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Article

A Model of the On-State Voltage across IGBT Modules Based on Physical Structure and Conduction Mechanisms

by
Qingyi Kong
1,
Mingxing Du
1,*,
Ziwei Ouyang
1,
Kexin Wei
1 and
William Gerard Hurley
1,2
1
Tianjin Key Laboratory of Control Theory and Applications in Complicated System, Tianjin University of Technology, Tianjin 300384, China
2
Department of Electrical Engineering, The National University of Ireland, H91 TK33 Galway, Ireland
*
Author to whom correspondence should be addressed.
Energies 2019, 12(5), 851; https://doi.org/10.3390/en12050851
Submission received: 22 January 2019 / Revised: 21 February 2019 / Accepted: 28 February 2019 / Published: 5 March 2019
Browse Figures
Versions Notes

Abstract

:
The on-state voltage is an important electrical parameter of insulated gate bipolar transistor (IGBT) modules. Due to limits in instrumentation and methods, it is difficult to ensure accurate measurements of the on-state voltage in practical working conditions. Based on the physical structure and conduction mechanism of the IGBT module, this paper models the on-state voltage and gives a detailed method for extracting the on-state voltage. Experiments not only demonstrate the feasibility of the on-state voltage separation method but also suggest a method for measuring and extracting the model parameters. Furthermore, on-state voltage measurements and simulation results certified the accuracy of this method.

1. Introduction

In recent years, power electronics technology has developed rapidly; it has been widely used in new energy power generation [1,2], electric vehicles [3,4], ship manufacturing [5], and aerospace [6]. In these fields, power electronics systems perform the important task of power conversion, which increases the requirements for their reliability. Studies have shown that power failures of semiconductor devices account for 31% of all faults in power electronics systems [7]. Therefore, the insulated gate bipolar transistor (IGBT) module, the most widely used power semiconductor [8], plays a decisive role in the reliability of power electronics systems. In some cases, IGBT modules have to endure more than five million power cycles [9]. During their service lifetime, the junction temperature fluctuates in a wide range [10] causing serve thermal stress [11], due to the different thermal expansion coefficients of different materials, which makes the failure inevitable. In addition, harsher operating environments also accelerate the failure process, high power [12,13], and high temperature [14,15], in particular.
IGBT module can be regarded as a switch in power electronics systems. Both transient characteristics [16,17] and steady characteristics have been researched. The on-state voltage, denoted as the voltage between the collector and the emitter in steady state [18,19] is the main parameter of the steady state characteristic and is important to the IGBT module. Measuring on-state voltage in on-line conditions contributes toward the monitoring of IGBT module working status and to improving the reliability of an entire power electronics system.
In engineering applications, which are restricted by manufacturing technology and operating conditions, IGBT modules are often insufficiently cooled, causing the junction temperature far higher than the operating temperature [20]. The influences of conditions for high junction temperature have been analyzed [16,21]. Such high junction temperatures increase the probability for failure of the IGBT module. Acquiring information about the junction temperature accurately [22,23,24] and applying the appropriate compensatory measures when necessary [25] can improve the stability of IGBT modules and, by extension, the whole system. The on-state voltage is a thermal sensitive parameter of the IGBT module [26]. Considering the relationship between the junction temperature and the on-state voltage, it is realizable to monitor IGBT module junction temperature in on-line condition [27].
As the module undergoes increasing numbers of power cycles, aging of internal components is inevitable. Aging effects can be divided into bond wire degradation [28,29] and solder fatigue [30,31]. The main effects of bond wire degradation are bond line liftoff and cracking [32]. When one of the bond wires fails, the others will suffer an increased current density, thus accelerating the aging process of the IGBT module and ultimately leading to the breakdown of the entire power electronics system. Studies have shown that bond wire failure will cause an increase in the resistance of bond wire [18], leading to an increase in the on-state voltage. Thus, measuring the on-state voltage while the IGBT is in operation [33,34] can predict bond wire failure.
Currently, IGBT module on-state voltage measurement methods can be divided into two main categories. First, additional circuits are installed realizing the on-line measurement which have been widely used in recent years and applied in junction temperature measurement [35] or bond wire failure prediction [36]. What is more, with the development of wide band-gap semiconductors and increasing switching speed, [37] provided a fast voltage clamp circuit with better accuracy and higher bandwidth but that suffered from disturbances. Reference [38] proposed an on-state voltage measurement circuit, which can analyze on-state behavior of power semiconductors and improve the accuracy of loss breakdown models of power converters. However, all these methods increase the complexity of the power electronics system. Second, the module is monitored with mathematical models and the external measurable signals of the module. Based on the physical structure of the module and the conduction mechanisms therein, Hefner and Blackburn modeled the IGBT in its operating state and proposed a method for calculating the on-state voltage [39]. Focusing the main characteristics of the IGBT module, [40] simplifies modeling problems based on the assumptions that separates on-stage voltage into four parts and offers a calculation method. Lauritzen and Ma introduced another modeling technique called lumped charge [41], which was applied to IGBT modules in [42], and offers an access to on-state voltage simulation realized into the SPICE modeling platform [43]. In [44,45], the model of the IGBT module based on physical structure is constructed as a combination of a metal–oxide–semiconductor field-effect transistor (MOSFET) part and a bipolar junction transistor (BJT) part. It not only provides an on-state voltage measurement method, but also describes the transient characteristic in detail. However, some parameters required in these methods are difficult to extract under realistic working conditions. Furthermore, the collector current density and junction temperature have a significant effect on the calculation results. Therefore, it is necessary to propose a “brief” model to measure IGBT module on-state voltage.
Another modeling method in [46] can be utilized to describe the characteristics of an IGBT module similar to the BJT-MOSFET model. In this method, the IGBT module is constructed as a PIN rectifier part and a MOSFET part which can provide an on-state voltage measurement method. To simplify the on-state voltage measurement, this paper considers the physical structure of the IGBT module and comes up with a model based on the PIN-MOSFET structure. The forward characteristic of the PIN rectifier can be modeled as a backward power (the threshold voltage) installs in series with a resistance. What is more, the IGBT module on-state voltage can be divided into a chip-level voltage drop and a package-level voltage drop. Thus, in this paper, the on-state voltage is separated into a more specific model (Vce-th, Von-chip, Vpackage) that allows us to model the IGBT module while it is in operation, and the conduction mechanisms generated in Von-chip are considered.
When the collector current is regarded as an independent variable, the on-state voltage drop across the chip (Von-chip) becomes a dependent variable, and the collector-emitter threshold voltage (Vce-th) and the package resistance (Rpackage) are independent variables. We then develop methods for extracting these independent parameters, and on-state voltage can be obtained after acquired the collector current (Ic). Experimental results and function simulations demonstrate the feasibility and accuracy of our model.
This paper is organized as follows: Section 2 analyzes the physical structure and conduction mechanism of the module in on-state status. An on-state voltage model is given after the theoretical analysis of IGBT module. Section 3 gives an extraction method for the parameters needed in the proposed model. Experimental results and function simulations demonstrate the accuracy of our model. Section 4 is a summary of the paper.

