Prognostic Reliability Analysis of Power Electronics...

International Journal of Performability Engineering Vol. 6, No. 5, September 2010, pp. 513-524.

© RAMS Consultants Printed in India

________________________________________

*Corresponding author’s email: [email protected] 513

Prognostic Reliability Analysis of Power Electronics Modules

CHUNYAN YIN1*

, HUA LU1, MAHERA MUSALLAM

2, CHRIS BAILEY

1 and

C MARK JOHNSON2

1School of Computing and Mathematical Sciences, University of Greenwich

30 Park Row, London, United Kingdom 2School of Electrical and Electric Engineering, University of Nottingham,

University Park, Nottingham, United Kingdom

(Received on October 02, 2009, revised on March 27, 2010)

Abstract: This paper describes a physics-of-failure (PoF) based prognostic method for

power electronics modules (PEMs). Differing from the traditional reliability prediction

methods, this approach allows the reliability performance of PEMs to be assessed in real

time. Four techniques have been used to develop this method, they are: (1) Compact

electro-thermal model (2) Rainflow counting algorithm (3) Compact thermo-mechanical

model and (4) Lifetime consumption model. As a demonstration, this method has been

applied to a typical IGBT half bridge module and solder joint fatigue was assumed as the

major failure mechanism. In this application, a random electric current load profile was

generated in laboratory environment and used to derive the thermal loading condition for

the module. Due to the randomness of the load profile, rainflow counting method was

used to reduce the continuous load profile into discrete sets of thermal cycles. The damage

induced in each temperature cycle was calculated via a compact thermo-mechanical

model, and used in the lifetime model to calculate the PEMs lifetimes under simple cyclic

loading conditions. Based on these predicted lifetimes and the linear damage accumulation

rule, the total consumed life of the PEMs over the whole period of usage was predicted.

Keywords: prognostic, reliability, power modules, physics-of-failure

1. Introduction

Power electronics modules (PEMs) are power electronics components that contain power

semiconductor devices such as the Insulated Gate Bipolar Transistor (IGBT) and

Thyristor. These components are used in industries and domestic appliances for the

control and conversion of electric currents. Due to the harsh working environments of

PEMs, the required reliability standard of such components is often very high [1][2].

In recent years, physics-of-failure (PoF) based reliability analysis and prediction

methods have played an increasingly important role in the PEM design and failure

analysis. By combining computer modeling and failure mode/mechanism analysis

methods, the reliability of PEMs can now be predicted for some common wear-out failure

mechanisms such as solder joint fatigue and wirebond lifting. The results of this modern

prediction method can be used to identify critical design parameters, and compared to

traditional handbook methods they have the potential to provide end users with more

accurate estimate of the mean lifetime of the components under qualification test

conditions or mission profiles. However, the qualification test conditions and mission

profiles are often made up of predetermined cyclic load profiles that in general are very

different from the load profiles in service loading condition.

Chunyan Yin, Hua Lu, Mahera Musallam, Chris Bailey and C Mark Johnson

514

Under in-service load conditions, load level and frequency change over time

irregularly. Obviously, this makes lifetime prediction methods that are based on

predetermined constant loading conditions not adequate for estimating the remaining life

of the components under the actual application conditions and this is where prognostic

reliability analysis method can play an important role.

The existing prognostic approaches for electronics can be classified into the following

four categories: (1) Fuses or Canaries, (2) Data Driven Methods, (3) Model Driven

Methods, and (4) Fusion technique, which is an integration of the above three methods.

Among these four types of techniques, Model Driven Methods such as the PoF lifetime

model based prognostic methods have been widely used for the lifetime prediction of

products where fatigue/wear out is the major failure mechanism [3][4]. In this method, the

loading conditions of the components are monitored for changes and the real-time

consumed/remaining lifetime of PEMs can be calculated at any time. In this work, this

kind of prognostic method has been applied to a typical IGBT half bridge module used in

aircraft applications, as shown in Figure 1. For PEMs, solder joint fatigue, wirebond

failure and substrate delamination etc., have been identified as the major failure

mechanisms [5][7]. In this work, however, only solder joint fatigue was taken into account

in the analysis.

2. Overview of the Prognostic System

The prognostic method presented in this paper is a model driven approach where PoF

models are used on the data gathered from the IGBT module to estimate the remaining

life. This method consists of four steps:

(1) Compact electro-thermal model: A reduced order electro-thermal model is

constructed to establish the relationship between the power dissipation and the

temperature in the PEM. Such relationship can be used for the calculation of the

junction temperatures and temperatures at each interface inside power modules

under variable operation conditions in real time.

