# Analysis of Voltage Variation in Silicon Carbide MOSFETs during Turn-On and Turn-Off

^{*}

## Abstract

**:**

_{DS}/dt) for SiC MOSFET during turn-on and turn-off has been performed theoretically and experimentally in this paper. Turn-off variation in voltage is not a strong function of temperature, whereas the turn-on variation in voltage has a monotonic relationship with temperature. The temperature dependence is a result of the competing effects between the positive temperature coefficient of the intrinsic carrier concentration and the negative temperature coefficient of the effective mobility of the electrons in SiC MOSFETs. The relationship between variation in voltage and supply voltage, load current, and gate resistance are also discussed. A temperature-based analytical model of dV

_{DS}/dt for SiC MOSFETs was derived in terms of internal parasitic capacitances during the charging and discharging processes at the voltage fall period during turn-on, and the rise period during turn-off. The calculation results were close to the experimental measurements. These results provide a potential junction temperature estimation approach for SiC MOSFETs. In SiC MOSFET-based practical applications, if the turn on dV

_{DS}/dt is sensed, the device temperature can be estimated from the relationship curve of turn on dV

_{DS}/dt versus temperature drawn in advance.

## 1. Introduction

_{DS}/dt and temperature for SiC MOSFET can be observed in some published reports [9,10,11,12,13,14]. In [9] and [14], the characterization and comparison of three types of 1.2 kV SiC MOSFETs produced by different manufacturers is presented at 25 °C and 175 °C. Similar measurements have also been performed in [10,11]. In [12], a SiC Implantation and Epitaxial MOSFET (SiC-IEMOSFET) has been evaluated at the temperatures of 25 °C and 125 °C. In reference [13], a behavioral model of SiC MOSFET in Pspice over a wide temperature range is provided. The static and dynamic behavior is simulated using the presented model and compared to the measured waveforms. However, the effects of temperature on switching characteristics were only examined at two temperature conditions. From the aforementioned literature, we don’t know if the dV

_{DS}/dt varies linearly with temperature due to the absence of measurement data. Furthermore, many issues still remain unclear, such as the effects of supply voltage, load current and gate resistance on dV

_{DS}/dt and the modeling of dV

_{DS}/dt. However, these are important for SiC MOSFET-based practical applications. It is necessary to investigate the effects of temperature on the switching characteristics, which is useful for understanding how the variation of voltage varies with temperature. Alternatively, in future SiC MOSFET-based practical applications, the junction temperature measurement will become an important topic. However, for SiC MOSFETs there is less temperature sensitivity for the same electrical parameters as in Si IGBTs owing to their unipolar nature. Because of the wider bandgap, the lower intrinsic carrier concentration and the faster switching speed, some conventional indicators of junction temperature estimation for Si devices would fail for SiC MOSFETs [15,16]. Hence, it is also important to find a temperature-sensitive electrical parameter to evaluate device temperature in SiC MOSFETs.

## 2. Model

#### 2.1. Overview of the Turn-On and Turn-Off Process

_{GD}), gate–source (C

_{GS}), and drain–source (C

_{DS}).

_{DS}, causing a drop in turn-on and a peak in turn-off, as a result of the induced positive voltages and negative voltages, respectively [17].

_{DS}of the SiC MOSFET, which usually cannot be observed outside the SiC MOSFET. During the turn-on process, the energy stored in C

_{DS}discharges through MOS channel, which causes the channel current I

_{channel}to be larger than the drain current I

_{D}measured outside. While at turn-off, the capacitance C

_{DS}is charged as the drain-source voltage V

_{DS}rises. In this process, a part of the load current flows to C

_{DS}, which causes I

_{channel}to be smaller than I

_{D}. As a result, the gate-source plateau voltage V

_{GP}in turn-on is higher than that in turn-off.

