## Abstract

Monitoring and predicting temperatures at critical locations of a power electronic system is important for safety, reliability, and efficiency. As the market share of vehicles with electric powertrains continues to increase, there is also an important economic cost of failing electronic components. For inverters present in such a drive system, exceeding the temperature limit for certain critical components, such as DC-link capacitors and Silicon carbide MOSFETs, can lead to failure of the system. In such an application, extracting the temperatures using sensors from locations such as dies and capacitors require expensive modifications and poses technical challenges. It is therefore necessary to create a thermal model for the inverter system to estimate the temperature at various components in order to ensure operation within temperature limits. The model approach is also suitable for predicting the effect on the component temperature and reliability of boundary conditions such as coolant, ambient temperature, and mission profile. This study assesses the reliability of a 250 kW liquid cooled inverter system designed for traction application. The critical failure areas are the DC-link capacitors, and the SiC MOSFET dies, which are rated at 175 °C. The system is modeled as a compact system by reasonably considering each component as a lumped capacitance and estimating the thermal resistance using physical dimensions. Results from the model are then compared against experimental data from constant power testing, and good agreement is observed for the cold plate and gate driver temperatures. With the model fidelity established, the model is then used to implement drive cycles from the Environmental Protection Agency for nonroad applications. The resulting temperature profile for each component is a series of temperature peaks and troughs that contribute to damage and failure. Rainflow counting algorithm is then used to quantify the damage per mini-cycles and used to estimate the predicted life for each component based on their manufacturer provided reliability qualification, and the mission profile is executed on the test bench for validation. The results are then used to generate a system risk matrix that relates the failure risk associated with a certain mission profile and the cooling scheme. It therefore demonstrates that an automotive inverter with SiC switching devices can be credibly assessed for failure risk using a compact model that is independent of boundary conditions, in combination with established reliability correlations and techniques.

## Introduction

Power modules are used widely in power inverters and converters in electric and hybrid vehicles and renewable energy systems [1,2]. The material limitations of silicon combined with a need for more reliable and efficient power conversion technologies are increasing the emphasis on the utilities of silicon carbide as an alternative semiconductor material in power modules [3]. The dramatically lower intrinsic carrier density in silicon carbide allows SiC-equipped devices more sustained operation at higher temperatures compared to silicon-based electronics [4]. One benefit of operating power modules at high temperatures is the reduction in size and cost of the cooling system [5]. SiC devices also tend to demonstrate radiation hardness and chemical inertness, which makes a good candidate for harsh environment electronics [6]. Despite these advantages, SiC devices do have reliability concerns at higher temperatures due to gate insulator breakdown [7].

Reliability assessment of power modules in switching applications has traditionally involved insulated gate bipolar transistor (IGBT)-based modules. Wire bond lift off and solder delamination between substrates and base plates were usually the two failure mechanisms under focus due to the limiting role they often play in such applications [8,9]. Sankaran et al. [10] studied aluminum wire bond liftoff failure and found junction temperature swings and manufacturing processes to be more important influences on lifetime rather than the junction temperature itself. Hamidi et al. [11] found no significant lifetime enhancement when nickel traces were added to the aluminum but did observe improvement when a molybdenum layer was added between the wire and chip. Held et al. [12] investigated the power cycling withstanding capability of IGBT modules and formulated a useful lifetime expression that combines the temperature swing, the mean temperature and material-specific parameters. Held's studies were meant to analyze the reliability of IGBTs, but because in all cases, the failure was observed in the wire bonds, and researchers have since used the model to estimate lifetime of wire bonds until failure. Matsunaga and Uegai [13] used Held's results for comparison as they came up with a subsequent empirical expression for wire bond life. The experimental findings agreed closely with Held's equation even though Matsunaga and Uegai studied wire bonds on a generic die and not on IGBTs as Held did. Held's model was also used by Bryant et al. [14], in conjunction with rainflow counting algorithm and Miner's rule [15] to develop a compact device model-based reliability assessment method for IGBT power devices for traction applications.

