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

energies

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

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; [email protected] (Q.K.); [email protected] (Z.O.); [email protected] (K.W.); [email protected] (W.G.H.) 2 Department of Electrical Engineering, The National University of Ireland, H91 TK33 Galway, Ireland * Correspondence: [email protected]; Tel.: +86-22-6021-4268

Received: 22 January 2019; Accepted: 28 February 2019; Published: 5 March 2019

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.

Keywords: IGBT module; on-state voltage; separation method; model

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

Energies 2019, 12, 851; doi:10.3390/en12050851 www.mdpi.com/journal/energies Energies 2019, 12, 851 2 of 15 module. Acquiring information about the junction temperature accurately [22–24] 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 Energies 2019, 12, x FOR PEER REVIEW 3 of 16 Energies 2019, 12, 851 3 of 15 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 collector current (Ic). Experimental results and function simulations demonstrate the feasibility and accuracy of our model. accuracy of our model. This paper is organized as follows: Section 2 analyzes the physical structure and conduction This paper is organized as follows: Section2 analyzes the physical structure and conduction mechanism of the module in on-state status. An on-state voltage model is given after the theoretical 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 analysis of IGBT module. Section3 gives an extraction method for the parameters needed in the proposed model. Experimental results and function simulations demonstrate the accuracy of our proposed model. Experimental results and function simulations demonstrate the accuracy of our model. Section 4 is a summary of the paper. model. Section4 is a summary of the paper.

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

2.1.2.1. Threshold Threshold Voltages Voltages and and Working Working Conditions Conditions of of the the IGBT IGBT Module Module TheThe physical physical structure structure of of the the IGBT IGBT module module is is shown shown in in Figure Figure 1.1 .The The module module is is equivalent equivalent to to a PINa PIN rectifier rectiﬁer combined combined with with a MOSFET. a MOSFET. The The on-state on-state behavior behavior is dominated is dominated by the by PIN the rectifier, PIN rectiﬁer, and theand switching the switching behavior behavior is determined is determined by the by MOSFET. the MOSFET. When When gate- gate-emitteremitter volta voltagege (Vge) is (V lowerge) is lower than thethan threshold the threshold voltage voltage Vth, theV Nth ,junction the N junction near the near emitter the emitter(denoted (denoted as NE), the as NP Ejunction), the P junctionnear the gate near (denotedthe gate (denoted as PG), and as P theG), andN– drift the N– region drift form region a form back- ato back-to-back-back PN junction, PN junction, which which causes causes a high a resistancehigh resistance between between the collector the collector and andthe theemitter. emitter. With With this this situation, situation, the the IGBT IGBT module module is is in in its its offoff-state.-state. In this this case, case, even even if if a large a large voltage voltage isapplied is applied to the to collector-emitter, the collector-emitter, the IGBT the module IGBT module cannot cannotbe switched be switched into the into on-state. the on-state.

FigureFigure 1. 1. PhysicalPhysical structure structure of of the the insulated insulated gate gate bipolar bipolar transistor transistor ( (IGBT)IGBT) module module..

When V crosses the threshold voltage, an inverse-layer channel is generated in the back-to-back When Vgege crosses the threshold voltage, an inverse-layer channel is generated in the PN junction, forming a connection between the N and N– drift regions. In this case, the IGBT module back-to-back PN junction, forming a connection Ebetween the NE and N– drift regions. In this case, theacts IGBT as an module open gate acts but as is an not open in its gate on-state. but is The not P junctionin its on near-state. the The collector P junction (called near P+ Cthe) and collector the N+ buffer make up another PN junction, which is equivalent to a PIN rectifier. A bias voltage must be (called P+C) and the N+ buffer make up another PN junction, which is equivalent to a PIN rectifier. A biasapplied voltage across must the be collector applied and across emitter the tocollector overcome and theemitter effect to of overcome the internal the electric effect of field, the ensuringinternal electricthat charge field, carriersensuring reach that charge the emitter carriers from reach the the collector. emitter Withfrom thisthe collector. bias voltage With applied, this bias the voltage IGBT applied,module isthe in IGBT its on-state. module is in its on-state. The IGBT module; therefore, has two threshold voltages: the gate threshold voltage, V , which The IGBT module; therefore, has two threshold voltages: the gate threshold voltage, Vth, which formsforms the the inverse-layer inverse-layer channel channel in the in power the power MOSFET MOSFET component, component, and the and collector-emitter the collector threshold-emitter voltage, V , which overcomes the internal electric field in the PIN rectifier component. threshold voltage,ce-th 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 Figure1.

