SPICE NIGBT

SPICE-compatible N-Channel insulated gate bipolar transistor

Since R2020a

• 

Libraries:
Simscape / Electrical / Additional Components / SPICE Semiconductors

Description

The SPICE NIGBT block models a SPICE n-type insulated gate bipolar transistor (IGBT).

SPICE, or Simulation Program with Integrated Circuit Emphasis, is a simulation tool for electronic circuits. You can convert some SPICE subcircuits into equivalent Simscape™ Electrical™ models using the Environment Parameters block and SPICE-compatible blocks from the Additional Components library. For more information, see subcircuit2ssc.

This figure shows the equivalent circuit for the SPICE NIGBT block:

Equations

Variables for the SPICE NIGBT block equations include:

• Variables that you define by specifying parameters for the SPICE NIGBT block.

• Temperature, T, which is 300.15 K by default. You can use a different value by specifying parameters for the SPICE NIGBT block or by specifying parameters for both the SPICE NIGBT block and an Environment Parameters block. For more information, see Transistor Temperature.

MOSFET Channel Current

This table shows the equations that define the relationship between the MOSFET channel current, I_mos, and the gate-source voltage, V_gs.

Applicable Range of Vgs Values	Corresponding Imos Equation
$$V_{gs}<VT$$	$$I_{mos}=GMIN*V_{ds}*SCALE$$
$$V_{ds}\le \frac{V_{gs}-VT}{KF}$$	$$I_{mos}=SCALE*\left(\frac{KF*KP\left[(V_{gs}-VT)V_{ds}-\frac{KF*V_{ds}{}^2}{2}\right]}{1+THETA*(V_{gs}-VT)}+GMIN*V_{ds}\right)$$
$$V_{ds}>\frac{(V_{gs}-VT)}{KF}$$	$$I_{mos}=SCALE*\left(\frac{KP{(V_{gs}-VT)}^2}{2\left[1+THETA*(V_{gs}-VT)\right]}+GMIN*V_{ds}\right)$$

In these equations:

• V_ds is the drain-source voltage.

• VT is the threshold voltage.

• KF is the triode region factor.

• KP is the mosfet transconductance.

• THETA is the transverse field factor.

Bipolar Steady-State Collector Current

This table shows the equations that define the relationship between the steady-state collector current, I_css, and the emitter-base capacitance, Q_eb.

Applicable Range of Qeb Values	Corresponding Icss Equation
$$Q_{eb}<0$$	$$I_{css}=0$$
$$Q_{eb}\ge 0$$	$$I_{css}=\left[\left(\frac{1}{1+b}\right)I_T+\left(\frac{b}{1+b}\right)\left(\frac{4D_p}{W^2}\right)Q_{eb}\right]*SCALE$$

In these equations:

• $$b=\frac{MUN}{MUP}$$ is the ambipolar mobility ratio.

• $$D_p=\frac{K_{B}T}{q}*MUP$$ is the diffusion coefficient for holes.

• $$W=WB-W_{bcj}$$ is the quasi-neutral base width, where:

  • WB is the metallurgical base width.

  • $$W_{bcj}=\sqrt{2{\epsilon }_{si}\frac{V_{bc}+V_{bi}}{q*NB}}$$ is the base-collector depletion width.

  • V_bc is the base-collector voltage.

  • V_bi is the built-in voltage, and it is equal to 0.6 V

Bipolar Steady-State Base Current

This table shows the equations that define the relationship between the steady-state base current, I_bss, and the emitter-base capacitance, Q_eb.

Applicable Range of Qeb Values	Corresponding Ibss Equation
$$Q_{eb}<0$$	$$I_{bss}=0$$
$$Q_{eb}\ge 0$$	$$I_{bss}=\frac{Q_{eb}}{TAU}+{\left(\frac{Q_{eb}}{Q_B}\right)}^2\left(\frac{4*N{B}^2}{n{i}^2}\right)JSNE*AREA*SCALE$$

In these equations:

• TAU is the ambipolar recombination lifetime.

• JSNE is the emitter saturation current density.

• ni is the intrinsic carrier concentration. At 300 K it is equal to 1.45*1010 1/cm3.

• $$Q_B=qW{N}_B*AREA$$ is the background mobile carrier base charge, where:

  • N_B is the base doping.

  • AREA is the area of the device.

Bipolar Emitter-Base Voltage

This table shows the equations that define the relationship between the emitter-base voltage, V_eb, and the emitter-base capacitance, Q_eb.

