Model N-Channel MOSFET using either Shichman-Hodges equation or surface-potential-based model

Semiconductor Devices

The N-Channel MOSFET block provides two main modeling variants:

Based on threshold voltage — Uses the Shichman-Hodges equation to represent the device. This modeling approach, based on threshold voltage, has the benefits of simple parameterization and simple current-voltage expressions. However, these models have difficulty in accurately capturing transitions across the threshold voltage and lack some important effects, such as velocity saturation. For details, see Threshold-Based Model.

Based on surface potential — Uses the surface-potential equation to represent the device. This modeling approach provides a greater level of model fidelity than the simple square-law (threshold-voltage-based) models can provide. The trade-off is that there are more parameters that require extraction. For details, see Surface-Potential-Based Model.

Together with the thermal port variants (see Thermal Port), the block therefore provides
you with four choices. To select the desired variant, right-click
the block in your model. From the context menu, select **Simscape** > **Block
choices**, and then one of the following options:

**Threshold-based**— Basic model, which represents the device using the Shichman-Hodges equation (based on threshold voltage) and does not simulate thermal effects. This is the default.**Threshold-based with thermal**— Model based on threshold voltage and with exposed thermal port.**Surface-potential-based**— Model based on surface potential. This model does not simulate thermal effects.**Surface-potential-based with thermal**— Thermal variant of the model based on surface potential.

The threshold-based variant of the 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, *I*_{DS},
depends on the region of operation:

In the off region (

*V*_{GS}<*V*_{th}), the drain-source current is:$${I}_{DS}=0$$

In the linear region (0 <

*V*_{DS}<*V*_{GS}–*V*_{th}), the drain-source current is:$${I}_{DS}=K\left(({V}_{GS}-{V}_{th}){V}_{DS}-{V}_{DS}{}^{2}/2\right)\left(1+\lambda \left|{V}_{DS}\right|\right)$$

In the saturated region (0 <

*V*_{GS}–*V*_{th}<*V*_{DS}), the drain-source current is:$${I}_{DS}=(K/2){({V}_{GS}-{V}_{th})}^{2}\left(1+\lambda \left|{V}_{DS}\right|\right)$$

In the preceding equations:

*K*is the transistor gain.*V*_{DS}is the positive drain-source voltage.*V*_{GS}is the gate-source voltage.*V*_{th}is the threshold voltage.*λ*is the channel modulation.

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 drain-source 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 drain-source 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 drain-source capacitance
```

)
when the datasheet provides a plot of junction capacitances as a function
of drain-source voltage. Using tabulated capacitance values gives
more accurate dynamic characteristics and avoids the need for interactive
tuning of parameters to fit the dynamics.

If you use the ```
Specify fixed gate-source, gate-drain
and drain-source capacitance
```

or ```
Specify
tabulated gate-source, gate-drain and drain-source capacitance
```

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

*C*_{GD}=*Crss**C*_{GS}=*Ciss*–*Crss**C*_{DS}=*Coss*–*Crss*

The two fixed capacitance options (```
Specify fixed
input, reverse transfer and output capacitance
```

