Real-Time Temperature Estimation of the Machine Drive SiC Modules Consisting of Parallel Chips per Switch for Reliability Modelling and Lifetime Prediction

Abstract

This paper presents a new methodical procedure to monitor in real time the junction temperature of SiC Power MOSFET modules of parallel-connected chips utilized in machine drive systems to develop their reliability modelling and predict their lifetime. The paper implements the on-line measurements of temperature-sensitive electrical parameters (TSEP) approach, particularly the quasi-threshold voltage and the on-state drain to source voltage, to estimate the junction temperature in real time. The proposed procedure firstly applied computational fluid dynamics analysis on the module under study to determine the chip which undergoes the maximum junction temperature during typical operation of the module. Then, a calibration phase, using double-pulse tests on the selected chip, is used to generate look-up tables to relate the TSEPs under study to the junction temperature. Next, the real-time estimation of junction temperature was accomplished during the on-line operation of the three-phase inverter, taking into account the induced distortion/noises due to operation of the parallel-connected chips in the module. After that, a comparison between the two TSEPs under study was provided to demonstrate their advantages/drawbacks. Finally, reliability modelling was developed to predict the lifetime of the studied module based on the estimated junction temperature under a predetermined mission profile.

1. Introduction

Recent technological advances in power semiconductors have made wide bandgap (WBG) power semiconductor devices, such as Silicon Carbide (SiC) or Gallium Nitride (GaN), an attractive substitute for their silicon counterparts, thanks to their potential higher power density, higher blocking voltage and less switching losses [1,2]. Moreover, the reliability of such devices becomes of paramount importance especially in critical applications such as aerospace and military fields. It is also well known that operating conditions significantly affect the reliability of these power electronic components. The most significant stress factors of power electronic modules are temperature and temperature cycling which result in thermo-mechanical stress due different coefficients of thermal expansions (CTEs) of materials in the modules [3,4]. Repetitive thermal cycling can eventually cause cracks, solder voids and delamination within module interconnection resulting in increased thermal resistance and ultimately even higher junction temperatures (T_j) [5]. Consequently, on-line estimation of junction temperature during the operation of a power electronic converter is therefore essential for its condition monitoring, which can potentially improve its reliability by providing real time up-to-date information for the devices’ health states, and ultimately predicting the remaining useful lifetime [6,7,8].

Real-time measurements of junction temperature (T_j) can be accomplished using one of three approaches [9,10]: optical approach, physical contact approach, or temperature-sensitive electrical parameters (TSEP) approach.

Table 1. Measurement approaches of junction temperature.

Approach	Comments	Method		Reference
Optical	Requires the chip to be optically connected to the detection system and therefore the protective dielectric gel has to be removed	Electroluminescence of MOSFET body diode		[11]
		Laser deflection		[12,13]
		Infrared radiation		[14,15]
Physical contact	Requires significant alterations to module packaging and dielectric gel to place the device as close as possible to the chip	Thermo-sensitive devices such as thermistors or thermocouples		[16]
TSEP	Provides a more practical solution for temperature monitoring since they rely on the thermal dependence of the electrical properties of the semiconductor devices to determine the Tj without modification to the module itself	Threshold voltage (Vth)	(i)  Good sensitivity with negative slope linearity over a wide operational range. (ii) Auxiliary Kelvin source measurement is required.	[17,18]
		On-state Voltage (VDSon)	(i)  Good sensitivity with positive slope linearity over a wide operational range. (ii) Current dependent.	[19,20,21]
		Internal gate resistance (Rg)	(i)  High-resolution ADC is required due to its low temperature sensitivity. (ii) Highly vulnerable to EMI	[22,23]

summarizes the number of applications for each of these approaches. It shows that the TSEP approach has the superiority over the other approaches since it provides on-line monitoring for T_j of the device without the need to modify its module. Furthermore, from the stated literature in Table 1, it demonstrates the advantageous V_th and V_DSon methods to capture the T_j due to their better sensitivity and higher resilience to the electromagnetic interference (EMI) over a wide operating range comparing to other TSEP methods.

Furthermore, some other recent papers have also investigated the application of TSEP methodologies in WBG power devices such as SiC power MOSFETs.

Table 2. TSEP implementation for SIC power MOSFETS.