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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

Energiesthe IGBT2019 module,, 12, 851 and it is marked in Figure 1. 4 of 15

2.2. On-State Conduction Mechanism of the IGBT Module 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 collectorWhen the and IGBT pass module through remains the N– in drift the on-state,region under carriers the (taking action holesof the aspositive an example) bias voltage begin atVce the-th. collectorThey finally and reach pass through the gate the region N– drift under region the underaction the of actiondiffusion. of the If positivewe compare bias voltagethe processVce-th .of They the ﬁnallycarriers reach passing the gate through region the under PIN therectifier action component of diffusion. with If we the compare movement the process of free electronsof the carriers in a passingconductor, through the concept the PIN of rectiﬁer resistance component can be introduced. with the movement In this paper, of free the electrons resistance in in aconductor, N region ( theN+ conceptbuffer and of resistanceN– drift region can be included) introduced. is expressed In this paper, as Ron the-N, resistanceand the voltage in Nregion drop is (N+ Von- bufferN. Later, and these N– driftholes regiondrift through included) the isinversion expressed channel as Ron-N of the, and power the voltageMOSFET drop component is Von-N .to Later, reach these the emitter. holes drift The throughchannel re thesistance inversion is R channelon-CH, and of the the voltage power drop MOSFET is Von component-CH. Figure 1 to marks reach the the positions emitter. The of R channelon-N and resistanceRon-CH. Moreover, is Ron-CH V,on and-N and the V voltageon-CH are dropalso iscomponentsVon-CH. Figure of the1 marks on-state the voltage positions drop of Racrosson-N and theR IGBTon-CH. Moreover,chip. Von-N and Von-CH are also components of the on-state voltage drop across the IGBT chip. To concludeconclude thisthis developmentdevelopment of the carrierscarriers behaviorbehavior withinwithin the IGBTIGBT module,module, the on-stateon-state model of of the the IGBT IGBT module module chip chip is expressed is expressed as the as equivalent the equivalent circuit circuit shown shown in Figure in2 . Figure This diagram 2. This isdiagram composed is composed of the collector-emitter of the collector threshold-emitter threshold voltage Vvoltagece-th, the Vce on-state-th, the on N-state region N region resistance resistanceRon-N-, andRon-N the-, and channel the channel resistance resistanceRon-CH .R Basedon-CH. Based on this on on-state this on- model,state model, the voltage the voltage drop acrossdrop across the chip the in chip the on-statein the on is-state calculated is calculated as follows: as follows:

Vchip = Vce-th + (Ron-N + Ron-CH) × Ic (1) Vchip = Vce-th + (Ron-N + Ron-CH) × Ic (1)

Figure 2. On-stateOn-state model of the IGBT module chip.

2.3. Model of the On-StateOn-State Voltage In the IGBT module, aluminum bond wires connect the silicon chip to to the the diode, diode, gate gate electrode, electrode, and the diode-emitterdiode-emitter structure. Each Each unit unit of the IGBT module shares three bus bars. If the IGBT module remains in its on on-state,-state, a voltage drop is caused by the current passing through the bus bars, bond wires,wires, andand soldersolder points. points. This This voltage voltage drop drop is is caused caused by by the the equivalent equivalent circuit circuit of the of modulethe module and is denoted as V . and is denoted packageas Vpackage. A 3D model of the the IGBT IGBT module module is is shown shown in in Figure Figure3 3.. The The silicon silicon chip chip (marked (marked in in orange) orange) determines both the on-stateon-state and transient characteristics of the IGBT module. The package circuit is marked in in purple. purple. The The free-wheeling free-wheeling diode diode (FWD), (FWD), direct direct copper copper bonding bon (DCB)ding plate, (DCB) and plate, baseplate and (Cu)baseplate are also (Cu) shown are also in Figure shown3. From in Figure the perspective 3. From the of this perspective physical ofstructure, this physical the on-state structure, voltage the can be separated into the chip-level voltage drop (V ) and the package-level voltage drop (V ), on-state voltage can be separated into the chip-levelchip voltage drop (Vchip) and the packagepackage-level as formulated by the following equation: voltage drop (Vpackage), as formulated by the following equation:

VceVce= =V Vchipchip ++ Vpackage (2)(2) Combined with the on-state chip voltage model of the IGBT module proposed above, the Combined with the on-state chip voltage model of the IGBT module proposed above, the on-state on-state model could be updated, as shown in Figure 4. Note that Ron-N+ and Ron-CH are rewritten as model could be updated, as shown in Figure4. Note that Ron-N+ and Ron-CH are rewritten as Ron-chip Ron-chip therein. The threshold voltage of the collector–emitter (Vce-th) remains constant as the collector 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 changes. At the same time, the chip-level voltage drop (V ) will increase as the collector current increases. on-chip current increases.

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FigureFigure 3. 3D 3. 3Dmodel model of the of theIGBT IGBT module. module.