Compared to IGBT, investigations into failure in SiC MOSFET power devices have been fewer and more recent. Santini et al. [16] investigated the threshold voltage degradation in SiC MOSFETs in order to develop a model for determining the remaining life. Qiu et al. [17] used reliability block diagrams, with wire bonds on each die in parallel and the dies themselves in series such that the module reliability function is the product of the each individual component reliability function. According to this model, having redundant wire bonds do not necessarily enhance reliability. Ceccarelli et al. [18] used mission profiles to estimate SiC MOSFET reliability using wire bond as the limiting failure. While all these works are interesting, few of them attempt to determine reliability when SiC MOSFET-based switching devices are used in a more demanding environment, such as in traction applications. In such cases, there are tangible advantages that Si brings over Si-based IGBTs, yet there is often other failure modes that may be triggered before failure in the modules and hence the increased reliability of SiC may not be fully utilized due to limiting failures in other parts of the system. This makes it important to investigate reliability of SiC devices not only as a discrete die but also as a module consisting of SiC dies under extreme conditions.

While there has been prior work done on the reliability of SiC MOSFET power module, the focus of this paper is on making use-condition specific reliability comparison with regard to traction inverters. For that purpose, a tractor drive schedule is used as a mission profile that provides a basis for reasonable comparison. The thermal performance is predicted using a computational lumped capacitance model that is validated with experimental data as well as compared to data from literature. The computational scheme is then used to estimate the thermal parameters using boundary conditions corresponding to extreme use conditions appropriate for traction application, such as high heat dissipation and high coolant temperatures.

The extracted damage parameters are used to compare the predicted reliability of the SiC MOSFET-based inverter to a hypothetical Si-IGBT-based inverter. Emphasis is put on the area deemed to be at highest risk: the switching dies and consequentially the power modules. The results and corresponding discussion make clear the limitations to system level reliability even when component reliability is enhanced, and possible ways of mitigating the reliability concerns are explored.

## Part A: System Description and Lumped Capacitance Model Validation

The traction inverter system is a 250 kW three-phase all-SiC three-level T-type inverter. The detailed system design can be found in Refs. [1921]. Figure 1 shows the schematic of this traction inverter. As can be seen from the figure, each phase consists of one half-bridge module shaded in blue and one common source module shaded in green. All modules include two switch position, e.g., in phase A, half bridge module is built by S1 and S4, and common source module is built by S2 and S3. To drive the modules, dual-channel isolated gate drivers from Wolfspeed are used. In addition, there are two 220 uF polypropylene (PP) film capacitor FFVE6K0227K connected in series in each phase. Laminated bus bar is used to make connections between modules and capacitors to achieve low impedance in order to reduce the voltage and current overshoots and high reliability. Table 1 shows the inverter system specifications.

Fig. 1
Fig. 1
Close modal
Table 1

Inverter system specifications

ParametersValue
Rated power250 kW
Phase current (root‐mean‐squared)300 A
Switching frequency20 kHz
ParametersValue
Rated power250 kW
Phase current (root‐mean‐squared)300 A
Switching frequency20 kHz

The modules are bolted through a commercially available aluminum cold plate (Wieland Microcool CP 3001, from Wieland MicroCool, Decatur, AL) connected to an external chiller (Fig. 2). The equivalent thermal circuit (Fig. 3) was turned into a matlab code to numerically compute the temperature of each component at discrete time intervals when subjected to an input power schedule. The thermal circuit diagram was modeled as a lumped resistor-capacitor circuit and numerically solved as a system of coupled first order differential equations in matlab. The key parameters have been added in Table 2. These values were obtained from a combination of physical dimensions, material properties and, where applicable (such as the module), manufacturer provided datasheet. The table provides the numerical values of the parameters from Fig. 3. The units of R and C would correspond to K/W and J/K, respectively.

Fig. 2
Fig. 2
Close modal
Fig. 3
Fig. 3
Close modal
Table 2

Values of parameters in Fig. 3 used in numerical computation

ParameterRParameterC
R_conv2.8 × 10−3C14385.8
R10.135C2126.3
R20.135C3674.7
R30.31C451.4
R40.1C51344
R_amb10.96
R_amb20.210
ParameterRParameterC
R_conv2.8 × 10−3C14385.8
R10.135C2126.3
R20.135C3674.7
R30.31C451.4
R40.1C51344
R_amb10.96
R_amb20.210