Paper	Features	Drawbacks
[24]	Quantifies the characteristics of some TSEP including Vth, VDSon, the turn-on transient characteristic (di/dt)	The quantification procedures took place only during the double-pulse test process and have not been verified in real-world operation scenarios
[25]	On-line junction temperature measurement for SiC MOSFET based on Vth extraction	The proposed Vth measurement is experimentally evaluated only through the double-pulse tests, not during real-world operation scenarios as well
[26]	Provides on-line junction temperature estimation using VDSon	It required a thermistor embedded in the module to measure the DBC temperature along with a shunt resistor in series with the switch to measure its current
[27]	Junction temperature monitoring using on-resistance with voltage clamp and current shunt	It required high bandwidth shunt approach integrated in the PCB board to detect the drain current
[28]	Utilizes the gate drive current (ig) during turn-on transients to estimate the Tj	The proposed approaches have high sensing offset 9–12 °C for Tj. In addition, they cannot directly regulate ig during the turn-on transient
[29]	Real-time junction temperature measurement for SiC MOSFETs using turn-on delay approach	It required sophisticated adjustable gate resistance circuit along with high resolution capture device to ensure proper results

highlights some of their features and drawbacks. On the other hand, the on-line estimation of junction temperature during the operation of parallel-connected chips in SiC MOSFETs modules using the TSEP techniques has not been demonstrated yet in the literature.

Recently, large SiC power MOSFET modules that are utilized in different machine drive applications are typically constructed by paralleling a number of dies in order to increase their output current capabilities. The operation of parallel-connected SiC power MOSFETs has been studied in previous papers, in which important issues such as the distribution of the power losses within the parallel devices, the induced resonances and the parasitic oscillations during their commutation, crosstalk and EMI are investigated and studied. Paper [30] presents the key parameters that play important roles in the performance of the parallel operation of the SiC MOSFETs with respect to the device characteristics as well as the circuit layout. In [31], the impact of the electrothermal variation between parallel-connected devices on overall avalanche ruggedness are analyzed. In addition, experimental losses analysis for two parallel-connected SiC MOSFETs is investigated through a double-pulse test in [32] as well as during the operation of DC/DC boost converter in [33].

Furthermore, even though SiC MOSFET have thermally oxidized insulating SiO₂ layers, which have superior dielectric properties, the V_th of such devices suffers from instabilities due to their bias temperature stress (BTS) behaviour. Their BTS causes trapping of carriers near the SiC/SiO₂ interface, which produces a variation in output characteristics of the devices. The presence of carbon atoms during the thermal oxidation of SiC causes a SiC/SiO₂ interface with higher magnitudes across the interface to trap density and oxide charges compared with the traditional Si/SiO₂ interface [34]. Additionally, the SiC/SiO₂ interface is also different from the Si/SiO₂ interface due to its narrower band offsets which reduces the barrier for carriers to scale that leads to the gate leakage current and the gate dielectric degradation. Due to this threshold voltage shift, the positive and negative bias temperature instability contributes to inhomogeneous current distributions in the system, which eventually degrades the commutation of the device and increases its temperature [35,36,37].

Despite of all these challenges in estimating the T_j of SiC MOSFETs devices by TSEP approach, especially in parallel-connected arrangements, this presented paper has achieved the real-time estimation of the T_j of such devices with high accuracy and minimum error with respect to the actual temperature measurements.

This paper presents a systematic route for real-time estimation for the T_j of SiC power MOSFETs modules consisting of paralleled chips per switch using the on-line measurements of V_th and V_DSon. V_DSon and V_th have been selected for estimating the T_j in this paper since they present better temperature sensitivities and higher noise immunities compared to other TSEPs utilized in T_j estimation of semiconductor devices, such as internal gate resistance, saturation current and the switching on/off times.

A measuring board has been designed in this research to cope with the operation of the modules of paralleled connected chips and capture the TSEP under study in a non-invasive manner during real-time inverter operation. The proposed TSEP monitoring is evaluated in a SiC MOSFET prototype module consisting of six paralleled chips per switch. In order to identify the chip to which the TSEP-based monitoring is applied, a computational fluid dynamics (CFD) analysis has been performed in Section 3 to determine the hottest chip during a typical operation. A calibration procedure, using double-pulse tests, is then used in Section 4 to construct look-up tables relating the proposed TSEPs with the T_j of the SiC MOSFET module under the study. In addition, the captured measurements of V_th during the double-pulse tests have gone through distribution and curve-fitting techniques in order to overcome the challenges associated with the V_th divergences in SiC MOSFETs devices due to the induced distortion/noise during the operation of paralleled chips. Subsequently, the real-time estimation of T_j has been implemented in Section 5 and validated for a SiC MOSFET-based three-phase power inverter. Moreover, the two proposed TSEPs under study are compared based on the outcomes of the real-time operation according to their performance and feasibility for modules of parallel-connected chips. Eventually, reliability modelling was then developed in Section 6 for the studied module based on the estimated T_j to predict its lifetime within a predefined mission profile. The lifetime prediction has been performed through Rainflow algorithm and histogram analysis along with the Coffin–Manson model based on the power cycling tests which have been undertaken by the module manufacture. At last, Section 7 discusses the influence of the ageing effects of the SiC power module on the studied TSEPs as well as a refinement process is proposed to amend the T_j estimation to include the deviations in the measured TSEP due to the degradation effects of the module.

