Lifetime Prediction for Power Electronics Module ... - IEEE Xplore

Lifetime Prediction for Power Electronics Module Substrate Mount-down Solder Interconnect a

Hua Lua†, Tim Tilforda, Chris Baileya, David.R.Newcombeb School of Computing and Mathematical Sciences, University of Greenwich, 30 Park Row, London SE10 9LS, UK b Dynex Semiconductor Ltd., Doddington Road, Lincoln, LN6 3LF, UK †Email: [email protected]

Abstract A numerical modeling method for the prediction of the lifetime of solder joints of relatively large solder area under cyclic thermal-mechanical loading conditions has been developed. The method is based on the Miner’s linear damage accumulation rule and the properties of the accumulated plastic strain in front of the crack in large area solder joint. The nonlinear distribution of the damage indicator in the solder joints have been taken into account. The method has been used to calculate the lifetime of the solder interconnect in a power module under mixed cyclic loading conditions found in railway traction control applications. The results show that the solder thickness is a parameter that has a strong influence on the damage and therefore the lifetime of the solder joint while the substrate width and the thickness of the baseplate are much less important for the lifetime. Introduction Despite recent progress in new interconnect materials such isotropic/anisotropic conductive adhesives, copper/gold columns etc, solder materials remain the most commonly used interconnect materials. Consequently the reliability of solder interconnects is still crucial in most modern electronics products. For the electronics packaging industry one of the greatest challenges is to accurately predict the lifetime of these interconnects. In recent years, a lot of studies have been carried to predict the lifetime of BGA and flip chip solder joints using experimental and computer modeling method. For example, Syed [1] derived a lifetime model which relates the accumulated plastic strain per cycle or the accumulated plastic work density per cycle to crack propagation rate in BGA or flip chip solder joints using Sn37Pb or SnAgCu solder alloys. Similarly, Shubert etc also presented a lifetime model for SnAgCu solder joints [2]. Usually, when this type of lifetime model is used in lifetime prediction, the average damage, be it the plastic strain or plastic work density in solder joints is used. This is adequate in many situations because the solder joint area is small compared to the solder thickness and also because it is simply too difficult to include the effects of the damage distribution in solder joints with cracks. For solder joints with relatively large solder area, however, the damage distribution becomes a problem. First of all, the damage distribution may vary too much from the crack tip to the area without macroscopic cracks to make the averaged damage indicator value a poor representation of the fatigue process. Secondly, when a crack propagates in a solder joint, the distribution of the damage indicator value may change as a result. Therefore, in order to calculate the lifetime of the solder joint, it is necessary to take these two factors into account.

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In this work, the aim is to devise a method that can be used in lifetime prediction for solder interconnect with a relatively large area. The method is based on the Miner’s linear damage accumulation rule which states that for a structure under cyclic loads with a mixture of different amplitudes, failure will occur if the following condition is met: k

ni

∑N i =1

=1

(1)

i

where Ni is the lifetime for the ith load profile, ni is the number of cycles the structure has been exposed to the ith load profile, and k is the total number of load profiles [3]. To use this rule effectively, the properties of the damage distribution have been studied and these properties have made the prediction of lifetime in large solder interconnect relatively simple. In order to use this lifetime prediction method, a fatigue lifetime model for SnAg solder interconnect, has also been derived from experimental lifetime data. To demonstrate the application of this method, the lifetimes of a solder interconnect in a power electronics module (PEM) have been calculated for railway power electronics applications. Power electronic modules are widely used in the aerospace and automotive industries for the electrical power conversion and control. A typical power module consists of several layers of insulator, conductor and semiconductor plus some metal wires, encapsulations, busbars and the casing components [4]. Theses different materials are assembled together in the packaging process to form power electronic circuits and the mechanical structure. Since PEMs contain many different materials, they are highly inhomogeneous, and there are many interfaces in these devices posing a great challenge to their designers. The PEM component failure mechanism that will be discussed in this work is the fatigue of the solder interconnect of the substrate mount-down. This is the solder layer connecting the isolation substrate to the baseplate. It is an important component because solder joint fatigue is one of the major failure mechanisms in PEMs [5]. In Figure 1, the scanning acoustic micrograph shows that after 8000 cycles under a cyclic thermal loading condition, much of the solder interconnect has cracked. The solder interconnect functions as the mechanical support of the substrate and as the heat conduction path. In service conditions, if the cracked area is too large compared to the total solder-substrate interfacial area, the thermal resistance may become too high and the temperature of the components on the substrate will not work reliability. Figure 2 shows a schematic of the structure of this component.