#### 2.2. Temperature-Based dV_{DS}/dt Model

_{GD}, C

_{GS}and C

_{DS}. The capacitances C

_{GD}and C

_{GS}govern the switching transient since they are charged and discharged during the turn-on and turn-off processes. The effect of capacitance C

_{DS}can’t also be neglected since it also charges and discharges. In Figure 2, the MOSFET is in the saturation region and V

_{GS}remains almost unchanged at the voltage fall period during turn-on. Consequently, the gate current deviates from the gate source capacitance C

_{GS}and the Miller capacitance C

_{GD}to mainly charge the C

_{GD}. In addition, the drain source capacitance C

_{DS}is discharged in this phase and the discharging currents will inject into the channel of the MOSFET. Similarly, the C

_{DS}is charged during the voltage rise period during turn-off, and a part of the load current will be shunt. Owing to the discharging/charging of terminal capacitances, the current flowing through MOSFET, named the channel current, is not equal to the current measured through the drain terminal, namely I

_{D,}which is larger or smaller than I

_{D}. Figure 3a shows the discharging of capacitances C

_{GD}during turn-on, whereas the charging of capacitances C

_{GD}is shown in Figure 3b. The discharging/charging process of Miller capacitance is also exhibited in this figure.

_{DS,sat}, defined as V

_{GS}− V

_{TH}, and the SiC MOSFET is in the saturation region [18,19]. The channel current is a function of saturation voltage V

_{DS,sat}and can be given as :

_{0}C

_{OX}/L is the transconductance parameter, W is the channel width, L is the channel length, V

_{TH}and V

_{GS}are the threshold voltage and gate-source voltage, respectively, λ is the channel length modulation parameter, μ

_{0}is the effective mobility of the electrons in the channel, and C

_{OX}is the gate–oxide capacitor.

_{GG}has become the low level V

_{GG_L}in this phase, and the gate source voltage V

_{GS}reaches its Miller plateau voltage that is equal to V

_{TH}+I

_{L}/g

_{m}, the gate drive current I

_{G}can be calculated as shown in Equation (2), where R

_{G}is the gate drive resistance, I

_{L}is the load current, and g

_{m}is the device’s transconductance:

_{DS}is a drain–source voltage V

_{DS}–sensitive parameter due to the variation in depletion region width of the drain–body junction with V

_{DS}, which is given by [20,21]:

_{SiC}is the dielectric constant in SiC, N

_{A}is the p-well region doping, A

_{DS}is the drain–source overlap area, V

_{bi}is the junction potential in drain-body junction, N

_{D}is the doping in drift region, and n

_{i}is the intrinsic carrier concentration of SiC.

_{GD}is consisted of the gate oxide capacitance C

_{OX}= ε

_{OX}A

_{GD}/t

_{ox}in series with the bias-dependent depletion capacitance under gate oxide C

_{GDJ}= A

_{GD}(qN

_{A}ε

_{SiC}/2V

_{DS})

^{1/2}, which is given by:

_{GS}, C

_{GD}, and C

_{DS}as seen in Figure 3, the variation in voltage can be calculated for the voltage rise period during turn-off:

_{GS}is gate-source capacitance and I

_{D}is drain current of the SiC MOSFET, which is equal to load current I

_{L}. According to different operating conditions, Mc Nutt et al. [22] found that capacitance C

_{GD}can be further simplified. Figure 4 shows how the capacitance C

_{GD}varies under different operating conditions. When gate-source voltage V

_{GS}is greater than threshold voltage, and drain-source voltage V

_{DS}is greater than zero, capacitance C

_{GD}is approximately equal to the gate oxide capacitance C

_{OX}because depletion capacitance C

_{GDJ}is far in excess of the C

_{OX}. Hence, Equation (6) can be further simplified by using C

_{OX}instead of C

_{GD}. Additionally, during turn-on, the expression of the variation in voltage can also be derived is similar to Equation (6), where gate current is defined as I

_{G}= (V

_{GG_H}− (I

_{L}/g

_{m}+ V

_{TH}))/R

_{G}.

