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# N-Channel IGBT

Model N-Channel IGBT

## Library

Semiconductor Devices

## Description

The N-Channel IGBT block models a PNP Bipolar transistor driven by an N-Channel MOSFET, as shown in the following figure:

The MOSFET source is connected to the bipolar transistor collector, and the MOSFET drain is connected to the bipolar transistor base. The MOSFET uses the equations shown in the N-Channel MOSFET block reference page. The bipolar transistor uses the equations shown in the PNP Bipolar Transistor block reference page, but with the addition of an emission coefficient parameter N that scales kT/q.

The N-Channel IGBT block uses the on and off characteristics you specify in the block dialog box to estimate the parameter values for the underlying N-Channel MOSFET and PNP bipolar transistor.

The block uses the off characteristics to calculate the base-emitter voltage, Vbe, and the saturation current, IS.

When the transistor is off, the gate-emitter voltage is zero and the IGBT base-collector voltage is large, so the PNP base and collector current equations simplify to:

where N is the Emission coefficient, N parameter value, VAF is the forward Early voltage, and Ic and Ib are defined as positive flowing into the collector and base, respectively. See the PNP Bipolar Transistor reference page for definitions of the remaining variables. The first equation can be solved for Vbe.

The base current is zero in the off-condition, and hence Ic = –Ices, where Ices is the Zero gate voltage collector current. The base-collector voltage, Vbc, is given by Vbc = Vces + Vces, where Vces is the voltage at which Ices is measured. Hence we can rewrite the second equation as follows:

The block sets βR and βF to typical values of 1 and 50, so these two equations can be used to solve for Vbe and IS:

 Note:   The block does not require an exact value for βF because it can adjust the MOSFET gain K to ensure the overall device gain is correct.

The block parameters Collector-emitter saturation voltage, Vce(sat) and Collector current at which Vce(sat) is defined are used to determine Vbe(sat) by solving the following equation:

Given this value, the block calculates the MOSFET gain, K, using the following equation:

where Vth is the Gate-emitter threshold voltage, Vge(th) parameter value and VGE(sat) is the Gate-emitter voltage at which Vce(sat) is defined parameter value.

Vds is related to the transistor voltages as Vds = VceVbe. The block substitutes this relationship for Vds, sets the base-emitter voltage and base current to their saturated values, and rearranges the MOSFET equation to give

where Vce(sat) is the Collector-emitter saturation voltage, Vce(sat) parameter value.

These calculations ensure the zero gate voltage collector current and collector-emitter saturation voltage are exactly met at these two specified conditions. However, the current-voltage plots are very sensitive to the emission coefficient N and the precise value of Vth. If the manufacturer datasheet gives current-voltage plots for different VGE values, then the N and Vth can be tuned by hand to improve the match.

### Charge Model

The block models gate junction capacitance as a fixed gate-emitter capacitance CGE and either a fixed or a nonlinear gate-collector capacitance CGC.

If you select Specify using equation parameters directly for the Parameterization parameter in the Junction Capacitance tab, you specify the Gate-emitter junction capacitance and Gate-collector junction capacitance parameters directly. Otherwise, the block derives them from the Input capacitance Cies and Reverse transfer capacitance Cres parameter values. The two parameterizations are related as follows:

• CGE = Cres

• CGC = CiesCres

If you select the Gate-collector charge function is nonlinear option for the Charge-voltage linearity parameter, then the gate-collector charge relationship is defined by the piecewise-linear function shown in the following figure.

With this nonlinear capacitance, the gate-emitter and collector-emitter voltage profiles take the form shown in the next figure, where the collector-emitter voltage fall has two regions (labeled 2 and 3) and the gate-emitter voltage has two time-constants (before and after the threshold voltage Vth):

You can determine the capacitor values for Cies, Cres, and Cox as follows, assuming that the IGBT gate is driven through an external resistance RG:

1. Set Cies to get correct time-constant for VGE in Region 1. The time constant is defined by the product of Cies and RG. Alternatively, you can use a datasheet value for Cies.

2. Set Cres so as to achieve the correct VCE gradient in Region 2. The gradient is given by (VGEVth)/(Cres · RG).

3. Set VCox to the voltage at which the VCE gradient changes minus the threshold voltage Vth.

4. Set Cox to get correct Miller length and time constant in Region 4.

Because the underlying model is a simplification of an actual charge distribution, some iteration of these four steps may be required to get a best overall fit to measured data. The collector current tail when the IGBT is turned off is determined by the Total forward transit time parameter.

