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Thermal fatigue life evaluation of SnAgCu solder joints in a multi-chip power module

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2017 J. Phys.: Conf. Ser. 841 012014

(http://iopscience.iop.org/1742-6596/841/1/012014)

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IOP Conf. Series: Journal of Physics: Conf. Series 841 (2017) 012014 doi :10.1088/1742-6596/841/1/012014

Thermal fatigue life evaluation of SnAgCu solder joints in a

multi-chip power module

C Barbagallo1, G L Malgioglio2, G Petrone1 and G Cammarata1

1University of Catania, Department of Industrial Engineering, Viale A. Doria 6,

95125, Catania, Italy

2STMicroelectronics, IPD R&D, Stradale Primosole 50, 95121, Catania, Italy

E-mail: gpetrone@dii.unict.it

Abstract. For power devices, the reliability of thermal fatigue induced by thermal cycling has

been prioritized as an important concern. The main target of this work is to apply a numerical

procedure to assess the fatigue life for lead-free solder joints, that represent, in general, the

weakest part of the electronic modules. Starting from a real multi-chip power module, FE-

based models were built-up by considering different conditions in model implementation in

order to simulate, from one hand, the worst working condition for the module and, from

another one, the module standing into a climatic test room performing thermal cycles.

Simulations were carried-out both in steady and transient conditions in order to estimate the

module thermal maps, the stress-strain distributions, the effective plastic strain distributions

and finally to assess the number of cycles to failure of the constitutive solder layers.

1. Introduction

Recently, various electrified vehicles are emerging. Power (inverter/converter) modules, based on

IGBTs and diodes, are one of the core components for such vehicles and convert battery or fuel-cell

power to drive motors. Power modules equipped in electrified vehicles often operate at harsh

conditions. Thermal stress is known to be one of the major factors resulting performance degradations

or damages in solder joints in power modules [1]. For that reason, demand of high power density

electronic converters calls for numerical methods to evaluate their reliability at the design stage. The

reliability of lead-free solder joints is one of the key factors in the reliability of the overall converter,

since they represent mechanical, electrical and often thermal connections between the electronic

components and the board [2]. Combined with the thermal expansion mismatch between the different

materials of the assembly, cyclic thermal loadings result in stress reversals and potential accumulation

of inelastic strain in the solder joint. This inelastic strain accumulates with repeated cycling and

ultimately causes solder joint cracking and interconnect failure [3]. Many authors [3,7,8] have studied

the fatigue behaviour of lead-free solders. There is a difference between a fatigue life evaluation that

uses power cycling and one that uses temperature cycling. During thermal cycling, the solder layer

reaches a uniform temperature. In case of the power cycle becomes short, this state is different from

the real active state of the power device, in fact the real temperature distribution on the solder layer is

not uniform. [4]. The damage of solder joints, which falls in the mechanical fatigue behavior of

materials, is a Low-Cycle-Fatigue (LCF) process. A characteristic of LCF is that significant plastic

strains occur on the macroscopic scale during each load cycle. Because of the demand for high power

density electronic converters, coupled thermo-mechanical analyses oriented to the solder joint fatigue

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IOP Conf. Series: Journal of Physics: Conf. Series 841 (2017) 012014 doi :10.1088/1742-6596/841/1/012014

life prediction are becoming a topic of very high interest. In this framework, a numerical analysis on

thermo-mechanical behaviour and fatigue life prediction for a power module is proposed.

2. Model implementation

Models were implemented and solved by a FE-based software devoted to multi-physical applications.

In our study, we numerically analysed thermal state, thermal-induced stress-strain and we carried-out a

LCF life prediction for a multi-chip power module. Model implementation and numerical solution are

presented in the following paragraphs.

2.1. Geometry of the numerical model

The geometry of the studied module and the related stratigraphy are shown in Fig. 1. The module is

mainly made by a copper baseplate where three power islands are arranged on. Each power island is

composed by several layers, such as lead-free solders, a packed 3-layers Direct Bond Copper (DBC),

the dies (IGBT and diode) equipped with front metals.

(a) (b)

Figure 1. Geometry of the numerical model (a) and related stratigraphy (b). Baseplate is shown in

grey, solders in magenta, DBC ceramic in cyan, DBC copper in red, dies in green and front metals in

blue.

The physical properties of materials considered in our study are reported in Tab. 1.

Table 1. The physical properties of materials (

ρ

density, k thermal conductivity, Cp specific heat at

constant pressure,

α

coefficient of volumetric thermal expansion, E Young’s modulus,

ν

Poisson’s

ratio, σy Yield strength).

