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Lifetime prediction on the base of mission profiles
Microelectronics Reliability 45 (2005) 1293–1298 www.elsevier.com/locate/microrel
Invited Paper
Lifetime Prediction on the Base of Mission Profiles Mauro Ciappa Swiss Federal Institute of Technology (ETH) Integrated Systems Laboratory Zurich, Switzerland
Abstract Realistic mission profiles represent a challenge for the lifetime prediction of complex devices and systems. This paper proposes several examples where this problem has been solved by proper analysis of the stresses, by dedicated physical modeling, and by efficient calculation tools. Ó 2005 Elsevier Ltd. All rights reserved.
1. Introduction The end-of-life period of complex devices is often defined by extrinsic failure mechanisms. The time-tothe-failure (lifetime) for these mechanisms is normally estimated on the base of deterministic models, which are calibrated usually with data extracted from accelerated tests and less frequently with field data. These estimates are referred to a given application profiles, which are specific to the technical systems under consideration (hybrid car, locomotive, airplane, oil field, etc.). Lifetime models for the main failure mechanisms are available as a function of the intensity either of a single or of multiple stress factors. These models usually provide the time-to-failure tf , the median (t50, arbitrary quantile), or the mean-time-to-failure (MTTF) of a time distribution. These values are normally provided in conjunction with additional parameters, which describe the shape of the distribution. The models are usually defined for time-independent or cyclic stresses and often refer to simple test structures. The task to use such physical models to predict the lifetime of complex devices operated under realistic conditions is very challenging, since one has to take into consideration time dependency of the stresses occurring during the real mission profile. In this paper, we will discuss some practical procedures to solve this
problem, with a special focus on thermo-mechanical failure mechanisms of power devices. 2. Mission profiles In the reliability field a mission profile is defined as the specific task, which must be fulfilled by an item during a stated time under given conditions. A first example of a mission profile are power converters used in airborne applications to drive electrical actuators in the close vicinity of the jet engine. In this case, the power devices are required to survive at the same time static environment temperatures of about 200°C during the flight and extreme thermal cycles between –55°C and 200°C with a rate of 10°C/min during landing and take off. The requested lifetime of the equipment is 50’000 hours corresponding to about 500 landing/take off cycles [1]. Another application imposing extreme working conditions to the electronic systems is the oilfield. The characterization of the formation properties (e.g. electrical resistivity) within the wellbore in order to make decision about drilling and production operations (Wireline log) requires electronic devices to operate for relatively short periods (typically 6 hours) in a temperature range extending from –25°C to 175°C and
0026-2714/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.microrel.2005.07.060
M. Ciappa / Microelectronics Reliability 45 (2005) 1293–1298
Power devices used in electrical hybrid vehicles are normally specified for a typical lifetime of 8’000 hours, which corresponds to several millions of power cycles with different duration and amplitude. In this case, the environment temperature strongly depends on the design of the cooling circuitry of the vehicle. If the power converter shares the same cooling circuitry with the thermal engine, a baseline temperature of 90°C up to 120°C can be expected. This leads to junction temperatures of the switching devices in the 200°C range. With a typical baseline temperature of 60°C, the working conditions of the devices are less severe in vehicles, which use for the converter a dedicated cooling circuitry. Up to now no standardized mission profile is available in the automotive field, which has been expressly developed for reliability prediction purposes. Car manufacturers are assessing the reliability performance of their products by using standardized driving cycles, which are originally intended for the measurement of exhaust emissions and of the fuel consumption (e.g. NMVEG, Artemis). Performing reliability tests in the field with the use of full-featured devices or systems is generally very expensive and in several cases it is also unfeasible. For this reason, lifetime tests are often performed using simple test structures developed expressly to investigate a given failure mechanism and under simplified test conditions. The extrapolation of the reliability data obtained under these circumstances to the real device and to the real operating conditions requires some particular skills. First, the stress conditions need to be representative of the stresses experienced by the systems in the field. Second, the model used to predict the reliability of the full-featured device has to take into consideration the reduced complexity of the test vehicle. Third a physical model and proper calculation tools are required that relate the simplified stress conditions to the stress situation encountered in the field. This basic approach will be demonstrated in the following sections by taking as an example the prediction of the lifetime of power devices for traction applications.