Applicable Range of Qeb Values	Corresponding Veb Equation
$$Q_{eb}<0$$	$$V_{eb}=V_{ebj}$$
$$Q_{bi}>Q_{eb}\ge 0$$	$$V_{ebmin}=\min (V_{ebj},V_{ebd})$$
$$Q_{eb}>Q_{bi}$$	$$V_{eb}=V_{ebd}$$

In these equations:

• $$V_{ebj}=V_{bi}-\frac{{\left(Q_{eb}-Q_{bi}\right)}^2}{2qNB{\epsilon }_{si}{A}^2}$$is the emitter-base depletion voltage.

• V_bi is the built-in voltage.

• $$Q_{bi}=AREA*\sqrt{2{\epsilon }_{si}qNB*V_{bi}}$$ is the emitter-base junction built-in voltage.

• $$V_{ebd}=\frac{kT}{q}\ln \left[\left(\frac{P_0}{n{i}^2}+\frac{1}{NB}\right)\left(NB+P_0\right)\right]-\frac{D_C}{{\mu }_{nc}}\ln \frac{P_0+NB}{NB}$$is the emitter-base diffusion voltage.

Anode Current

The anode current is obtained from this equation:

$$I_T=\frac{V_{ae}}{R_b}*SCALE,$$

where:

• V_ae is the applied anode-emitter voltage.

• R_b is the conductivity-modulated base resistance.

This table shows the equations that define the relationship between the conductivity-modulated base resistance, R_b, and the emitter-base capacitance, Q_eb.

Applicable Range of Qeb Values	Corresponding Rb Equation
$$Q_{eb}<0$$	$$R_b=\frac{W}{q*MUN*AREA*NB}$$
$$Q_{eb}\ge 0$$	$$R_b=\frac{W}{q*{\mu }_{eff}*AREA*n_{eff}}$$

In these equations:

• μ_eff is the effective carrier mobility.

• n_eff is the effective base doping concentration.

• MUN is the electron mobility.

μ_eff and n_eff are obtained using these equations:

$$\begin{array}{l}{\mu }_{nc}=\frac{1}{\left(\frac{1}{{\mu }_n}+\frac{1}{{\mu }_c}\right)}\\ {\mu }_{pc}=\frac{1}{\left(\frac{1}{{\mu }_p}+\frac{1}{{\mu }_c}\right)}\\ {\mu }_{eff}={\mu }_{nc}+\frac{{\mu }_{pc}{Q}_{eb}}{\left(Q_{eb}+Q_B\right)}\\ D_c=2\frac{kT}{q}\frac{{\mu }_{nc}{\mu }_{pc}}{{\mu }_{nc}+{\mu }_{pc}}\\ L=\sqrt{D_c*TAU}\\ P_0=\frac{Q}{q*AREA*L\tanh \frac{W}{2L}}\\ n_{eff}=\frac{\frac{W}{2L}\sqrt{N_B^2+P_0^{2}csch\left(\frac{W}{L}\right)}}{arctanh\left[\frac{\sqrt{N_B^2+P_0^{2}csch\left(\frac{W}{L}\right)}\tanh \left(\frac{W}{2L}\right)}{N_B+P_{0}csch\left(\frac{W}{L}\right)\tanh \left(\frac{W}{2L}\right)}\right]}\\ {\overline{\delta }}_p=\frac{P_0\sinh \left(\frac{W}{2L}\right)}{\sinh \left(\frac{W}{L}\right)}\end{array}$$

where:

• μ_nc is the electron carrier scattering mobility.

• μ_pc is the hole carrier scattering mobility.

• D_c is the carrier-carrier scattering diffusivity.

• L is the ambipolar diffusion length.

• P₀ is the carrier concentration at emitter's end of the base.

• $$\overline{{\delta }_p}$$ is the average carrier concentration in base.

Avalanche Multiplication Current

The avalanche multiplication current is obtained from this equation:

$$I_{mult}=\left(M-1\right)\left(I_{mos}+I_{css}+I_{ccer}\right)+M*I_{gen},$$

where:

• $$I_{gen}=\frac{SCALE}{TAU}q{n}_{i}AREA\sqrt{2{\epsilon }_{si}\frac{V_{bc}}{q{N}_B}}$$is the collector-base thermally generated current.

• I_css is the steady-state collector current.

• I_mos is the MOSFET channel current.

• I_ccer is the collector-emitter redistribution current.