FigureFigure 4. On 4. -On-stateOnstate-state model model of the of theIGBT IGBT module. module. However, the conductivity modulation in the semiconductor will also affect the on-state chip However,However, the the conductivity conductivity modulation modulation in thein the semiconductor semiconductor will will also also affect affect the the on -onstate-state chip chip resistance. When the positive current flowing through the PN junction (PIN rectifier area in Figure1) resistance.resistance. WhenWhen the the positive positive current current flowing flowing through through the the PN P junctionN junction (PIN (PIN rectifier rectifier area area in Figure in Figure 1) 1) increases, the concentration of minority carriers injected and accumulated in the N– drift region increases,increases, the th concentratione concentration of minorityof minority carriers carriers injected injected and and accumulated accumulated in thein the N– Ndrift– drift region region becomes very large. In order to maintain the semiconductor electrically neutral, the concentration of becomesbecomes very very large. large. In orderIn order to maintainto maintain the the semiconductor semiconductor electrically electrically neutral, neutral, the the concentration concentration of of majority carriers will also be greatly increased, resulting in a significant decrease in its resistivity, that majoritymajority carriers carriers will will also also be greatlybe greatly increased, increased, resulting resulting in ain significant a significant decrease decrease in itsin itsresistivity, resistivity, is, a significant increase in its conductivity, which is the conductivity modulation effect. As the collector thatthat is, ais, significant a significant increase increase in itsin conductivity,its conductivity, which which is the is the conductivity conductivity modulation modulation effect. effect. As Asthe the currentcollector (I c current) increases, (Ic) theincreases, enhanced the conductivity enhanced conductivity modulation modulation will gradually will reduce gradually the on-state reduce chip the collector current (Ic) increases, the enhanced conductivity modulation will gradually reduce the resistance.on-state chip Thus, resistance.Ron-chip Thus,defined Ron in-chip this defined paper in isthis closely paper related is closely to I crelatedand their to Ic relation and their is describedrelation is on-state chip resistance. Thus, Ron-chip defined in this paper is closely related to Ic and their relation is usingdescribedFRon-chip using(Ic F).Ron-chip (Ic). described using FRon-chip (Ic). From the analysisanalysis above,above, thethe on-stateon-state modelmodel ofof thethe IGBTIGBT modulemodule isisproposed, proposed, where where both bothV Vce-thce-th From the analysis above, the on-state model of the IGBT module is proposed, where both Vce-th and Rpackage areare constant, constant, and and th thee on on-state-state chip chip resistance resistance is is a dependent variable that indicates the and Rpackage are constant, and the on-state chip resistance is a dependent variable that indicates the collector current: collectorcollector current: current: Vce = Vce-th + [FRon-chip (Ic) + Rpackage] × Ic (3) Vce = Vce-th + [FRon-chip (Ic) + Rpackage] × Ic (3) Vce = Vce-th + [FRon-chip (Ic) + Rpackage] × Ic (3) 3. Experimental Results 3. Experimental Results 3. Experimental3.1. Measurements Results of the Collector-Emitter Threshold

3.1.3.1. Measurements MeasurementsWe tested of an the of IGBT theCollector Collector module-Emitter-Emitter produced Threshold Threshold by SEMIKON (SKM75GB12T4) in an experiment shown in Figure5. Its rated voltage was 1200 V, and its rated current was 75 A. According to the datasheet WeWe tested tested an anIGBT IGBT module module produced produced by bySEMIKON SEMIKON (SKM75GB12T4) (SKM75GB12T4) in anin experimentan experiment shown shown provided by the manufacturer [47], the gate-emitter voltage was set to 15 V and the environment in Figurein Figure 5. Its 5. ratedIts rated voltage voltage was was 1200 1200 V, andV, and its ratedits rated current current was was 75 A.75 AccordingA. According to theto the datasheet datasheet temperature was room temperature (25 ◦C). Figure6 shows a photograph of the semiconductor providedprovided by bythe the manufacturer manufacturer [47 ][,47 the], thegate gate-emitter-emitter voltage voltage was was set setto 15to V15 andV and the the environment environment parameter test system we used (PCT-2), which was composed of the 2651A high-power source meter, temperaturetemperature was was room room temperature temperature (25 (25 °C ) °C. Figure). Figure 6 shows 6 shows a photograph a photograph of theof the semiconductor semiconductor the 2636B system source meter, the 8010 high-power test device, and a computer. The V-I curve of parameterparameter test test system system we we used used (PCT (PCT-2),- 2), which which was was composed composed of theof the 2651A 2651A high high-power-power source source the IGBT module was measured using ACS software (V2.0 Release, Keithley Instruments, Cleveland, meter,meter, the the 2636B 2636B system system source source meter, meter, the the 8010 8010 high high-power-power test test device, device, and and a computer. a computer. The The V- IV -I OH, USA). curvecurve of theof the IGBT IGBT module module was was measured measured using using ACS ACS software software (V 2.0(V 2.0Rele Releasease, Ke, iKethleyithley Instruments Instruments, , ClevelandCleveland, Ohio, Ohio, USA, USA). ).

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FigureFigureFigure 5. 5. 5. The The The IGBTIGBT IGBT module module used used for forfor testing. testing.