3. Analysis of mission profiles In many power systems, e.g. in automotive applications, the power electronic modules consist of single packaged chips that are cooled by forced convection in dedicated water/glycol cooling circuits. Not surprisingly, the complexity of these assemblies represents a major limitation in terms of efficiency, compactness, weight, cost, and reliability of the vehicle. Simple lifetime prediction models, based on the bimetallic approximation for the thermo-mechanical stresses, and based on the principle of a linear accumulation of the damage related to cyclic fatigue have been proposed and investigated in the past [3,4,5]. Under the simple assumption of linear accumulation of the cyclic fatigue damage, a fatigue function can be defined as Q ( T ) =
N ( T ) N f ( T )
where is the number of cycles performed at a given temperature excursion T and N f is the number of cycles to failure at the same T, respectively. Differentiation and integration of Q [5] over a complete mission temperature profile yields Q ( after 1 mission profile) =
g ( T ) 1 - d ( T ) a T min T q T max
where g(T) represents the frequency distribution of the thermal excursions inside one mission profile. Equation (XX) already includes the assumed dependency of Nf on T according to a Coffin-Manson law with coefficient a and exponent q, to be determined experimentally by accelerated tests.
80
300 Junction Temperature normalized speed
70 60
200
50 40 30
100
Speed [rel. units]
to survive up to 2000 mechanical shocks with accelerations reaching 250 g. The acquisition of several physical parameters while drilling (Measurement while drilling), including the pressure, the temperature, and the wellbore trajectory requires electronic devices able to operate at least for 1000 hours at 150°C and to survive typically 100’000 shocks at 250 g. Additional activities, like reservoir monitoring are less stringent in terms of mechanical shocks but they impose an almost constant operating temperature of 150°C for a period of 5 years [2].
Junction Temperature [°C]
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20 10 0 0
200
400
600
800
0 1000
Time [sec]
Fig. 1 Time evolution of the junction temperature of an IGBT of a hybrid car operated according to the driving cycle Artemis [6].
M. Ciappa / Microelectronics Reliability 45 (2005) 1293–1298
(a)
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(b)
Fig. 2 Frequency of the temperature cycles from Fig. 1 (1000 s) as a function of the cycle excursion and cycle duration (a) according to the cycle definition A [5], (b) according to the cycle definition B [5].
The ratio 1/Q returns the lifetime of the system under investigation expressed in number of missions profile to failure. The next step is the extraction the number, the amplitude and the duration of the thermal cycles, which are experienced by the system when it is submitted to a given mission profile to define the frequency function g( T). After assuming a proper definition for the thermal excursion [5] and a suitable procedure for processing the data, the g( T) is extracted from the temperature profile in Figure 1. This represents the evolution of the junction temperature of an insulated gate bipolar transistor (IGBT) device in a power module, operated within a hybrid car, which is driven according to a standard mission profile (Artemis [6]) in an urban environment. In spite of the fact that the junction temperature has been acquired with a sampling period of 500 ms, these data represent a reasonable estimate of the real junction temperature. In fact, the junction temperature increase due to power dissipation spikes (e.g., switching losses) whose duration is much shorter than the typical thermal time constant of the whole system (typically several seconds) is almost negligible. The extracted function can be either analytical or numerical. The analytical form can be obtained by fitting the empirical distribution with the usual statistical distributions, i.e., Normal, Lognormal,or Weibull. Figure 2a and 2b represent such a distribution for the cycle definition A and B introduced in [5], as a function of the cycle amplitude and of the cycle duration. It can be observed that the highest bin corresponds to thermal cycles having a temperature excursion lower than 5 K and a duration shorter than 5 s. About 80% of the temperature cycles are lower than 25 K, while their duration does not exceed 15 s. The observed maximum
temperature swing is 65 K, the maximum cycle duration is 35 s, and the total number of cycles is 206 (for a driving period of 1000 s). This means that with a specified lifetime of 8’000 hours the vehicle experiences up to 5 millions of cycles with different amplitude and duration. 4. Modeling the degradation during the mission profile In order to overcome the problems involved with the arbitrary definition of the thermal cycle encountered in Section 3, prediction models have been developed, which make use of the fundamental thermomechanical equations describing the creep mechanics in materials submitted to cyclic loads [7,8]. In particular, the proposed model assumes that stresses above the yield point cause a plastic irreversible deformation, which turns into a hysteresis loop in the stress-strain representation.