This equation defines the relationship between the base-collector voltage, V_bc, and the avalanche multiplication factor, M:

$$M=\frac{1}{1-{\left(\frac{V_{bc}}{B{V}_{cbo}}\right)}^{BVN}},$$

where:

• $$B{V}_{cbo}=BVF*5.34e13*N{B}^{-0.75}$$is the open-base collector-emitter breakdown voltage.

• BVF is the avalanche uniformity factor.

• BVN is the avalanche multiplication exponent.

Capacitance Model

The gate source capacitance is obtained from this equation:

$$Q_{gs}=CGS*V_{gs}*SCALE.$$

The drain source capacitance is obtained from this equation:

$$Q_{ds}=q(AREA-AGD)*NB*W_{dsj}*SCALE,$$

where W_dsj = W_bcj is the drain-source depletion width.

This table shows the equations that define the relationship between the gate-drain capacitance, Q_dg, and the drain-gate voltage, V_dg

Applicable Range of Vdg Values	Corresponding Qdg Equation
$$V_{dg}+VTD\le 0$$	$$Q_{dg}=C_{gdo}*V_{dg}*SCALE$$
$$V_{dg}+VTD>0$$	$$Q_{dg}=\left[\frac{qNB{\epsilon }_{si}AGD}{COXD}\left(\frac{COXD*W_{dgj}}{{\epsilon }_{si}}\log \left(1+\frac{COXD*W_{dgj}}{{\epsilon }_{si}}\right)\right)-C_{gdo}*VTD\right]*SCALE$$

In these equations:

• $$C_{gdo}=COXD*AGD$$ is the gate-drain overlap oxide capacitance.

• V_dg is the drain-gate voltage.

• ε_si is the permittivity of silicon.

• $$W_{dgj}=\sqrt{2{\epsilon }_{si}\frac{\left(V_{dg}+VTD\right)}{qNB}}$$ is the drain-gate overlap depletion width.

• VTD is the Gate-drain overlap depletion threshold, VTD.

• COXD is the Gate-drain oxide capacitance per unit area, COXD.

• AGD is the Gate-drain overlap area, AGD.

• NB is the Base doping, NB.

This equation shows the relationship between the collector-emitter redistribution current, I_ccer, and the collector-emitter redistribution capacitance, C_cer:

$$I_{ccer}=C_{cer}*\frac{d{V}_{ec}}{dt}*SCALE,$$

where V_ec is the emitter-collector voltage.

This table shows the equations that define the relationship between the collector-emitter redistribution capacitance, C_cer, and the emitter-base capacitance, Q_eb.

Applicable Range of Qeb Values	Corresponding Ccer Equation
$$Q_{eb}>0$$	$$C_{cer}=\frac{Q_{eb}{C}_{bcj}}{3Q_B}+C_{min}*AREA$$
$$Q_{eb}\le 0$$	$$C_{cer}=C_{min}AREA$$

In these equations:

• C_bcj is the base-collector depletion capacitance.

• $$Q_B=qW{N}_B*AREA$$ is the background mobile carrier base charge.

The implicit emitter-base capacitor current is obtained from this equation:

$$I_{qeb}=\frac{d{Q}_{eb}}{dt}*SCALE.$$

Transistor Temperature

You can use these options to define transistor temperature, T:

• Fixed temperature — The block uses a temperature that is independent of the circuit temperature when the Model temperature dependence using parameter in the Temperature settings of the SPICE NIGBT block is set to Fixed temperature. For this model, the block sets T equal to TFIXED.

• Device temperature — The block uses a temperature that depends on circuit temperature when the Model temperature dependence using parameter in the Temperature settings of the SPICE NIGBT block is set to Device temperature. For this model, the block defines temperature as

  $$T=T_C+TOFFSET$$

  where:

  • T_C is the circuit temperature.

    If there is not an Environment Parameters block in the circuit, T_C is equal to 300.15 K.

    If there is an Environment Parameters block in the circuit, T_C is equal to the value that you specify for the Temperature parameter in the SPICE settings of the Environment Parameters block. The default value for the Temperature parameter is 300.15 K.

  • TOFFSET is the offset local circuit temperature.

Ports

Refer to the figure for port locations.

Conserving

gx — Gate terminal

electrical

Electrical conserving port associated with the IGBT gate terminal.

cx — Collector terminal

electrical

Electrical conserving port associated with the IGBT collector terminal.

ex — Emitter terminal

electrical

Electrical conserving port associated with the IGBT emitter terminal.

Parameters

Dimensions

Gate-drain overlap area, AGD — Gate-drain overlap area

5.0e-6 m^2 (default) | positive scalar

Gate-drain overlap area. The value must be greater than 0.