2. Proposed Methodical Procedure for the T_j Estimation

A measuring board has been developed in this research for on-line capturing of the V_DSon and V_th for the modules of multiple chips per switch. The developed board emphasizes the non-invasive monitoring of the TSEPs under study during the real-time operation of the three-phase inverter, taking into consideration the induced noises due to the operation of module, which consists of parallel chips per switch.

Schematic circuits for capturing the V_DSon and V_th are demonstrated in Figure 1 and Figure 2, respectively. The V_DSon is acquired during the on-state period. The switch Q1 in Figure 1 is used to disconnect the low voltage measuring circuit from the high voltage drain of the power MOSFET during turn-off. A signal conditioning circuit is also utilized to scale the measured signal to a suitable range for the measuring ADC channels. Figure 2 illustrates the schematic of the triggering circuit that is employed to trigger the ADC channel measuring the gate-to-source voltage (V_GS). The main challenge in on-line measurement of V_th lies in the capturing of the gate voltage at the correct instant at the start of the device conduction time. In this paper, the voltage across the parasitic inductance between the auxiliary Kelvin source (S’) and the source (S) is employed to capture the required V_th signal [38]. This voltage (V_S’S) is generated when the device current I_DS starts to rise during device turn-on. The rising edge of the V_S’S across the parasitic inductance can be then used to trigger the ADC channel measuring the gate–source V_GS effectively at the start of conduction and therefore acquire the V_th measurement. Accordingly, the measurement of the drain-to-source current I_DS is not needed to detect the V_th value in this approach.

Moreover, ferrite beads have been included after each voltage regulator in the measuring board to reduce the oscillations in the generated voltage levels due to the parasitic oscillations between the connected chips [39], and an additional opto-isolation circuit has been implemented between the control and the gate drive circuits to minimize the ground loop in the system [40].

Accordingly, the flow chart of the proposed methodical procedure in this paper for estimating the T_j of the parallel-connected SiC power modules in real time is demonstrated in Figure 3 to be utilized, ultimately, to develop their reliability modelling and predict their lifetime.

3. Thermal Analysis for the SiC MOSFET Module

The power module used in this work, Figure 4, is a SiC MOSFET-based half-bridge. The module has been designed and manufactured by Siemens AG, to provide a power electronic building block (PEBB) for a 99% efficient three-phase power converter with a power-to-weight ratio of 10 kW/kg. Figure 5 shows the CAD drawings of the half-bridge wire-bond-less power module. Twelve MOSFETs were sintered using a silver sintering paste onto the direct copper bonded (DBC) substrate. Since each switch is obtained by parallel connection of six MOSFET dies, in order to identify the device to be monitored in the final application, a computational fluid dynamics (CFD) simulation analysis has been carried out for the module under the study to identify the device with the highest T_j.

The simulation has been established in the ANSYS 2021 R2 Icepak CFD tool to solve the conjugate heat transfer (CHT) phenomena between the different components in the module and the surroundings. The configurations of the utilized CFD simulation are as follows:

• The inlet air temperature is at 40 °C with a fixed airflow rate of 4 m/s.
• SiC chips with thermal conductivity of 150 W/mK.
• Since the thermal conductivity of SiC is temperature dependent and decreases with temperature, the worst-case value for conductivity has been chosen in this paper at T_j = 125 °C [41,42].
• Silver sintering simulated as a solid with thermal conductivity of 250 W/mK [43] and thickness of 100 µm.
• DBC copper Si₃N₄ layers with thermal conductivities 398 and 85 W/mK.

The thermal analysis shown in Figure 6 demonstrates that chip number 9 suffers from the highest T_j in steady-state conditions with total power losses of 150 W, equivalent to 12.5 W per chip. Therefore, this chip will be chosen for the TSEP monitoring in this paper by capturing its V_DSon and V_th to be utilized for the proposed estimation of the T_j in the paper.

4. Double-Pulse Tests

Double-pulse tests have been performed on the SiC Power MOSFET module under study for the purpose of directly correlating the measured TSEPs with a known device temperature and therefore provide calibration look-up tables to be used in real-time implementation. The experimental setup utilized in the double-pulse test is shown in Figure 7 along with its schematic circuit in Figure 8 in which the nominated MOSFET chip implemented in the TSPE under study is indicated with its V_S’S measurement.

A hot plate, as shown in the experimental setup, is used to accurately control the junction temperature of the MOSFET module during the tests. Direct measurement of the junction temperature is performed using a thermal camera capturing the die temperature of the module. The module upper surface is accessible in the given experimental setup through a gap in the gate drive interface board as shown in Figure 7. In this experimental setup, an air-cored inductor (170 μH) is used as load (L) and film capacitor (C) of 600 uF–900 V and has been inserted across the DC bus. A gate drive board (Prodrive Technologies PT62SCMD12) has been used in these tests.