Fig. 3 Stress-strain plot for the mission profile of Fig. 1.
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M. Ciappa / Microelectronics Reliability 45 (2005) 1293–1298
The uniaxial strain is computed from the thermal expansion of the bimetallic system, while the corresponding shear stress is derived from the creep relation. Once represented in the strain-stress plane, these values provide the deformation energy dissipated during a thermal cycle of arbitrary shape. In fact, it can be easily demonstrated that the deformation energy is proportional to the area included within the corresponding hysteresis loop [8]. The lifetime of the system can be computed under the assumption that the system reaches its end-of-life as soon as a total amount of deformation work, Wtot, has been accumulated. Thus, the lifetime of the system (expressed in number of mission profiles) can be computed by calculating the ratio between Wtot and the deformation work associated with a given mission profile. Based on these principles, we have proposed two different models for the creep behavior of solder materials. The first model includes only the dependency of the shear stress on the temperature gradient. The second model takes also into account the dependency of the creep behavior on the instantaneous temperature. Once calibrated [14], the model applied to the mission profile of Figure 1 returns the instantaneous strainstress values, which are plotted with the time as a parameter in Figure 3. The area enclosed within every single loop represents the total plastic deformation work associated with the mission profile. In spite of its apparent complexity, the model based on the creep behavior is robust and returns lifetimes that are not strongly dependent on the uncertainty of the assumed parameters. Furthermore, the lifetime can be easily extrapolated by standard numerical procedures. The main limitation of the new model consists of the fact that, similar to the Coffin-Mansonapproach, it fails in predicting the decrease of the module lifetime when operated at higher average temperatures. This is due to the assumption that creep is the only plastic deformation mechanism, which leads to the thermal cycling damage. More complicated models can be developed, which take into account additional mechanisms as for instance stress relaxation, anisotropic effects, and microstructural changes. Unfortunately, the number of free parameters associated with these approaches would make the calibration of those models virtually impossible. 5. Efficient computational tools for long mission profiles A brute-force numerical simulation of a complete power system is beyond the capabilities of current computer environments. For this reason, a hierarchical approach has been developed for power system
modeling. As an example of this approach, an Integrated Starter Generator (ISG) topology is considered, which makes use of a highly-integrated design, and which shares the cooling circuitry with the internal combustion engine with the cooling fluid being at a typical steady-state temperature of 90°C. This assumption implies the use of high-temperature semiconductors (with junction temperature up to 180°C) and the optimization of the thermal management with the aim to dissipate the time-dependent power losses of the devices and to avoid inefficient thermal interfaces (e.g. thermal grease).
Fig. 4 Finite element model of the ISG with 93217 nodes
Figure 4 presents the finite element simulation model of the 6 kW ISG. It consists of a threephase MOSFET half-bridge inverter with six multi-chip modules soldered on a common AlSiC base plate (which is an integral part of the cooling system. Four OPTIMOS transistors are mounted on every single bare multi-chip substrate [9]. All thermal management considerations are based on the standardized NMVEG driving cycle [10]. The related power mission profile represented in Figure 5 has been measured on the ISG described above, that is by assuming a power rating of 6 kW, the start-stop function, boosting, and regenerative braking. As shown elsewhere [11] the power losses are proportional to the square of the rms phase current when conduction losses are dominant. Since the transient thermal simulation of complex 3D finite element models is not feasible with sufficient accuracy for the long driving cycles required by the automotive applications (several minutes), the traditional extraction procedure was based on the measurement of the experimental thermal impedance of the system by the cooling curve technique [3]. The analytical form of the thermal impedance was then obtained in an empirical way by fitting the measured curve with a linear
M. Ciappa / Microelectronics Reliability 45 (2005) 1293–1298
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Fig. 5 (a) Power consumption of the ISG in Fig. 4 during an NMVEG cycle and the power losses of the MOSFETs. (b) Calculated junction temperature of a MOSFET of the ISG.
