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# N-Channel MOSFET

Model N-Channel MOSFET using Shichman-Hodges equation

## Library

Semiconductor Devices

## Description

The N-Channel MOSFET block uses the Shichman and Hodges equations [1] for an insulated-gate field-effect transistor to represent an N-Channel MOSFET.

The drain-source current, IDS, depends on the region of operation:

• In the off region (VGS < Vth) the drain-source current is:

${I}_{DS}=0$

• In the linear region (0 < VDS < VGSVth) the drain-source current is:

${I}_{DS}=K\left(\left({V}_{GS}-{V}_{th}\right){V}_{DS}-{V}_{DS}{}^{2}/2\right)\left(1+\lambda |{V}_{DS}|\right)$

• In the saturated region (0 < VGSVth < VDS) the drain-source current is:

${I}_{DS}=\left(K/2\right){\left({V}_{GS}-{V}_{th}\right)}^{2}\left(1+\lambda |{V}_{DS}|\right)$

In the preceding equations:

• K is the transistor gain.

• VDS is the positive drain-source voltage.

• VGS is the gate-source voltage.

• Vth is the threshold voltage.

• λ is the channel modulation.

### Charge Model

The block models junction capacitances either by fixed capacitance values, or by tabulated values as a function of the drain-source voltage. In either case, you can either directly specify the gate-source and gate-drain junction capacitance values, or let the block derive them from the input and reverse transfer capacitance values. Therefore, the Parameterization options for charge model on the Junction Capacitance tab are:

• Specify fixed input, reverse transfer and output capacitance — Provide fixed parameter values from datasheet and let the block convert the input and reverse transfer capacitance values to junction capacitance values, as described below. This is the default method.

• Specify fixed gate-source, gate-drain and output capacitance — Provide fixed values for junction capacitance parameters directly.

• Specify tabulated input, reverse transfer and output capacitance — Provide tabulated capacitance and drain-source voltage values based on datasheet plots. The block converts the input and reverse transfer capacitance values to junction capacitance values, as described below.

• Specify tabulated gate-source, gate-drain and output capacitance — Provide tabulated values for junction capacitances and drain-source voltage.

Use one of the tabulated capacitance options (Specify tabulated input, reverse transfer and output capacitance or Specify tabulated gate-source, gate-drain and output capacitance) when the datasheet provides a plot of junction capacitances as a function of drain-source voltage. Using tabulated capacitance values will give more accurate dynamic characteristics, and avoids the need to iteratively tune parameters to fit the dynamics.

If you use the Specify fixed gate-source, gate-drain and output capacitance or Specify tabulated gate-source, gate-drain and output capacitance option, the Junction Capacitance tab lets you specify the Gate-drain junction capacitance and Gate-source junction capacitance parameter values (fixed or tabulated) directly. Otherwise, the block derives them from the Input capacitance, Ciss and Reverse transfer capacitance, Crss parameter values. These two parameterization methods are related as follows:

The two fixed capacitance options (Specify fixed input, reverse transfer and output capacitance or Specify fixed gate-source, gate-drain and output capacitance) let you model gate junction capacitance as a fixed gate-source capacitance CGS and either a fixed or a nonlinear gate-drain capacitance CGD. If you select the Gate-drain charge function is nonlinear option for the Charge-voltage linearity parameter, then the gate-drain charge relationship is defined by the piecewise-linear function shown in the following figure.

For instructions on how to map a time response to device capacitance values, see the N-Channel IGBT block reference page. However, this mapping is only approximate because the Miller voltage typically varies more from the threshold voltage than in the case for the IGBT.

 Note:   Because this block implementation includes a charge model, you must model the impedance of the circuit driving the gate to obtain representative turn-on and turn-off dynamics. Therefore, if you are simplifying the gate drive circuit by representing it as a controlled voltage source, you must include a suitable series resistor between the voltage source and the gate.

### 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.

When including temperature dependence, the transistor defining equations remain the same. The gain, K, and the threshold voltage, Vth, become a function of temperature according to the following equations:

${K}_{Ts}={K}_{Tm1}{\left(\frac{{T}_{s}}{{T}_{m1}}\right)}^{BEX}$

Vths = Vth1 + α ( TsTm1)

where:

• Tm1 is the temperature at which the transistor parameters are specified, as defined by the Measurement temperature parameter value.

• Ts is the simulation temperature.

• KTm1 is the transistor gain at the measurement temperature.

• KTs is the transistor gain at the simulation temperature. This is the transistor gain value used in the MOSFET equations when temperature dependence is modeled.

• Vth1 is the threshold voltage at the measurement temperature.

• Vths is the threshold voltage at the simulation temperature. This is the threshold voltage value used in the MOSFET equations when temperature dependence is modeled.