2. Theoretical Analysis of the IGBT Module Model in On-State Status

2.1. Threshold Voltages and Working Conditions of the IGBT Module

The physical structure of the IGBT module is shown in Figure 1. The module is equivalent to a PIN rectifier combined with a MOSFET. The on-state behavior is dominated by the PIN rectifier, and the switching behavior is determined by the MOSFET. When gate-emitter voltage (Vge) is lower than the threshold voltage Vth, the N junction near the emitter (denoted as NE), the P junction near the gate (denoted as PG), and the N– drift region form a back-to-back PN junction, which causes a high resistance between the collector and the emitter. With this situation, the IGBT module is in its off-state. In this case, even if a large voltage is applied to the collector-emitter, the IGBT module cannot be switched into the on-state.
When Vge crosses the threshold voltage, an inverse-layer channel is generated in the back-to-back PN junction, forming a connection between the NE and N– drift regions. In this case, the IGBT module acts as an open gate but is not in its on-state. The P junction near the collector (called P+C) and the N+ buffer make up another PN junction, which is equivalent to a PIN rectifier. A bias voltage must be applied across the collector and emitter to overcome the effect of the internal electric field, ensuring that charge carriers reach the emitter from the collector. With this bias voltage applied, the IGBT module is in its on-state.
The IGBT module; therefore, has two threshold voltages: the gate threshold voltage, Vth, which forms the inverse-layer channel in the power MOSFET component, and the collector-emitter threshold voltage, Vce-th, which overcomes the internal electric field in the PIN rectifier component.
The IGBT module requires that the Vce-th bias voltage be consistent to remain in the on-state. Therefore, Vce-th can be regarded as a part of the on-state chip voltage drop in the collector-emitter of the IGBT module, and it is marked in Figure 1.