combination of multiple exponential curves (usually with 5 to 6 different time constants). This traditional approach presented several practical problems. The most limiting factor is that the system has to be completely realized (increasing the prototyping costs and the development cycle) and, in order to acquire the thermal impedance curve, it must be able to be switched at very low frequencies (tenths of Hertz). Furthermore, the nodes of the compact model extracted by the least squares fit procedure had no physical meaning, such that the compact model just described the evolution of the junction temperature. This implies that it could not be used for computing the timedependent temperature of intermediate interfaces (e.g. solder layers), inhibiting its use for reliability prediction purposes [3]. The procedure we demonstrate here is very robust. It does not require that the converter be completely realized, or that it operates at very low frequencies. This represents a very efficient way to reduce the development cycle of a converter by the quantitative use of CAD tools and it enables at the same time an implementation of a built-in reliability program [3]. The starting point of the procedure [12,14] is a static 3D finite element model of the converter including the module and the heat sink. This model is initially calibrated with experimental data acquired either by infrared thermography, or by internal thermometry techniques [3]. Once calibrated, the 3D finite element model is used to extract the thermal impedance of the system. This is done by computing the transient step response of the system powered in different configurations, in order to take into account the thermal coupling between the different heat sources. This step just requires a few transient simulations with computational times in the range of
two to three hours, depending on the complexityof the system and the available computing resources. The step response of the system obtained in this way is processed according to an optimized algorithm [12], which renders both the thermal impedance of every heat source, as well the functions describing their mutual thermal interference. This is done such that every node of the compact model still represents a physical interface of the converter. The data representing the complex thermal impedance are saved in a matrix form for efficient numerical processing. The whole procedure is automatic and requires just a few minutes of computation time. The junction temperature of every chip (or the temperature at an arbitrary interface) of the converter submitted to an arbitrary application profile can be computed in the time domain as soon the related power function (static and switching losses as function of the time) is known.
Fig. 6 Simulated step response at the different interfaces of a MOSFET in the ISG in Fig. 4.
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This is the case of the standard NMVEG mission profile [10] represented in Figure 5a. This method is very fast, as for example a simulation of a 20min cycle takes only seconds or minutes depending on the required accuracy.
[6]
[7]
6. Summary and conclusions In this paper, we discussed the current status and the open issues related to the lifetime prediction of devices operated according to complex mission profiles. The available techniques have been applied to challenging problems of from the field of the power devices for traction applications. It has been shown that the multidisciplinary problems encountered in lifetime prediction activities cannot be tackled by the exact solution of fundamental equations. Purpose-oriented physical models in conjunction with dedicated experimental procedures and proper computational tools are the pragmatic way to the success. The author would like to thank Kari Oila, Flavio Carbognani, Matteo Ferrari for their contributions. We also acknowledge all the partners of the European project HIMRATE, in particular Eckhard Wolfgang and Norbert Seliger (Siemens Corp. Research), Frederic Lecoq (Renault), and Gérard Coquery (INRETS).
References [1]
[2]
Z. Khatir, G. Coquery, S. Lefebvre Fiabilité des dispositifs semi-conducteurs de puissance synergies de recherches entre applications automobiles et aéronautiques, Proc. of the 2 èmes Journées du RTP, 1516 mars 2004, Carry le Rouet (France) B. Parmentier Reliability of lead free solder for high temperature applications, Proc. of the 2 èmes Journées du RTP, 15-16 mars 2004, Carry le Rouet (France)
[3]
M. Ciappa Some reliability aspects of IGBT modules for high power applications, Hartung-Gorre Printing House, Konstanz, Germany (2001)
[4]
M. Ciappa and W. Fichtner Lifetime prediction of IGBT modules for traction applications, IEEE Int. Reliab. Physics Symp. 38, 210 (2000)
[5]
M. Ciappa, F. Carbognani, P. Cova, W. Fichtner A Novel thermo-mechanics-based lifetime prediction model for cycle fatigue failure mechanisms in power semiconductors, IEEE Trans. on Dev. and Mat. Reliability 3 191-196 (2003)