• BEX is the mobility temperature exponent. A typical value of BEX is -1.5.

• α is the gate threshold voltage temperature coefficient, dVth/dT.

For most MOSFETS, you can use the default value of -1.5 for BEX. Some datasheets quote the value for α, but most typically they provide the temperature dependence for drain-source on resistance, RDS(on). Depending on the block parameterization method, you have two ways of specifying α:

• If you parameterize the block from a datasheet, you have to provide RDS(on) at a second measurement temperature. The block then calculates the value for α based on this data.

• If you parameterize by specifying equation parameters, you have to provide the value for α directly.

If you have more data comprising drain current as a function of gate-source voltage for more than one temperature, then you can also use Simulink® Design Optimization™ software to help tune the values for α and BEX.

### 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

When modeling temperature dependence, consider the following:

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

• When you specify RDS(on) at a second measurement temperature, it must be quoted for the same working point (that is, the same drain current and gate-source voltage) as for the other RDS(on) value. Inconsistent values for RDS(on) at the higher temperature will result in unphysical values for α and unrepresentative simulation results. Typically RDS(on) increases by a factor of about 1.5 for a hundred degree increase in temperature.

• You may need to tune the values of BEX and threshold voltage, Vth, to replicate the VDS-VGS relationship (if available) for a given device. Increasing Vth moves the VDS-VGS plots to the right. The value of BEX affects whether the VDS-VGS curves for different temperatures cross each other, or not, for the ranges of VDS and VGS considered. Therefore, an inappropriate value can result in the different temperature curves appearing to be reordered. Quoting RDS(on) values for higher currents, preferably close to the current at which it will operate in your circuit, will reduce sensitivity to the precise value of BEX.

## Dialog Box and Parameters

### Main Tab

Parameterization

Select one of the following methods for block parameterization:

• Specify from a datasheet — Provide the drain-source on resistance and the corresponding drain current and gate-source voltage. The block calculates the transistor gain for the Shichman and Hodges equations from this information. This is the default method.

• Specify using equation parameters directly — Provide the transistor gain.

Drain-source on resistance, R_DS(on)

The ratio of the drain-source voltage to the drain current for specified values of drain current and gate-source voltage. RDS(on) should have a positive value. This parameter is only visible when you select Specify from a datasheet for the Parameterization parameter. The default value is 0.025 Ω.

Drain current, Ids, for R_DS(on)

The drain current the block uses to calculate the value of the drain-source resistance. IDS should have a positive value. This parameter is only visible when you select Specify from a datasheet for the Parameterization parameter. The default value is 6 A.

Gate-source voltage, Vgs, for R_DS(on)

The gate-source voltage the block uses to calculate the value of the drain-source resistance. VGS should have a positive value. This parameter is only visible when you select Specify from a datasheet for the Parameterization parameter. The default value is 10 V.

Gain, K

Positive constant gain coefficient for the Shichman and Hodges equations. This parameter is only visible when you select Specify using equation parameters directly for the Parameterization parameter. The default value is 5 A/V2.

Gate-source threshold voltage, Vth

Gate-source threshold voltage Vth in the Shichman and Hodges equations. For an enhancement device, Vth should be positive. For a depletion mode device, Vth should be negative. The default value is 1.7 V.

Channel modulation, L

The channel-length modulation, usually denoted by the mathematical symbol λ. When in the saturated region, it is the rate of change of drain current with drain-source voltage. The effect on drain current is typically small, and the effect is neglected if calculating transistor gain K from drain-source on-resistance, RDS(on). A typical value is 0.02, but the effect can be ignored in most circuit simulations. However, in some circuits a small nonzero value may help numerical convergence. The default value is 0 1/V.

Measurement temperature

Temperature Tm1 at which Drain-source on resistance, R_DS(on) is measured. This parameter is only visible when you select Model temperature dependence for the Parameterization parameter on the Temperature Dependence tab. The default value is 25 C.

### Ohmic Resistance Tab

Source ohmic resistance

The transistor source resistance. The default value is 1e-4 Ω. The value must be greater than or equal to 0.

Drain ohmic resistance

The transistor drain resistance. The default value is 0.001 Ω. The value must be greater than or equal to 0.

### Junction Capacitance Tab

Parameterization

Select one of the following methods for capacitance parameterization:

• Specify fixed input, reverse transfer and output capacitance — Provide fixed parameter values from datasheet and let the block convert the input and reverse transfer capacitance values to junction capacitance values, as described below. This is the default method.

• Specify fixed gate-source, gate-drain and output capacitance — Provide fixed values for junction capacitance parameters directly.

• Specify tabulated input, reverse transfer and output capacitance — Provide tabulated capacitance and drain-source voltage values based on datasheet plots. The block converts the input and reverse transfer capacitance values to junction capacitance values, as described below.