2.2. On-State Conduction Mechanism of the IGBT Module

When the IGBT module remains in the on-state, carriers (taking holes as an example) begin at the collector and pass through the N– drift region under the action of the positive bias voltage Vce-th. They finally reach the gate region under the action of diffusion. If we compare the process of the carriers passing through the PIN rectifier component with the movement of free electrons in a conductor, the concept of resistance can be introduced. In this paper, the resistance in N region (N+ buffer and N– drift region included) is expressed as Ron-N, and the voltage drop is Von-N. Later, these holes drift through the inversion channel of the power MOSFET component to reach the emitter. The channel resistance is Ron-CH, and the voltage drop is Von-CH. Figure 1 marks the positions of Ron-N and Ron-CH. Moreover, Von-N and Von-CH are also components of the on-state voltage drop across the IGBT chip.
To conclude this development of the carriers behavior within the IGBT module, the on-state model of the IGBT module chip is expressed as the equivalent circuit shown in Figure 2. This diagram is composed of the collector-emitter threshold voltage Vce-th, the on-state N region resistance Ron-N-, and the channel resistance Ron-CH. Based on this on-state model, the voltage drop across the chip in the on-state is calculated as follows:
Vchip = Vce-th + (Ron-N + Ron-CH) × Ic

2.3. Model of the On-State Voltage

In the IGBT module, aluminum bond wires connect the silicon chip to the diode, gate electrode, and the diode-emitter structure. Each unit of the IGBT module shares three bus bars. If the IGBT module remains in its on-state, a voltage drop is caused by the current passing through the bus bars, bond wires, and solder points. This voltage drop is caused by the equivalent circuit of the module and is denoted as Vpackage.
A 3D model of the IGBT module is shown in Figure 3. The silicon chip (marked in orange) determines both the on-state and transient characteristics of the IGBT module. The package circuit is marked in purple. The free-wheeling diode (FWD), direct copper bonding (DCB) plate, and baseplate (Cu) are also shown in Figure 3. From the perspective of this physical structure, the on-state voltage can be separated into the chip-level voltage drop (Vchip) and the package-level voltage drop (Vpackage), as formulated by the following equation:
Vce = Vchip + Vpackage
Combined with the on-state chip voltage model of the IGBT module proposed above, the on-state model could be updated, as shown in Figure 4. Note that Ron-N+ and Ron-CH are rewritten as Ron-chip therein. The threshold voltage of the collector–emitter (Vce-th) remains constant as the collector current changes. At the same time, the chip-level voltage drop (Von-chip) will increase as the collector current increases.
However, the conductivity modulation in the semiconductor will also affect the on-state chip resistance. When the positive current flowing through the PN junction (PIN rectifier area in Figure 1) increases, the concentration of minority carriers injected and accumulated in the N– drift region becomes very large. In order to maintain the semiconductor electrically neutral, the concentration of majority carriers will also be greatly increased, resulting in a significant decrease in its resistivity, that is, a significant increase in its conductivity, which is the conductivity modulation effect. As the collector current (Ic) increases, the enhanced conductivity modulation will gradually reduce the on-state chip resistance. Thus, Ron-chip defined in this paper is closely related to Ic and their relation is described using FRon-chip (Ic).
From the analysis above, the on-state model of the IGBT module is proposed, where both Vce-th and Rpackage are constant, and the on-state chip resistance is a dependent variable that indicates the collector current:
Vce = Vce-th + [FRon-chip (Ic) + Rpackage] × Ic