FigureFigureFigure 6. 6. 6.Semiconductor Semiconductor Semiconductor testing testing equipment. equipment.equipment. Figure 6. Semiconductor testing equipment. AsAsAs shown shown shown in in in Figure Figure Figure7, 7, the7, the the V-I VV- characteristicI- I characteristiccharacteristic curve curve curve of of of the the the IGBT IGBT IGBT module, module, as as as tested tested at at at room room room temperature,temperature,temperature,As shown had had had in a Figure segmentationa a segmentation segmentation 7, the andV and -andI thecharacteristic the the voltage voltage voltage at at at the curvethe the inﬂection inflection inflection of the pointpoint IGBTpoint waswas was module, V Vcece-thce-th-th. .. When Whenas When tested V VVcece wasce was atwas less roomless less temperature,thanthanthanVce-th V Vcece-,th-th the, ,the thehad IGBT IGBT IGBT a segmentation module module module waswas was inin andin thethe the the off off-state. off voltage-state.-state. Some SomeSome at the leakage leakage inflection currents currents currents point led led ledwas to to to a aV small a cesmall small-th. When slope slope slope Vin ince inthe wasthe the V V -lessI- V-I I characteristic, indicating high resistance. When Vcece was higher than Vcece-th-th, the IGBT module was in the thancharacteristic,characteristic, Vce-th, the IGBT indicating indicating module high high was resistance. resistance. in the off When When-state.V VSomece waswas leakage higher than currents VVce-th, ledthe, the toIGBT IGBT a small module module slope was wasin in the inthe V the -I on-state, and the collector–emitter resistance decreased, causing an increase in the curve slope that characteristic,on-state,on-state, and and theindicating the collector–emitter collector high–emitter resistance. resistanceresistance When decreased, Vce was higher causing causing than an an Vincreasece increase-th, the IGBTin in the the modulecurve curve slope was slope thatin that the indicatesindicates linear linear behavior. behavior. However, However, it it was was quite quite rare rare to to be be able able to to extract extract V Vcece-th-th directly directly from from the the V V-I- I onindicates-state, and linear the behavior. collector– However,emitter resistance it was quite decreased, rare tobe causing able to an extract increaseVce-th in directlythe curve from slope the that V-I characteristiccharacteristic curve. curve. indicatescharacteristic linear curve. behavior. However, it was quite rare to be able to extract Vce-th directly from the V-I characteristic curve.

1010

10 88

(A)

I I

6 44

(A)

c I 4 22

V Vce-thce-th 2 00 0.00.0 0.50.5 1.01.0 1.51.5 2.02.0 2.52.5 V (V) V Vcece (V) ce-th 0 Figure0.0FigureFigure 7. 7. 7.V-I V V0.5-I-characteristic Icharacteristic characteristic1.0 curve curve 1.5at at room roomroom temperature. temperature.temperature.2.0 2.5 V (V) ce Figure 7. V-I characteristic curve at room temperature.

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To ensure the accuracy of measurements of the collector-emitter threshold voltage, a linear ToTo ensure ensure the the accuracyaccuracy of ofmeasurements measurements of of the the collector-emitter collector-emitter threshold threshold voltage, voltage, a a linear linear function (y = ax + b) could be used to describe the on-state V-I characteristic curve. The intersection functionfunction (y (y = = axax + + b)b) couldcould bebe usedused toto describe describe the the on-state on-state V-I V-I characteristic characteristic curve. curve. The The intersection intersection point between the obtained function and the voltage axis was Vce-th (see Figure 8). point between the obtained function and the voltage axis was Vce-th (see Figure 8). point between the obtained function and the voltage axis was Vce-th (see Figure8).

10 10

8 8

6 6

y=ax+b

(A)

c y=ax+b

(A) c I 4 4

2 2

0 00.0 0.5 V 1.0 1.5 2.0 2.5 0.0 0.5 Vce-th 1.0 1.5 2.0 2.5 ce-th V (V) Vce (V) ce Figure 8. Method for extracting collector-emitter threshold voltage (Vce-th). FigureFigure 8. 8.Method Method for for extracting extracting collector-emitter collector-emitter threshold threshold voltage voltage (V (Vce-thce-th).).

When extracting the coefficients of these fitting functions from the data, optimizing the selected WhenWhen extracting extracting the the coefficients coefficients of of these these fitting fitting functions functions from from the the data, data, optimizing optimizing the the selected selected data can improve the function fitting results and the resulting accuracy of Vce-th. The primary function datadata can can improve improve the the function function fitting fitting results results and and the the resulting resulting accuracy accuracy of ofV ce-thVce-th..The The primaryprimary functionfunction F1 (x) obtained with the selection value of 0.6 V as a starting point is shown in Figure 9a. The FF11(x) (x) obtained obtained with with the the selection selection value value of 0.6 of V 0.6as a V starting as a starting point is shown point is in shown Figure9 ina. The Figure R-squared 9a. The R-squared determination coefficient for this function was 0.99342. Since the initial value of the determinationR-squared determination coefficient for coefficient this function for was this 0.99342. functionSince was the 0.99342. initial Since value the of the initial selected value voltage of the selected voltage point was improved continuously, the determination coefficient for the primary pointselected was voltage improved point continuously, was improved the determination continuously, coefficient the determination for the primary coefficient function for was the tested primary for function was tested for extracting Vce-th. When the selected value reached 1.4 V, R-square = 0.9994, extractingfunction wasVce-th test. Whened for the extracting selected valueVce-th. When reached the 1.4 selected V, R-square value = 0.9994,reached and 1.4 theV, R resulting-square primary= 0.9994, and the resulting primary function F2 (x) is also shown in Figure 9a. Therefore, changing the starting functionand the resultingF2 (x) is also primary shown function in Figure F29 (x)a. Therefore,is also shown changing in Figure the 9a. starting Therefore, point changing of the data the used starting for point of the data used for curve fitting effectively improved the fitting result and the accuracy of the curvepoint fittingof the data effectively used for improved curve fitting the fitting effectively result improved and the accuracy the fitting of result the V ce-thandextraction. the accuracy Table of the1 Vce-th extraction. Table 1 exhibits the parameters of the liner function applied in V–I characteristic exhibitsVce-th extraction. the parameters Table 1of exhibits the liner the function parameters applied of in the V–I liner characteristic function applied curve fitting. in V–I characteristic curve fitting. curve fitting. 12 12 I 10 Ic 10 c F1 (x) F1 (x) 8 F2 (x) 8 F2 (x) F (x) 3 ) F3 (x 6