G. Coquery, S. Carubelli, J.P. Ousten, R. Lallemand, F. Lecoq, D. Lhotellier, V. de Viry, P. Dupuy Power module lifetime estimation from chip temperature direct measurement in an automotive traction inverter Microelectronics Reliability 41 1695-1700(2001) A. Schubert, H. Walter, R Dudek, B. Michel, G. Lefranc, J. Otto, G. Mitic Thermo-Mechanical Properties and Creep Deformation of Lead-Containing and Lead-Free Solders, Proc. of the 34th Int. Symposium on Microelectronics IMAPS (2001)
[8]
D. Rubesa Lifetime prediction and constitutive modelling for creepfatigue interaction, Bornträger, Berlin 1991
[9]
N. Seliger, J. Rackles, H. Schwarzenbauer, W. Kiffe, and S. Bolz, Compact and robust power electronic packaging interconnection technology for an integrated starter generator, Haus der Technik Fachbuch Band 14, Expert, Essen 2002, pp. 248-255
[10] R. Knorr, M. Bienert, S. Bolz, G. Lugert, and P. Skotzek Überblick und Perspektiven des 14/42V Bordnetzes Komponenten, Architektur und Möglichkeiten Elektronik im Kraftfahrzeug, VDI Gesellschaft Fahrzeug- und Verkehrstechnik, Düsseldorf (2000) [11] N. Seliger, E. Wolfgang, G. Lefranc, H. Berg, and T. Licht, Reliable power electronics for automotive applications, Microelectronics Reliability 42, 1597-1604 (2002) [12] T. Kojima, Y. Yamada, M. Ciappa, M. Chiavarini, W. Fichtner, A novel electro-thermal simulation approach of power IGBT modules for automotive traction applications Proc. of the International Power Semiconductor Devices and ICs (ISPSD) 16 289-292(2004) [13] M. Ciappa, F. Carbognani, P. Cova, and W. Fichtner A novel thermomechanics-based lifetime prediction model for cycle fatigue failure mechanisms in power semiconductors, Microelectronics Reliability 42 1653-1658(2002) [14] C. Yun, P. Malberti, M. Ciappa, W. Fichtner Thermal component model for electrothermal analysis of IGBT module systems IEEE Trans. on Adv. Packaging AP-24, 401-406 (2001)
Invited Paper
Lifetime Prediction on the Base of Mission Profiles Mauro Ciappa Swiss Federal Institute of Technology (ETH) Integrated Systems Laboratory Zurich, Switzerland
Abstract Realistic mission profiles represent a challenge for the lifetime prediction of complex devices and systems. This paper proposes several examples where this problem has been solved by proper analysis of the stresses, by dedicated physical modeling, and by efficient calculation tools. Ó 2005 Elsevier Ltd. All rights reserved.
1. Introduction The end-of-life period of complex devices is often defined by extrinsic failure mechanisms. The time-tothe-failure (lifetime) for these mechanisms is normally estimated on the base of deterministic models, which are calibrated usually with data extracted from accelerated tests and less frequently with field data. These estimates are referred to a given application profiles, which are specific to the technical systems under consideration (hybrid car, locomotive, airplane, oil field, etc.). Lifetime models for the main failure mechanisms are available as a function of the intensity either of a single or of multiple stress factors. These models usually provide the time-to-failure tf , the median (t50, arbitrary quantile), or the mean-time-to-failure (MTTF) of a time distribution. These values are normally provided in conjunction with additional parameters, which describe the shape of the distribution. The models are usually defined for time-independent or cyclic stresses and often refer to simple test structures. The task to use such physical models to predict the lifetime of complex devices operated under realistic conditions is very challenging, since one has to take into consideration time dependency of the stresses occurring during the real mission profile. In this paper, we will discuss some practical procedures to solve this
problem, with a special focus on thermo-mechanical failure mechanisms of power devices. 2. Mission profiles In the reliability field a mission profile is defined as the specific task, which must be fulfilled by an item during a stated time under given conditions. A first example of a mission profile are power converters used in airborne applications to drive electrical actuators in the close vicinity of the jet engine. In this case, the power devices are required to survive at the same time static environment temperatures of about 200°C during the flight and extreme thermal cycles between –55°C and 200°C with a rate of 10°C/min during landing and take off. The requested lifetime of the equipment is 50’000 hours corresponding to about 500 landing/take off cycles [1]. Another application imposing extreme working conditions to the electronic systems is the oilfield. The characterization of the formation properties (e.g. electrical resistivity) within the wellbore in order to make decision about drilling and production operations (Wireline log) requires electronic devices to operate for relatively short periods (typically 6 hours) in a temperature range extending from –25°C to 175°C and