#### 2.3. Dependency Analysis

_{B}is Fermi-potential, Q

_{f}is the fixed oxide charges, and φ

_{ms}is the work function difference between metal and semiconductor [23]:

_{ms}and fixed oxide charges Q

_{f}being essentially independent of temperature, the threshold voltage temperature dependency can be given through differentiating Equation (7) with respect to temperature:

_{DS}, it is known that C

_{DS}varying with temperature is dominated by the temperature dependency of V

_{bi}. In the expression of V

_{bi}in Equation (4), as temperature T increases, kT/q rises and $\mathrm{ln}({N}_{A}{N}_{D}/{n}_{i}^{2})$ decreases. Hence, the more dominant parameter will determine how C

_{DS}changes with temperature. Theoretically, the $\mathrm{ln}({N}_{A}{N}_{D}/{n}_{i}^{2})$ term dominates the temperature dependency of C

_{DS}since V

_{bi}decreases with temperature shown in Figure 5, where the drift region doping N

_{D}is 3.8 × 10

^{15}cm

^{−3}. From Figure 5, C

_{DS}increases with temperature owing to its inverse proportional relationship with V

_{bi}, according to Equation (4). As reported by Chen et al. [7], experimentally, the C-V characteristics of SiC MOSFET almost overlap under different temperatures. Hence, the temperature dependency of C

_{DS}is neglected in the following analysis. Additionally, the C

_{GS}and C

_{OX}are generally considered to be constant.

_{DS}/dt can be obtained, as shown in Equation (10):

_{DS}/dt can be derived via the temperature dependency of threshold voltage and effective mobility. From Equation (13), mobility μ

_{0}possesses a negative temperature coefficient and decreases with temperature. However, for SiC MOSFET, dμ

_{0}/dT is very low and can be neglected due to its wide band-gap characteristics as reported in Hasanuzzaman et al. [24]. Hence, the temperature sensitivity of dV

_{DS}/dt is dominated by dV

_{TH}/dT and is negative because the temperature coefficient of threshold voltage is negative. Hence, turn-off dV

_{DS}/dt decreases as temperature increases. Similarly, the variation tendency of dV

_{DS}/dt under different temperatures during the turn-on process can also be predicted.

_{DS}/dt with respect to the load current is positive, as shown in Equation (14), it has a positive impact on the variation in voltage, which means the variation in voltage increases with increasing load current:

_{DS}varies under different voltages, as described in Equation (3). As seen from Equation (2), the higher the gate resistance, the lower the gate current. Hence, the variation in voltage decreases with increasing gate resistance. Likewise, for the voltage fall period during turn-on, the variation in voltage also depends on the gate resistance, load current, voltage, and temperature, and their impacts on variation in voltage can be obtained through a similar analysis process as for turn-off. A flow diagram for the proposed temperature-based analytical model, described in function blocks, is given in Figure 6. The temperature dependency of variation in voltage is a result of the variation of the intrinsic carrier concentration n

_{i}and the effective mobility of the electrons μ

_{0}with temperature. Owing to the positive temperature effect of the intrinsic carrier concentration n

_{i}and the negative temperature effect of effective mobility of the electrons μ

_{0}, dV

_{DS}/dt decreases with temperature for turn-off and increases for turn-on. Since SiC MOSFET has wider band-gap energy, the temperature sensitivity of the effective mobility of the electrons μ

_{0}can be neglected and can be considered approximately constant in the model.

## 3. Experiment Details

## 4. Experimental Results

#### 4.1. Static Characteristics under Different Temperatures

_{VT}is about −6.37 mV/°C. If nominal threshold voltage V

_{TH}

_{0}at room temperature is known, a simple expression can be used to describe threshold voltage at any measured temperature T:

_{0}. As aforementioned analysis, the dμ

_{0}/dT of SiC MOSFET is very low and can be neglected due to its wide band-gap characteristics. Hence, the temperature dependency of transconductance gm is also not considered.