or ```
Specify
fixed gate-source, gate-drain and drain-source capacitance
```

)
let you model gate junction capacitance as a fixed gate-source capacitance *C*_{GS} and
either a fixed or a nonlinear gate-drain capacitance *C*_{GD}.
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.

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.

The surface-potential-based variant of the block provides a greater level of model fidelity than the simple square-law (threshold-voltage-based) model. The surface-potential-based block variant includes the following effects:

Fully nonlinear capacitance model (including the nonlinear Miller capacitance)

Charge conservation inside the model, so you can use the model for charge sensitive simulations

Velocity saturation and channel-length modulation

The intrinsic body diode

Reverse recovery in the body diode model

Temperature scaling of physical parameters

For the thermal variant, dynamic self-heating (that is, you can simulate the effect of self-heating on the electrical characteristics of the device)

This model is a minimal version of the world-standard PSP model (see http://nsti.org/Nanotech2005/WCM2005/WCM2005-GGildenblat.pdf), including only certain effects from the PSP model in order to strike a balance between model fidelity and complexity. For details of the physical background to the phenomena included in this model, see [2].

The basis of the model is Poisson equation:

$$\frac{{\partial}^{2}\psi}{\partial {x}^{2}}+\frac{{\partial}^{2}\psi}{\partial {y}^{2}}=\frac{q{N}_{A}}{{\epsilon}_{Si}}\left[1-\mathrm{exp}\left(\frac{-\psi}{{\varphi}_{T}}\right)+\mathrm{exp}\left(\frac{\psi -2{\varphi}_{B}-{V}_{CB}}{{\varphi}_{T}}\right)\right]$$

$${\varphi}_{T}=\frac{{k}_{B}T}{q}$$

where:

*ψ*is the electrostatic potential.*q*is the magnitude of the electronic charge.*N*_{A}is the density of acceptors in the substrate.*ɛ*_{Si}is the dielectric permittivity of the semiconductor material (for example, silicon).*ϕ*_{B}is the difference between the intrinsic Fermi level and the Fermi level in the bulk silicon.*V*_{CB}is the quasi-Fermi potential of the surface layer referenced to the bulk.*ϕ*_{T}is the thermal voltage.*k*_{B}is Boltzmann’s constant.*T*is temperature.

Poisson equation is used to derive the surface-potential equation:

$${\left({V}_{GB}-{V}_{FB}-{\psi}_{s}\right)}^{2}={\gamma}^{2}\left[{\psi}_{s}+{\varphi}_{T}\left(\mathrm{exp}\left(\frac{-{\psi}_{s}}{{\varphi}_{T}}\right)-1\right)+{\varphi}_{T}\mathrm{exp}\left(-\frac{2{\varphi}_{B}+{V}_{CB}}{{\varphi}_{T}}\right)\left(\mathrm{exp}\left(\frac{{\psi}_{s}}{{\varphi}_{T}}\right)-1\right)\right]$$

where:

*V*_{GB}is the applied gate-body voltage.*V*_{FB}is the flatband voltage.*ψ*_{s}is the surface potential.*γ*is the body factor,

$$\gamma =\frac{\sqrt{2q{\epsilon}_{Si}{N}_{A}}}{{C}_{ox}}$$

*C*_{ox}is the capacitance per unit area.

The block uses an explicit approximation to the surface-potential equation, to avoid the need for numerical solution to this implicit equation.

Once the surface potential is known, the drain current *I*_{D} is
given by

$${I}_{D}=\frac{W{\mu}_{0}}{L{G}_{\Delta L}{G}_{mob}\sqrt{1+{\left({\theta}_{sat}\Delta \psi \right)}^{2}}}\left[-{\overline{Q}}_{inv}\Delta \psi +{\varphi}_{T}\left({Q}_{invL}-{Q}_{inv0}\right)\right]$$

where:

*W*is the device width.*L*is the channel length.*μ*_{0}is the low-field mobility.*θ*_{sat}is the velocity saturation.*Δψ*is the difference in the surface potential between the drain and the source.*Q*_{inv0}and*Q*_{invL}are the inversion charge densities at the source and drain, respectively.$${\overline{Q}}_{inv}$$ is the average inversion charge density across the channel.

*G*_{mob}is the mobility reduction factor. For more information, see the**Surface roughness scattering factor**parameter description in the Main Tab (Surface-Potential-Based Variant) section.*G*_{ΔL}is the channel-length modulation.

$${G}_{\Delta L}=1-\frac{\Delta L}{L}=1-\alpha \mathrm{ln}\left[\frac{{V}_{DB}-{V}_{DB,eff}+\sqrt{{\left({V}_{DB}-{V}_{DB,eff}\right)}^{2}+{V}_{p}^{2}}}{{V}_{p}}\right]$$

where:

*α*is the channel-length modulation factor.*V*_{DB}is the drain-body voltage.*V*_{DB,eff}is the drain-body voltage clipped to a maximum value corresponding to velocity saturation or pinch-off (whichever occurs first).*V*_{p}is the channel-length modulation voltage.