Proceedings of HDP’07

Table I. Mechanical properties of the substrate mountdown component. The temperature T is in Celsius. E(GPa) CTE(ppm/K) ν Alumina 270 0.22 7.4 Cu 103 0.3 17.3 SnAg 54.05-0.193T 21.85+0.02039T

(a) Figure 1. Scanning Acoustic Micrograph of the isolation substrate solder joint (8000 cycles wth delta T of 80°C). The lighter area is the cracked area.

copper ceramic copper solder

(b)

copper baseplate

Figure 2. The cross section of the substrate mountdown solder interconnect. Numerical modeling method In this work, finite element analysis (FEA) method is used to calculate the stress, strain and damage indicators in solder under cyclic thermal-mechanical loading. The dimensions of the isolation substrate that has been analyzed in this work are 56x50mm2. The thickness of the ceramic, the copper and the baseplate are 0.38, 0.3 and 5 mm respectively. A 3D FEA model of the device is shown in Figure 3. Because of the symmetry only a quarter of the device need to be modeled. This model contains about 60,000 8-noded elements. Usually, for a static linear elastic FEA analysis, this model size is not considered excessively large for modern computers. But in this work many transient analysis simulations have to be run, and each analysis has to model at least three thermal cycles and each cycle has to be divided into many time steps and this means that total CPU time can be very long. Therefore, this 3D model has been used for a linear analysis for qualitative assessment of problem only. The mechanical properties of the materials are listed in Table I. In this linear analysis, an arbitrary thermal load of -120°C is applied and the resulting von Mises stress distribution is shown in Figure 3(b). The results show that for in the whole structure the stress is the highest in the ceramic. In the solder layer, the stress is the highest near the edge and at the copper-solder interface and this is where cracks initiate and propagate in thermal cycling tests (Figure 1).

Figure 3: (a) A quarter of the structure and (b) the stress distribution under thermal load. In the simulations that are used for lifetime prediction of the solder joint, a 2D FEA model is used. This model represents the cross section of the device along the length of the device. Figure 4 shows the mesh around the edge of the isolation substrate. A crack is included in the model because the solder joint area is relative large and crack initiation should be just a fraction of the total lifetime and crack propagation is more representative of the state of the solder interconnect during thermal cycling and in service. In this simulation nonlinear material properties of the SnAg solder are used. The visco-plastic/creep constitutive equation for SnAg alloy is, •

ε

cr

= A × sinh n (ασ e ) exp(

−Q ) RT

(2)

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 II [6]. Table II: Creep parameters for solder materials.

SnAg

A(s)

n

α (1/MPa)

Q/R

9.00E+05

5.5

0.06527

8690


0.018 0.016

crack

plastic strain per cycle

Cu Alumina ceramic Cu

Cu baseplate

crack length = 0.6 mm

0.014


0.012


0.010 0.008 0.006 0.004 0.002

Figure 4. The mesh of the 2D model near the crack tip.

0. 0

0. 4

1. 2 0. 8

1. 6

2. 4 2. 0

2. 8

3. 2

4. 0 3. 6

distance from crack tip (mm)

Figure 6: Accumulated plastic strain per cycle in front of the crack tip.