Area of the device, AREA — Device area

1.0e-5 m^2 (default) | positive scalar

Area of the device. The value must be greater than 0.

Number of parallel devices, SCALE — Number of parallel devices

1 (default) | positive integer

Number of parallel transistors the block represents. The value must be an integer greater than 0.

General

Electron mobility, MUN — Mobility of electron

1.5e3 cm^2/s/V (default) | scalar

Mobility of the electrons.

Hole mobility, MUP — Mobility of hole

4.5e2 cm^2/s/V (default) | scalar

Mobility of the hole.

Base doping, NB — Doping of base

2e14 1/cm^3 (default) | scalar

Doping of the base.

MOSFET

Triode region factor, KF — Factor of triode region

1 (default)

Factor of the triode region.

MOS transconductance, KP — MOS transconductance

0.38 A/V^2 (default) | scalar

The derivative of the drain current with respect to the gate voltage. The value must be greater than or equal to 0

Threshold voltage, VT — Threshold voltage

4.7 V (default) | scalar

Threshold voltage.

Transverse field factor, THETA — Transverse field factor

0.02 1/V (default) | scalar

Transverse field factor.

BJT

Ambipolar recombination lifetime, TAU — Ambipolar recombination lifetime

7.1e-6 s (default) | scalar

Ambipolar recombination lifetime.

Metallurgical base width, WB — Width of metallurgical base

9.0e-5 m (default) | scalar

Width of the metallurgical base.

Emitter saturation current density, JSNE — Density of emitter saturation current

6.5e-13 A/cm^2 (default) | scalar

Density of the emitter saturation current.

Avalanche uniformity factor, BVF — Avalanche uniformity factor

1 (default) | scalar

Avalanche uniformity factor.

Avalanche multiplication exponent, BVN — Avalanche multiplication exponent

4 (default) | scalar

Avalanche multiplication exponent.

Capacitance

Gate-source capacitance per unit area, CGS — Gate-source capacitance per unit area

1.24e-8 F/cm^2 (default) | scalar

Gate-source capacitance per unit area.

Gate-drain oxide capacitance per unit area, COXD — Gate-drain oxide capacitance per unit area

3.5e-8 F/cm^2 (default) | scalar

Gate-drain oxide capacitance per unit area.

Gate-drain overlap depletion threshold, VTD — Gate-drain overlap depletion threshold

1e-3 V (default) | scalar

Gate-drain overlap depletion threshold.

Specify initial condition — Whether to specify initial condition

No (default) | Yes

Whether to specify initial condition.

Initial condition voltage ICVGE — Initial condition voltage ICVGE

0 V (default) | scalar

Initial condition voltage ICVGE.

Dependencies

To enable this parameter, set Specify initial condition to Yes.

Initial condition voltage ICVCE — Initial condition voltage ICVCE

0 V (default) | scalar

Initial condition voltage ICVCE.

Dependencies

To enable this parameter, set Specify initial condition to Yes.

Temperature

Model temperature dependence using — Temperature dependence model

Device temperature (default) | Fixed temperature

Options for modeling the transistor temperature dependence:

• Device temperature — Use the device temperature to model temperature dependence.

• Fixed temperature — Use a temperature that is independent of the circuit temperature to model temperature dependence.

For more information, see Temperature Dependence.

Fixed circuit temperature, TFIXED — Fixed circuit temperature

300.15 K (default) | positive scalar

Transistor simulation temperature. The value must be greater than 0 K.

Dependencies

To enable this parameter, set Model temperature dependence using to Fixed temperature.

Parameter extraction temperature, TMEAS — Parameter extraction temperature

300.15 K (default) | positive scalar

Temperature at which the transistor parameters are measured. The value must be greater than 0 K.

Offset local circuit temperature, TOFFSET — Local circuit temperature offset

0 K (default) | scalar

Amount by which the transistor temperature differs from the circuit temperature.

Dependencies

To enable this parameter, set Model temperature dependence using to Device temperature.

References

[1] Hefner, A.R. and Diebolt, D.M. An experimentally verified IGBT model implemented in the Saber circuit simulator. IEEE transactions on Power Electronics 9, no. 5 (September 1994): 532-42. https://doi.org/10.1109/63.321038.

[2] Hefner, A.R., Jr. Semiconductor measurement technology: INSTANT - IGBT Network Simulation and Transient ANalysis Tool. U.S. Department of Commerce/Technology Administration, National Institute of Standards and Technology. 1992.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2020a