The block computes the inversion charge densities directly from the surface potential.

The block also computes the nonlinear capacitances from the surface potential. Source and drain charge contributions are assigned via a bias-dependent Ward-Dutton charge-partitioning scheme, as described in [3]. These charges are computed explicitly, so this model is charge-conserving. The capacitive currents are computed by taking the time derivatives of the relevant charges. In practice, the charges within the simulation are normalized to the oxide capacitance and computed in units of volts.

The MOSFET gain, β, is given by

$$\beta =\frac{W{\mu}_{0}{C}_{ox}}{L}$$

The threshold voltage for a short-circuited source-bulk connection is approximately given by

$${V}_{T}={V}_{FB}+2{\varphi}_{B}+2{\varphi}_{T}+\gamma \sqrt{2{\varphi}_{B}+2{\varphi}_{T}}$$

where:

2

*ϕ*_{B}is the surface potential at strong inversion.

The overall model consists of an intrinsic MOSFET defined by the surface-potential formulation, a body diode, series resistances, and fixed overlap capacitances, as shown in the schematic.

The block models the body diode as an ideal, exponential diode with both junction and diffusion capacitances:

$${I}_{dio}={I}_{s}\left[\mathrm{exp}\left(-\frac{{V}_{DB}}{n{\varphi}_{T}}\right)-1\right]$$

$${C}_{j}=\frac{{C}_{j0}}{\sqrt{1+\frac{{V}_{DB}}{{V}_{bi}}}}$$

$${C}_{diff}=\frac{\tau {I}_{s}}{n{\varphi}_{T}}\mathrm{exp}\left(-\frac{{V}_{DB}}{n{\varphi}_{T}}\right)$$

where:

*I*_{dio}is the current through the diode.*I*_{s}is the reverse saturation current.*V*_{DB}is the drain-body voltage.*n*is the ideality factor.*ϕ*_{T}is the thermal voltage.*C*_{j}is the junction capacitance of the diode.*C*_{j0}is the zero-bias junction capacitance.*V*_{bi}is the built-in voltage.*C*_{diff}is the diffusion capacitance of the diode.*τ*is the transit time.

The capacitances are defined through an explicit calculation of charges, which are then differentiated to give the capacitive expressions above. The block computes the capacitive diode currents as time derivatives of the relevant charges, similar to the computation in the surface-potential-based MOSFET model.

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. To model the dependence on temperature
during simulation, select `Model temperature dependence`

for
the **Parameterization** parameter on the **Temperature
Dependence** tab.

**Threshold-Based Model**

For threshold-based variant, you can 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, *V*_{th},
become a function of temperature according to the following equations:

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

*V*_{ths} = *V*_{th1} + *α* (*T*_{s} – *T*_{m1})

where:

*T*_{m1}is the temperature at which the transistor parameters are specified, as defined by the**Measurement temperature**parameter value.*T*_{s}is the simulation temperature.*K*_{Tm1}is the transistor gain at the measurement temperature.*K*_{Ts}is the transistor gain at the simulation temperature. This is the transistor gain value used in the MOSFET equations when temperature dependence is modeled.*V*_{th1}is the threshold voltage at the measurement temperature.*V*_{ths}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,*d**V*_{th}/*d**T*.

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, *R _{DS}(on)*.
Depending on the block parameterization method, you have two ways
of specifying

If you parameterize the block from a datasheet, you have to provide

*R*at a second measurement temperature. The block then calculates the value for_{DS}(on)*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*.

**Surface-Potential-Based Model**

The surface-potential-based model includes temperature effects on the capacitance characteristics, as well as modeling the dependence of the transistor static behavior on temperature during simulation.

The **Measurement temperature** parameter on
the **Main** tab specifies temperature *T*_{m1} at
which the other device parameters have been extracted. The **Temperature
Dependence** tab provides the simulation temperature, *T*_{s},
and the temperature-scaling coefficients for the other device parameters.
For more information, see Temperature Dependence Tab (Surface-Potential-Based Variant).

