Junction Temperature Measurement Based on the Internal Gate Resistance for a Wide Range of Power Semiconductors

This paper presents research results on the junction temperature measurement via the internal gate resistance in converter operation for IGBTs and its applicability to other types of active power semiconductors. A junction temperature monitor has been developed to determine the value of the temperature-dependent internal gate resistance by using a sinusoidal voltage superimposed on the gate voltage at the resonance frequency. The device enables a simple and robust junction temperature measurement in inverter operation, which is in excellent agreement with an infrared reference measurement. The method's applicability to semiconductors other than Si-IGBTs, such as SiC-MOSFETs, JFETs, and GaN devices, is verified by gate impedance measurements using a network analyzer. The gate impedance's quality factor is decisive. Other temperature-sensitive electrical parameters (TSEPs) related to the switching behavior depend on the internal gate resistance. Therefore, the findings presented are relevant for many junction temperature measurement methods.


I. INTRODUCTION
Measuring the junction temperature of power semiconductors in practical operation can be relevant for several reasons. First, temperature measurement can detect faulty system conditions and stop operation when the maximum junction temperature is exceeded to avoid catastrophic failure. In addition, the temperature measurement during the converter operation can help to decide whether the system design is over-or even under-rated in terms of the performance of the semiconductors. The design of power electronic circuits is typically based on laboratory loss and temperature measurements and calculations based on specific load profiles [2]. The temperature measurement under real operating conditions can verify the complete design processes. In addition, temperature measurement is suggested to monitor the system's health or to detect degradation [3], [4], [5].
Power semiconductor modules often use negative or positive temperature coefficient sensors, usually soldered near the chips on the DBC ceramic substrate. The sensor value represents the base plate temperature for modules with a base plate. Sensors in modules without a base plate measure the approximate heat sink temperature. These sensors cannot capture the junction temperature because they are located too far away.
The most promising TSEP methods are either based on the forward voltage, the internal gate resistance, or changes in the dynamic switching behavior. The forward voltage can only be measured when current is flowing through the device. It also depends on the semiconductor current, which can be either a small sense or a load current. For thermal impedance measurements and degradation tests, a small sense current at a defined level is usually injected [12], [26], [27]. In converter operation, the small sense current can only be injected in idle phases [28]. An additional, accurate current sensor is necessary for online monitoring during converter operation. The temperature can be determined with a two-dimensional matching depending on measured load current, and forward voltage [29], [30], [31]. Additionally, the gate voltage can be varied to determine the temperature from the forward voltage at an equivalent current level [29]. The forward voltage can also be measured with additional diodes on the chip area, connected to a small current source [32], [33].
The problem of the current dependency does not arise with the internal gate resistor as TSEP. To prevent oscillations between parallel connected chips, many power semiconductor chips contain an internal gate resistor, typically consisting of polysilicon and located directly on the chip. Thus, the resistance value depends on the chip temperature. The internal gate resistor method cannot be applied to passive power semiconductor devices like the anti-parallel diode in IGBT inverters. Still, with the increased use of SiC-MOSFETs without parallel diodes, the significance of this drawback will decrease. The main part of the internal gate resistance normally consists of a polysilicon resistor, which is located on the semiconductor chip and has a positive temperature coefficient. The measurement of the internal gate resistance can be based on a superimposed high-frequency measurement signal on the gate voltage in either on-or off-state [11], [13], [34], [35], via DC gate current injection [36] or via measurement of the peak gate current [37], [38].
Another group of TSEPs is based on changes in the dynamic switching characteristic, which also depends on the temperature and the value of the internal gate resistance. The turn-on respectively turn-off delay as TSEP has been investigated in [16], [17], [18], [19], [39], [40], [41]. The threshold voltage can also be applied as reported in [14], [29], [42], [43], [44]. The voltage or duration of the Miller voltage plateau have also been analyzed in [40], [45]. Other dynamic switching parameters like the reverse recovery behavior [46] or the short-circuit current [47] have also been proposed as TSEPs. Most of these TSEPs based on the dynamic switching behavior have only been tested in a double pulse laboratory setup and for a specific type of semiconductor.
The internal gate resistance and the transfer characteristic of devices of the same type can vary slightly due to tolerances. The highest measuring accuracy can be achieved through a component-specific calibration for these TSEP methods. The junction temperature measurement based on the internal gate resistance is superior to other TSEPs, due to the independence from the current and the applicability to many semiconductors. In addition, it does not require high dynamic accuracy of the measuring equipment. This article shows how well the junction temperature measurement with the T J -R Gi -monitor works in converter operation with IGBTs and what needs to be considered. In addition, it is investigated and successfully demonstrated whether this method can be transferred to other semiconductor types.
The rest of the paper is organized as follows. Section II explains the operating principle of the junction temperature monitor based on the internal gate resistance. Measurement results in inverter operation with IGBTs are presented in Section III. The applicability to other semiconductor types is investigated by gate impedance measurements with a network analyzer in Section IV. In Section V, the knowledge gained from the impedance measurement is transferred to a SiC MOSFET. The temperature is recorded with the T J -R Gimonitor during the heating and cooling phase to demonstrate how easily the thermal impedance can be determined. Finally, Section VI concludes this article.