140 120 von Mises Stress (MPa)

4. 4

4. 8

0.000

100

3D 2D

80 60 40 20 0 0

1

2 3 4 distance from edge (mm)

5

6

Another property of the damage distribution for a large area solder interconnect is that the size of the substrate has limited effect on the distribution in the solder joint. As shown in Figure 7, for a fixed crack length of 0.6 mm, the damage profile in front of the crack tip does not change as the substrate size changes from 28 to 56 mm. Therefore, the damage profile calculated for the 28 mm substrate can also be used for lifetime prediction of any substrate size in this size range. But of course, this conclusion is made for this particular range of substrate sizes, and it is expected to be invalid if the substrate becomes too small.

Figure 5. The von-Mises stress value along the soldersubstrate interface in 2D and 3D models.

0.016 plastic strain per cycle

0.014 0.012

Substrate size=56 mm

0.010

Substrate size=28 mm

0.008 0.006 0.004 0.002 0.000 4. 8 4. 4 4. 0 3. 6 3. 2 2. 8 2. 4 2. 0 1. 6 1. 2 0. 8 0. 4 0. 0

The damage indicator used in this work is the accumulated plastic work per thermal cycle, ∆εp. This quantity can be determined through experiments or computer modeling. Generally speaking, the distribution of ∆εp changes with location as well as the time as the crack develops in a solder joint. For large area solder joints, however, the distribution has a special characteristic that can be exploited to simply the lifetime calculation. As shown in Figure 6, the accumulated plastic strain distributions in models with different crack length are almost identical. This proves that the damage indicator value at a location on the crack path, i.e. the soldersubstrate interface, is only dependent on its distance to the crack tip, not the crack length. Consequently, only one damage distribution for a fixed crack length needs to be obtained from the modeling and it can be used for models with any crack length.

0.018

distance from crack tip

Figure 7. The distribution of the accumulated plastic strain per cycle in the 28 mm and 56 mm substrate. To quantify the impact of the dimensional changes on the damage in the substrate mount-down solder interconnect, a simple sensitivity analysis has been carried out. Three geometric parameters have been chosen for this analysis. They are the solder thickness (x1), substrate width (x2) and the baseplate thickness (x3). A composite design of experiment method has been used to select 15 points in the design space and finite element analysis simulations are carried out at these


points. The resulting values of accumulated plastic strain per cycle, ∆εp, for all the design points are used for a quadratic response surface fit. The response surface equation has 10 coefficients as shown bellow.

Δε p = c0 + c1 x1 + c2 x2 + c3 x3 +

c12 x1 x2 + c13 x1 x3 + c23 x2 x3 +

(3)

c11 x12 + c22 x22 + c33 x32 In this equation the values of the variables are normalized so that the coefficients can be compared. The values of the coefficients are listed in Table III. Table III. The coefficients of the response surface equation. Coeffs. values c0 0.0092 c1 -0.00416 c2 1.00E-06 c3 0.000445 c12 -2.50E-07 c13 -0.00027 c23 -5.0E-07 c11 0.0019 c22 -1.99E-05 c33 -0.00015 The values of the coefficients represent their relative importance of the respective design variables. It is evident that the coefficients that are linked to the terms with x1 in them are significantly greater than other coefficients. This means that a change in x1 value affects the change in ∆εp more significantly than the changes in other design parameters and therefore, x1, i.e. the solder thickness is the most important design parameter so far as the reliability of the solder interconnect is concerned. It is also clear that the least important variable is the isolation substrate width, x2. Lifetime model In the 2D FEA model, the crack path is one-dimensional, the cracked area of the solder interconnect can be represented by the crack length. For a solder interconnect with length L, if the damage indicator has an average value of ∆εp, the lifetime of this solder interconnect NL is assumed to have the following Coffin Manson form.

NL =

L

a ( Δε p )

b

(4)

where L is in millimeters, a and b are constants. This is an empirical equation and the constant a and b have to be determined through experiments and computer modeling. In order to determine a and b, the experimental lifetime data described in [7] are used. In that experiment, the failure was defined as the number of cycles at which there is an increase in the relative thermal resistance by 20% between the substrate and the baseplate.