According to the schematic circuit in Figure 8 the lower side switch (Sw_low) is the main switch under study, in which its TSEPs are monitored and captured during the tests using the measuring board. On the other hand, the upper side switch (Sw_up) will act as a diode by providing negative voltage to its gate. Furthermore, Figure 8 illustrates the voltage V_S’S over the parasitic inductance which is used to trigger the ADC channel of the V_th measurement.

Figure 9 and Figure 10 illustrate, at the junction temperature 100 °C and 20 °C, respectively, the V_GS measurement and the voltage signal V_trig1 of the circuit of Figure 2, which is used to trigger the ADC channel of the V_th measurement. As shown in both figures, the main distinction between the two different T_j is in the initiation time of the V_trig1 with respect to V_GS value and its dependence on the T_j. As the T_j increases, the switch will be able to create a conductive channel between drain and source faster than that at lower T_j condition with the same DC bus voltage. This eventually leads to lower V_th voltage value with increasing of the T_j. Accordingly, the V_trig1 signal is generated sooner in the case of T_j = 100 °C and the corresponding ADC will then initiate conversion earlier, i.e., with V_GS =3.45 V as shown in Figure 9, compared to V_GS = 3.85 V for the 20 °C case in Figure 10. The captured measurements by the ADC channels are transferred to a graphical user interface (GUI) through a serial peripheral interface (SPI) communication.

The acquired measurements for V_th at the 100 °C and 20 °C by the ADC channel are illustrated in Figure 11 and Figure 12, respectively. It is worth noting that there is an offset of approximately 0.55 V between the V_th captured by the ADC channels (Figure 11 and Figure 12) and those illustrated by the oscilloscope and the voltage probes (Figure 9 and Figure 10). This is mainly due to the low pass filter effect of the larger input capacitance of the voltage probes on the captured signals, which causes a delay in measuring the signals by the oscilloscope.

It is also worth to mention that the sampling frequency that has been used in the paper for the double-pulse tests (as well as the following real-time operation) is 10 kHz, equivalent to 100 usec sample time, while the required ADC conversion and measuring times during the tests typically take 0.92 usec. Consequently, the ADC process is almost undertaken within 1% of the sample time of the testing operations, so the error due to these ADC processing times is avoided. On the other hand, the total delay time, from applying the triggering signal of V_S’S at the input of the trigger circuit (Figure 2) until the ADC unit initiates its conversion process, is taken around 5.3 nsec only so that an accurate measurement of V_th is achieved from the V_GS profile during the turning-on of the SiC device given that the rise time of the V_GS during the turn-on period is around 200–300 nsec.

Figure 13 and Figure 14 show the V_DSon signals captured by the ADC channel at 100 °C and 20 °C, respectively. Since the on-state resistance (R_DSon) has a positive temperature coefficient, i.e., it increases as T_j increases, consequently the V_DSon also increases with T_j but with a potentially nonlinear and current-dependent relationship.

Accordingly, based on the captured measurements through Figure 11, Figure 12, Figure 13 and Figure 14, it is demonstrated that the captured TSEP, V_th and V_DS-on, are mostly steady and constant across the measuring interval taking into the account the same operation and temperature condition. Figure 11 and Figure 12 illustrated a maximum deviation of 5% had occurred for V_th measurements, while Figure 13 and Figure 14 shows a maximum deviation of 1% had taken place in V_DSon measurement.

Figure 15 shows that the gate driver adapter board, mounted on the power module, features a cut-out that allows direct visual and physical access to three of the twelve SiC MOSFET dies in the module. The top surface of the module is coated with boron nitride paint to provide a high emissivity surface for the thermal camera. The temperature measurements for the three visible dies are illustrated in Figure 16 which indicates the temperature variations within these three dies to be around 5%. Figure 15 also illustrates the micro-coaxial contact, SM, in the gate driver adaptor board that enables the access to measure the V_SS’.

A series of double-pulse tests have been carried out on the SiC Power MOSFET module under the study at 500 V DC throughout different T_j and different drain-to-source currents (I_DS). The T_j has been independently measured using a thermal camera as shown in Figure 17 and Figure 18. The thermal imaging is calibrated via the thermal camera software by taking the average temperature across the MOSFET die under study. Examples of thermal measurement error analysis is illustrated in Figure 17 and Figure 18 as well using a boxplot approach.

An example of the waveforms of the V_GS, V_DS, I_DS and the load current (I_out) during one double-pulse test at 19 °C T_j is shown in Figure 19 in which the magnitude of the I_out is controlled by the width of the first pulse of the test. However, the second pulse is used to maintain the current at the required value during acquiring the TSEP by the measuring board. I_out is captured using the LECROY-CP150 current probe; however, I_DS is acquired using CWT Ultra-mini Rogowski coil.