3. Experimental Results

3.1. Measurements of the Collector-Emitter Threshold

We tested an IGBT module produced by SEMIKON (SKM75GB12T4) in an experiment shown in Figure 5. Its rated voltage was 1200 V, and its rated current was 75 A. According to the datasheet provided by the manufacturer [47], the gate-emitter voltage was set to 15 V and the environment temperature was room temperature (25 °C). Figure 6 shows a photograph of the semiconductor parameter test system we used (PCT-2), which was composed of the 2651A high-power source meter, the 2636B system source meter, the 8010 high-power test device, and a computer. The V-I curve of the IGBT module was measured using ACS software (V2.0 Release, Keithley Instruments, Cleveland, OH, USA).
As shown in Figure 7, the V-I characteristic curve of the IGBT module, as tested at room temperature, had a segmentation and the voltage at the inflection point was Vce-th. When Vce was less than Vce-th, the IGBT module was in the off-state. Some leakage currents led to a small slope in the V-I characteristic, indicating high resistance. When Vce was higher than Vce-th, the IGBT module was in the on-state, and the collector–emitter resistance decreased, causing an increase in the curve slope that indicates linear behavior. However, it was quite rare to be able to extract Vce-th directly from the V-I characteristic curve.
To ensure the accuracy of measurements of the collector-emitter threshold voltage, a linear function (y = ax + b) could be used to describe the on-state V-I characteristic curve. The intersection point between the obtained function and the voltage axis was Vce-th (see Figure 8).
When extracting the coefficients of these fitting functions from the data, optimizing the selected data can improve the function fitting results and the resulting accuracy of Vce-th. The primary function F1 (x) obtained with the selection value of 0.6 V as a starting point is shown in Figure 9a. The R-squared determination coefficient for this function was 0.99342. Since the initial value of the selected voltage point was improved continuously, the determination coefficient for the primary function was tested for extracting Vce-th. When the selected value reached 1.4 V, R-square = 0.9994, and the resulting primary function F2 (x) is also shown in Figure 9a. Therefore, changing the starting point of the data used for curve fitting effectively improved the fitting result and the accuracy of the Vce-th extraction. Table 1 exhibits the parameters of the liner function applied in V–I characteristic curve fitting.
However, Figure 9b reveals that the high R-square obtained in curve fitting sacrificed the fitting accuracy in the area near the collector-emitter threshold voltage, which also caused the error in the Vce-th measurement. Herein, Vce-th was obtained when the R-square reached 0.998 and the obtained functions are shown in Figure 9b as F3 (x). At this point, a (the slope of the function)= 5.97575, b (the Y-intercept of the function)= −3.91408, and Vce-th = 0.6549 V.

3.2. Extraction of the Package Resistance

The chip-level voltage drop in the on-state could be calculated with Equation (4). When the collector injection current was in a lower range, the PIN diode dominated the on-state voltage, and the contribution of the MOSFET could be ignored. With increasing injection current, the voltage drop caused by the MOSFET should become noticeable [46]. Therefore, when the collector–emitter voltage of the IGBT module was near the threshold voltage Vce-th, the voltage drops generated in the N+ buffer, N– drift region, and the channel of the chip could be approximated as zero. With these assumptions, Equation (4) could be rewritten as:
V c e   =   2 K T q ln [ J C W N 4 q D a n i F ( W N / 2 L a ) ]   +   p L C H J C H μ n i C O X ( V G − V T H )
Vce = Vce-th + Ic Rpackage
where K is the Boltzmann constant, T is the absolute temperature, q is the electronic charge, WN is the width of the N+ drift region, Jc is the current density, ni is the intrinsic carrier concentration, Da is the ambipolar diffusion coefficient, La is the ambipolar diffusion length, Lch is the ambipolar diffusion coefficient, Cox is the channel length, p is the indicated cell pitch, Vge is the gate voltage, Vth is the threshold voltage, and μni is the inverse layer mobility [46].
Figure 10 shows a photograph of our on-state voltage acquisition system. The high-power programmable DC power supply and programmable electronic load (120 V/60 A/250 W) were connected in series and linked at the terminal of the collector-emitter. Another programmable DC power supply was connected in series with the terminal of the IGBT module’s gate-emitter and provided the voltage that produced the inverse-layer channel, which ensured that the IGBT module remained in the on-state. Because of the inevitable resistance generated in the test circuit, the IGBT module could not take in the entire voltage produced by the high-power DC supplier. We therefore adjusted the output voltage of the high-power DC supplier constantly until the IGBT module reached the on-state, which was judged using a high-accuracy digital multimeter. The collector current (Ic) was acquired by a programmable electronic load. When the reading of high-power DC supplier was 0.67 V, Vce = 0.6584 V and Ic = 0.3311 A, and according to Equation (5), Rpackage = 10.287 mΩ.