#### 4.2. Temperature Dependency of dV_{DS}/dt

_{DS}/dt depends on device temperature, load current, gate resistors, and voltage. Here, the effects of these factors are investigated and the results are shown in Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, Figure 18 and Figure 19, where the turn-off waveforms of drain voltage are shown in Figure 12, Figure 13, Figure 14 and Figure 15, and the turn-on waveforms are shown in Figure 16, Figure 17, Figure 18 and Figure 19. The test conditions were set to voltages of 200, 400 and 600 V, and load currents of 10, 15 and 20 A. The gate resistor varied from 10 Ω to 150 Ω and the temperature ranged from 25 °C to 175 °C. An external drive system with 24/–5 voltage was used in the test and a double pulse signal was generated by a pulse generator. The current was measured using a Pearson current sensor. As seen, load current, voltage, temperature, and gate resistor have different impacts on dV

_{DS}/dt during turn-off and turn-on. During turn-off, the relationship between dV

_{DS}/dt and temperature is strongly dependent on the gate resistor. With larger values for the gate resistor, the curves nearly overlap under different temperatures. With smaller values for the gate resistor, the variation in voltage barely changed as temperature increased. However, the time at which the voltage rose obviously increased with temperature, which means the delay time varied as temperature increased.

_{DS}/dt, which varies with temperature under different measurement conditions, were obtained. The results are shown from Figure 20, Figure 21, Figure 22, Figure 23, Figure 24 and Figure 25, where Figure 20, Figure 21 and Figure 22 are the results for turn-off, and Figure 23, Figure 24 and Figure 25 are for turn-on. The calculated values are also shown in these figures. In the calculations, the values of C

_{GS}and C

_{OX}are 2.192 nF and 3.387 nF, respectively, extracted by a constant gate current circuit during turn-on. Indeed, for a SiC MOSFET the relative change in channel length is very small comparing with the long channel, λ can be treated as zero. According to some points in the device output characteristic saturation region, the values of W and L were obtained. The drain–source overlap area A

_{DS}was 5.3676 mm

^{2}. Equation (15) was adopted as the expression of threshold voltage under different temperatures.

_{DS}/dt and temperature under different load currents is presented in Figure 20. Figure 21 shows the temperature dependence of dV

_{DS}/dt under different voltages at 15 A load current of and 10 Ω gate resistance. Note that dV

_{DS}/dt has little fluctuation as the temperature increases, meaning that turn-off dV

_{DS}/dt is not a strong function of temperature. The dV

_{DS}/dt also increases with load current and supply voltage. The positive voltage coefficient of dV

_{DS}/dt is due to the fact that drain-source capacitance and Miller capacitance reduce with increasing supply voltage. The Miller capacitance is consisted of a fixed oxide capacitance and a depletion capacitance that varies with voltage. The depletion width increases as voltage increases resulting in a small depletion capacitance and hence the Miller capacitance declines at a large voltage. While, drain-source capacitance is comprised of the depletion region capacitance of drain-body junction and the region width also increases with voltage. Hence drain-source capacitance decreases. The calculated results show dV

_{DS}/dt is minimally temperature sensitive and decreases with temperature. Some discrepancies can be found between the measurements and calculations. The reason for this may be the temperature dependence of the effective mobility compensating for the temperature dependence of the threshold voltage in realistic experimental conditions. Furthermore, the impact of the gate resistors on the temperature dependence of dV

_{DS}/dt was also measured at 400 V and 15 A. The results are exhibited in Figure 22. The dV

_{DS}/dt varied with different resistors, and was large with smaller resistor values and was small with larger resistor values. The reason results from the variation of gate current at different resistors observed in aforementioned analysis.

_{DS}/dt and temperature, under different load currents, at 400 V and 10 Ω, is presented in Figure 23. For different voltages, the relationship at 15 A and 10 Ω is shown in Figure 24. Notably, dV

_{DS}/dt is less than zero and its magnitude increases with temperature, as expected. Moreover, the temperature dependency of dV

_{DS}/dt exhibits near-linear characteristics. The results are interesting since the monotonic relationship may be a potential indictor for junction potential measurement for SiC MOSFET. At the same temperature, a larger load current results in a smaller dV

_{DS}/dt. For voltage, the magnitude of dV

_{DS}/dt is larger for a larger voltage. To evaluate the effects of gate resistors on the temperature dependency of turn-on dV

_{DS}/dt, the temperature dependency of turn-on dV

_{DS}/dt was measured at 400 V and 15 A under different gate resistor values. The results are shown in Figure 25. A variation in dV

_{DS}/dt can be observed in Figure 25 for different gate resistors at the same temperature. A smaller gate resistor results in a larger magnitude of dV

_{DS}/dt. Moreover, in the above figures, the calculated and measured values show good agreement at the evaluated temperature range.