The block has an optional thermal port, hidden by default. To expose the thermal port, right-click the block in your model, and select the appropriate block variant:

For a model based on threshold voltage and with exposed thermal port, select

**Simscape**>**Block choices**>**Threshold-based with thermal**.For a thermal variant of the model based on surface potential, select

**Simscape**>**Block choices**>**Surface-potential-based with thermal**.

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.

When modeling temperature dependence for threshold-based block variant, consider the following:

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

When you specify

*R*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_{DS}(on)*R*value. Inconsistent values for_{DS}(on)*R*at the higher temperature will result in unphysical values for_{DS}(on)*α*and unrepresentative simulation results. Typically*R*increases by a factor of about 1.5 for a hundred degree increase in temperature._{DS}(on)You may need to tune the values of

*BEX*and threshold voltage,*V*_{th}, to replicate the*I*_{DS}–*V*_{GS}relationship (if available) for a given device. Increasing*V*_{th}moves the*I*_{DS}-*–V*_{GS}plots to the right. The value of*BEX*affects whether the*I*_{DS}–*V*_{GS}curves for different temperatures cross each other, or not, for the ranges of*V*_{DS}and*V*_{GS}considered. Therefore, an inappropriate value can result in the different temperature curves appearing to be reordered. Quoting*R*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_{DS}(on)*BEX*.

This configuration of the **Main** tab corresponds
to the threshold-based block variant, which is the default. If you
are using the surface-potential-based variant of the block, see Main Tab (Surface-Potential-Based Variant).

**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.

*R*should have a positive value. This parameter is only visible when you select_{DS}(on)`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.

*I*_{DS}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.

*V*_{GS}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/V^{2}.**Gate-source threshold voltage, Vth**Gate-source threshold voltage

*V*_{th}in the Shichman and Hodges equations. For an enhancement device,*V*_{th}should be positive. For a depletion mode device,*V*_{th}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,*R*. 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_{DS}(on)`0`

1/V.**Measurement temperature**Temperature

*T*_{m1}at which**Drain-source on resistance, R_DS(on)**is measured. The default value is`25`

°C.

This configuration of the **Main** tab corresponds
to the surface-potential-based block variant. If you are using the
threshold-based variant of the block, based on the Shichman and Hodges
equations, see Main Tab (Threshold-Based Variant).

**Gain**The MOSFET gain,

*β*. This parameter primarily defines the linear region of operation on an*I*_{D}–*V*_{DS}characteristic. The value must be greater than 0. The default value is`18`

A/V^{2}.**Flatband voltage**The flatband voltage,

*V*_{FB}, defines the gate bias that must be applied in order to achieve the flatband condition at the surface of the silicon. The default value is`-1.1`

V. You can also use this parameter to arbitrarily shift the threshold voltage due to material work function differences, and to trapped interface or oxide charges. In practice, however, it is usually recommended to modify the threshold voltage by using the**Body factor**and**Surface potential at strong inversion**parameters first, and only use this parameter for fine-tuning.**Body factor**Body factor,

*γ*, in the surface-potential equation. This parameter primarily impacts the threshold voltage. The default value is`3.5`

V^{1/2}.**Surface potential at strong inversion**The 2

*ϕ*_{B}term in the surface-potential equation. This parameter also primarily impacts the threshold voltage. The default value is`1`

V.**Velocity saturation factor**Velocity saturation,

*θ*_{sat}, in the drain-current equation. Use this parameter in cases where a good fit to linear operation leads to a saturation current that is too high. By increasing this parameter value, you reduce the saturation current. For high-voltage devices, it is often the case that a good fit to linear operation leads to a saturation current that is too low. In such a case, either increase both the gain and the drain ohmic resistance or use an N-Channel LDMOS FET block instead. The default value is`0.4`