To validate the accuracy of the lumped model, the inverter is loaded to 75 kW on a testbed (Fig. 4) with thermocouples, which are connected to a data acquisition system, placed at the cold plate while a FLIR A550 infrared thermal imaging camera (Teledyne FLIR, Wilsonville, OR) is setup to monitor and record the temperature on the gate driver. Water at 12.8 °C is circulated as the coolant. The resulting temperature profile for the cold plate, when compared to the predicted cold plate temperature profile from the lumped model, show close agreement for the final steady-state temperature but differ for the time constant (Fig. 5). There are several possible reasons for this discrepancy, among which are the approximations regarding the internal volume of the cold plate and the surface area subject to convection by the coolant. Both affect the thermal resistance and capacitance values used in the model and therefore would affect the numerically calculated temperature. For the gate drivers, the temperature plotted in Fig. 5 is the hot spot temperatures (Fig. 6), which is the probable cause behind the difference with the model predictions. However, there is still reasonable agreement, especially for temperature values (Table 3), and therefore, the general fidelity of the model is confirmed.

Fig. 4
Fig. 4
Close modal
Fig. 5
Fig. 5
Close modal
Table 3

Comparison of steady-state temperature and rise time for cold plate and gate drivers

ExperimentalModel% difference
Gate driver39.037.80.06%
Cold plate13.913.80.04%
Rise time (s) (99% of steady state)
Gate driver18022022%
Cold plate38027028%
ExperimentalModel% difference
Gate driver39.037.80.06%
Cold plate13.913.80.04%
Rise time (s) (99% of steady state)
Gate driver18022022%
Cold plate38027028%

The main factors affecting the cold plate temperature in the experiment were:

• The heat dissipated in the dies

• The coolant inlet temperature

• The effective coefficient of heat transfer (h)

• Exchange of heat with surroundings (for cold plate)

Ideally, part (d) should be negligible. To be certain, an energy analysis of the system was carried out based on the coolant inlet/outlet temperature. Heat flow (heat carried away by the coolant) was measured over a repetitive interval using numerical integration, and just assuming that to be all the heat dissipated resulted in a calculated efficiency of 98.9%, which is very close to the predicted efficiency of 99%. The heat lost to (or gained from) the surroundings, in this case, is negligible.

Fig. 6
Fig. 6
Close modal

## Part B: Thermal Performance Based on Lumped Capacitance Model and Thermal Resistance

With the validity of the model established, the next step is to use the model to predict thermal and reliability indicators under use conditions. For this purpose, an Environmental Protection Agency recommended off-road drive schedule for agricultural tractors is chosen as a cases study. The drive schedule is scaled and extended end-to-end (Fig. 7) to make it a good representation of stable operation. The drive schedule was scaled to the maximum per-module power loss of about 700 W. This value was arrived at by applying the target conditions including current, voltage, power factor, switching speed, fundamental frequency, and modulating method. It is to be noted that only the common source modules will be subject to this dissipation, and the normal modules are to be subject to a lower dissipation, whereas in this study, the dissipation is taken to be same in all the modules, and the estimates can be considered conservative. The difference between this drive schedule and those for more conventional vehicles (such as the highway fuel efficiency test cycle, HWFET) is in the amplitude of the temperature swings as well as the number per time. Table 4 gives a brief comparison between the two. The off road schedule would result in greater damage per cycle, and the electronics subject to it need more rigorous reliability demands.

Fig. 7
Fig. 7
Close modal
Table 4

Comparison of off road tractor drive cycle with HWFET drive cycle

Largest power swing (%)79%55%
Average number of swings per minute9.814.35
Largest power swing (%)79%55%
Average number of swings per minute9.814.35

The power dissipation schedule is then set as the input signal into the model, and the output signal provides the transient temperature profile of each component (Fig. 8). Coolant temperature is set at 70 and 105 °C and the ambient temperature at 70 °C, in order to provide the most conservative estimate possible. For a 1:1 water-ethylene glycol (antifreeze) mixture, which is the intended coolant for the system, the boiling point is at 106 °C, and therefore 105 °C is practically the highest temperature it can operate in as part of a single-phase cooling system. The modules are the hottest component in the system as they are source of the dissipation, and the cold plate at the lowest temperature due to its thermal proximity to the coolant. Due to their high thermal capacity, the capacitors have a significantly longer lag time before they reach their temperature peaks. The mean component temperatures after the system reaches a repetitive state is given in Table 5.