II. OPERATING PRINCIPLE OF THE JUNCTION TEMPERATURE MONITOR
Measuring the internal gate resistance R Gi enables the determination of the junction temperature of power semiconductors. The measured temperature usually correlates to the temperature of the dedicated polysilicon R Gi near the gate pad. The temperature dependence of R Gi is almost linear for most DUTs and has a temperature coefficient of about ( 1 ) The principle of the measurement method has been first described in [48]. A driver-integrated solution has been demonstrated in [34] and a plug-and-measure device in [11]. It is outlined in Fig. 2. By excitation with a sinusoidal voltage source, knowing u 1 and u 2 , the absolute value of the gate impedance Z can be measured at an adjustable DC-gate voltage u gs . If the frequency of the signal source u 1 corresponds to the resonant frequency f res of the gate circuit (typically 1 to 40 MHz), the internal gate resistance R Gi and the parasitic resistances R p in the gate circuit are measured, since the imaginary parts of the parasitic stray inductance of the gate circuit L p and the input capacitance C iss cancel each other. It is: At resonance frequency ω res = 1/ L p C iss it is: The internal gate resistance on the chip has to be the dominant part of the resistance, and the parasitic resistance of, e.g., bond wires from the package pins to the die, has to be small for an excellent junction temperature measurement (R p << R Gi (T j )) [49]. This is typically the case for most internal gate resistors with a value greater than 1 . Further details are given in Section IV. The absolute value and the real part of an exemplary IGBT gate impedance measured with a vector network analyzer Bode 100 from OMICRON Lab, depending on the frequency and temperature, are shown in Fig. 3(a). The real part increases with frequency due to the skin effect. By adopting the sinusoidal oscillation frequency to the resonance frequency f res , the ratio of measured stimulation voltage and the resulting current is equal to the real part, mainly formed by the internal gate resistance.
Based on this principle, the T J -R Gi -monitor has been designed as a measurement device, which can be installed between the gate driver and the DUT (see Fig. 4) [11]. During the measurement phase, the gate voltage is superimposed with a sinusoidal small voltage source u 1 with an amplitude of 600 mV. The current is determined via an additional measurement resistor R m and the voltage u 3 . After RMS and ADC processing, the internal gate resistance and thus temperature are calculated by a microcontroller STM32F303RET6 and transmitted to a PC via a fiber optic USB interface. The measurement phase is normally during the DUTs off-state in converter operation but can also be configured in on-state for thermal impedance measurements. Thus, the coupling switches S 1 and S 2 must be bidirectional. The mostly linear relationship between internal resistance and temperature (see Fig. 3(b)) typically enables a two-point calibration on a heating plate. For several semiconductors of the same type, it has been shown that the temperature coefficient is very similar. However, the absolute value of the internal gate resistance can vary slightly. For industrial use, at least a one-point calibration must be carried out, e.g., when starting the device.
The power loss within the internal gate resistance due to the superimposed measurement voltage is in the lower milliwatt range. The conduction and switching loss in the regular operation of the chip is in the range of several watts. Thus, the self-heating due to the superimposed measurement voltage can be neglected.
The measured temperature is equal to the temperature at the location of the internal gate resistance, which is typically in the center of the chip. In contrast, the temperature based on the forward voltage measurement equals the mean temperature over the total active chip area [50]. For the regular operation of chips without degradation [51], both temperatures are relatively close, as shown in the infrared measurement in Fig. 5. The infrared image of a power semiconductor with a non-uniform chip surface temperature also makes it clear that there is no single accurate junction temperature. The virtual junction temperature is sometimes used as an equivalent value determined by the forward voltage method.