In order to disregard the false triggering events in measuring the V_th in the SiC MOSFET devices, a filtering based on a voltage band around the expected values of V_th is applied. In addition to that, the captured values of both V_th and V_DSon have also been post-processed to develop the best relationship that correlates the T_j to TSEP under study with the lowest error to overcome the variations in both TSEPs due to the induced distortions during the operation of the paralleled connected chips. Figure 20 and Figure 21 present an example of these applied post-processing analyses in this paper.

Figure 20a–d show the number of captured samples of the TESPs under study at T_j equals 90 °C with different load currents 20 A, 40 A and 60 A. Figure 21 illustrates the applied distribution fitting approach to process the captured V_th samples of Figure 20a. Firstly, the histogram of the captured samples is developed to designate the best probability distribution function that could fit the captures values.

As shown in Figure 21, the normal distribution function is a better candidate to represent the captured values based on the developed histogram. After that, the mean value of the estimated distribution function is then calculated to represent the value of the V_th at this testing instance. Similar to the V_DSon captured samples, but this is repeated at each output current value (I_O) as illustrated in Figure 20b–d, since this parameter is current dependant. Accordingly, this distribution-fitting technique has been carried out for all captured samples of the TSEP under study in order to select the proper value that could represent the measured TSEP at each testing condition. It has also been recognized that the variance of the fitted distributions for the captured samples of the two TSEPs are relatively increasing with the increase of I_out as well as T_j since both factors contribute to raising the effect of the induced noise and parasitic oscillations generated during the operation of the parallel chips of the module. Finally, a curve-fitting technique was developed to predict the best relationships with lowest errors between mean values for each TESP and the measured T_j. These relationships are then employed in the upcoming real-time estimation of the T_j in Section 5.

Some of the developed curve-fitting relationships from the applied double-pulse tests are provided in Figure 22 for the V_DSon and Figure 23 for the V_th versus different T_j as well as different I_O. A good linearity for V_DSon with respect to T_j is demonstrated in Figure 22. Sensitives of approximately 1.45 mV/°C and 1 mV/°C are estimated at output currents 60 A and 40 A, respectively. The single-chip datasheet [44] provides a sensitivity of at 5.5 mV/°C at I_DS of 50 A, which results in approx. 0.92 mV/°C for six chips per switch, assuming symmetric current sharing between the parallel chips.

The expected negative temperature coefficient of V_th is confirmed along with the invariance to load current as demonstrated in Figure 23. A relatively good linearity is observed. Good sensitivity of around 6.6 mV/°C is comparable to approximately 5 mV/°C given in the device datasheet. The main reasons for this discrepancy are the approach to capture the V_th in the datasheet compared to the method implemented here in this paper.

5. Real-Time Inverter Operation

The proposed on-line estimation for junction temperature for SiC MOSFET under the study is evaluated in the real-time operation of a three-phase inverter. The three-phase inverter used for this study is a three-leg half-bridge-based converter used to supply a three-phase RL load. The layout of the three-phase inverter is provided in Figure 24 along with its schematic circuit in Figure 25. Due to the availability of prototype module under the study, the inverter was constructed using only a single prototype module (M₁) and the remaining two legs of the converter were implemented using commercial off-the-shelf modules (CREE CAS300M) (M₂ and M₃). A table of components utilized in this inverter circuit are listed in

Table 3. Components of the three-phase inverter.

Components	Description/Values
MOSFET module (M1)	SiC MOSFET Module under study
MOSFET module (M2 and M3)	CREE CAS300M12BM2
DC Link Capacitor (C1)	600 µF Film capacitor
Module mounted Capacitors (C2, C3, C4)	2.2 µF Polypropylene
Load Inductor (L)	3 Phase 320 µH Inductor
Current sensors	LEM LF 205-S
Gate Driver Boards	Prodrive PT62SCMD12

with their descriptions and values. During testing, the inverter was driven so as to output a sinusoidal output current at a frequency of 200 Hz into the load with a 10 kHz switching frequency. To validate the temperature values predicted by the TSEP, a thermal camera has been utilized to measure the die temperature of the module during the inverter operation.

5.1. On-Line T_j Estimation Based on the V_th Measurements

Figure 26 illustrates the waveforms of the gate-to-source voltages (V_GS) of the three switches in the lower sides of the three MOSFET modules (legs) in the three-phase inverter. The voltage across the parasitic inductance (V_S’S), which is used to trigger the ADC channel to capture the V_th as discussed in previous sections, is shown in the bottom trace in Figure 26.

Figure 27a illustrates the signal captured directly by the ADC channel for the V_th measurement. This signal does not present the actual value for the V_th since there is a signal conditioning circuit between the measured point on the V_GS and the ADC channel in the measuring board in order to adjust the measured signal to be within the measuring scale of the ADC channel. After suitable scaling, the actual measured V_th is shown in Figure 27b. It is worth noting that during the on-line acquisition of the V_th measurement, false triggering instances for the ADC channel took place, as illustrated in Figure 27a. The main causes of these events are the switching events of other device/chips in the module and the other phases, EMI noise within the system and parasitic module. As shown in Figure 27a, these false triggering events will result in measurements of V_th outside of the typical range and therefore can be discarded from further processing using a filtering based on a voltage band around the expected values of V_th.