Fig. 8
Fig. 8
Close modal
Table 5

Components and their mean temperatures when system achieves stability

ComponentTemperature (C)
Module131.3
Gate driver125.3
Capacitor123.5
Cold plate105.8
ComponentTemperature (C)
Module131.3
Gate driver125.3
Capacitor123.5
Cold plate105.8

Fuentes, Kouro and Bernet [22] compared the thermal performances of SiC-MOSFET and Si-IGBT modules under identical test setup conditions and found that the losses in the Si-IGBT module at 2 kHz was roughly the same as the losses in the SiC MOSFET at 20 kHz at power factor = 1, which is the switching frequency used in the experimental validation. Using the lumped capacitance method along with the case-to-junction thermal resistance, the junction temperatures of the two dies are compared. The junction temperature of the Si die is a few degrees lower than the SiC die, which agrees with the data presented by Fuentes et al. The estimated junction temperatures for the two different coolant temperatures, as well as data from Fuentes, are presented in Table 6.

Table 6

Comparison of lumped capacitance model predictions and Fuentes et al. [22]

Rth (junction to case) (C/W)Tj (Fuentes [22])Tj (Lumped) at 70 C coolantTj (Lumped) at 105 C coolant
Si-IGBT0.083103 C144 C176 C
Si-Diode (IGBT module)0.11487 C121 C150 C
SiC-MOSFET0.100110 C156.3 C190.3 C
Si-Diode (MOSFET module)0.11081 C118 C149 C
Rth (junction to case) (C/W)Tj (Fuentes [22])Tj (Lumped) at 70 C coolantTj (Lumped) at 105 C coolant
Si-IGBT0.083103 C144 C176 C
Si-Diode (IGBT module)0.11487 C121 C150 C
SiC-MOSFET0.100110 C156.3 C190.3 C
Si-Diode (MOSFET module)0.11081 C118 C149 C

The SiC devices are rated for higher maximum temperature of operation due to the its wide band gap. The junction temperature, even though it is greater than that of the Si-IGBT in this instance, is significantly lower than its rated maximum, which is 175 C for 70 C coolant flow. For the Si-IGBT, however, the temperature is very close to 150 C, which is around the maximum demonstrated operating temperature for such devices.

The lifetimes are calculated based on Held's Arrhenius Coffin-Manson model [12, Eq. (1)], with the ‘off’ temperature taken to be at 22 C
$Nf=A ΔTαexp(QRTm)$
(1)

Here, Nf is the no. of cycles to failure, ΔT is the temperature swing, and Tm is the medium temperature. The parameters consistent for Aluminum bond wires are given in Table 7.

Table 7

Parameters used in Eq. (1)

ParameterValue
A5.1 × 109
α−5
Q29,900
R8.314
ParameterValue
A5.1 × 109
α−5
Q29,900
R8.314

The problem with using Held's model in this situation is that it only takes into account the temperature swing. The material properties, and differences thereof, are not accounted for, resulting in a simplistic first pass of analysis. These results are therefore compared to a stress based model that integrates the material properties for thermal and mechanical stresses. A finite element based model is developed which uses the input from the thermal simulations to compute the stresses. The stresses at the peak temperature are compared to the stresses at the storage condition of 22 C, and the difference gives the stress differential, which is the primary failure executor in this model. The analysis is first carried out at the module level, and then the die with greatest stress differential is used for a submodel analysis with aluminum bond wires. The stresses in the bond wires provide the final parameters that are fed into the lifetime model.

The material properties used in the finite element model to compute the von Mises stresses are given in Table 8. The geometries for the finite lement analysis are a widely used commercially available Si IGBT-based power module (Fig. 9), and the same SiC MOSFET-based module used in the experimental testing discussed in the earlier section. Even though the comparison is not universal, they offer a relative assessment of the two technologies as a useful case study. The lifetime model used here is the Basquin's equation [23,24, Eq. (2)], which uses the stress range, Δσ, as the damage metric
$Nf=C (Δσ)−K$
(2)

where the constants C and K are 3.84e23 and 10.34 [25].