III. JUNCTION TEMPERATURE MONITOR APPLICATION WITH IGBTS A. ONLINE JUNCTION TEMPERATURE MEASUREMENT IN CONVERTER OPERATION
The internal gate resistance is typically measured in the switch's off-state with the T J -R Gi -monitor in converter operation (see Fig. 6). Simplified, the measurement phase with duration t meas starts after a delay time t delay after the transition into the switch's off-state. Normally, only a single measurement value is obtained per measurement phase during the length of the ADC window t ADC , which is normally at the end of t meas due to a ring buffer structure implemented in the microcontroller. The ADC sample rate is 4 Megasamples per second. Optionally, consecutive ADC windows can be set to filter common mode disturbances due to other switching semiconductors within an inverter [1]. All three times t meas , t delay  and t ADC can be adjusted with the T J -R Gi -monitor. The measurement phase also includes a coupling and decoupling time, which is necessary to insert the measurement circuit between the gate driver and the DUT gate circuit (see Fig. 4(a)). If the measurement phase is longer than the switch's off time, then the T J -R Gi -monitor is immediately decoupled within 200 ns, and the measurement value is discarded. The sampling rate of the temperature measurement depends on the switching frequency, as the measurement is only once per switching period. Further limits are the transmission rate to the PC and the capability of the microcontroller, but sufficient temperature sampling rates in the range of 1 kHz to 10 kHz are feasible.
All presented temperature measurements have been obtained with a six-pack IGBT module FS200R12PT4 in singleor three-phase inverter operation with inductive load (3x 1 mH inductors) depicted in Fig. 7. The switching frequency is 2.5 kHz. The DC-link voltage is adjusted to match the allowable current rating depending on the impedance, which varies with the output frequency.
Temperature measurements at a small output frequency of f out = 1 Hz are helpful for a characterization of the thermal impedance because they show a relatively large ripple. The load current and temperature measurements in single-phase inverter operation are presented in Fig. 8.
Three-phase inverter temperature measurements at output frequency f out = 50 Hz and varying modulation index are depicted in Fig. 9 at various time levels. Next to the T J -R Gimonitor temperature value, the IR-pyrometer temperature is shown. For the IR-pyrometer measurement, the IGBT module is open and blackened (see Fig. 7) to demonstrate the perfect matching with the T J -R Gi -monitor temperature values.
The IR temperature values have a sample rate of 10 kHz. The average sampling rate of the T J -R Gi -monitor values is  lower due to the inverter switching frequency of 2.5 kHz limiting the measurement phase rate. The measurement shows that the T J -R Gi -monitor enables a simple and robust temperature measurement during converter operation with varying load profiles. This is confirmed by an almost perfect match with the IR-pyrometer reference measurement of a specially prepared module. The associated measurement at f out = 50 Hz of the three-phase currents and a single output voltage of three-phase inverter operation is presented in Fig. 10.

B. SELECTING A DISTURBANCE-FREE GATE VOLTAGE
The internal gate resistance is part of the gate impedance, which is depending on the frequency due to the gate capacitance and parasitic stray inductance (see Fig. 4(a)). The gate capacitance is voltage dependent. All gate capacitances in this subsection have been measured with a Keysight Technologies  power device analyzer B1506A. The flat-band effect, which shows a decreased gate capacitance in the gate voltage range of zero to five volts measured at zero blocking voltage, is well known (see Fig. 11).
But there can also be a dependency on the blocking voltage for some ranges of the gate voltage (see curve tracer measurements in Fig. 12(a) to (c)). For a gate voltage U GE of 0 V or −10 V, the gate-emitter capacitance, which forms the main part of the input capacitance, is different but independent of the blocking voltage U CE . For gate voltages between these boundaries, the capacitance has a blocking voltage-dependent shift. The varying capacitance leads to a shift of the resonance frequency of the gate impedance recorded with a network analyzer (see Fig. 13). Thus, the measured value of the internal gate resistance can not only depend on the chip temperature but also undesirably on parameters like the blocking voltage, which can fluctuate in real converter operation.
The effect of a wrong and good calibrated temperature measurement with the T J -R Gi -monitor in single-phase inverter operation at 50 Hz output frequency is shown in Fig. 14. With only −5 V gate voltage, the gate capacitance depends on the blocking voltage, and a 100 Hz temperature ripple due to the DC-link voltage ripple appears on the   temperature measurement. With −9 V gate voltage, only the 50 Hz ripple due to the natural thermal ripple is measured.
The optimum strategy to avoid undesired dependencies is to analyze the gate impedance with several system parameters and to choose a negative gate voltage and frequency of the superimposed measurement signal to match a point of the gate impedance, which is only temperature dependent.