(2) Classification of thermal cycles: Because the stochastic nature of the loading that

has been applied, the temperature profile consists of temperature cycles with

different amplitude and mean value. Cycle counting algorithm such as the

rainflow method is used to analyze the temperature profile, so that the number of

cycles for any temperature range can be calculated.

(3) Compact thermo-mechanical model: A reduced order thermo-mechanical model,

which relates the damage indicator (∆εp) to the temperature changes, is

constructed. This model enables the fast calculation of the damage indicator ∆εp

Figure 1: The IGBT power module that was used in the experiment

Prognostic Reliability Analysis of Power Electronics Modules 515

in the PEM. Such damage information can be used in the following lifetime

consumption model for lifetime prediction.

(4) Lifetime consumption model: This relates the lifetime consumption or remaining

life in the PEM to the damage indicators. PoF lifetime models and the linear

damage accumulation rule are applied in this model. The functional block diagram of the whole system is show in Figure 2.

3. Construction of the Compact Electro-thermal Model

High temperature and cyclic temperature changes can dramatically reduce the lifetime

of power electronic modules. Therefore, real time systems which can predict the

temperature inside the PEMs are highly desirable in reliability analysis. In this work, a

real time compact thermal model which represents the relationship between the power

dissipation and junction temperatures has been constructed. Figure 3 illustrates the real

Figure 2: Function diagram of the prognostic system

30%

T (°C)

1 11 12 1

2 21 22 2

1

1 2 2

_ 2

_ 1

1 2

J N

J N

in

JN N N NN in

A

Solder

Substrate Nin

Solder

Baseplate M M MN

T a a a

T a a a

P

T a a a PT

T

T P

T

T a a a

= +

K

L

M M

L

M

M

M

Analyse Load Profile

(Rainflow Counting Algorithm)

Calculate Damage

(Compact Thermo-mechanical Model)

Generate Load Profile

(Compact Electro-thermal models)

Calculate Life Consumption

(Lifetime consumption Model)

Damage Metric (Strain, Energy etc)

516 Chunyan Yin, Hua Lu, Mahera Musallam, Chris Bailey and C Mark Johnson

time implementation of the compact thermal model. This model was developed in

MATLAB/Simulink using the real time software toolbox and implemented on a DSPACE

real time system that incorporates a Pulse Width Modulation card [8].

In order to develop the compact thermal model, the junction temperature of each

active component was measured using infrared thermometer for given power dissipation.

In locations that are hidden from view, numerical analysis using FLOTHERM software

package has been carried out to predict the temperatures. The thermal parameters of the

heat transfer path from any heat source, i.e., the dies, to the hidden layers were

determined. In the end, an N by M transfer function matrix was constructed to represent

the thermal behavior of the whole module as shown in (1), where the terms a11….aMN

represent the transfer function of each heat transfer path, TA is the ambient temperature,

P1in… PNin are the heat sources, TJ1…TJN are the junction temperatures and T_solder_2

etc., are temperatures at other locations within the module [9].

Once the transfer function is constructed for a certain type of PEM, Equation (1) can

be used as an efficient and simple way to calculate the junction temperature and the

temperature inside the PEM in real time. The efficiency and accuracy of this compact

thermal model was tested using several test cases and the details can be found in [8][9].

Figure 3: Real time implementation of compact thermal model

Converter

Controller

Power

Electronic

Converter

Power

dissipation in

Component #1

Power

dissipation in

Component #N

Compact

thermal

model

fs/N

Estimated

temperature

s

1 11 12 1

2 21 22 2

1

1 2 2

_ 2

_1

1 2

(1)

J N

J N

in

JN N N NN in

A

Solder

Substrate Nin

Solder

Baseplate M M MN

T a a a

T a a a

P

T a a a PT

T

T P

T

T a a a

= +

K

L

M M

L

M

M

M

L


The output of the compact thermal model is a time series of temperatures that change

with the input electric current and the environment conditions. Cycle counting algorithms

such as the rainflow counting method, can be used to analyze the temperature vs. time

data to extract the occurrence frequencies of different thermal cycling ranges. This

information can then be used in the reduced-order thermo-mechanical model and the

lifetime prediction model to calculate the accumulated physical damage in the PEM. The

rainflow counting method is well described in the literature [10][14].