Fig. 9
Fig. 9
Close modal
Table 8

Material properties of Si and SiC used to evaluate die stresses in the finite element model

E (GPa)Coefficient of thermal expansion (10 × 10−6 per K)Density (kg/m3)Poisson's ratio
Si1202.623300.29
SiC410431600.14
E (GPa)Coefficient of thermal expansion (10 × 10−6 per K)Density (kg/m3)Poisson's ratio
Si1202.623300.29
SiC410431600.14

## Part C: Die and Module Reliability and Comparison Between Si-Insulated Gate Bipolar Transistor and SiC-MOSFET

The expected reliability of the dies are determined from their cycles to failure value by assuming exponential distribution of failure and taking the cycles to failure predicted by the models to be the mean times to failure (Fig. 10). Here, the reliability stands for the probability of survival based on the mean estimate. The switching dies (MOSFETs and IGBTs) are more susceptible to failure than diodes or any other components, because of their high junction temperatures and associated thermomechanical stresses. The relative comparison shows the Held model agreeing closely with the stress-based model for the IGBT but differing significantly for the SiC MOSFET device. This is reasonable because Held's empirical model was based on studies on Si IGBTs, whereas SiC MOSFETs have very different mechanical properties, which cause them to deviate. In addition, the MOSFET dies having smaller dimensions is a possible reason they developed lower stresses than the IGBT dies. The modules must operate as series/parallel combinations of dies that need to operate together. The reliability of the module is thus a result of the component reliability as well as their configuration. Both modules have dies connected in electrically parallel, which can also be taken to be paralleled in a reliability configuration. The current carrying capacity of each switching die is considered, resulting in a k-out-of-n system. For a current carrying capacity of 15 A for each switching diodes, the commercial SiC MOSFET-based module with 14 switching dies, the system can be seen as two 4-out-of-7 systems connected in series (Fig. 11). This approach is also taken for the IGBT module, and the results are plotted in Fig. 12.

Fig. 10
Fig. 10
Close modal
Fig. 11
Fig. 11
Close modal
Fig. 12
Fig. 12
Close modal

There are other reliability considerations, particularly when the reliability of the system as a whole is assessed. The lowest rated temperature component is the PPFE DC-link capacitors, which therefore may play a limiting role for the entire system. One way to manage that would be by introducing a secondary cooling loop where the capacitors are exposed to basic air cooling. Other solutions may involve using capacitors of higher rated temperatures, but the options there are limited. The results in Fig. 13 are from a parametric analysis of the system discussed in this paper, which shows that introducing a secondary cooling loop for the capacitors is the most effective way to improve system reliability. The capacitor reliability was predicted from manufacturer provided datasheet. Figure 14 gives results of an analysis of system redundancy. This shows how adding just five bond wires per module (for five separate switching dies) would improve reliability almost as much as adding an extra module. This is based on the k-out-of-n system analysis discussed previously.

Fig. 13
Fig. 13
Close modal
Fig. 14
Fig. 14
Close modal

## Conclusion and Future Work

In this case study, the predicted reliability of SiC-MOSFET-based modules in inverter application under off-road, traction mission profile is compared to that of a widely used, commercially available IGBT based module, and the analyses show the conditions to be slightly more suited to reliable operation of the SiC MOSFET than Si-IGBT based ones. The results are not independent of the approach of analysis, as a purely temperature swing-based (Held Arrhenius model) reliability prediction appears to predict higher reliability than a stress-based (Basquin) approach. The two approaches differ little for Si-IGBT, but significant differences are observed for SiC. For the same power dissipation, the SiC die junctions experience junction temperatures that are significantly below its maximum rated temperature, whereas Si devices would nearly reach their limit. This translates to the module level, with the SiC device expected to last about 30% longer in terms of thermal cycles. This implies that SiC devices are suitable for applications where high temperatures can not be avoided, such as for very high power density requirements or where cooling system is restricted due to logistical factors. As this analysis is meant to be a case study of two common modules with different switching device technologies, the dies differ not only in their semiconductor material, but also in die geometry, size and module configuration.

## Acknowledgment

The authors are grateful to Dr. Alan Mantooth and his team at the department of Electrical Engineering, University of Arkansas, and Dr. Chris Farnell of the National Center for Reliable Electric Power Transmission (NCREPT) for facilitating the electrical and thermal testing necessary for this project. The information, data, or work present herein was funded in part by the Advanced Research Projects Agency-Energy (ARPA-E), U.S. Department of Energy, under Award No. DE-AR0000895. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

## Funding Data

• Advanced Research Projects Agency—Energy (Grant No. DE-AR0000895; Funder ID: 10.13039/100006133).

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