### Fine-Tuning the Current-Voltage Characteristics

Use the parameters on the Advanced tab to fine-tune the current-voltage characteristics of the modeled device. To use these additional parameters effectively, you will need a manufacturer datasheet that provides plots of the collector current versus collector-emitter voltage for different values of gate-emitter voltage. The parameters on the Advanced tab have the following effects:

• The Emission coefficient, N parameter controls the shape of the current-voltage curves around the origin.

• The Collector resistance, RC and Emitter resistance, RE parameters affect the slope of the current-voltage curve at higher currents, and when fully turned on by a high gate-emitter voltage.

• The Forward Early voltage, VAF parameter affects the shape of the current-voltage curves for gate-emitter voltages around the Gate-emitter threshold voltage, Vge(th).

### Modeling Temperature Dependence

The default behavior is that dependence on temperature is not modeled, and the device is simulated at the temperature for which you provide block parameters. You can optionally include modeling the dependence of the transistor static behavior on temperature during simulation. Temperature dependence of the junction capacitances is not modeled, this being a much smaller effect.

Temperature dependence is modeled by the temperature dependence of the constituent components. See the N-Channel MOSFET and PNP Bipolar Transistor block reference pages for further information on the defining equations.

Some datasheets do not provide information on the zero gate voltage collector current, Ices, at a higher measurement temperature. In this case, you can alternatively specify the energy gap, EG, for the device, using a typical value for the semiconductor type. For silicon, the energy gap is usually 1.11 eV.

### Thermal Port

The block has an optional thermal port, hidden by default. To expose the thermal port, right-click the block in your model, and then from the context menu select Simscape block choices > Show thermal port. This action displays the thermal port H on the block icon, and adds the Thermal port tab to the block dialog box.

Use the thermal port to simulate the effects of generated heat and device temperature. For more information on using thermal ports and on the Thermal port tab parameters, see Simulating Thermal Effects in Semiconductors.

## Basic Assumptions and Limitations

The model is based on the following assumptions:

• This block does not allow you to specify initial conditions on the junction capacitances. If you select the Start simulation from steady state option in the Solver Configuration block, the block solves the initial voltages to be consistent with the calculated steady state. Otherwise, voltages are zero at the start of the simulation.

• You may need to use nonzero junction capacitance values to prevent numerical simulation issues, but the simulation may run faster with these values set to zero.

• The block does not account for temperature-dependent effects on the junction capacitances.

## Dialog Box and Parameters

### Main Tab

Zero gate voltage collector current, Ices

The collector current that flows when the gate-emitter voltage is set to zero, and a large collector-emitter voltage is applied, that is, the device is in the off-state. The value of the large collector-emitter voltage is defined by the parameter Voltage at which Ices is defined. The default value is 2 mA.

Voltage at which Ices is defined

The voltage used when measuring the Zero gate voltage collector current, Ices. The default value is 600 V.

Gate-emitter threshold voltage, Vge(th)

The threshold voltage used in the MOSFET equations. The default value is 6 V.

Collector-emitter saturation voltage, Vce(sat)

The collector-emitter voltage for a typical on-state as specified by the manufacturer. The default value is 2.8 V.

Collector current at which Vce(sat) is defined

The collector-emitter current when the gate-emitter voltage is Vge(sat) and collector-emitter voltage is Vce(sat). The default value is 400 A.

Gate-emitter voltage at which Vce(sat) is defined

The gate voltage used when measuring Vce(sat) and Ice(sat). The default value is 10 V.

Measurement temperature

The temperature for which the parameters are quoted. The default value is 25 C.

### Junction Capacitance Tab

Parameterization

Select one of the following methods for block parameterization:

• Specify from a datasheet — Provide parameters that the block converts to junction capacitance values. This is the default method.

• Specify using equation parameters directly — Provide junction capacitance parameters directly.

Input capacitance, Cies

The gate-emitter capacitance with the collector shorted to the source. This parameter is only visible when you select Specify from a datasheet for the Model junction capacitance parameter. The default value is 26.4 nF.

Reverse transfer capacitance, Cres

The collector-gate capacitance with the emitter connected to ground. This parameter is only visible when you select Specify from a datasheet for the Model junction capacitance parameter. The default value is 2.7 nF.

