79510

FR4 (Interposer) 15(X); 16(Y); 50(Z) 23000

Die att. adhesive 65 1500

Solder mask 60 3500

Cu 16,7 130000

FR4 (PCB) 12(X); 17(Y); 45(Z) 23000

Two variants of moulding compounds, which are

identified as LS#1 (Low Stress) and LS#2, are chosen for the investigations. Moulding compound LS#1 has a low Tg and as consequence the CTE difference is high at high temperatures (Fig. 4a).

-50 0 50 100 1500

1x10-5

2x10-5

3x10-5

4x10-5

5x10-5

6x10-5

0

5000

10000

15000

20000

25000

30000 LS#1 (CTE) FR4 (CTEX) FR4 (CTEY)

You

ng's

mod

ulus

, MP

a

Temperature, °C

CTE

, ppm

/K

LS#1 (Young's modulus)

Fig.4a CTE of moulding compound LS#1 [2]

The second moulding compound has lower CTE than the substrate at all simulated temperatures (Fig4.b).

Temperature dependent values of CTE (22ppm/K@25°C) and Young’s modulus (50GPa@25°C) for SnAgCu solder were found in literature [3].

-50 0 50 100 150 2000

1x10-5

2x10-5

3x10-5

0

5000

10000

15000

20000

25000

30000

LS#2 (CTE) FR4 (CTEX) FR4 (CTEY)

You

ng's

mod

ulus

, MP

a

Temperature, °C

CTE

, ppm

/K LS#2 (Young's modulus)

Fig.4b CTE of moulding compound LS#2

The mechanical properties of solder alloys are non-linear. For modelling the creep deformation of solder materials in FE-simulations, the well-known generalized Garofaldo equation [4] was used. The inelastic strain rate is given as

[ ]

−=

TCCC

dtd Ccr 4

21 exp)sinh( 3σε (1)

σ is von-Mises stress. During the last years, several constitutive models for

Sn95.5Ag3.8Cu0.7 were published, but there is yet no material model, which is accepted as general standard. The analysis of published creep data was performed with five test simulations. The corresponding constants of steady-state creep deformation are shown in the Table 2.

Table 2. Deformation constants of steady-state creep for SnAg3.8Cu0.7 and SnAg3.8Cu1 [10] alloy

C1[1/s] C2 [1/MPa] C3 C4 [K] Reference

3.20E+04 0.037 5.10 6525 [5]

2.78E+05 0.024 6.41 6500 [6]

5.01E+02 0.032 4.96 5434 [7]

9.81E+03 0.045 8.03 8547 [8]

8.78E+08 0.052 5.13 11210 [9]

2.60E-03 0.185 3.00 4655 [10]

For comparison, the isothermal lines of the different

data sets from Table 2 are plotted in Figs. 5a and 5b. The plotted data cover a wide range of stress levels and creep rates [6]. The graph corresponding to [8] shows higher creep resistance than the other models. The largest differences between the data sets are observed at low stresses and low strains.

1 10 10010-1110-1010-910-810-710-610-510-410-310-210-1100

[5] [6] [7] [8] [9] [10]

S

econ

dary

Cre

ep R

ate

(1/s

ec)

Stress (MPa)

Fig.5a Creep strain rate versus von-Mises stress for Sn95.5Ag3.8Cu0.7 at -40°C

1 10 10010-1110-1010-910-810-710-610-510-410-310-210-1100

[5] [6] [7] [8] [9] [10]

Sec

onda

ry C

reep

Rat

e (1

/sec

)

Stress (MPa)

Fig.5b Creep strain rate versus von-Mises stress for Sn95.5Ag3.8Cu0.7 at 125°C

The corresponding hysteresis loops for simulated shear stress versus creep shear strain in Sn95.5Ag3.8Cu0.7 solder joints of BGAs are plotted in Fig.6 for thermal cycles between -40°C and 125°C.

-0,004 -0,003 -0,002 -0,001 0,000-2

-1

0

1

2

3 [5] [6] [7] [8] [9] [10]

She

ar s

tress

(MP

a)

Shear strain

Fig. 6 Simulation of shear stress vs. shear strain creep hystereses for Micro-BGA packages

The simulated equivalent creep strain amplitude and the predicted life cycles for each creep models for are given in Table 3. Table 3. Equivalent creep strain amplitude and number of cycles to failure computed with Equation 3

∆εcr Nf Reference 1.33E-2 1215 [5] 1.26E-2 1300 [6] 1.21E-2 1365 [7] 1.02E-2 1700 [8] 1.02E-2 1698 [9] 1.54E-2 998 [10]

From the life prediction results, it becomes evident

that the data have some scattering. The creep-fatigue lives of µBGA solder joints predicted with [8] and [9] are higher than those predicted with [5], [6], [7] and [10]. In the authors´ opinion the data from [6] represent average values for the considered sinh-model parameters and therefore these data are used for our FE-simulations.