4. Construction of the Reduced Order Thermo-mechanical Model

4.1 Computational Modeling of the IGBT power module

A typical PEM consists of several layers of different materials that are assembled

together in the packaging process to form power electronic circuits and the mechanical

structure. Due to the mismatch of the coefficients of thermal expansion (CTE) in the

structure, high level stress can be created during temperature changes which can cause

crack initiation, propagation, and eventually failure, especially at the interface between the

different materials. In qualification tests and in-service conditions, the solder joint

degradation and wire bond lift-off are identified as the most common failure mechanisms

in the PEMs [5][6][7].

The reliability of PEMs can be predicted using finite element (FE) method. For low

cycle fatigue failure, this is achieved by calculating the stress and strain in the solder joint

under cyclic thermal loading and then using the accumulated plastic strain to predict the

lifetime of the structure.

The internal structure of the IGBT power module is shown in Figure 4. It consists of

nine layers and five different materials. There are two layers of solder connections, one is

underneath of the silicon die and another one connects the substrate to the base-plate. A

2D FE model of this device was constructed, as shown in Figure 5. The total number of

elements is about 8000.

Heat sink

Base plate

Substrate

Die

Silicon

SnAg solder

Copper

Alumina

Thermal grease

Figure 4: Internal structure of studied IGBT module


This 2D model represents the cross section of the device along the length direction. A

previous study [11] has already proved that there is almost no difference in the von-Mises

stress prediction along the solder substrate interface in 2D and 3D models. In the model,

the thermal grease layer and heat sink were neglected. Instead, their existence was

represented by appropriate boundary conditions on the bottom surface of the base-plate,

i.e., the surface is free to move on the XZ plane, but fixed in the Y direction. A small

crack was also included in the model.

In the simulation, nonlinear material properties of the SnAg solder were used. The

visco-plastic/creep constitutive equation for the SnAg alloy is

( )sinh exp (2)n

cr e

QA

RTε ασ

− = ×

&

where R is the gas constant, T is the temperature in Kelvin, σe is the von Mises equivalent

stress. A, n, α, Q are material constants and their values are listed in Table 1.

Table 1: Creep parameters for solder material [11]

A(s) n α (1/MPa) Q/R

SnAg 9.00E+05 5.5 0.06527 8690

The measured IGBT junction temperature in the lab environment was used as the

loading profile in the computer simulations, as shown in Figure 6.

Figure 6: Measured IGBT junction temperature

Figure 5: 2D FE model of half of the IGBT module

IGBT junction temperature measurements (ºC)

20

30

40

50

60

70

80

0 50 100 150 200

Time (s)

Tem

pera

ture

(C)


As mentioned earlier, there are two solder interconnects in the IGBT module. The

lifetimes of these solder layers depend on the stress/stain level, size of the contact area and

temperature variation. Since the solder interconnect underneath the silicon die has much

smaller contact area than the one underneath the substrate in this application, it has been

found to be the interconnect that failed first. Therefore, the damage indicator for the PEM

was defined as the accumulated plastic strain in the solder interconnect underneath the

silicon die. The distribution of the accumulated plastic strain in this solder interconnect at

the end of the third temperature cycle is shown in Figure 7.

4.2 Design of Experiments (DoE) Method

FE is a powerful tool in reliability prediction, but it is not suitable for real time

analysis because it is time consuming. In order to solve this problem, an approximate

compact model has been built using the FE results and the Design of Experiment (DoE)

method. The purpose of DoE analysis is to identify the set of design points at which finite

element analysis will be undertaken to provide predictions for constructing the response

surface (i.e., reduced order model). In this study, a full quadratic function was used to

approximate the response surface. If the number of design variable is two, the

construction of such a polynomial function requires solving linear equations with 6

unknown variables. This means that at least 6 experimental points are required to identify

these coefficients. The DoE method that has been used in this analysis is a composite, full

factorial, D-optimal design with 9 design points.

The two design variables investigated are the mean temperature Tm and temperature

variation ∆T in one electrical switching cycle. The accumulated plastic strain ∆εp in the

solder interconnect was chosen as the damage indicator. As shown in Table 2, 9 points in

the design space were chosen and finite element calculations were carried out at these

design points. The predicted ∆εp and its natural logarithmic values are shown in Table 2.