(A)

c I 4 4

2 2

0 0 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 Vce-th 1.0 1.5 2.0 2.5 Vce-th V (V) Vce (V) ce (a) (a) Figure 9. Cont.

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5.0

Ic 4.5 F1 (x) 4.0 F2 (x) 3.5 ) F3 (x

3.0

(A)

c I 2.5

2.0

1.5

1.0 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 V (V) ce (b)

FigureFigure 9.9.Fitting Fitting resultsresults for forV Vce-thce-th using variousvarious data:data: (a)) TheThe wholewhole effecteffect ofof functionfunction ﬁtting;fitting; ((bb)) thethe enlargedenlarged view view of of function function ﬁtting. fitting.

Table 1. Accuracy of V extraction using various data. However, Figure 9b reveals that the highce-th R-square obtained in curve fitting sacrificed the fitting

accuracyVoltage in (V) the area anear the Standard collector Error-emitter threshold b voltage, Standard which Error also R-Square caused theV ce-therror(V) in the Vce-th measurement.0.6 5.61701 Herein, Vce- 0.01724th was obtained− 3.25972when the R-square 0.027 reached 0.993420.998 and the 0.5803 obtained functions0.9 are shown 5.94661 in Figure 9b 0.01148 as F3 (x). At this−3.85935 point, a (the 0.01933 slope of the function 0.99783)= 5.97575, 0.6490 b ( the 0.92 5.96143 0.01129 −3.88716 0.0191 0.99793 0.6520 Y-intercept of the function)= −3.91408, and Vce-th = 0.6549 V. 0.93 5.96969 0.01119 −3.90269 0.01898 0.99799 0.6537 − 0.94 5.97575Table 1. 0.01113 Accuracy of Vce-th3.91408 extraction using 0.01891 various data. 0.99803 0.6549 1.4 6.30752 0.00789 −4.56373 0.01497 0.9994 0.7235

Voltage (V) a Standard Error b Standard Error R-Square Vce-th (V) However,0.6 Figure5.617019b reveals that0.01724 the high R-square−3.25972 obtained 0.027 in curve fitting0.99342 sacrificed 0.5803 the fitting accuracy in0.9 the area5.94661 near the collector-emitter0.01148 threshold−3.85935 voltage,0.01933 which also0.99783 caused the error0.6490 in the Vce-th measurement.0.92 5.96143 Herein, Vce-th0.01129was obtained −3.88716 when the R-square0.0191 reached 0.99793 0.998 and the0.6520 obtained functions0.93 are shown5.96969 in Figure 9b0.01119 as F3 (x). At−3.90269 this point, a0.01898 (the slope of the0.99799 function)= 0.6537 5.97575, b (the Y-intercept0.94 of5.97575 the function)= 0.01113−3.91408, and−3.91408Vce-th = 0.65490.01891 V. 0.99803 0.6549 1.4 6.30752 0.00789 −4.56373 0.01497 0.9994 0.7235 3.2. Extraction of the Package Resistance 3.2. ExtractionThe chip-level of the voltagePackage Resistance 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 chip-level voltage drop in the on-state could be calculated with Equation (4). When the the contribution of the MOSFET could be ignored. With increasing injection current, the voltage drop collector injection current was in a lower range, the PIN diode dominated the on-state voltage, and caused by the MOSFET should become noticeable [46]. Therefore, when the collector–emitter voltage the contribution of the MOSFET could be ignored. With increasing injection current, the voltage of the IGBT module was near the threshold voltage V , the voltage drops generated in the N+ buffer, drop caused by the MOSFET should become noticeablece-th [46]. Therefore, when the collector–emitter N– drift region, and the channel of the chip could be approximated as zero. With these assumptions, voltage of the IGBT module was near the threshold voltage Vce-th, the voltage drops generated in the Equation (4) could be rewritten as: N+ buffer, N– drift region, and the channel of the chip could be approximated as zero. With these assumptions, Equation (4) could2KT be rewrittenJ W as: pL J V = ln[ C N ] + CH CH (4) ce ( ) ( − ) q 2KT4qDani F WJCWN/2N La µniCOXpLCHVJCHG VTH Vce = ln [ ] + (4) q 4qD n F(W /2L ) μ C (V -V ) a i N a ni OX G TH Vce = Vce-th + Ic Rpackage (5) where K is the Boltzmann constant, T is theVce absolute = Vce-th + temperature, Ic Rpackage q is the electronic charge, WN is the(5) width of the N+ drift region, Jc is the current density, ni is the intrinsic carrier concentration, Da is the where K is the Boltzmann constant, T is the absolute temperature, q is the electronic charge, WN is ambipolar diffusion coefficient, La is the ambipolar diffusion length, Lch is the ambipolar diffusion the width of the N+ drift region, Jc is the current density, ni is the intrinsic carrier concentration, Da is coefficient, Cox is the channel length, p is the indicated cell pitch, Vge is the gate voltage, Vth is the the ambipolar diffusion coefficient, La is the ambipolar diffusion length, Lch is the ambipolar threshold voltage, and µni is the inverse layer mobility [46].