3. Input parameters and loads Material properties and geometry data are used as

analysis inputs. Geometric features exhibit variations, which are caused by manufacturing and assembly processes. Among these are the component placement accuracy on the substrate (diagonal distance from corner joint to corner joint), screen-printing process variations and solder paste parameters like the standoff height. Some geometry parameters and material properties influence the solder joint reliability significantly. For example, the materials and geometry, that define the package structure, have influence on the effective CTE of the package. Therefore, CTE is a function of the coefficients of thermal expansion of the materials, the thickness and the moduli of elasticity [11, 12].

As shown in Fig. 7 a cyclic thermal load is defined by a temperature transient from –40°C to 125°C, with 30 min dwell time and 10 s ramp time.

0 1000 2000 3000 4000 5000 6000 7000 8000-60-40-20

020406080

100120140

Tem

peta

ture

,°C

Zeit,s

Fig.7 Passive temperature loading cycle used in simulations

For creep analysis, it is important to study the responses for multiple thermal cycles until the hysteresis loops become stabilized. In our simulations creep shear strain is stabilized after the second cycle. Therefore only two thermal cycles were simulated. 4. Results and Discussion 4.1 Fatigue model

For strain-based analysis, Coffin-Manson fatigue models [13-15] are widely used for low cycle fatigue analysis.

αε apl NC ⋅=∆ (2)

Here ∆εpl is the effective von-Mises viscoplastic strain range and α and C are temperature-dependent parameters, which can be obtained experimentally from strain-cycling tests. In practice, for experimental or analytical determination of the creep strain amplitude ∆εcr can be used at high homologous temperatures in the Coffin-Manson equations for the prediction of the number of cycles to failure Nf.

Inelastic strain and stress in µBGAs and VQFNs sol-der joints are taken from FEA. For the evaluation of assembly lifetime, the following damage model [16] was applied:

295.1)(5.4 −∆= crfN ε . (3)

In thermal cycling tests on many components the

times or numbers of cycles to failure will be distributed over rather large intervals. The two-parameter Weibull function is considered as a suitable distribution function for failure times or cycles fN of the assemblies:

β

α

β

α

−

−

−=−=fN

f

t

eNForetF 1)(1)( (4)

Cycles to failure distributions for Weibull plots can be

obtained from thermal cycling simulations only when distributed input parameters are used.

4.2 Probabilistic sensitivity analysis

Probabilistic sensitivities are important in order to improve a design toward a more reliable version. From Monte Carlo simulations, sensitivities can be derived by calculation of correlation coefficients between input variables and output parameters. A frequently used non-parametric correlation tests for sensitivity calculation is the Spearman test based on rank-order correlation [4].

∑∑

∑

−−

−−=

n

ii

n

ii

n

iii

s

SSRR

SSRRr

22 )()(

))(( (5)

There Ri is the rank of xi within the set of observations [x1,x2,…..xn], Si is the rank of yi within the set of

[y1,y2,….yn], and RS , are average ranks of a Ri and Si respectively. Values of sensitivity rS can be distributed in a range from +1 (perfect correlation), through 0 (no correlation), to -1 (perfect negative correlation).

4.3 Effect of solder pad opening size and area ratio

The geometric characteristics can have a significant effect on the thermo-mechanical reliability. Two variants of ball geometry were regarded: NSMD pads on boards and SMD pads on package substrates. For both types the ball radius (225 µm) and the connection radius on the package side (170 µm) are the same and pad radii on the substrate side are different (150 µm and 200 µm respectively). So for variant #1 (small substrate pad) Rs>Rp, while for variant #2 (large substrate pad) Rs<Rp.

Fig.8 Solder ball models with different copper pad designs.

The two-parameter Weibull distribution was used to characterize the lifetime distribution of assembled packages. Smaller pads lead to higher reliability while larger pads have lower lifetime and a higher failure probability.

500 1000 2000

0.02

0.05

0.10

0.25

0.50

0.75 0.90 0.96

Life time, No. of cycles

Failu

re p

roba

bilit

y, %

Fig.9 Computed cycles to failure distributions for two different solder pad opening size (µBGA49)

Sensitivities of lifetime to the change of such input variables as package pad opening radius (Rp) and sub-strate pad radius (Rs) were calculated. Comparison of these coefficients shows that the pad opening radius is a powerful parameter for package reliability optimisation.