The real-time estimation of the T_j using the V_th is evaluated throughout the operation of the three-phase inverter over a period of 20 min. The inverter has a 500 V DC input and outputs 90 Arms current at 200 Hz. The measured T_j along with the post-processed value of V_th (V_{th post-pro}) is illustrated in Figure 28. During this test, T_j increases from approximately 30 °C up to 120 °C, while V_th decreases from 2.65 V down to 2.05 V. The measured V_th values are utilized to estimate the T_j based on the look-up table produced with the double-pulse tests. Figure 29 shows the measured and the estimated junction temperatures during the test. Figure 29 validates the effectiveness and the accuracy of the proposed approach for the on-line estimation of the T_j using the V_th measurements, where a maximum divergence of approximately 2~3 °C is found between the estimated and the measured T_j values over a whole duration of the running test of the inverter operation.

5.2. On-Line T_j Estimation Based on the V_DSon Measurements

The proposed approach to estimate the T_j using the measurements of V_DSon is graphically shown in Figure 30. The off-line double-pulse tests are utilized to generate a 3D look-up table of R_DSon = V_DSon/I_DSon as a function of I_DSon and T_j. An inverse look-up table T_j (R_DSon,I_DSon) is then generated off-line using the MATLAB 2023-a curve-fitting toolbox and utilized afterwards for the on-line estimation process of the T_j. I_DSon can be assumed equal to the load current.

Samples of the real-time measurements of V_DSon during the on-line operation of the three-phase inverter are provided in Figure 31 for two different T_j, (55 °C and 125 °C). The waveforms illustrate the sinusoidal pattern of the measured V_DSon, which reflects the sinusoidal output phase current during three-phase inverter operation. Only the positive half of the V_DSon waveform is captured in the implemented measuring board in this study in order to increase the resolution for utilizing the available input range of the measuring ADC channel.

The proposed real-time estimation of T_j is eventually performed as demonstrated in Figure 32. Figure 32 illustrates the measured T_j as well as the post-processed values of V_DSon (V_{DSon post-pro}) during the test of the inverter operation at 500 V DC input voltage and 90 Arms, 200 Hz AC output current. During this test, T_j increases from around 60 °C up to 125 °C. Similarly, the V_DSon has also increased from approximately 430 mV up to 590 mV. Figure 33 shows the same measured T_j but along with the measured R_DSon during the test.

Finally, the measured T_j and the estimated T_j using the developed look-up table T_j (R_DSon,I_DSon) are compared in Figure 34 and Figure 35 as functions of the experiment time and R_DSon, respectively. Accordingly, an advantageous and good T_j estimation has been demonstrated based on the proposed approach of the measurement of the V_DSon in this study, where a maximum of 5~6 °C difference took place between the measured and the estimated T_j during the whole running operation period.

5.3. Comparisons Between the TSEPs Under Study

In addition to the common steps that have to carried out to implement both TSEPs under study in modules of parallel-connected chips,

Table 4. Comparisons between V_th and V_DSon as TSEP based on the demonstrated case studies.

	Vth	VDSon
Requirements	The VS’S measurement to trigger the measuring ADC channel for the Vth	The VS’S measurement to trigger the measuring ADC channel for VDS after a predefined time delay Additional high voltage switch is required to block the high turn-off voltage from the measuring circuit Additional current sensor to measure the IDS current through the chip to which the TSEP method is applied (1)
Dependents	Temperature	Temperature and IDS current
Performance	Linear with negative slope characteristics Sensitivity of 5~6.6 mV/°C	Semi-linear with positive slope characteristics Sensitivity of 1~1.45 mV/°C
Estimated error	Maximum divergence of 2~3 °C between the estimated and the measured Tj	Maximum divergence of 5~6 °C between the estimated and the measured Tj

⁽¹⁾ Not applicable in most of the modules of paralleled chips per switch.

provides a summary for the differences between these two parameters with respect to their individual requirements for implementation, along with analyses for their performances and feasibilities in modules of parallel-connected chips based on the demonstrated case studies in the paper.

Since the I_DS current through one chip is normally not accessible in the majority of the modules of paralleled chips unless an alteration is performed in the module configuration, so it is assumed in this paper that the total I_DS current is equally distributed in the parallel chips. However, this could be challenging for the TSEP approach using the V_DSon measurement since the current through paralleled chips are varied due to the individual temperature of each chip. Accordingly, based on Table 4 as well as the previous statement, it is shown that the V_th is a better candidate to be utilized for the T_j estimation based on TSEP approach for modules of paralleled chips as it has lower requirements and less estimated error along with better performance and sensitivity compared to the implementation of V_DSon as TSEP. As a result, the measurement of V_th is designated to be employed for estimating the T_j of the module under study for the forthcoming reliability modelling and lifetime prediction analysis.