0026-2714/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.microrel.2005.07.060
M. Ciappa / Microelectronics Reliability 45 (2005) 1293–1298
Power devices used in electrical hybrid vehicles are normally specified for a typical lifetime of 8’000 hours, which corresponds to several millions of power cycles with different duration and amplitude. In this case, the environment temperature strongly depends on the design of the cooling circuitry of the vehicle. If the power converter shares the same cooling circuitry with the thermal engine, a baseline temperature of 90°C up to 120°C can be expected. This leads to junction temperatures of the switching devices in the 200°C range. With a typical baseline temperature of 60°C, the working conditions of the devices are less severe in vehicles, which use for the converter a dedicated cooling circuitry. Up to now no standardized mission profile is available in the automotive field, which has been expressly developed for reliability prediction purposes. Car manufacturers are assessing the reliability performance of their products by using standardized driving cycles, which are originally intended for the measurement of exhaust emissions and of the fuel consumption (e.g. NMVEG, Artemis). Performing reliability tests in the field with the use of full-featured devices or systems is generally very expensive and in several cases it is also unfeasible. For this reason, lifetime tests are often performed using simple test structures developed expressly to investigate a given failure mechanism and under simplified test conditions. The extrapolation of the reliability data obtained under these circumstances to the real device and to the real operating conditions requires some particular skills. First, the stress conditions need to be representative of the stresses experienced by the systems in the field. Second, the model used to predict the reliability of the full-featured device has to take into consideration the reduced complexity of the test vehicle. Third a physical model and proper calculation tools are required that relate the simplified stress conditions to the stress situation encountered in the field. This basic approach will be demonstrated in the following sections by taking as an example the prediction of the lifetime of power devices for traction applications.
3. Analysis of mission profiles In many power systems, e.g. in automotive applications, the power electronic modules consist of single packaged chips that are cooled by forced convection in dedicated water/glycol cooling circuits. Not surprisingly, the complexity of these assemblies represents a major limitation in terms of efficiency, compactness, weight, cost, and reliability of the vehicle. Simple lifetime prediction models, based on the bimetallic approximation for the thermo-mechanical stresses, and based on the principle of a linear accumulation of the damage related to cyclic fatigue have been proposed and investigated in the past [3,4,5]. Under the simple assumption of linear accumulation of the cyclic fatigue damage, a fatigue function can be defined as Q ( T ) =
N ( T ) N f ( T )
where is the number of cycles performed at a given temperature excursion T and N f is the number of cycles to failure at the same T, respectively. Differentiation and integration of Q [5] over a complete mission temperature profile yields Q ( after 1 mission profile) =
g ( T ) 1 - d ( T ) a T min T q T max
where g(T) represents the frequency distribution of the thermal excursions inside one mission profile. Equation (XX) already includes the assumed dependency of Nf on T according to a Coffin-Manson law with coefficient a and exponent q, to be determined experimentally by accelerated tests.
80
300 Junction Temperature normalized speed
70 60
200
50 40 30
100
Speed [rel. units]
to survive up to 2000 mechanical shocks with accelerations reaching 250 g. The acquisition of several physical parameters while drilling (Measurement while drilling), including the pressure, the temperature, and the wellbore trajectory requires electronic devices able to operate at least for 1000 hours at 150°C and to survive typically 100’000 shocks at 250 g. Additional activities, like reservoir monitoring are less stringent in terms of mechanical shocks but they impose an almost constant operating temperature of 150°C for a period of 5 years [2].
Junction Temperature [°C]
1294
20 10 0 0
200
400
600
800
0 1000
Time [sec]
Fig. 1 Time evolution of the junction temperature of an IGBT of a hybrid car operated according to the driving cycle Artemis [6].
M. Ciappa / Microelectronics Reliability 45 (2005) 1293–1298
(a)
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(b)
Fig. 2 Frequency of the temperature cycles from Fig. 1 (1000 s) as a function of the cycle excursion and cycle duration (a) according to the cycle definition A [5], (b) according to the cycle definition B [5].