Energies 2019, 12, x FOR PEER REVIEW 9 of 16

Energiesdiffusion2019 coefficient,, 12, 851 Cox is the channel length, p is the indicated cell pitch, Vge is the gate voltage,9 of V 15th 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 programmableFigure 10 shows DC power a photograph supply and of our programmable on-state voltage electronic acquisition load (120 system. V/60 The A/250 high-power W) were programmableconnected in series DC powerand linked supply at the and terminal programmable of the collector electronic-emitter. load Another (120 V/60 programmable A/250 W) were DC connectedpower supply in series was and connected linked inat theseries terminal with the of the terminal collector-emitter. of the IGBT Another module’s programmable gate-emitter and DC powerprovided supply the voltage was connected that produced in series the inverse with the-layer terminal channel, of thewhich IGBT ensured module’s that the gate-emitter IGBT module and providedremained thein the voltage on-state. that producedBecause of the the inverse-layer inevitable resistance channel, generated which ensured in the that test thecircuit, IGBT the module IGBT remainedmodule could in the not on-state. take in Becausethe entire of voltage the inevitable produced resistance by the high generated-power inDC the supplier. test circuit, We thetherefore IGBT moduleadjusted could the output not take voltage in the entire of the voltage high-power produced DC by supplier the high-power constantly DC until supplier. the IGBT We therefore module adjustedreached the output on-state, voltage which of was the high-power judged using DC a supplier high-accuracy constantly digital until mult the IGBTimeter. module The collector reached the on-state, which was judged using a high-accuracy digital multimeter. The collector current (I ) was current (Ic) was acquired by a programmable electronic load. When the reading of high-powerc DC acquired by a programmable electronic load. When the reading of high-power DC supplier was 0.67 V, supplier was 0.67 V, Vce = 0.6584 V and Ic = 0.3311 A, and according to Equation (5), Rpackage = 10.287 VmΩ.ce = 0.6584 V and Ic = 0.3311 A, and according to Equation (5), Rpackage = 10.287 mΩ.

Figure 10. Apparatus for measuringmeasuring on-stateon-state voltage. 3.3. The Acquisition Method of On-State Chip Resistance 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 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): decreased as the collector current increased. Ron-chip can be calculated with Equation (6):

Ron-chipRon-chip= (=V (ceV−ce −V Vce-thce-th)/IIcc −− RRpackagepackage (6)(6)

The high-powerhigh-power DC supply in Figure 10 and the programmable load were set to the constantconstant current (CC)(CC) mode, mode, and and the the gate gate voltage voltage was was set set to to 15 15 V. ToV. obtainTo obtain the fullthe relationfull relation between between on-state on-state chip chip resistance and collector current completely, Ic was set from 10 to 74 A in this experiment. The resistance and collector current completely, Ic was set from 10 to 74 A in this experiment. The electronic loadelectronic used load for package used for resistance package resistance extraction extraction was substituted was substituted by a high-power by a high equipment-power equipment (600 V/ (600 V/240 A/12 KW). The relation between Ron-chip and Ic was then obtained by adjusting the output 240 A/12 KW). The relation between Ron-chip and Ic was then obtained by adjusting the output current providedcurrent provided by the DC by power the DC supply power continuously. supply continuously. Note that the Note preset that value the of preset the programmable value of the electronicprogrammable load shouldelectronic be keptload consistentshould be withkept theconsistent DC power with supplier. the DC power supplier. Figure 11 shows shows the the variation variation of of the the on-state on-state voltage, voltage, the the chip-level chip-level voltage voltage drop, drop, and and the the package-levelpackage-level voltagevoltage drop drop as as the the collector collector current current increased. increased. With With the the increase increase of collectorof collector current, current, the IGBTthe IGBT module module on-state on-state voltage voltage obviously obviously increased, increased, because because of the changeof the change in the chip-level in the chi voltagep-level dropvoltage and drop the package-leveland the package voltage-level drop. voltage Figure drop. 12 Figure shows 12 the shows relationship the relationship between between the on-state the chipon-state resistance, chip resistance, package resistance,package resistance, and the collector and the current.collector The current. on-state The chip on- resistancestate chip decreasedresistance exponentiallydecreased exponentially as the collector as the current collector increased, current due inc toreased, the conductance due to the modulation. conductance Simultaneously, modulation. thisSimultaneously, trend also explained this trend why also theexplained package-level why the voltage package drop-level increased voltage drop more increased than the more chip-level than voltagethe chip drop.-level voltage drop.