• Specify tabulated gate-source, gate-drain and output capacitance — Provide tabulated values for junction capacitances and drain-source voltage.

Input capacitance, Ciss

The gate-source capacitance with the drain shorted to the source. This parameter is visible only for the following two values for the Parameterization parameter:

• If you select Specify fixed input, reverse transfer and output capacitance, the default value is 350 pF.

• If you select Specify tabulated input, reverse transfer and output capacitance, the default value is [720 700 590 470 390 310] pF.

The drain-gate capacitance with the source connected to ground. This parameter is visible only for the following two values for the Parameterization parameter:

• If you select Specify fixed input, reverse transfer and output capacitance, the default value is 80 pF.

• If you select Specify tabulated input, reverse transfer and output capacitance, the default value is [450 400 300 190 95 55] pF.

Gate-source junction capacitance

The value of the capacitance placed between the gate and the source. This parameter is visible only for the following two values for the Parameterization parameter:

• If you select Specify fixed gate-source, gate-drain and output capacitance, the default value is 270 pF.

• If you select Specify tabulated gate-source, gate-drain and output capacitance, the default value is [270 300 290 280 295 255] pF.

Gate-drain junction capacitance

The value of the capacitance placed between the gate and the drain. This parameter is visible only for the following two values for the Parameterization parameter:

• If you select Specify fixed gate-source, gate-drain and output capacitance, the default value is 80 pF.

• If you select Specify tabulated gate-source, gate-drain and output capacitance, the default value is [450 400 300 190 95 55] pF.

Output capacitance, Coss

The output capacitance applied across the drain-source ports. For fixed capacitance models, the default value is 0 pF. For tabulated capacitance models, the default value is [900 810 690 420 270 170] pF.

Corresponding drain-source voltages

The drain-source voltages corresponding to the tabulated capacitance values. This parameter is visible only for tabulated capacitance models (Specify tabulated input, reverse transfer and output capacitance or Specify tabulated gate-source, gate-drain and output capacitance). The default value is [0.1 0.3 1 3 10 30] V.

Charge-voltage linearity

Select whether gate-drain capacitance is fixed or nonlinear:

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

Gate-drain oxide capacitance

The gate-drain capacitance when the device is on and the drain-gate voltage is small. This parameter is only visible when you select Gate-drain charge function is nonlinear for the Charge-voltage linearity parameter. The default value is 200 pF.

Drain-gate voltage at which oxide capacitance becomes active

The drain-gate voltage at which the drain-gate capacitance switches between off-state (CGD) and on-state (Cox) capacitance values. This parameter is only visible when you select Gate-drain charge function is nonlinear for the Charge-voltage linearity parameter. The default value is -0.5 V.

### 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. This is the default method.

• Model temperature dependence — Model temperature-dependent effects. Provide a value for simulation temperature, Ts, a value for BEX, and a value for the measurement temperature Tm1 (using the Measurement temperature parameter on the Main tab). You also have to provide a value for α using one of two methods, depending on the value of the Parameterization parameter on the Main tab. If you parameterize the block from a datasheet, you have to provide RDS(on) at a second measurement temperature, and the block will calculate α based on that. If you parameterize by specifying equation parameters, you have to provide the value for α directly.

Drain-source on resistance, R_DS(on), at second measurement temperature

The ratio of the drain-source voltage to the drain current for specified values of drain current and gate-source voltage at second measurement temperature. This parameter is only visible when you select Specify from a datasheet for the Parameterization parameter on the Main tab. It must be quoted for the same working point (drain current and gate-source voltage) as the Drain-source on resistance, R_DS(on) parameter on the Main tab. The default value is 0.037 Ω.

Second measurement temperature

Second temperature Tm2 at which Drain-source on resistance, R_DS(on), at second measurement temperature is measured. This parameter is only visible when you select Specify from a datasheet for the Parameterization parameter on the Main tab. The default value is 125 C.

Gate threshold voltage temperature coefficient, dVth/dT

The rate of change of gate threshold voltage with temperature. This parameter is only visible when you select Specify using equation parameters directly for the Parameterization parameter on the Main tab. The default value is -6 mV/K.

Mobility temperature exponent, BEX

Mobility temperature coefficient value. You can use the default value for most MOSFETs. See the Basic Assumptions and Limitations section for additional considerations. 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:

G

Electrical conserving port associated with the transistor gate terminal

D

Electrical conserving port associated with the transistor drain terminal

S

Electrical conserving port associated with the transistor source terminal

## References

[1] H. Shichman and D. A. Hodges. "Modeling and simulation of insulated-gate field-effect transistor switching circuits." IEEE J. Solid State Circuits, SC-3, 1968.