The ratio 1/Q returns the lifetime of the system under investigation expressed in number of missions profile to failure. The next step is the extraction the number, the amplitude and the duration of the thermal cycles, which are experienced by the system when it is submitted to a given mission profile to define the frequency function g( T). After assuming a proper definition for the thermal excursion [5] and a suitable procedure for processing the data, the g( T) is extracted from the temperature profile in Figure 1. This represents the evolution of the junction temperature of an insulated gate bipolar transistor (IGBT) device in a power module, operated within a hybrid car, which is driven according to a standard mission profile (Artemis [6]) in an urban environment. In spite of the fact that the junction temperature has been acquired with a sampling period of 500 ms, these data represent a reasonable estimate of the real junction temperature. In fact, the junction temperature increase due to power dissipation spikes (e.g., switching losses) whose duration is much shorter than the typical thermal time constant of the whole system (typically several seconds) is almost negligible. The extracted function can be either analytical or numerical. The analytical form can be obtained by fitting the empirical distribution with the usual statistical distributions, i.e., Normal, Lognormal,or Weibull. Figure 2a and 2b represent such a distribution for the cycle definition A and B introduced in [5], as a function of the cycle amplitude and of the cycle duration. It can be observed that the highest bin corresponds to thermal cycles having a temperature excursion lower than 5 K and a duration shorter than 5 s. About 80% of the temperature cycles are lower than 25 K, while their duration does not exceed 15 s. The observed maximum
temperature swing is 65 K, the maximum cycle duration is 35 s, and the total number of cycles is 206 (for a driving period of 1000 s). This means that with a specified lifetime of 8’000 hours the vehicle experiences up to 5 millions of cycles with different amplitude and duration. 4. Modeling the degradation during the mission profile In order to overcome the problems involved with the arbitrary definition of the thermal cycle encountered in Section 3, prediction models have been developed, which make use of the fundamental thermomechanical equations describing the creep mechanics in materials submitted to cyclic loads [7,8]. In particular, the proposed model assumes that stresses above the yield point cause a plastic irreversible deformation, which turns into a hysteresis loop in the stress-strain representation.
Fig. 3 Stress-strain plot for the mission profile of Fig. 1.
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M. Ciappa / Microelectronics Reliability 45 (2005) 1293–1298
The uniaxial strain is computed from the thermal expansion of the bimetallic system, while the corresponding shear stress is derived from the creep relation. Once represented in the strain-stress plane, these values provide the deformation energy dissipated during a thermal cycle of arbitrary shape. In fact, it can be easily demonstrated that the deformation energy is proportional to the area included within the corresponding hysteresis loop [8]. The lifetime of the system can be computed under the assumption that the system reaches its end-of-life as soon as a total amount of deformation work, Wtot, has been accumulated. Thus, the lifetime of the system (expressed in number of mission profiles) can be computed by calculating the ratio between Wtot and the deformation work associated with a given mission profile. Based on these principles, we have proposed two different models for the creep behavior of solder materials. The first model includes only the dependency of the shear stress on the temperature gradient. The second model takes also into account the dependency of the creep behavior on the instantaneous temperature. Once calibrated [14], the model applied to the mission profile of Figure 1 returns the instantaneous strainstress values, which are plotted with the time as a parameter in Figure 3. The area enclosed within every single loop represents the total plastic deformation work associated with the mission profile. In spite of its apparent complexity, the model based on the creep behavior is robust and returns lifetimes that are not strongly dependent on the uncertainty of the assumed parameters. Furthermore, the lifetime can be easily extrapolated by standard numerical procedures. The main limitation of the new model consists of the fact that, similar to the Coffin-Mansonapproach, it fails in predicting the decrease of the module lifetime when operated at higher average temperatures. This is due to the assumption that creep is the only plastic deformation mechanism, which leads to the thermal cycling damage. More complicated models can be developed, which take into account additional mechanisms as for instance stress relaxation, anisotropic effects, and microstructural changes. Unfortunately, the number of free parameters associated with these approaches would make the calibration of those models virtually impossible. 5. Efficient computational tools for long mission profiles A brute-force numerical simulation of a complete power system is beyond the capabilities of current computer environments. For this reason, a hierarchical approach has been developed for power system
modeling. As an example of this approach, an Integrated Starter Generator (ISG) topology is considered, which makes use of a highly-integrated design, and which shares the cooling circuitry with the internal combustion engine with the cooling fluid being at a typical steady-state temperature of 90°C. This assumption implies the use of high-temperature semiconductors (with junction temperature up to 180°C) and the optimization of the thermal management with the aim to dissipate the time-dependent power losses of the devices and to avoid inefficient thermal interfaces (e.g. thermal grease).
