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Thermal impedance spectroscopy of power modules A. Hensler a,⇑, D. Wingert a, Ch. Herold a, J. Lutz a, M. Thoben b a b

Chemnitz University of Technology, Chemnitz, Germany Inﬁneon Technologies AG, Warstein, Germany

a r t i c l e

i n f o

Article history: Received 30 May 2011 Received in revised form 23 June 2011 Accepted 28 June 2011 Available online 23 July 2011

a b s t r a c t In this paper, a method of thermal impedance spectroscopy for power modules is presented. This method enables a high resolution non-destructive analysis of the power module by means of electrical measurement and subsequent mathematical evaluation. The result provides a separation of partial thermal resistances corresponding material layers and facilitates a plausible estimation of geometrical dimensions of the power module package within the heat ﬂow path. This method is applied for localization of failures during power cycling test. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction The reliability of power modules at power cycling load is determined besides bond wire lift-off by deterioration of different layers within heat ﬂow path (Fig. 1). In order to detect this failure during reliability tests, today the quasi steady state thermal resistance between junction and heat sink or coolant is monitored. This measurement delivers no information which layer of the power module is degraded. Thus for detailed information about speciﬁc failure mechanism, subsequent time consuming and often destructive failure analyses are needed, e.g. metallographic preparation. Thermal impedance spectroscopy of power modules promises a simpler and faster method for the failure localization. 2. Method description The thermal impedance spectroscopy analysis method is based on the method from [1] used in the ﬁeld of microelectronics. For the power module application this method was modiﬁed. With modiﬁcations the derivative of the Zth(t) function was avoided. This method is described in the following.

reached, the load current is switched off and the cooling behavior is measured until the junction temperature is equal to the reference temperature. The junction temperature Tj(t) is measured with the VCE(T)-method as described in [1]. The sensor for the reference temperature is usually a thermocouple. Power losses Pv are determined by means of forward voltage and load current of the power device, which are measured shortly before load current turn off at the end of the heating phase. With determined values Tj(t), Tref(t) and Pv the thermal impedance function is calculated with the following equation:

Z th;cooling ðtÞ ¼

T j ðtÞ T ref ðtÞ Pm

ð1Þ

The Zth,cooling(t) function describes the cooling behavior of the junction. With the assumption that the cooling curve describes analogously the heating behavior of the junction following transformation can be performed to determine the heating thermal impedance function Zth,heating.

Z th;heating ðtÞ ¼ Z th; cooling ðtÞ ð1Þ þ Z th; cooling ðt ¼ 0Þ

ð2Þ

This function is the starting point for the thermal impedance spectroscopy method. For further steps the heating function is deﬁned as the general thermal impedance Zth(t).

2.1. Deﬁnition of thermal impedance spectrum

Z th ðtÞ ¼ Z th; heating ðtÞ

The transient thermal behavior of power modules is usually given between the junction and a reference temperature Tref (case, heat sink or ambient). This function is determined by means of step response. For it the power device is exposed to an active power pulse Pv generated with load current. After the steady state is

In applications this function is used to estimate the junction temperature of the power device depending on power losses and pulse time. This measured transient thermal behavior is approximated with an equivalent Foster network as shown in Fig. 2. The mathematical description is given in the following equation

⇑ Corresponding author. E-mail address: [email protected] (A. Hensler). 0026-2714/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.microrel.2011.06.039

Z th ðtÞ ¼

n X i¼1

ð3Þ

t

Ri ð1 e si Þ;

si ¼ Ri C i

ð4Þ

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0,15 0,10 0,05 0,00 1,0E-05 1,0E-04 1,0E-03 1,0E-02 1,0E-01 1,0E+00 1,0E+01 1,0E+02 Fig. 1. Typical power module with base plate.

Datasheet

Solver

Fig. 3. Zth(t) of a standard power module and corresponding approximation.

ðxj ni Þ aji ¼ 1 ee

Eq. (8) can be written as the following matrix equation Eq. (10). In this equation vector ‘‘z’’ is the measured thermal impedance Zth(t) and ‘‘A’’ the known matrix given in Eq. (9). The vector ‘‘r’’ is the thermal impedance spectrum to be calculated.

Fig. 2. Equivalent Foster network.