ρ

[kg/m3]

k

[W/(m·K)]

Cp

[J/(kg·K)]

α

[K-1]

E

[MPa]

ν

[-]

σY

[MPa]

Copper

8900

360

393

1.6E-5

1.2E5

0.34

48

Solder (SnAgCu)

7370

75

220

2.2E-5

5.0E4

0.36

26

Ceramic

3260

150

734

4.5E-6

3.3E5

0.24

32

Silicon

2340

135

735

2.5E-6

1.8E5

0.22

40

Aluminium

2710

202

871

2.3E-5

7.0E4

0.33

11

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2.2. Thermo-mechanical model

In the first step of our investigation, labelled from now Case A, a thermo-mechanical simulation was

carried-out for the device, both in steady and transient conditions. It consisted in solving the following

governing equations:

!!!

!"

!" !!!!"# !!

(1)

!!!!!!!!!!!!!!"!!

(2)

Eq. (1) represents the energy equation, where T is the temperature and Q is the volumetric heat

generation. Eq. (2) is the Hooke’s law relating the stress-strain of material, where

σ

is the stress

tensor,

σ

0 and

ε

0 are initial stress and strain, C is the fourth order elasticity tensor, “:” stands for the

double-dot tensor product and

ε

represents the total strain tensor, defined as:

!!

!

!

!" !!!"!!

!

(3)

where s is the displacement. Other symbols in eqns. (1) and (2) are referred to the caption of Tab.

1. Eqns. (2) and (3) were solved in order to detect the stress-strain thermally induced on the

constitutive materials. The term

θ

appearing in eq. (2) denotes the difference between the local

temperature T and the strain reference one Tref, that corresponds to the baseplate temperature. This

analysis was performed considering the worst working conditions in order to compute the maximum

temperature and related stress-strain during the module functioning. To this goal, the bottom surface of

the baseplate was held at constant temperature Tref and a volumetric heat source was applied to all

devices. Values of thermal heat sources correspond to the maximum power supplied to the devices

during the module functioning. On all other boundaries, an insulation condition was applied. From the

mechanical point of view, a fixed constraint was chosen for the bottom baseplate surface, maintaining

free all other boundaries of the model. The structural load was related to the thermal computed state

only.

2.3. Thermal fatigue model

In a second step of our investigation, labelled as Case B, a thermal fatigue life prediction was carried-

out for the module. The target of this analysis was to assess the fatigue life of solder joints subjected to

thermal cycles. The model proposed for predicting the fatigue life of solder layers is plastic strain

based. As usually done when applying a plastic strain approach, time-independent plastic strain

conditions are applied and the resulting stresses within a component are analysed.

2.3.1. Thermal cycle test

The computational model was built considering a thermal cycle between two environmental fixed

temperatures. To this goal, and differently from what previously described for model implementation,

we solved the energy equation in “passive” conditions. That means we applied different external

conditions as thermal load to the device. In particular, no internal heat source was considered, while

we applied two different thermal states (Tc = -40 °C and Th = 125 °C) to the entire device external

boundaries. This procedure simulates the module standing inside a climatic test room, held at two

different constant control temperatures (cold temperature, Tc, and hot temperature, Th). By means of

this approach, the plastic strain range, ∆

ε

p, was evaluated by using the achieved thermal states. The

ε

p

is defined as the effective plastic strain, computed as a component of the total strain.

Then, in analogy to the Basquin equation, we applied the Coffin-Manson equation [5] to compute

the number of cycles to failure, reading as follows:

!!!

!

!!!

!!!!!

!!

(4)

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where ɛ'f is the fatigue ductility coefficient and c is the fatigue ductility exponent of the solder

material and finally Nf is the number of cycles to failure.

3. Numerical solution

Continuous equations were spatially discretized by a Finite Element approach based on the Galerkin

method on non-uniform and non-structured computational grids made of tetrahedral Lagrange

elements of order 2. Influence of spatial discretization was preliminary studied in order to assure

mesh-independent results. A computational grid made of about 1230500 elements was retained for

computations, giving 7835500 degrees of freedom. This mesh determines a maximum relative error of

4% with respect to the finer grid used for the preliminary mesh test made for this analysis. A snapshot

of the used mesh is presented in Fig. 2. Steady solutions of discretized equations were carried-out by

applying an iterative dumped Newton-Raphson scheme [6], classically based on the discretized PDE

linearization by a first-order Taylor expansion. Algebraic systems of equations coming from

differential operators discretization have been solved by an Unsymmetrical Multi-Frontal package, a

direct solver particularly efficient in order to solve unsymmetrical sparse matrixes by a LU

decomposition method. For time-marching simulations we adopted an Implicit Differential-Algebraic

(IDA) solver based on a variable-order and variable-step-size Backward Differentiation Formulas

(BDF) [6]. Computations were carried-out on computational node made of 2 x 64 bit quad-core

processors speeding up to 3.3 GHz of frequency and handling 512 GB of RAM.

Figure 2. Mesh of the numerical model.