## 5. Discussion

_{DS}/dt and temperature for SiC MOSFET can be also seen in previous studies. In Chen et al. [9] and DiMarino et al. [14], the measurements were performed at a supply voltage of 600 V and load current of 10 A with 10 Ω gate resistance. The impact of temperature is clear and the magnitude of dV

_{DS}/dt decreases as temperature increases for turn-off, but increases with increasing temperature for turn-on. Othman et al. [11] experimentally showed the temperature-sensitivity of turn-off dV

_{DS}/dt is very low and approximately constant under 400 V, 15 A, and 28 Ω gate resistance test conditions. When temperature ranges from 25 °C up to 175 °C, the value of dV

_{DS}/dt is approximately 10.44 V/ns. However, for turn-on dV

_{DS}/dt, the magnitude increases from 4.6 V/ns at 25 °C to 6.62 V/ns at 175 °C. As reported by Takao et al. [12], the same conclusions were drawn from the switching waveforms of SiC MOSFETs at 25 °C and 175 °C at 600 V, 10 A, with 11.36 Ω gate resistance. The magnitude of turn-on dV

_{DS}/dt is approximately 12 V/ns at 25 °C and 15 V/ns for 175 °C, whereas the values of turn-off dV

_{DS}/dt are all approximately 29.11 V/ns for both 25 °C and 175 °C. These provide a potential solution for SiC MOSFET junction temperature estimation.

_{CE}/dt under different temperatures has been reported by Bryant et al. [25]. The dV

_{CE}/dt possesses a negative temperature coefficient and decreases with temperature decreases. For different load currents, the slope is the same and its value is 6.75 V/(μs°C). Because of this fixed sensitivity and linearity, turn-off dV

_{CE}/dt can be used as an effective indicator for junction temperature measurement of an IGBT. However, for a SiC MOSFET, turn-off dV

_{DS}/dt is not strongly correlated with temperature. Hence, monitoring turn-off dV

_{DS}/dt seems to be infeasible for junction temperature measurement of a SiC MOSFET.

_{DS}/dt are the threshold voltage and the effective mobility. For Si MOSFET, the effective mobility decreases with temperature and its temperature dependency is negative. But for SiC MOSFETs, as reported in [24], the temperature dependency of effective mobility can be neglected and be considered approximately constant due to its wide band-gap characteristics. Hence, it can be concluded theoretically that the temperature dependency of dV

_{DS}/dt in Si MOSFETs is less than that in SiC MOSFETs owing to the compensating effects of the temperature characteristic of the effective mobility to the temperature characteristic of the threshold voltage in Si MOSFETs. However, it is hard to find the experimental measurements on the temperature dependency of dV

_{DS}/dt for Si MOSFETs in previous literature. A comprehensive comparison between Si MOSFETs and SiC MOSFETs, regarding the dependency of the dV

_{DS}/dt on temperature, load current and gate resistor, will be performed experimentally in the next step.

_{DS}/dt is shown to have good temperature sensitivity and is approximately linear. The results are interesting and significant because it may be a potential indicator for junction temperature measurement of a SiC MOSFET. Others factors can also effect turn-on dV

_{DS}/dt, as shown in Figure 23, Figure 24 and Figure 25, but this is not an issue. Because the type of device and system parameters, such as voltage, load current, and gate resistance, are usually fixed in practical SiC MOSFET-based applications, and turn-on dV

_{DS}/dt is only dominated by temperature. Before the turn-on dV

_{DS}/dt–based method is used for temperature assessment, the calibration curves between dV

_{DS}/dt and temperature should be drawn experimentally and used as a lookup table. Indeed, the lookup table is easily implemented by digital signal processing (DSP). The dV

_{DS}/dt can also be easily measured by a RC high-pass connected to the drain and source terminals of device from the switching waveforms. After the dV

_{DS}/dt is measured, the corresponding junction temperature can be estimated from the lookup table.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Cross structure of a silicon carbide (SiC) metal–oxide–semiconductor field-effect transistor (MOSFET).