In most cases few RC elements are sufﬁcient to describe the thermal system properly, e.g., in data sheet for the thermal impedance between junction and case (bottom side of the base plate) four elements are used. In Ref. [2] from Eq. (4) the time-constant spectrum is derived. The deﬁnition is: time constants si are on the x-coordinate, magnitudes Ri are on the y-coordinate. This deﬁnition is used for the description of the thermal impedance spectrum. Example of this function is shown in Fig. 4. 2.2. Calculation algorithm of thermal impedance spectrum Typically the thermal systems of power modules are described with few RC elements of the equivalent Foster network. Values of the RC elements are calculated using the method of least squares. Due to complex thermal processes, e.g., thermal spreading, thermal systems are of ‘‘distributed nature’’. These networks are characterized by a continuous spectrum of time constants [2]. Here, the target of the mathematical extraction of the thermal impedance spectrum is to achieve a solution with many RC elements of the Foster network to reproduce the continuous thermal spectrum. The basis for the mathematical extraction of the thermal spectrum is a measured or simulated Zth(t) function from Eq. (3). The ﬁrst step is the introduction of the logarithmic time axis and time constant axis, Eqs. (5) and (6).

x ¼ lnðtÞ

ð5Þ

n ¼ lnðsÞ

ð6Þ

With these logarithmic deﬁnitions the Zth(t) function from Eq. (4) is expressed with Eq. (7), which represents discrete convolution. Thereby the index ‘‘j’’ discretize the time axis x and index ‘‘i’’ the time constant axis n.

Z th ðxÞ ¼

n X

ð7Þ

Other notation of Eq. (7) is as follows:

Z th ðx1 Þ B. B .. B B B Z th ðxj Þ B B. B. @.

1

0

a11 C B. C B .. C B C B C ¼ B aj1 C B C B. C B. A @. am1 Z th ðxm Þ

where as aij is

. . . a1i .. . . . . aji

. . . ami

Z ¼Ar

ð10Þ

For the solution of this equation the ‘‘Bayesian deconvolution’’ algorithm is used as described in Ref. [3]. The implementation of this algorithm is given with Eq. (11), where ‘‘p’’ is the number of iterations.

X aji r zj 1 i ¼P P ðpÞ j a ji j k ajk r k ðpÞ

ðpþ1Þ

ri

ð11Þ

The solver algorithm for the extraction of the quasi continuous thermal impedance spectrum was veriﬁed with the Zthjc(t) curve given in the data sheet of a standard power module. Fig. 3 shows the approximation of the algorithm in comparison to the original Zth(t) function. Fig. 4 shows the quasi continuous thermal impedance spectrum calculated with described solver algorithm. This function represents the Foster network with n = 100 RC elements. This solution was reached after 2,0E4 iterations of Eq. (11). 2.3. Differential and cumulative structure function In [2,4] two functions are given for the physical description of the heat ﬂow path: the differential and cumulative structure function. First, the calculated thermal impedance spectrum (Foster network) has to be transformed into Cauer network, Fig. 5. This transformation is performed with the method of the recursively rapid Foster–Cauer circuit transformation described in Ref. [5]. With ri and ci values of the Cauer network the structure functions are calculated with following equations. Eq. (12) gives the

2,5E-02

ðxj ni Þ Rðni Þ 1 ee

i¼1

0

ð9Þ

1 10 Rðn1 Þ . . . a1n C B. .. C C B . C C CB .. C CB B Rðni Þ C . . . ajn C C CB C B . . .. C C CB .. . . [email protected] . A . . . amn Rðnn Þ

2,0E-02 1,5E-02 1,0E-02

ð8Þ

5,0E-03 0,0E+00 -10,0

-8,0

-6,0

-4,0

-2,0

0,0

2,0

4,0

Fig. 4. Thermal impedance spectrum of a standard power module.

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r1

rn

c1

PV

Table 1 Material constants from [6].

cn

Fig. 5. Equivalent Cauer network.

Material

Heat conductivity k (W/(m K))

Volumetric heat capacity s (W s/(m3 K))

Si Cu A12O3 Solder

148 394 24 70

1.65E+06 3.40E+06 3.03E+06 1.67E+06

1,0E+07

Rthjc

1,0E+06

Table 2 Relation of measurement points to material layers.

5

1,0E+05 1,0E+04 1,0E+03

4

2 1

3

1,0E+02 1,0E+01 1,0E+00 1,0E-01 0,00

0,02

0,04

0,06

0,08

0,10

0,12

0,14

1,0E+04

Rthjc 5

1,0E+02

1

2

3

4

5

Material K ((W2 s)/K2) C (W s/K)

Si 1.5E+01 2.4E02

Cu 1.5E+02 1.1E01

A12O3 3.4E+01 2.7E01

Solder 9.0E+02 1.8E+00

Cu 7.6E+04 1.3E+02

KðqÞ ¼ k s A2

ð14Þ

CðqÞ ¼ s A d

ð15Þ

where A is the heat conduction area, k is heat conductivity, s is volumetric heat capacity, and d is the thickness of material layer. Constants k and s of the package materials are listed in Table 1. Corresponding to Eqs. (14), (15) and material constants given in Table 1 marked measurement points of the construction functions can be referred to speciﬁc material layers of the power module from Fig. 1. Determined relations are shown in Table 2. Measured values K and C provide an estimation of the geometric dimension for heat ﬂow material layers. For example with the point ‘‘1’’ chip dimensions are determined in the following.

Fig. 6. Differential structure function of a 650 A/1200 V power module.

1,0E+03

Point no.