1/V.**Channel-length modulation factor**The factor, α, multiplying the logarithmic term in the

*G*_{ΔL}equation. This parameter describes the onset of channel-length modulation. For device characteristics that exhibit a positive conductance in saturation, increase the parameter value to fit this behavior. The default value is`0`

, which means that channel-length modulation is off by default.**Channel-length modulation voltage**The voltage

*V*_{p}in the*G*_{ΔL}equation. This parameter controls the drain-voltage at which channel-length modulation starts to become active. The default value is`50`

mV.**Surface roughness scattering factor**Indicates the strength of the mobility reduction. The mobility is

*μ*=*μ*_{0}/*G*_{mob}, where*μ*_{0}is the low-field mobility without the effect of surface scattering. The mobility reduction factor,*G*_{mob}, is given by $${G}_{mob}=\sqrt{1+{\left({\theta}_{sr}{V}_{eff}\right)}^{4}}$$, where*θ*_{sr}is the surface roughness scattering factor and*V*_{eff}is a voltage that is indicative of the effective vertical electric field strength in the channel,*E*_{eff}. For high vertical electric fields, the mobility is roughly proportional to*E*_{eff}^2 for electrons. The default parameter value is`0`

1/V.**Linear-to-saturation transition coefficient**This parameter controls how smoothly the MOSFET transitions from linear into saturation, particularly when velocity saturation is enabled. This parameter can usually be left at its default value, but you can use it to fine-tune the knee of the

*I*_{D}–*V*_{DS}characteristic. The expected range for this parameter value is between 2 and 8. The default value is`8`

.**Measurement temperature**Temperature

*T*_{m1}at which the block parameters are measured. If the**Device simulation temperature**parameter on the**Temperature Dependence**tab differs from this value, then device parameters will be scaled from their defined values according to the simulation and reference temperatures. For more information, see Temperature Dependence Tab (Surface-Potential-Based Variant). The default value is`25`

°C.

**Source ohmic resistance**The transistor source resistance, that is, the series resistance associated with the source contact. The value must be greater than or equal to

`0`

. The default value for threshold-based variants is`1e-4`

Ω. The default value for surface-potential-based variants is`2e-3`

Ω.**Drain ohmic resistance**The transistor drain resistance, that is, the series resistance associated with the drain contact. The value must be greater than or equal to

`0`

. The default value for threshold-based variants is`0.01`

Ω. The default value for surface-potential-based variants is`0.17`

Ω.**Gate ohmic resistance**The transistor gate resistance, that is, the series resistance associated with the gate contact. This parameter is visible only for the surface-potential-based block variants. The value must be greater than or equal to

`0`

. The default value is`8.4`

Ω.

This tab is visible only for the threshold-based variant of the block.

**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, output, and reverse transfer capacitance values to junction capacitance values, as described in Charge Model for Threshold-Based Variant. This is the default method.`Specify fixed gate-source, gate-drain and drain-source 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, output, and reverse transfer capacitance values to junction capacitance values, as described in Charge Model for Threshold-Based Variant.`Specify tabulated gate-source, gate-drain and drain-source 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.

**Reverse transfer capacitance, Crss**The drain-gate capacitance with the source connected to ground, also known as the Miller capacitance. 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.

**Output capacitance, Coss**The drain-source capacitance with the gate and source shorted. 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`0`

pF.If you select

`Specify tabulated input, reverse transfer and output capacitance`

, the default value is`[900 810 690 420 270 170]`

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 drain-source capacitance`