6. Reliability Modelling and Lifetime Prediction

The on-line estimation of the T_j represents the cornerstone to establish the reliability modelling and lifetime prediction for the new designed SiC MOSFET module under study which has been manufactured with the new wire-bond-free planar technology. A lifetime model for the studied module has been developed based on the Rainflow counting analysis using the power cycling tests performed by module manufacture. A mission profile representative of a machine drive operation utilized for aircraft flight has been used to provide a quantification of the estimated lifetime.

Figure 36 illustrates a flow chart with the steps to perform the proposed lifetime prediction of the SiC MOSFET module. Firstly, for a given mission profile, the estimated T_j profile (as a stress profile) is acquired along with the associated maximum T_j as well as the maximum case temperature (T_C). Next, the estimated T_j profile is then processed through the Rainflow cycle counting algorithm to estimate the local maxima and minima (extremes) of the given T_j profile. These extremes are then utilized in the following histogram analysis to evaluate the number of cycles (n_i) per amplitude of junction temperature cycles (ΔT_j-i) through the T_j profile. On the other hand, power cycling tests have been developed to acquire the numbers of cycles to failure (N_f) for different ΔT_j so that the relationship between N_f and the ΔT_j could be then achieved based on the Coffin–Manson model [45,46]. As a result, based on the outcomes of the developed histogram analysis as well as the Coffin–Manson model, N_fi for each ΔT_j-i is estimated which are used in evaluating the lifetime consumption (LC_i) corresponding to each ΔT_j-i. Finally, by applying Palmgren–Miner linear damage accumulation rule, the total lifetime consumption (LC) is calculated so that the anticipated lifetime becomes the inverse of the value in load cycle units. These successive steps are demonstrated thoroughly in the following figures.

Based on the defined mission profile, the estimated T_j profile of the module under study is developed as shown in Figure 37. This estimated temperature profile is utilized subsequently in the Rainflow analysis. Rainflow cycle counting algorithm has been performed in order to estimate the local extremes of the developed temperature profile. Figure 38 shows the estimated extremes. The following step is to establish the histogram analysis for these extremes and define for each histogram bin its temperature amplitude (ΔT_j-i) as well as the associated number of cycles (n_i) for each ΔT_j-i. Figure 39 demonstrates the developed histogram analysis for the estimated extremes from the Rainflow algorithm.

Module manufacture has provided results of power cycling tests for the studied module prototype, so the N_f versus different ΔT_j are given at the predefined maxima of T_j and T_C. Consequently, the Coffin–Manson model is then developed to evaluate the relationship between N_f and ΔT_j where the model coefficients are estimated statistically based on provided data from manufacture power cycling tests.

Figure 40 illustrates the given data from the power cycling tests along with the Coffin–Manson model relating the N_fi and T_j-i as follows:

$$N_{fi}=k {\left(∆T_{j\text{-}i}\right)}^{-m}$$

(1)

where

k = 7.6854 × 10⁸

m = 2.188

Figure 40. Coffin–Manson Model between N_f and ΔT_j.

Figure 40. Coffin–Manson Model between N_f and ΔT_j.

Table 5. Life consumption and lifetime evaluation for the module under study.

∆Ti	5.2	22	55.6	80.8
ni	3	1	2.5	0.5
Nfi	2.08 × 107	8.88 × 105	1.17 × 105	5.16 × 104
LCi	1.44 × 10−7	1.13 × 10−6	2.14 × 10−5	9.70 × 10−6
LCtotal	3.2373 × 10−5
Lifetime	30,890 (load cycles) ≈ 70,275 h

provides the predicted N_fi for each of the defined ΔT_i from histogram analysis of Figure 39. It is shown that the predicted N_f, resulted from ΔT_j at 80.8 °C, is equal to 5.16 × 10⁴ cycles, while the experimental N_f plotted in Figure 40 at 82.2 °C reached 5.76 × 10⁴ cycles, which gave around 10% variance in such condition.

The final steps towards the evaluation of the lifetime are also demonstrated in Table 5 based on the developed histogram bins in Figure 39 and the estimated Coffin–Manson model in Figure 40. The lifetime consumption (LC_i) corresponding to each ΔT_j-i in Table 5 is calculated in

$${LC}_i={\displaystyle \frac{n_i}{N_{fi}}}$$

(2)

As a result, the total combined lifetime consumption (LC) from the different ΔT_j from Table 5 becomes

$$LC={\sum }_i{\displaystyle \frac{n_i}{N_{fi}}}$$

(3)

where i is from 1 to 4.