**Figure 3.**Terminal capacitances charging and discharging at: (

**a**) the voltage fall phase and (

**b**) the rise phase.

**Figure 4.**The gate–drain capacitance (C

_{GD}) varies under different operating conditions. (

**a**) V

_{GS}= 0, V

_{DS}= 0; (

**b**) V

_{GS}> V

_{TH}, V

_{DS}> 0; (

**c**) V

_{GS}< V

_{TH}, V

_{DS}> 0.

**Figure 12.**Turn-off waveforms for drain-source voltage (V

_{DS}) at a voltage of 200 V, a load current 15 A, and at different temperatures with a gate drive resistance (R

_{G}) = 10 Ω.

**Figure 13.**Turn-off waveforms for V

_{DS}at a voltage of 400 V, a load current 15 A, and at different temperatures with R

_{G}= 10 Ω.

**Figure 14.**Turn-off waveforms for V

_{DS}at a voltage of 400 V, a load current 20 A, and at different temperatures with R

_{G}= 10 Ω.

**Figure 15.**Turn-off waveforms for V

_{DS}at a voltage of 400 V, a load current 20 A, and at different temperatures with R

_{G}= 150 Ω.

**Figure 16.**Turn-on waveforms for V

_{DS}at a voltage of 200 V, a load current 15 A, and at different temperatures with R

_{G}= 10 Ω.

**Figure 17.**Turn-on waveforms for V

_{DS}at a voltage of 400 V, a load current 15 A, and at different temperatures with R

_{G}= 10 Ω.

**Figure 18.**Turn-on waveforms for V

_{DS}at a voltage of 400 V, a load current 20 A, and at different temperatures with R

_{G}= 10 Ω.

**Figure 19.**Turn-on waveforms for V

_{DS}at a voltage of 400 V, a load current 20 A, and at different temperatures with R

_{G}= 150 Ω.

**Figure 20.**Measured and calculated dV

_{DS}/dt as a function of temperature at a voltage of 400 V and a gate resistor of 10 Ω during turn-off, shown for different load currents.

**Figure 21.**Measured and calculated dV

_{DS}/dt as a function of temperature at a load current of 15 A and a gate resistor of 10 Ω during turn-off, shown for different voltages.

**Figure 22.**Measured dV

_{DS}/dt as a function of temperature at a voltage of 400 V and a load current 15 A during turn-off, shown for different gate resistances.

**Figure 23.**Measured and calculated dV

_{DS}/dt as a function of temperature at a voltage of 400 V and a gate resistor of 10 Ω during turn-on, shown for different load currents.

**Figure 24.**Measured and calculated dV

_{DS}/dt as a function of temperature at a voltage of 15 A and a gate resistor of 10 Ω during turn-on, shown for different voltages.

**Figure 25.**Measured and calculated dV

_{DS}/dt as a function of temperature at a voltage of 400 V and a load current 15 A during turn-on, shown for different gate resistances.

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Li, H.; Liao, X.; Hu, Y.; Huang, Z.; Wang, K.
Analysis of Voltage Variation in Silicon Carbide MOSFETs during Turn-On and Turn-Off. *Energies* **2017**, *10*, 1456.
https://doi.org/10.3390/en10101456

**AMA Style**

Li H, Liao X, Hu Y, Huang Z, Wang K.
Analysis of Voltage Variation in Silicon Carbide MOSFETs during Turn-On and Turn-Off. *Energies*. 2017; 10(10):1456.
https://doi.org/10.3390/en10101456

**Chicago/Turabian Style**

Li, Hui, Xinglin Liao, Yaogang Hu, Zhangjian Huang, and Kun Wang.
2017. "Analysis of Voltage Variation in Silicon Carbide MOSFETs during Turn-On and Turn-Off" *Energies* 10, no. 10: 1456.
https://doi.org/10.3390/en10101456