, the default value is`270`

pF.If you select

`Specify tabulated gate-source, gate-drain and drain-source 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 drain-source capacitance`

, the default value is`80`

pF.If you select

`Specify tabulated gate-source, gate-drain and drain-source capacitance`

, the default value is`[450 400 300 190 95 55]`

pF.

**Drain-source junction capacitance**The value of the capacitance placed between the drain 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 drain-source capacitance`

, the default value is`0`

pF.If you select

`Specify tabulated gate-source, gate-drain and drain-source capacitance`

, the default value is`[450 410 390 230 175 115]`

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.**Gate-source voltage, Vgs, for tabulated capacitances**For tabulated capacitance models, this parameter controls the voltage dependence of the

**Reverse transfer capacitance, Crss**or the**Gate-drain junction capacitance**parameter (depending on the selected parameterization option). These capacitances are a function of the drain-gate voltage. The block calculates drain-gate voltages by subtracting this gate-source voltage value from the values specified for the**Corresponding drain-source voltages**parameter. The default value is`0`

V. 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`

).**Charge-voltage linearity**The two fixed capacitance options (

`Specify fixed input, reverse transfer and output capacitance`

or`Specify fixed gate-source, gate-drain and drain-source capacitance`

) let you model gate junction capacitance as a fixed gate-source capacitance*C*_{GS}and either a fixed or a nonlinear gate-drain capacitance*C*_{GD}. Select whether the 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 for Threshold-Based Variant. Two additional parameters appear to let you define the gate-drain charge function.

**Gate-drain oxide capacitance**The gate-drain capacitance when the drain-gate voltage is less than the

**Drain-gate voltage at which oxide capacitance becomes active**parameter value. This parameter is visible only 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 (

*C*_{GD}) and on-state (*C*_{ox}) 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.

This tab is visible only for the surface-potential-based variant of the block.

**Oxide capacitance**The parallel plate gate-channel capacitance. The default value is

`1500`

pF.**Gate-source overlap capacitance**The fixed, linear capacitance associated with the overlap of the gate electrode with the source well. The default value is

`100`

pF.**Gate-drain overlap capacitance**The fixed, linear capacitance associated with the overlap of the gate electrode with the drain well. The default value is

`14`

pF.

**Reverse saturation current**The current designated by the

*I*_{s}symbol in the body-diode equations. The default value for threshold-based variant is`0`

A. The default value for surface-potential-based variant is`5.2e-13`

A.**Built-in voltage**The built-in voltage of the diode, designated by the

*V*_{bi}symbol in the body-diode equations. Built-in voltage has an impact only on the junction capacitance equation. It does not affect the conduction current. The default value is`0.6`

V.**Ideality factor**The factor designated by the

*n*symbol in the body-diode equations. The default value is`1`

.**Zero-bias junction capacitance**The capacitance between the drain and bulk contacts at zero-bias due to the body diode alone. It is designated by the

*C*_{j0}symbol in the body-diode equations. The default value for threshold-based variant is`0`

pF. The default value for surface-potential-based variant is`480`

pF.**Transit time**The time designated by the

*τ*symbol in the body-diode equations. The default value is`50`

ns.

This configuration of the **Temperature Dependence** tab
corresponds to the threshold-based block variant, which is the default.
If you are using the surface-potential-based variant of the block,
see Temperature Dependence Tab (Surface-Potential-Based Variant)

**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,*T*_{s}, a value for*BEX*, and a value for the measurement temperature*T*_{m1}(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*R*at a second measurement temperature, and the block will calculate_{DS}(on)*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

*T*_{m2}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`