To determine the values of a and b, the first step is to carry out FEA computer simulations to predict the damage indicator ∆εp values in the solder joint for each and every temperature profile that has been used in the experiment [7]. Then, lifetime values are calculated for each temperature profile with a and b as adjustable parameters. The values of a and b are adjusted until the squared sum of the difference between the calculated lifetime values and the experimental values are minimized. The lifetime calculation method will be described in the following section. In the modeling, the failure of a solder joint is defined as the time it takes for the crack to have an area that is 20% of the total solder interconnect area. The final values of a and b have been found to be 0.0056 and 1.023 respectively. Lifetime prediction method In order to calculate the lifetime of the substrate mountdown solder joint model, the expected crack path is divided into a number of sections. For simplicity, these sections are chosen so that they coincide with the FEA model’s mesh elements on the crack path. The values of ∆εp at these sections are obtained from the modeling. The section that is closest to the crack tip has the greatest damage per cycle and the lifetime is NF1=N1. Equation 4 can be used to estimate this lifetime: b N1 = L1 / ⎡⎢ a ( Δε p ) ⎤⎥ ⎣ ⎦

(5)

where L1 is the length of the section that is closest to the crack tip. For the next section along the crack path, it is not as close as the first section to the crack tip so the value of the damage ∆εp is smaller and according to Equation 4 the lifetime N2 should have a value greater than N1 if the damage value remains unchanged at all the times. However, the damage value ∆εp does change because after the failure of the first section the crack tip moves closer to the second section so this second section becomes the one at the crack tip after N1 cycles and the damage changes as the result. In the following, the real lifetime of the second section is denoted as NF2. Its value can be calculated using the Miner’s rule expressed in Equation 1. Since there are only two stress states, this equation can be simplified to obtain Equation 5.

n1 n2 + =1 N1 N 2

(6)

where n1 and n2 are the number of cycles this section of the crack path has experienced at the time of failure of this section under the two load levels respectively. Obviously, in this case n2=N1 and the lifetime of this section, NF2, is given by

⎛ N ⎞ NF2 = n1 + n2 = n1 + N1 = N1 ⎜ 2 − 1 ⎟ N2 ⎠ ⎝

(7)

As expected, the lifetime of this section of the solder joint is greater than N1 but smaller than 2N1. This is because after the first N1 cycles of loading, though the second section has not failed (because N2 is greater than N1) it has already


experienced N1 cycles of damage at a lower stress level and therefore it has a remaining lifetime that is smaller than N1. Equation 7 can be generalized to calculate the lifetime of any solder section along a crack path that has been divided into k sections. Assuming that at the ith section, the value of ∆εp for this section is used to calculate the value Ni which is the lifetime of this section if ∆εp does not change over time, then the real lifetime for each section can be obtained by solving the following set of simultaneous linear equations.

0 ... 0 ⎞⎛ NF1 ⎞ ⎛ 1N1 ⎞ ⎛ α1 ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ α 2 α1 ... 0 ⎟⎜ NF2 ⎟ = ⎜ 2 N1 ⎟ (8) ⎜ ... ... ... ... ⎟⎜ ... ⎟ ⎜ ... ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎝ α k α k −1 ... α1 ⎠⎝ NFk ⎠ ⎝ kN1 ⎠ where α i = N1 / N i , and NFi is the real lifetime of the ith section after the crack tip movement has been taken into account. Results and discussions For the railway traction control applications of power electronics modules, the customer has specified two load conditions or mission profiles [7]. The first condition is for the mass transit application and the second one is for the high speed application. For each load condition, there are several cyclic load profiles. Each profile is characterized by the minimum and maximum temperatures as well as the number of cycles per day. In total there are four distinctive load profiles. Of the four profiles only three of them will be used for lifetime calculation because the temperature change in the cruise profile is only 1°C and it does not contribute to the total lifetime value. Table IV: Traction application: mass transit load condition. Status Shed stops Station Stops Cruise

Tmin -40°C +80°C +80°C

Tmax +80°C +100°C +81°C

Cycles/day 1 1080 6E6

Table V: Traction application: high speed. Status Shed stops Station Stops Speed Control Cruise