4. Results

Results were carried-out for different geometrical and constitutive configurations of the power

module. In particular, different layer thickness were investigated and different physical properties

were considered in solving the governing equations. In the following we present an extract of those

results.

4.1. Thermo-mechanical analysis results

The thermal distribution obtained for a steady simulation of the module, when all devices are

switched on and the maximum power (50 W for each IGBT and 10 W for each diode) is supplied

through chips front metals, is shown in Fig. 3a (left side). In the enlargement of the picture, we report

the maximum junction temperature value (Tjc(MAX) = 41.6 °C) detected by simulation on the front

metal of IGBT. The von Mises stress distribution, caused by the thermal load in Case A configuration,

is shown in Fig. 3b (right side). The maximum value of von Mises stress computed for each module

layer was compared to the ultimate strength of the constitutive materials. From comparison, tensile

resistance results widely verified in spite of the worst thermal case considered.

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(a) (b)

Figure 3. Thermal map [°C] (a) and stress distribution [MPa] (b) on the device and enlargements close

to the central power island (Case A).

4.2. Thermal cycle test analysis results

Thermal states computed in Case B configuration were exploited for estimating the effective plastic

strain distribution. The maximum value of

ε

p was detected on the solder layer, joining the baseplate

and the packed DBC. In particular, the most critical value of the effective plastic strain was detected in

correspondence of the solder DBC corners. This is maybe due to the geometrical singularity.

Fig. 4a (left side) shows the effective plastic strain distribution in proximity of one of the solder

DBC corner, where the highest value of

ε

p was found in both environmental thermal conditions (Tc and

Th). This result well agrees with experimental evidences obtained by experimental activities developed

on the power module. Fig. 4b (right side) shows two front-views of the module taken by a Scanning

Acoustic Microscope (SAM). Pictures were taken at different time instants during a “thermal cycle”

testing activity on the module. Environmental conditions applied in the climatic rooms during the

experimental tests correspond to thermal levels used in computations. From experimental data

reported in Fig. 4b it is possible to observe the damage produced on the module by the cyclic thermal

load, in particular on the DBC solder. White regions (highlighted by the red arrows in the Fig. 4b)

represent portions of the module where contact between layers fails. As attended, those regions were

found in correspondence of the solder DBC corners. This establishment well agrees with some other

findings of literature [7, 8].

As previously mentioned, from plastic strain evaluation it is possible to numerically assess the

potential number of cycles to failure. In consequence, we were able to estimate the expected number

of cycles to failure for SnAgCu solder layers, that are well-known the weakest part of the module from

this point of view. From our investigation, the fatigue life prediction is approximatively 1632 cycles

for the solder die and 383 cycles for the solder DBC. Those results are in agreement with experimental

evidences (solder DBC damaged between 300 and 600 cycles, solder die damaged after 1100 cycles).

Successively a comparison study between SnAgCu and SnPb solder joints fatigue life was performed.

From results, the fatigue life prediction for SnPb solder die is approximately 162672 cycles and 3071

for solder DBC. Those results well agree with evidences in literature showing that the fatigue life of

SnAgCu solders is considerably lower than that of SnPb solder layers [9]. Experimental results that

have been found in ref. [9] in similar tests indicate that at high board level strains SnPb solder out

performs SnAgCu solder; in particular, the characteristic life was 19500 cycles for SnPb solder and

7730 cycles for SnAgCu solder.

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(a) (b)

Figure 4. Effective plastic strain for one of the solder DBC corner, evaluated for Tc=125 °C (Case B)

(a). SAM front-view of the module during a “thermal cycle” testing (b): pictures are reported for

initial conditions (picture on top) and after 300 cycles (bottom picture). Red arrows indicate some

detected damaged regions.

5. Conclusions

This work highlights the opportunity to exploit a numerical approach in order to simulate, from one

hand, the thermo-mechanical behaviour of power module and, from another one, the fatigue life of

module performing thermal cycles a two environmental fixed temperature inside a climatic test room.

From results, it appears that thermal and thermo-mechanical levels are lower than potential critical

values for constitutive materials, even in the worst working conditions. The fatigue life prediction

results in good agreement with literature evidences and experimental findings. Module portions

subjected by the highest plastic strain are regions closed to solder DBC corners. This is maybe due to

the geometrical singularity. The fatigue life of SnAgCu solders is considerably lower than that of SnPb

solders: for solder DBC it is one order of magnitude shorter, and two orders shorter for solder die.

References

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[3] Sun Z, Benabou L and Dahoo P R En. Fract. Mech. 107 pp 48-60

[4] Shinohara K and Yu Q 2011 Int. J. Fatigue 33 pp 1221-34

[5] Manson S S 1966 (New York: McGraw-Hill)

[6] Hindmarsh A C, Brown P N, Grant K E, Lee S L, Serban R, Shumaker D E and Woodward C S

2005 ACM Trans. Math. Software 31 pp 363-396

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