Energies 2019, 12, x FOR PEER REVIEW 10 of 16 Energies 2019, 12, 851 10 of 15 Energies 2019, 12, x FOR PEER REVIEW 10 of 16 2.0 2.0 1.8 Vce 1.8 V 1.6 Vceon-chip

1.6 V Von-chip 1.4 package V 1.4 package 1.2 1.2

(V) 1.0

0.8

Voltage 0.8

0.6 Voltage 0.6 0.4 0.4 0.2 0.2 0.0 0 10 20 30 40 50 60 70 80 0.0 0 10 20 30 I40 (A) 50 60 70 80 c I (A) c Figure 11. Relationship between each voltage drop within the IGBT module and the collector current. FigureFigure 11.11. Relationship betweenbetween eacheach voltagevoltage dropdrop withinwithin thethe IGBT module and the collector current.

22 22 20 Rpackage 20 R package 18 Ron-chip 18 R 16 on-chip 16

(mΩ) 14

12 12

Resistance 10

Resistance 10 8 8 6 6 0 10 20 30 40 50 60 70 80 0 10 20 30 I40 (A) 50 60 70 80 c I (A) Figure 12. Relationship between each resistance withinc the IGBT module and the collector current. Figure 12. Relationship between each resistance within the IGBT module and the collector current. 3.4. MethodFigure for12. CalculatingRelationship On-Statebetween each Voltage resistance within the IGBT module and the collector current. 3.4. Method for Calculating On-State Voltage 3.4. MethodIt seems for that Calculating the on-state On- chipState resistanceVoltage and the collector current are related with the exponential functionIt seemsunder the that effect the of on the-state conductivity chip resistance modulation and introduce the collector in Section current2 and are the related relationship with isthe It seems that the on-state chip resistance and the collector current are related with the denotedexponential as Equation function (7). under The experimentalthe effect of the results conductivity were analyzed modulation with MATLAB introduce scripts in Section and ﬁtted 2 and with the exponential function under the effect of the conductivity modulation introduce in Section 2 and the thisrelationship exponential is function. denoted When as Equation the on-state (7). The chip experimental resistance is setresults to milliohms, were analyzed a = 94.19, with b = MA−0.6434,TLAB relationship is denoted as Equation (7). The experimental results were analyzed with MATLAB andscripts R-squared and fitted = 0.9982. with this exponential function. When the on-state chip resistance is set to scripts and fitted with this exponential function. When the on-state chip resistance is set to milliohms,Upon comparing a = 94.19, b the = −0.6434, experimental and R measurement-squared = 0.9982. and simulation values (Figure 13), it was found milliohms, a = 94.19, b = −0.6434, and R-squared = 0.9982. that theUpon simulation comparing data owed the experiment an ideal matched-degreeal measurement in a and lower simulation current range values (less (Figure than 60 13), A, 80% it was of Upon comparing the experimental measurement and simulation values (Figure 13), it was thefound rated that current). the simulation When it comes data owed to a higher an ideal level, matched the on-state-degree chip in resistance a lower current reduced range inconspicuously. (less than 60 found that the simulation data owed an ideal matched-degree in a lower current range (less than 60 AssumingA, 80% of thatthe Rrated current).keeps constant When it in comes high currentto a higher condition level, (80%the on of-state the ratedchip resistance current I reduced), we A, 80% of the ratedon-chip current). When it comes to a higher level, the on-state chip resistancerated reduced concludedinconspicuously. that on-state Assuming chip resistancethat Ron-chip had keeps an exponentialconstant in relationshiphigh current with condition collector (80% current. of the Thus, rated inconspicuously. Assuming that Ron-chip keeps constant in high current condition (80% of the rated on-statecurrent voltageIrated), we for concludedthe module that we tested on-state could; chip therefore, resistance be calculated had an exponential with Equations relationship (8) and (9). with currentcollector Irated current.), we Thus, concluded on-state that voltage on-state for the chip module resistance we tested had ancould; exponential therefore, relationshipbe calculated with with collector current. Thus, on-state voltage for the module web tested could; therefore, be calculated with Equations (8) and (9). Ron-chip = aIc (7) Equations (8) and (9). Ron-chip = aIcb (7) V = V + 94.19I −0.6463 + R I (8) ce ce-th Ron-chipc = aIcb package c (7) −0.6463−0.6463 Vce = Vce-thVce =+ V 94.19(0.8ce-th + 94.19IIratedc ) + R+packageRpackage Ic Ic (9)(8) Vce = Vce-th + 94.19Ic−0.6463 + Rpackage Ic (8)