IV. TESTING THE APPLICABILITY TO OTHER SEMICONDUCTORS BY GATE IMPEDANCE MEASUREMENT
The applicability of the R Gi -method to other semiconductors than IGBTs like SiC-MOSFETs or GaN devices is analyzed in this section by gate impedance measurements with a vector network analyzer Bode 100 from OMICRON Lab. The network analyzer can determine the absolute value and the real part of the gate impedance. However, the accuracy of the real part far from the resonant point drops significantly. In a simple LCR series resonant circuit, the real part corresponds to the ohmic part of the impedance.

A. SILICONE CARBIDE MOSFETS
In [11] a characteristic of the gate impedance of SiC-MOSFETs was described, which cannot be justified with a simple series connection of LCR. A decrease of the real part at lower frequencies and a change in the sign of the temperature coefficient have been reported. Reasons for this can be gate interference traps or the base material of the gate resistor with other properties. This characteristic of the real part can be modeled by adding a parallel RC element in series with the LCR element (see Fig. 15) [49].
The gate impedance of several 1.2 kVSiC-MOSFETs from different manufacturers has been analyzed. Relevant parameters of the semiconductors are listed in Table 1. Fig. 16    gives an overview of the general characteristic of the 1.2 kV SiC-MOSFET gate impedance curves at room temperature. The impedance at resonance is in the range of 1 to 4 and the resonance frequency varies between 17 MHz to 34 MHz. The temperature dependency of the impedance at resonance frequency is illustrated in Fig. 17.
Detailed views of the measured gate impedance including absolute value and and real part at various temperatures are shown in Fig. 18. The present state-of-the-art types of all four investigated manufacturers (see Fig. 18(a) to (e)) show that there is a mostly linear temperature dependency in the range of the resonance frequency, which can be utilized for temperature measurement with the T J -R Gi -monitor. The package layout with an additional Kelvin source pin has no significant influence on the shape of the measured curves except a higher resonance frequency due to the smaller gate inductance (see Fig. 18(c) versus Fig. 18(e)). The older chip generation of Infineon shows a more pronounced effect of the isothermal point with a shift of the sign of the temperature coefficient (see Fig. 18(d) versus Fig. 18(f)). The outdated generation in Fig. 18(g) shows, in contrast to all other samples, a negative temperature coefficient over the total frequency range. The frequency f res and the resistance R res at resonance have been measured with a network analyzer. The input capacitance C iss has been determined with a curve tracer at −5 V gate and 100 V blocking voltage. The gate circuit inductance L and the quality factor Q have been calculated from these three values based on a serial LCR network and constant parameters.
With SiC-MOSFETs, as with all other semiconductors, an analysis of the gate impedance must be carried out to ensure that there is only a temperature dependency by selecting a suitable gate voltage.

B. JFETS
The unique feature of the gate circuit of the JFET compared to IGBT and MOSFET is the nonexistent oxide and, instead, the blocking diode with its capacitance. The measured gate impedance of a 1.2 kV SiC JFET is depicted in Fig. 19. Further details on the normally-on SiC JFET are given in Table 2. The temperature sensitivity of the gate impedance (see also Fig. 24) enables temperature measurement with the T J -R Gi -monitor.

C. GAN
GaN devices are designed to have a very low inductance gate and commutation loop [52] in the range of less than 10 nH. In conjunction with a minimal input capacitance, this leads to very high resonance frequencies, which make a measurement with the T J -R Gi -monitor difficult. Fig. 20 illustrates the measured gate impedance of a 600 V enhancement GaN from Infineon (see Table 2) with an additional inductance of 190 nH and 350 m at 18.9 MHz. Without this additional gate inductance, the resonance frequency is far beyond the maximum frequency of the OMICRON Lab Bode 100 network analyzer. The gate impedance shows a temperature dependency, but with the additional inductance, the quality factor of the LCR network increases and results in a very sharp impedance curve according to:

D. CASCODE STRUCTURE DEVICES
Cascode structures are applied to convert normally-on devices like JFETs or depletion mode GaN HEMTs to normallyoff devices. Therefore, a Si MOSFET is connected in series (see Fig. 21). This MOSFET determines the gate impedance characteristic. The temperature dependency of a GaN HEMT cascode is shown in Fig. 22(a) and of a SiC JFET cascode in  Fig. 22(b). Both characteristics enable a temperature measurement via the internal gate resistance.