Die

Substrate

Solder

Crack tip

Figure 7: Accumulated plastic strain distribution


Table 2: Design points and correspondent plastic strain

Run No ∆T Tm ∆εp Ln(∆εp)

1 6 38 8.7e-7 -13.954

2 6 48 1.81e-6 -13.22

3 6 58 3.4e-6 -12.59

4 18 38 5.3e-5 -9.845

5 18 48 6.7e-5 -9.611

6 18 58 8.65e-5 -9.355

7 30 38 5.1e-4 -7.581

8 30 48 8.1e-4 -7.118

9 30 58 1.17e-3 -6.75

4.3 Response Surface (RS) Modeling

Once the responses at the designs points are obtained, the next step is to construct an

approximation model to the accumulated plastic strain ∆εp using the least square fitting

technique. The constructed response surface equation of ∆εp related to the two design

parameters is expressed as:

The quality of the RS approximation can be evaluated using a number of techniques in

order to estimate its predictive power and accuracy. The one that is used here is the

coefficient of determination R2, the higher the value of R

2, the better the fitting of the

approximation model. For the above RS function, R2=98.94%. The definition of the

coefficient of determination can be found in Ref. [12].

In order to identify a better fitting function, the RS function of Ln(∆εp) related to the

two design parameters was also constructed, which is

The R2 of this RS function is 99.84%, which indicates that this is a better fitting

function than equation (3) in this design space. Therefore, the RS function (equation 4)

was used to calculate the accumulated plastic strain ∆εp approximately at any points in the

design space, and the predicted ∆εp can be used subsequently in the lifetime prediction

model to estimate the reliability of the PEM in terms of number of cycles to failure. Once

the reduced order model is constructed finite element simulations are not needed any more

and this will greatly reduce the computing time.

5. Lifetime consumption calculation

In order to calculate the lifetime of the solder interconnect, the following strain based

lifetime prediction model for SnAg solder material was used.

where L (mm) is the length of the solder interconnect, NL is the number of cycles needed

for the crack length to reach L, ∆εp is the accumulated plastic strain per cycle, α and b are

material constants, which are 0.00562 and 1.023 respectively [11].

2

2

(558.2 115.8 1.22 2.396

0.1158 1.335 ) /10 6 (3)

p m

m m

T T T

T TT e

ε∆ = − ∆ − + ∆ −

+ ∆

2

2

( ) 15.16 0.4447 0.07882 0.004081

0.00145 0.0009074 (4)

p m

m m

Ln T T T

T TT

ε∆ = − + ∆ − − ∆

+ − ∆

(5)( )

L b

p

LN

a ε=

∆


In this particular application, the size of the solder interconnect underneath of the

silicon die is 12 by 12 mm2, the damage criteria of a solder interconnect was defined as

the time it took for the crack to have an area that is 20% of the total solder interconnect

area. Accordingly, the length to crack (L) in the lifetime prediction model was defined as

0.635 mm. Equation (5) was used to calculate the PEM lifetimes under constant loading

conditions. Together with the number of temperature cycles calculated from rainflow

counting analysis, the life consumed for each constant loading profile was obtained. Based

on the Palmgren-Miner’s rule, the total life consumed in the PEM is calculated as:

number of cycles

the structure has been exposed to the ith load profile, which can be achieved from rainflow

counting analysis, Nfi represents the expected lifetime for the ith load profile, which can be

calculated from the stain based lifetime prediction model, i.e., equation (5).

6. Application Example

The above prognostic method was applied to the IGBT power module. In order to take

into account the stochastic property of the loading profile in the actual application

environment, a load profile which consists of a series of steps of random amplitude and

width was created, as shown in Figure 8.

The transfer function matrix (equation 1) was constructed for this IGBT power module

and applied to the above loading profile. The estimated solder layer temperature under this

loading condition is shown in Figure 9.

This temperature profile, which is considered as one load cycle afterward, consists of

cycles of different temperature change amplitudes and mean values. The rainflow

counting algorithm was applied to extract the numbers of cycles with certain temperature

ranges.

Figure 8: Sample of load current profile [13]

31 2

1 2 3

.... (6)k

i k

i fi f f f fk

N N NN NLC

N N N N N= = + +∑


After the PEM went through this loading profile for five times, the life consumed was

predicted using the above prognostic method, and the results are summarized in Table 3.