3.3. The Acquisition Method of On-State Chip Resistance

Because of the existence of conductivity modulation, the IGBT module’s on-state chip resistance decreased as the collector current increased. Ron-chip can be calculated with Equation (6):
Ron-chip = (Vce − Vce-th)/Ic − Rpackage
The high-power DC supply in Figure 10 and the programmable load were set to the constant current (CC) mode, and the gate voltage was set to 15 V. To obtain the full relation between on-state chip resistance and collector current completely, Ic was set from 10 to 74 A in this experiment. The electronic load used for package resistance extraction was substituted by a high-power equipment (600 V/240 A/12 KW). The relation between Ron-chip and Ic was then obtained by adjusting the output current provided by the DC power supply continuously. Note that the preset value of the programmable electronic load should be kept consistent with the DC power supplier.
Figure 11 shows the variation of the on-state voltage, the chip-level voltage drop, and the package-level voltage drop as the collector current increased. With the increase of collector current, the IGBT module on-state voltage obviously increased, because of the change in the chip-level voltage drop and the package-level voltage drop. Figure 12 shows the relationship between the on-state chip resistance, package resistance, and the collector current. The on-state chip resistance decreased exponentially as the collector current increased, due to the conductance modulation. Simultaneously, this trend also explained why the package-level voltage drop increased more than the chip-level voltage drop.

3.4. Method for Calculating On-State Voltage

It seems that the on-state chip resistance and the collector current are related with the exponential function under the effect of the conductivity modulation introduce in Section 2 and the relationship is denoted as Equation (7). The experimental results were analyzed with MATLAB scripts and fitted with this exponential function. When the on-state chip resistance is set to milliohms, a = 94.19, b = −0.6434, and R-squared = 0.9982.
Upon comparing the experimental measurement and simulation values (Figure 13), it was found that the simulation data owed an ideal matched-degree in a lower current range (less than 60 A, 80% of the rated current). When it comes to a higher level, the on-state chip resistance reduced inconspicuously. Assuming that Ron-chip keeps constant in high current condition (80% of the rated current Irated), we concluded that on-state chip resistance had an exponential relationship with collector current. Thus, on-state voltage for the module we tested could; therefore, be calculated with Equations (8) and (9).
Ron-chip = aIcb
Vce = Vce-th + 94.19Ic−0.6463 + Rpackage Ic
Vce = Vce-th + 94.19(0.8Irated)−0.6463 + Rpackage Ic
Measuring the IGBT module on-state voltage under different currents allows us to verify the accuracy of applying the model proposed above. Collector currents (Ic) of 20, 40, 60, and 75 A were used in tests for this validation. The measured voltages (Vce-mea) and the calculated voltages (Vce-cal) are listed in Table 2.
Referring to the data sheet provided by manufacturer, the on-state voltage of the SKM75GB12T4 module was between 1.85 V and 2.1 V when operating at this current. This agreement between our experimental observation of the on-state voltage and the manufacturer’s specification for a brand-new module shows that our model is valid for its intended purpose.
To demonstrate the validity of the proposed methods, we tested another IGBT module manufactured by Guoyang Electronics (WGL100B65F23). Parameters required in the on-state voltage model were obtained in the same way. Some crucial data are shown in the following figures and Table 3. The threshold voltage was 0.6428 obtained from Figure 14a; Figure 14b exhibits the simulation result using the exponential function (Ron-chip = 52.14 Ic−0.4202) and Rpackage = 2.146 mΩ; Figure 14c shows the on-state voltages obtained by different methods and the accuracy was proved.

4. Conclusions

Based on the physical structure and conduction mechanisms within the IGBT module, we separated the on-state voltage into three parts: the collector-emitter threshold voltage, Vce-th, the chip voltage drop, Vchip-on, and the package voltage drop, Vpackage. We used these measurements to formulate an equivalent circuit of the IGBT module in its on-state. This model allowed us to measure relevant indicators and extract the different parts of the on-state voltage. When the collector current in the circuit increases, Vce-th remains constant. The on-state chip resistance Ron-chip is affected by the conductance modulation and has an exponential relation to Ic, so Von-chip has a nonlinear relationship with Ic. Since the resistance of the package circuit is constant, Vpackage is linear against Ic.
If the collector current is measured, the model in this paper can be applied for monitoring the on-state voltage of an on-line IGBT module. The accuracy of the proposed method was verified by comparison of the experimental measurements of Vce and the manufacturer’s data sheet.

Author Contributions

Operation of the experiments, analysis, and writing of the paper, Q.K.; guidance of theoretical analysis and writing, M.D.; guidance and optimization of experiments, K.W.; modification of manuscript, Z.O. and W.G.H.

Funding

The authors would like to acknowledge the financial support of the “New Energy Vehicle” Key Special Project of the National Key Research and Development Plan (No. 2017YFB0102500) and the Tianjin Natural Science Foundation of China (No. 17JCYBJC21300).