Fig. 4 Finite element model of the ISG with 93217 nodes
Figure 4 presents the finite element simulation model of the 6 kW ISG. It consists of a threephase MOSFET half-bridge inverter with six multi-chip modules soldered on a common AlSiC base plate (which is an integral part of the cooling system. Four OPTIMOS transistors are mounted on every single bare multi-chip substrate [9]. All thermal management considerations are based on the standardized NMVEG driving cycle [10]. The related power mission profile represented in Figure 5 has been measured on the ISG described above, that is by assuming a power rating of 6 kW, the start-stop function, boosting, and regenerative braking. As shown elsewhere [11] the power losses are proportional to the square of the rms phase current when conduction losses are dominant. Since the transient thermal simulation of complex 3D finite element models is not feasible with sufficient accuracy for the long driving cycles required by the automotive applications (several minutes), the traditional extraction procedure was based on the measurement of the experimental thermal impedance of the system by the cooling curve technique [3]. The analytical form of the thermal impedance was then obtained in an empirical way by fitting the measured curve with a linear
M. Ciappa / Microelectronics Reliability 45 (2005) 1293–1298
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(b)
Fig. 5 (a) Power consumption of the ISG in Fig. 4 during an NMVEG cycle and the power losses of the MOSFETs. (b) Calculated junction temperature of a MOSFET of the ISG.
combination of multiple exponential curves (usually with 5 to 6 different time constants). This traditional approach presented several practical problems. The most limiting factor is that the system has to be completely realized (increasing the prototyping costs and the development cycle) and, in order to acquire the thermal impedance curve, it must be able to be switched at very low frequencies (tenths of Hertz). Furthermore, the nodes of the compact model extracted by the least squares fit procedure had no physical meaning, such that the compact model just described the evolution of the junction temperature. This implies that it could not be used for computing the timedependent temperature of intermediate interfaces (e.g. solder layers), inhibiting its use for reliability prediction purposes [3]. The procedure we demonstrate here is very robust. It does not require that the converter be completely realized, or that it operates at very low frequencies. This represents a very efficient way to reduce the development cycle of a converter by the quantitative use of CAD tools and it enables at the same time an implementation of a built-in reliability program [3]. The starting point of the procedure [12,14] is a static 3D finite element model of the converter including the module and the heat sink. This model is initially calibrated with experimental data acquired either by infrared thermography, or by internal thermometry techniques [3]. Once calibrated, the 3D finite element model is used to extract the thermal impedance of the system. This is done by computing the transient step response of the system powered in different configurations, in order to take into account the thermal coupling between the different heat sources. This step just requires a few transient simulations with computational times in the range of
two to three hours, depending on the complexityof the system and the available computing resources. The step response of the system obtained in this way is processed according to an optimized algorithm [12], which renders both the thermal impedance of every heat source, as well the functions describing their mutual thermal interference. This is done such that every node of the compact model still represents a physical interface of the converter. The data representing the complex thermal impedance are saved in a matrix form for efficient numerical processing. The whole procedure is automatic and requires just a few minutes of computation time. The junction temperature of every chip (or the temperature at an arbitrary interface) of the converter submitted to an arbitrary application profile can be computed in the time domain as soon the related power function (static and switching losses as function of the time) is known.
Fig. 6 Simulated step response at the different interfaces of a MOSFET in the ISG in Fig. 4.
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This is the case of the standard NMVEG mission profile [10] represented in Figure 5a. This method is very fast, as for example a simulation of a 20min cycle takes only seconds or minutes depending on the required accuracy.
[6]
[7]
6. Summary and conclusions In this paper, we discussed the current status and the open issues related to the lifetime prediction of devices operated according to complex mission profiles. The available techniques have been applied to challenging problems of from the field of the power devices for traction applications. It has been shown that the multidisciplinary problems encountered in lifetime prediction activities cannot be tackled by the exact solution of fundamental equations. Purpose-oriented physical models in conjunction with dedicated experimental procedures and proper computational tools are the pragmatic way to the success. The author would like to thank Kari Oila, Flavio Carbognani, Matteo Ferrari for their contributions. We also acknowledge all the partners of the European project HIMRATE, in particular Eckhard Wolfgang and Norbert Seliger (Siemens Corp. Research), Frederic Lecoq (Renault), and Gérard Coquery (INRETS).
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