Vce = Vce-th + 94.19(0.8Irated)−0.6463 + Rpackage Ic (9) Vce = Vce-th + 94.19(0.8Irated)−0.6463 + Rpackage Ic (9)

Energies 2019, 12, 851 11 of 15 Energies 2019, 12, x FOR PEER REVIEW 11 of 16

20 Experimental Measurement 18 Function Simulation

(mΩ)

Resistance 8

4 0 10 20 30 40 50 60 70 80 I (A) c (a)

2.0 Experimental Measurement 1.8 Function Simulation

1.6

(V) 1.4

ce V

1.2

1.0

0.8 0 10 20 30 40 50 60 70 80

I (A) c (b)

FigureFigure 13. 13.Experimental Experimental observations observations and simulation and simulation values: (a values:) On-state (a chip) On resistance-state chip measurement resistance andmeasurement simulation; and (b) simulation; on-state voltage (b) on measurement-state voltage and measurement simulation. and simulation.

MeasuringMeasuring thethe IGBTIGBT modulemodule on-stateon-state voltagevoltage underunder differentdifferent currentscurrents allowsallows usus toto verifyverify thethe accuracyaccuracy ofof applyingapplying thethe modelmodel proposedproposed above.above. CollectorCollector currentscurrents (I(cIc)) ofof 20,20, 40,40, 60,60, andand 7575 AA werewere usedused inin teststests forfor thisthis validation.validation. The measured voltages ( (Vcece-mea-mea) and) and the the calculated calculated voltages voltages (V (ceV-calce-cal) are) arelisted listed in Table in Table 2. 2.

Table 2. Data comparison. Table 2. Data comparison

Ic (A) Ron-chip (mΩ) Vce-cal (V) Vce-mea (V) Error (%) Ic (A) Ron-chip (mΩ) Vce-cal (V) Vce-mea (V) Error (%) 2020 13.5899 13.5899 1.13221.1322 1.12941.1294 0.51350.5135 40 8.6814 1.4133 1.4112 0.1488 40 8.6814 1.4133 1.4112 0.1488 60 6.6801 1.6725 1.6957 −1.3681 6075 6.6801 6.6801 1.92091.6725 1.92611.6957 −0.2855−1.3681 75 6.6801 1.9209 1.9261 −0.2855

Referring to the data sheet provided by manufacturer, the on-state voltage of the SKM75GB12T4 Referring to the data sheet provided by manufacturer, the on-state voltage of the module was between 1.85 V and 2.1 V when operating at this current. This agreement between our SKM75GB12T4 module was between 1.85 V and 2.1 V when operating at this current. This experimental observation of the on-state voltage and the manufacturer’s speciﬁcation for a brand-new agreement between our experimental observation of the on-state voltage and the manufacturer’s module shows that our model is valid for its intended purpose. specification for a brand-new module shows that our model is valid for its intended purpose.

Energies 2019, 12, 851 12 of 15

Energies 2019, 12, x FOR PEER REVIEW 12 of 16 To demonstrate the validity of the proposed methods, we tested another IGBT module manufacturedTo demonstrate by Guoyang the validity Electronics of the (WGL100B65F23). proposed methods, Parameters we tested required another in the IGBT on-state module voltage modelmanufactured were obtained by in Guoyang the same Electronics way. Some (WGL100B65F23). crucial data are Parameters shown in required the following in the onﬁgures-state and Table3voltage. The threshold model were voltage obtained was in 0.6428 the same obtained way. Some from crucial Figure data 14 a;are Figure shown 14 inb the exhibits following the simulationfigures and Table 3. The threshold voltage was 0.6428 obtained− 0.4202) from Figure 14a; Figure 14b exhibits the result using the exponential function (Ron-chip = 52.14 Ic and Rpackage = 2.146 mΩ; Figure 14c simulation result using the exponential function (Ron-chip = 52.14 Ic−0.4202) and Rpackage = 2.146 mΩ; Figure shows the on-state voltages obtained by different methods and the accuracy was proved. 14c shows the on-state voltages obtained by different methods and the accuracy was proved.

I 10 c Function Fitting

(A)

c I

0 0.0 0.5 1.0 1.5 2.0 2.5 V (V) ce (a)

22 Experimental Measurement 20 Function Simulation 18

(mΩ) 14

10 Resistance

4 0 10 20 30 40 50 60 70 80 90 100 110 I (A) c (b) 1.8

Experimental Measurement 1.6 Function Simulation

1.4

(V)

V 1.2

1.0

0.8 0 10 20 30 40 50 60 70 80 90 100 110 I (A) c (c)

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. Energies 2019, 12, 851 13 of 15

Table 3. Data comparison.

Ic (A) Ron-chip (mΩ) Vce-cal (V) Vce-mea (V) Error (%) 20 13.5899 0.9946 0.9811 1.37 40 10.6344 1.1903 1.1540 3.14 60 9.1791 1.3555 1.3223 2.51 80 8.5702 1.5043 1.5001 0.27 100 8.5702 1.7197 1.7019 1.04

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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