Tmin -40°C

Tmax +80°C

Cycles/day 1

+80°C

+100°C

20

+80°C

+85°C

3240

+80°C

+81°C

6E6

The first step is the calculation of ∆εp distribution along the crack path, the lifetime for each crack path section, and the lifetime for each distinctive load profile. By using the accumulated plastic strain values for each load profile and Equations 5 and 8, lifetimes can be calculated. In order to study the effect of solder thickness on lifetime three solder

joint thickness values are used. The results are listed in Table VI. Table VI: Predicted lifetime for each single load temperature profile. Solder shed speed Station Thickness 0.1 mm

6.94E+03

1.25E+09

2.24E+05

0.2 mm

8.26E+03

1.50E+09

2.64E+05

0.3 mm

8.99E+03

1.61E+09

2.84E+05

The lifetimes calculated for each profile can then be used in the Miner’s rule to calculate the lifetimes of the solder joints for the two applications. The results are listed in Table VII. Table VII: Calculated lifetime for the high speed and mass transit applications. high speed mass transit solder thickness (years) (years) 0.1 mm 11.61 0.55 0.2 mm 13.76 0.65 0.3 mm 14.93 0.70 The results show that lifetimes increase significantly for both applications and for the mass transit application the lifetimes are much shorter than these for the high speed application. On close examination, it has been determined that that this difference is mainly caused by difference in the number of station stops of the applications: the mass transit application has a much greater number of station stops and therefore a much shorter lifetime. Conclusions A methodology for the calculation of the lifetime of relative large area solder joint has been developed. The methodology is based on the linear damage accumulation rule and it can best be used in solder joint where the profile of the damage indicator does not change significantly. As an example, the methodology has been used in the calculation of the lifetimes of the substrate solder interconnect in power modules for railway traction applications. The sensitivity of the lifetime to the changes in solder thickness has been obtained and the number of station stops in the applications has been identified as the cause of the short lifetime for the mass transit load profile. The methodology can be generalized to accommodate any damage accumulation rule for mixed amplitude loading but Equation 8 would have to be modified. Acknowledgments The authors wish to acknowledge the support of the Innovative electronics Manufacturing Research Centre (IeMRC) and the United Kingdom Department of Trade and Industry for the project ‘Modelling of Power Modules for Lifetime, Accelerated Testing, Reliability and Risk’. The authors would like to thank project partners Semelab Ltd,


Dynex Semiconductor Ltd., Goodrich Engine Control Raytheon Systems Ltd., SR Drives Ltd., and Areva T&D Ltd. for their contribution to the project. The authors would also like to thank Prof. Mark Johnson and his colleagues at the University of Sheffield and University of Nottingham for their support. References 1. Syed, A., “Accumulated creep strain and energy density based thermal fatigue life prediction models for SnAgCu solder joints”, Proceedings of the 54th Electronic Components and Technology Conference, pp.737-746, (2004) 2. Schubert, A., Dudek, R., Auerswald, E., Gollhardt, A., Michel, B., Reichl, H., “Fatigue life models for SnAgCu and SnPb solder joints evaluated by experiments and simulation”, 53rd Electronic Components & Technology Conference, 2003 Proceedings : pp.603-610, (2003) 3. S. Suresh, Fatigue of Materials, Cambridge University Press (1991), p.133 4. Sheng, W.W. and Colino, R.P., Power Electronic Modules, CRC Press (2005) 5. Pooch, M.-H., Dittmer, K.J., Gabisch, D., “Investigations on the damage mechanism of aluminum wire bonds used for high power applications”, Proc. EUPAC 96, (1996) pp. 128-131 6. Lau, J.H. (editor), Ball Grid Array Technology, McGrawHill (1995), p.396 7. Newcombe, D.R., Bailey, C. and Lu, H, “Rapid Solutions for Application Specific IGBT Module Design”, Proceedings of International Exhibition & Conference for Power Electronics Inteligent Motion Power Quality (PCIM), 22-24 May 2007, Nuremberg, 2007.