E. OVERVIEW
The general characteristic of several gate impedance curves at room temperature of selected devices GaN, SiC JFET, and cascode devices from Tables 1 and 2 is illustrated in Fig. 23. The impedance curve becomes flatter with decreasing quality factor. A flatter impedance curve makes it easier to measure the temperature with the T J -R Gi -monitor since the resonance point does not have to be hit precisely. By inserting an additional inductance in the measurement circuit, the resonance frequency can be decreased, but as a disadvantage, the quality factor and the temperature sensitivity decrease due to the parasitic resistance of the inductance. The temperature sensitivity  of the measured devices at resonance frequency is illustrated in Fig. 24.

V. JUNCTION TEMPERATURE MONITOR APPLICATION WITH SIC MOSFET
Based on the findings of the gate impedance measurements from the previous section, the applicability of the T J -R Gimonitor to wide-bandgap semiconductors is now shown using a SiC MOSFET as an example. In contrast to inverter operation, as in Section III, another application example shows how easily the thermal impedance can be determined with the T J -R Gi -monitor by recording cooling or heating curves.   The junction temperature is usually measured by the forward voltage on a small sense current during a cooling down period after heating the device to a steady state to determine the thermal impedance of power semiconductors. For on-state SiC MOSFETs with small measurement currents, the voltage to be measured is very low due to the lack of threshold voltage and low R DS,on [10]. In the off state, the body diode can be used in the reverse direction. To do this, the gate voltage must be sufficiently negative for the prevention of the influence of the channel [9]. The thermal impedance Z th (t ) can be calculated from the cooling temperature curve T (t ), the initial temperature in stationary mode T init and the heating power P, which the product of collector current and forward voltage can determine: To enable a fast commutation between a large heating current and a small sense current typically in the range of 1 to 100 mA, an additional serial and parallel switch are added to the test setup. Nevertheless, there can be a short blind time with the forward voltage method, e.g., due to the recombination of charge carriers in IGBTs within the first hundreds of microseconds [27], [50], [53], [54]. A linear evolution can obtain the relevant starting temperature with the square root of time [53], [55], [56], which is a good approximation for a power density up to 300 Wcm −2 .
Alternatively, the junction temperature can be measured with the T J -R Gi -monitor. Here, the T J -R Gi -monitor is configured for measurement during the on-state of the DUT at a positive gate voltage (see Fig. 25). The SiC-MOSFET C3M0016120D within a TO package is here mounted on a copper heating plate for the calibration of the T J -R Gi -monitor. The linear dependency of the resistance on the temperature of the gate impedance measurements (see Fig. 17) can be confirmed with the T J -R Gi -monitor. Fig. 26 shows the measured heating and cool-down temperature of the SiC-MOSFET within a TO package. The heating plate for the calibration has been removed, and the device is heated by a current of 13 A in permanent on mode. The sample rate of the raw data is 200 Hz and can be increased to 50 kHz for the first samples after triggering the measurement. The bottle neck is the transfer rate of the T J -R Gi -monitor to the PC. A filter like a moving average can significantly remove the large temperature ripple of the raw data. The R Gi -method enables a continuous temperature measurement during the heating and cooling phases. In contrast, the forward voltage method typically only measures cooling down phases and has a blind time of 150 µs to 1 ms after load current turn-off due to the recombination time from the high heating current to the small sense current [53]. A √ t-extrapolation has to be applied to determine the initial temperature for the forward voltage method. The T J -R Gi -monitor can measure the temperature at all times.
The thermal impedance junction to the ambient of the TO package without any cooling plate based on the cooldown temperature measurement is depicted in Fig. 27. The T J -R Gimonitor enables a fast and straightforward method of thermal impedance measurement without any additional switches to speed up the recombination process between heating and sense current or extrapolation to the starting value.

VI. CONCLUSION
The junction temperature measurement via the internal gate resistance is a promising method, which requires no modification of the package and enables a fast integration in existing converter configurations with the presented T J -R Gi -monitor.
The problem of further dependencies on system variables like e.g. the blocking voltage is presented in this paper for several IGBT voltage classes. This unwanted effect can be excluded by an analysis of the gate impedance and the choice of an optimal gate voltage in the off-state, where the internal gate resistance is measured.
The investigation of the gate impedance of several semiconductor types from various manufacturers has shown, that the junction temperature monitor can be applied to a wide range of devices.