1,0E+01

K ¼ 1:5E þ 01 W2 s=K2 ! Asi ¼ 248 mm2

4 1,0E+00

3 1,0E-01

C ¼ 2:4E 01 W2 s=K2 ! d ¼ 59 lm

2 1

1,0E-02 0,00

0,02

0,04

0,06

0,08

0,10

0,12

0,14

Fig. 7. Cumulative structure function of a 650 A/1200 V power module.

deﬁnition of the differential structure function; Eq. (13) describes the cumulative structure function.

KðqÞ;

C ð qÞ;

Kn ¼

Cn ¼

cn ; rn n X i¼1

qn

n X

ri

In the considered power module two IGBT chips are in parallel. So the measurement leads to the chip of 11.1 mm 11.1 mm 59 lm. It conforms with good accuracy to the real power device (length = 11 mm, width = 11 mm, thickness = 70lm). Analogical estimation of other identiﬁed layers delivers plausible dimensions. Further, it can be identiﬁed, that the dominant partial thermal resistance is caused by the A12O3 layer. This partial Rth (part between point ‘‘3’’ and ‘‘4’’ in Fig. 6) amounts to 67% of the whole Rthjc. It is in agree to the real power module package [7].

ð12Þ

i¼1

ci ;

qn ¼

n X

ri

ð13Þ

i¼1

Both structure functions were calculated for the data sheet Zth(t) curve of the power module in Fig. 3. The two following diagrams, Figs. 6 and 7, show the results. Five points are marked in the diagrams. In Fig. 6 peaks, in Fig. 7 plateaus have to be considered. These points can be referred to speciﬁc material layers within the heat ﬂow path of the power module. From Ref. [4] following physical interpretations Eqs. (14), (15) of K and C are used for further considerations.

DUT

Fig. 8. DUT (IGBT of standard power module).

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1,0E+07

Rthja

1,0E+06 1,0E+05 1,0E+04 1,0E+03

∆

1,0E+02

Fig. 9. Measured temperature cycle of the junction.

1,0E+01

3. Experimental application

1,0E+00

The method was applied during power cycling tests for the localization of solder layer degradation within the heat ﬂow path of the power module. The device under test was a standard power module of Inﬁneon Technologies AG, Fig. 8. During the reliability test the DUT was loaded with active thermal cycles induced by cycling direct current. The temperature cycle of the junction is depicted in Fig. 9. Test parameters in detail are:

1,0E-01 0,00

0,05

0,10

DUT before Test

0,15

0,20

0,25

0,30

DUT aer Test

Fig. 11. Thermal impedance spectroscopy of DUT before and after test.

ILoad ¼ 400 A; ton ¼ 0:7 s; t off ¼ 3:1 s; T jmax ¼ 175 C; DT j ¼ 105 K During the test the steady state thermal resistance Rth between junction and coolant was measured. The trend of the Rth is shown in Fig. 10. At the end of the test the degradation process can be identiﬁed. However, this measurement provides no information which failure mechanism causes the Rth increase. Degraded layer can be identiﬁed with the thermal impedance spectroscopy. Before and after the power cycling test the DUT was analyzed with the described analysis method. For it the thermal impedance Zthja was measured between junction and coolant. This measurement was performed with the cooling curve technique. The power module was heated with load current of 220 A until the steady state. After it, the load current was switched off and the cooling curve of the junction was measured by means of VCE(T)-method. At that the coolant temperature was held constant. Power losses were measured at the end of the heating phase with values of the forward voltage and load current. The thermal impedance function was calculated with the Eq. (1). In the next step this measured cooling curve was transformed into the heating curve with the Eq. (2). This calculated heating thermal impedance function is the basis for the described method for the thermal impedance spectroscopy. The result for the tested power module is shown in Fig. 11. The failure within the heat ﬂow path can be clearly identiﬁed with the thermal impedance spectroscopy. The partial thermal resistance between chip and Cu (top side of the DCB) is increased

130 125 120 115 110 105 100 95 90 85 80

Fig. 12. Left: system solder layer after test without degradation, middle: degraded chip solder layer after test, right: unstressed chip solder layer.

after the test, marked with D. According to that the failure occurred within the chip solder layer. It was conﬁrmed with the scanning acoustic microscopy as shown in Fig. 12. Bright regions of the middle image show the degradation. 4. Conclusion The thermal impedance spectroscopy is an appropriate nondestructive failure analysis method for power modules. This method provides the separation of partial thermal resistances and a plausible estimation of geometric dimensions of material layers within the heat ﬂow path. With this method typical failures can be clearly identiﬁed in power cycling tests. The application of this method is not restricted only for failure analysis during power cycling tests. This method also can be applied for ﬁeld measurements, for controlling of power module production processes. For these purposes the accuracy of the thermal impedance spectroscopy should be veriﬁed. Acknowledgment The work was supported by grants of the German Federal Ministry of Economics and Technology (BMWi). References

0

10000

20000

30000

Fig. 10. Rth monitoring of the DUT.

40000

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