Gate-emitter junction capacitance

The value of the capacitance placed between the gate and the emitter. This parameter is only visible when you select Specify using equation parameters directly for the Model junction capacitance parameter. The default value is 23.7 nF.

Gate-collector junction capacitance

The value of the capacitance placed between the gate and the collector. This parameter is only visible when you select Specify using equation parameters directly for the Model junction capacitance parameter. The default value is 2.7 nF.

Charge-voltage linearity

Select whether gate-drain capacitance is fixed or nonlinear:

• Gate-collector capacitance is constant — The capacitance value is constant and defined according to the selected parameterization option, either directly or derived from a datasheet. This is the default method.

• Gate-collector charge function is nonlinear — The gate-collector charge relationship is defined according to the piecewise-nonlinear function described in Charge Model. Two additional parameters appear to let you define the gate-collector charge function.

Gate-collector oxide capacitance

The gate-collector capacitance when the device is on and the collector-gate voltage is small. This parameter is only visible when you select Gate-collector charge function is nonlinear for the Charge-voltage linearity parameter. The default value is 20 nF.

Collector-gate voltage below which oxide capacitance becomes active

The collector-gate voltage at which the collector-gate capacitance switches between off-state (CGC) and on-state (Cox) capacitance values. This parameter is only visible when you select Gate-collector charge function is nonlinear for the Charge-voltage linearity parameter. The default value is -5 V.

Total forward transit time

The forward transit time for the PNP transistor used as part of the underlying IGBT model. It affects how quickly charge is removed from the channel when the IGBT is turned off. The default value is 0 μs.

Emission coefficient, N

The emission coefficient or ideality factor of the bipolar transistor. The default value is 1.

Forward Early voltage, VAF

The forward Early voltage for the PNP transistor used in the IGBT model. See the PNP Bipolar Transistor block reference page for more information. The default value is 200 V.

Collector resistance, RC

Resistance at the collector. The default value is 0.001 Ohm.

Emitter resistance, RE

Resistance at the emitter. The default value is 0.001 Ohm.

Forward current transfer ratio BF

Ideal maximum forward current gain for the PNP transistor used in the IGBT model. See the PNP Bipolar Transistor block reference page for more information. The default value is 50.

### Temperature Dependence Tab

Parameterization

Select one of the following methods for temperature dependence parameterization:

• None — Simulate at parameter measurement temperature — Temperature dependence is not modeled, and none of the other parameters on this tab are visible. This is the default method.

• Specify Ices and Vce(sat) at second measurement temperature — Model temperature-dependent effects by providing values for the zero gate voltage collector current, Ices, and collector-emitter voltage, Vce(sat), at the second measurement temperature.

• Specify Vce(sat) at second measurement temperature plus the energy gap, EG — Use this option when the datasheet does not provide information on the zero gate voltage collector current, Ices, at a higher measurement temperature.

Energy gap, EG

Energy gap value. This parameter is only visible when you select Specify Vce(sat) at second measurement temperature plus the energy gap, EG for the Parameterization parameter. The default value is 1.11 eV.

Zero gate voltage collector current, Ices, at second measurement temperature

The zero gate collector current value at the second measurement temperature. This parameter is only visible when you select Specify Ices and Vce(sat) at second measurement temperature for the Parameterization parameter. The default value is 100 mA.

Collector-emitter saturation voltage, Vce(sat), at second measurement temperature

The collector-emitter saturation voltage value at the second measurement temperature, and when the collector current and gate-emitter voltage are as defined by the corresponding parameters on the Main tab. The default value is 3 V.

Second measurement temperature

Second temperature Tm2 at which Zero gate voltage collector current, Ices, at second measurement temperature and Collector-emitter saturation voltage, Vce(sat), at second measurement temperature are measured. The default value is 125 C.

Saturation current temperature exponent, XTI

The saturation current exponent value for your device type. If you have graphical data for the value of Ices as a function of temperature, you can use it to fine-tune the value of XTI. The default value is 3.

Mobility temperature exponent, BEX

Mobility temperature coefficient value. You can use the default value for most devices. If you have graphical data for Vce(sat) at different temperatures, you can use it to fine-tune the value of BEX. The default value is -1.5.

Device simulation temperature

Temperature Ts at which the device is simulated. The default value is 25 C.

## Ports

The block has the following ports:

C

Electrical conserving port associated with the PNP emitter terminal.

G

Electrical conserving port associated with the MOSFET gate terminal.

E

Electrical conserving port associated with the PNP collector terminal.