Finally, the lifetime is estimated as follows:

$$lifetime={\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$LC$}\right.},\text{in load cycles}$$

(4)

Based on the developed reliability model, it is estimated that the device can survive approximately 30,890 load cycles at the specified mission profile which is equivalent to 70,275 flight hours based on the given load cycle of 136.5 min.

In view of that, this section presents how the estimated T_j from the previous sections can be employed to model the reliability of the SiC module under study and predict its lifetime based on a given mission profile. Even though there are other statistical component-level models as given in [47] that can also be adopted to perform the lifetime prediction, they also still require monitoring the T_j as a degradation indicator in real time to update their models’ parameters which were developed in the offline environment.

7. Influence of the Aging of the SIC MOSFETS on the Studied TSEPs

Both TSEPs under study are relatively influenced by the aging effects of the SiC power module in which their values are increasing with the device aging at the same operating T_j due to the gate oxidation degradation that increases the interface trapped charge Q_it [48]. On the other hand, to ensure that the degradation tests are representative to the real-world operational conditions as well as the deviations in the TSEP are reflecting only the aging effects, it has to accurately implement the expected environmental factors and conditions that the module will encounter during its lifespan. This involves selecting appropriate accelerated aging techniques, considering environmental factors like temperature, humidity, pressure, electromagnetic interference, etc.

Accordingly, a refinement arrangement is demonstrated in Figure 41 to compensate the divergences in the TSEP under study due to the module degrading effects. This process will include additional accelerated power cycle tests to be applied on the modules under test to correlate the deviations in the TESP under study to T_j as well as to the number of the power cycles (N_cyc) that will be performed on a module till it fails [48]. These accelerated power cycle tests can be applied using sequences of DC or AC power cycle tests till the module under test fails [48,49]. The relationship between the deviations in the TSEP, T_j and N_cyc is established after reaching the failure of one of the modules. This relationship will be then fed to the T_i estimation procedure for other healthy similar modules during its real-time operation in which the number of executed N_cyc will be involved in the estimation process of the T_j to compensate the variations in the TSEP under study due to the module aging effects.

The black route in the illustrated diagram of Figure 39 shows the original procedure for estimating the T_j for the modules of paralleled connected chips without taking into account the deviations in the TSEP under study due to the aging effects of the module. The outcome of this procedure will be denoted as (T_jest). On the other hand, the red route demonstrates the additional refinement process in order to take into consideration the module aging effects in which the number of the executed N_cyc on the module is utilized as well as the estimated T_j to predict the deviation in the TSEP (TSEP_dev) based on the look-up tables established by the accelerated power cycle tests. The N_cyc is calculated in this process by defining maximum and minimum boundaries for the T_jest (which are identical to those that are chosen for the accelerated power cycles); consequently, the variation in the T_jest across these boundaries are used to estimate how many N_cyc are executed on the module during its real-time operation. The resultant TSEP_dev will then amend the measured TSEP during the real-time operation of the module to evaluate the correct value of the estimated T_j. The outcome of this final process will be labelled as (T_{j corr}) which will be continuously updated through the refinement procedure of the red route. This proposed refinement procedure is planned to be evaluated in the ongoing future work when additional modules become available from the manufacture side since this module as a new designed prototype is currently under limited availability.

8. Conclusions

This paper presents a systematic procedure to estimate in real time the T_j of the SiC MOSFET modules of paralleled connected chips utilized in the new machine drive systems in order to develop their reliability modelling and predict their lifetime. A measuring board has been designed in this research to capture correctly the TSEP under study: V_th and V_DSon, to be used in the on-line estimation of the required T_j. The developed approaches were able to cope with the induced resonances and the parasitic oscillations during the commutation of the parallel chips and captured the correct TSEP values. Both TSEP approaches have then been evaluated and validated in a realistic high power application of a three-phase inverter. It is concluded that both approaches provide adequate sensitivity and linearity between the respective TSEP and the T_j (sensitivity of 5~6.6 mV/°C for V_th and 1~1.45 mV/°C for V_DSon). The temperature estimation based on V_th, however, appears simpler in implementation as it does not require output current measurement and it also provides a lower estimation error of 2~3 °C compared to 5~6 °C for V_DSon. Eventually, reliability modelling and lifetime prediction was developed for the SiC module under study based on the estimated T_j as well as the power cycle tests provided by the manufacturer. The lifetime has been predicted using Rainflow and histogram analyses under a predefined mission profile representing an aircraft flight. It shows that the module can operate up to 70,275 h which is equivalent to 30,890 cycles of the given load mission profiles. Lastly, a divergence of 2~3 °C in T_j estimation using V_th approach resulted in a maximum deviation of 10% in the predicted lifetime. On the other hand, with a divergence of 5~6 °C in T_j estimation using V_DSon approach, a maximum deviation of 17% in the predicted lifetime occurred. Furthermore, based on the available experimental power cycling tests carried out by the module manufacturer, it is shown that the predicted lifetime of 70,275 h is attributed to around 90% confidence level.