In order to reduce the size of the table, the contributions from the small temperature

change (∆T < 5°C) cycles were ignored, these temperature cycles often result in very

small accumulated strain per cycle and have little contribution to the whole lifetime

consumption. Table 3: Output from the PoF based prognostic method

∆T(°C) (Temperature amplitude) 24.6 25.4 12.4 11.7 < 5

Tm(°C) (Mean temperature) 53.2 53.1 48.1 48.3

No. of cycle (rainflow algorithm) 5 5 5 5 29

Predicted damage ∆εp 3.47e-4 4.02e-4 1.29e-5 1.06e-5

Predicted cycle to failure Nf 3.92e5 3.38e5 1.13e7 1.39e7

Life consumed 1.27e-5 1.48e-5 4.42e-7 4.72e-7

Life consumed total 0.000284%

The lifetime consumption due to the historical usage also indicates how much lifetime

the device has got left if the loading conditions remain the same.

7. Conclusions

PEMs are often used under severe working conditions and in hash environment, the

reliability performance of such devices is a big concern. Traditional reliability methods

developed using constant loading conditions do not take into account the randomness of

service loading conditions, therefore they are not suitable to be used for lifetime

prediction for the products in real time. The prognostic method presented in this paper

allows the reliability performance of PEMs to be assessed in real time. It was developed

using four techniques: Compact electro-thermal model, Cycle counting algorithm,

Compact thermo-mechanical model and Lifetime model. As a demonstration, this method

was applied to an IGBT module for aerospace applications. A random load current profile

Figure 9: Estimated solder layer temperature [13]

IGBT Substrate Solder temperature estimates (°C)

Ambient temperature (°C)


was generated in the laboratory environment; the accumulated damage in the PEM over

this usage period was predicted.

Acknowledgment: The authors would like to acknowledge the financial support of the

Innovative electronics Manufacturing Research Centre (IeMRC) for supporting the project

“A Prognostic and Diagnostic Environment for High Reliability Electronic Systems”

(SP/06/03). The authors would like to thank project partners Goodrich Corporation, GE

Aviation, Raytheon System Ltd, Dynex Semiconductor Ltd, Flomerics Ltd, Areva T&D

Ltd and Semelab Ltd for their contribution to the project.

References

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Chunyan Yin, Hua Lu, Mahera Musallam, Chris Bailey and C Mark Johnson

524

Chunyan Yin received her Master degree in material engineering from Harbin Institute of

Technology, China in 1999 and Ph.D. degree in computational science and engineering

from the University of Greenwich, U.K., in 2006. Since 2007, she has been working as a

research fellow within the School of Computer Sciences and Mathematics at the

University of Greenwich. Her current research interests are prognostic, reliability

predictions methods for power electronics.

Hua Lu received his M.Sc. degree in condensed matter physics from Wuhan University,

China in 1988, and he received his Ph.D. degree in computational physics from the

University of Edinburgh, U.K., in 1992. His current research areas are computer

modeling of electronic components, reliability prediction methods, design and

manufacturing optimization methods and their applications. He is now working as a

Reader (Associate Professor) in computational science at the University of Greenwich.

Mahera Musallam received her B.A. degree in electrical engineering from Birzeit

University in Palestine. In 2001 and 2005 she got her Masters degree in ‘Automation and

Control’ and her Ph.D. Degree in ‘Power Electronics and Control’ respectively from the

school of electrical and electronic engineering at Newcastle Upon Tyne University, U.K.

Since 2006 she has been a Research Fellow with the Department of Electrical and

Electronic Engineering, University of Nottingham, U.K. Her current research interests are

prognostics, thermal management and reliability of power electronics in real-time

applications.

Chris Bailey (for his biographical sketch, please refer to page 512 of this issue).

C Mark Johnson received the B.A. degree in engineering and the Ph.D. degree in

electrical engineering from the University of Cambridge, U.K., in 1986 and 1991

respectively. From 1992 to 2003 he was a Lecturer and later Reader at the University of

Newcastle where he led research into Silicon Carbide electronics. In 2003, he was

appointed as Rolls-Royce/RAEng Research Professor of Power Electronic Systems at the

University of Sheffield and in 2006 he was appointed to a personal chair at the University

of Nottingham, where he leads research into power semiconductor devices, power device

packaging, reliability, and thermal management, power module technologies and power

electronic applications. He is a member of the executive committee of the UK IeMRC and

is project manager for the Flagship Project in Power Electronics.

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