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Physical structure of the insulated gate bipolar transistor (IGBT) module.
Figure 1. Physical structure of the insulated gate bipolar transistor (IGBT) module.
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Figure 2. On-state model of the IGBT module chip.
Figure 2. On-state model of the IGBT module chip.
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Figure 3. 3D model of the IGBT module.
Figure 3. 3D model of the IGBT module.
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Figure 4. On-state model of the IGBT module.
Figure 4. On-state model of the IGBT module.
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Figure 5. The IGBT module used for testing.
Figure 5. The IGBT module used for testing.
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Figure 6. Semiconductor testing equipment.
Figure 6. Semiconductor testing equipment.
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Figure 7. V-I characteristic curve at room temperature.
Figure 7. V-I characteristic curve at room temperature.
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Figure 8. Method for extracting collector-emitter threshold voltage (Vce-th).
Figure 8. Method for extracting collector-emitter threshold voltage (Vce-th).
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Figure 9. Fitting results for Vce-th using various data: (a) The whole effect of function fitting; (b) the enlarged view of function fitting.
Figure 9. Fitting results for Vce-th using various data: (a) The whole effect of function fitting; (b) the enlarged view of function fitting.
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Figure 10. Apparatus for measuring on-state voltage.
Figure 10. Apparatus for measuring on-state voltage.
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Figure 11. Relationship between each voltage drop within the IGBT module and the collector current.
Figure 11. Relationship between each voltage drop within the IGBT module and the collector current.
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Figure 12. Relationship between each resistance within the IGBT module and the collector current.
Figure 12. Relationship between each resistance within the IGBT module and the collector current.
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Figure 13. Experimental observations and simulation values: (a) On-state chip resistance measurement and simulation; (b) on-state voltage measurement and simulation.
Figure 13. Experimental observations and simulation values: (a) On-state chip resistance measurement and simulation; (b) on-state voltage measurement and simulation.
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Figure 14. Experimental curves of the IGBT module (WGL100B65F23): (a) V-I characteristic curve and function fitting; (b) on-state chip resistance measurement and simulation; (c) on-state voltage measurement and simulation.
Figure 14. Experimental curves of the IGBT module (WGL100B65F23): (a) V-I characteristic curve and function fitting; (b) on-state chip resistance measurement and simulation; (c) on-state voltage measurement and simulation.
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Table
Table 1. Accuracy of Vce-th extraction using various data.
Table 1. Accuracy of Vce-th extraction using various data.
Voltage (V)aStandard ErrorbStandard ErrorR-SquareVce-th (V)
0.65.617010.01724−3.259720.0270.993420.5803
0.95.946610.01148−3.859350.019330.997830.6490
0.925.961430.01129−3.887160.01910.997930.6520
0.935.969690.01119−3.902690.018980.997990.6537
0.945.975750.01113−3.914080.018910.998030.6549
1.46.307520.00789−4.563730.014970.99940.7235
Table
Table 2. Data comparison.
Table 2. Data comparison.
Ic (A)Ron-chip (mΩ)Vce-cal (V)Vce-mea (V)Error (%)
2013.58991.13221.12940.5135
408.68141.41331.41120.1488
606.68011.67251.6957−1.3681
756.68011.92091.9261−0.2855
Table
Table 3. Data comparison.
Table 3. Data comparison.
Ic (A)Ron-chip (mΩ)Vce-cal (V)Vce-mea (V)Error (%)
2013.58990.99460.98111.37
4010.63441.19031.15403.14
609.17911.35551.32232.51
808.57021.50431.50010.27
1008.57021.71971.70191.04

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MDPI and ACS Style

Kong, Q.; Du, M.; Ouyang, Z.; Wei, K.; Hurley, W.G. A Model of the On-State Voltage across IGBT Modules Based on Physical Structure and Conduction Mechanisms. Energies 2019, 12, 851. https://doi.org/10.3390/en12050851

AMA Style

Kong Q, Du M, Ouyang Z, Wei K, Hurley WG. A Model of the On-State Voltage across IGBT Modules Based on Physical Structure and Conduction Mechanisms. Energies. 2019; 12(5):851. https://doi.org/10.3390/en12050851

Chicago/Turabian Style

Kong, Qingyi, Mingxing Du, Ziwei Ouyang, Kexin Wei, and William Gerard Hurley. 2019. "A Model of the On-State Voltage across IGBT Modules Based on Physical Structure and Conduction Mechanisms" Energies 12, no. 5: 851. https://doi.org/10.3390/en12050851

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