0,13 0,14 0,15 0,16 0,17 0,18 0,19

500

1000

1500

2000

2500

3000

3500 rs=0.57

Life

time,

cyc

le

Rp, µm

Fig.10a Sensitivity of lifetime to package pad opening radius (µBGA49)

0,12 0,13 0,14 0,15 0,16 0,17 0,18

500

1000

1500

2000

2500

3000

3500 rs=-0.1

Life

time,

cyc

le

Rs, µm

Fig.10b Sensitivity of lifetime to substrate pad radius (µBGA49)

For comparison, we have investigated the influence of QFN solder joint geometry parameters on package lifetime.

Fig.11 Interconnect geometry parameters on VQFN

For VQFN the fatigue life of soldered joints shows a positive sensitivity to increasing Cu-pad dimensions, which determine solder joint geometry. However, PCB pad width Ys has the strongest influence (rs=0.33) on the

large pad small pad

Rp Rp

Rs Rs

Xp

Xs

Ys

Yp

small pad

large pad

lifetime. Therefore, the increase of solder pads and solder land areas leads to increasing solder joint reliability.

Xp

Xs

Yp

Ys

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35Sensitivity

Fig.12 Lifetime sensitivity plot of interconnect geometry variables for the FE-model of an QFN

It is shown, that µBGAs with larger solder mask opening size and QFNs with longer peripheral lead length have longer fatigue lives.

4.4 Effect of moulding compound CTE on fatigue life The material data of the moulding compound can be

important for the assembly reliability. Both properties Young’s modulus and CTE values change dramatically around the glass transition temperature. Therefore, the influence of the variance of the moulding compounds´ CTE on the package lifetime was investigated.

A higher CTE of a moulding compound increases the effective package CTE and reduces the CTE mismatch with PCB. This factor which tends to increase the fatigue life. We have investigated two variants: In one case, the CTE of the moulding compound is lower than that of the PCB (LS#2). In the second case (LS#1) the difference in CTEs between moulding compound und PCB was inverse in a high temperature range, αMC > αPCB .

µBGA QFN

LS#1

LS#2

Fig.13a Package deformations for two different moulding compounds at -40°C (displacement scale factor=50)

A qualitative comparison of the thermal-mechanical

behaviour of packages with different moulding compound CTEs is shown in Fig. 13. It can be seen, that at –40°C

both variants of mould compound show the same modes of package deformation.

At 125°C, the deformation behaviour of assemblies with both moulding compounds is different. For packages with inverse ∆α (αMC>αPCB), the stress of moulding compound in the die overhang area increases due to an increase of the thermal expansion of the moulding compound in the die overhang area.

µBGA QFN

LS#1

LS#2

Fig.13b Package deformations for two different moulding compound CTEs at 125°C (displacement scale factor=50)

Finite elements modelling indicated that LS#1 would

improve fatigue life compared with LS#2 (Fig. 14).

3000 5000 70000.02

0.05

0.10

0.25

0.50

0.75

0.90 0.96

Life time, No. of cycles

Failu

re p

roba

bilit

y, %

Fig. 14 Cycles to failure for two different moulding compounds (temperature cycling -40°C to +125°C for VQFN-40)

Another interesting fact is that for LS #1 the location

of the critical zone is changed due to the influence of the CTE of the moulding compound. In order to investigate the effect of the variability of geometry and material properties a Monte Carlo simulation was conducted. All input values were changed according to their distributions and strain-based fatigue life predictions were made. In the case when LS#2 was used for the µBGA, the critical zone with the highest strain range was found in the corner balls for all simulations. For LS#1, the critical zone was

Lead pad length

PCB pad length

Lead pad width

LS#1

LS#2

PCB pad width

displaced to the next ball in the diagonal inward direction. Nevertheless for some geometry value sets the zone of maximum strain appeared in the corner balls.

µBGA QFN

LS#1

LS#2

Fig.15 Location of the critical zone for two different moulding compound CTEs (displacement scale factor=50)

5. Conclusions A comparative analysis of µBGA and QFN is

undertaken regarding geometric and material parameters. Stress and creep analyses were utilized to predict the reliability of lead free solder joints during thermal cycling. Simulations results coupled with sensitivity analyses show the same behaviour for both types of packages.

• Increase of solder mask opening sizes for µBGA and peripheral lead length for QFN increased also package fatigue life.

• Values of the CTE difference between moulding compounds and substrates can change the location of the critical zones

• It is important use optimal moulding compound CTE, in order to prevent inverse CTE difference.

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.

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