.**Body diode reverse saturation current temperature exponent**The reverse saturation current for the body diode is assumed to be proportional to the square of the intrinsic carrier concentration,

*n*_{i}=*N*_{C}exp(–*E*_{G}/2*k*_{B}*T*).*N*_{C}is the temperature-dependent effective density of states and*E*_{G}is the temperature-dependent bandgap for the semiconductor material. To avoid introducing another temperature-scaling parameter, the block neglects the temperature dependence of the bandgap and uses the bandgap of silicon at 300K (1.12eV) for all device types. Therefore, the temperature-scaled reverse saturation current is given by$${I}_{s}={I}_{s,m1}{\left(\frac{{T}_{s}}{{T}_{m1}}\right)}^{{\eta}_{Is}}\cdot \mathrm{exp}\left(\frac{{E}_{G}}{{k}_{B}}\cdot \left(\frac{1}{{T}_{m1}}-\frac{1}{{T}_{s}}\right)\right).$$

*I*_{s,m1}is the value of the**Reverse saturation current**parameter from the**Body Diode**tab,*k*_{B}is Boltzmann’s constant (8.617x10-5eV/K), and*η*_{Is}is the**Body diode reverse saturation current temperature exponent**. The default value is`3`

, because*N*_{C}for silicon is roughly proportional to T^{3/2}. You can remedy the effect of neglecting the temperature-dependence of the bandgap by a pragmatic choice of*η*_{Is}.**Device simulation temperature**Temperature

*T*_{s}at which the device is simulated. The default value is`25`

°C.

This configuration of the **Temperature Dependence** tab
corresponds to the surface-potential-based block variant. If you are
using the threshold-based variant of the block, see Temperature Dependence Tab (Threshold-Based Variant)

**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 the device simulation temperature,*T*_{s}, and the temperature-scaling coefficients for other block parameters.

**Gain temperature exponent**The MOSFET gain,

*β*, is assumed to scale exponentially with temperature,*β*=*β*_{m1}(*T*_{m1}/*T*_{s})^*η*_{β}.*β*_{m1}is the value of the**Gain**parameter from the**Main**tab and*η*_{β}is the**Gain temperature exponent**. The default value is`1.3`

.**Flatband voltage temperature coefficient**The flatband voltage,

*V*_{FB}, is assumed to scale linearly with temperature,*V*_{FB}=*V*_{FBm1}+ (*T*_{s}–*T*_{m1})*S*_{T,VFB}.*V*_{FBm1}is the value of the**Flatband voltage**parameter from the**Main**tab and*S*_{T,VFB}is the**Flatband voltage temperature coefficient**. The default value is`5e-4`

V/K.**Surface potential at strong inversion temperature coefficient**The surface potential at strong inversion, 2

*ϕ*_{B}, is assumed to scale linearly with temperature,*2ϕ*_{B}= 2*ϕ*_{Bm1}+ (*T*_{s}–*T*_{m1})*S*_{T,ϕB}. 2*ϕ*_{Bm1}is the value of the**Surface potential at strong inversion**parameter from the**Main**tab and*S*_{T,ϕB}is the**Surface potential at strong inversion temperature coefficient**. The default value is`-8.5e-4`

V/K.**Velocity saturation temperature exponent**The velocity saturation,

*θ*_{sat}, is assumed to scale exponentially with temperature,*θ*_{sat}=*θ*_{sat,m1}(*T*_{m1}/*T*_{s})^*η*_{θ}.*θ*_{sat,m1}is the value of the**Velocity saturation factor**parameter from the**Main**tab and*η*_{θ}is the**Velocity saturation temperature exponent**. The default value is`1.04`

.**Surface roughness scattering temperature exponent**This parameter leads to a temperature-dependent reduction in the MOSFET transconductance at high gate voltage. The surface roughness scattering,

*θ*_{sr}, is assumed to scale exponentially with temperature,*θ*_{sr}=*θ*_{sr,m1}(*T*_{m1}/*T*_{s})^*η*_{sr}.*θ*_{sr,m1}is the value of the**Surface roughness scattering factor**parameter from the**Main**tab and*η*_{sr}is the**Surface roughness scattering temperature exponent**. The default value is`0.65`

.**Resistance temperature exponent**The series resistances are assumed to correspond to semiconductor resistances. Therefore, they decrease exponentially with increasing temperature.

*R*_{i}=*R*_{i,m1}(*T*_{m1}/*T*_{s})^*η*_{R}, where*i*is S, D, or G, for the source, drain, or gate series resistance, respectively.*R*_{i,m1}is the value of the corresponding series resistance parameter from the**Ohmic Resistance**tab and*η*_{R}is the**Resistance temperature exponent**. The default value is`0.95`

.**Body diode reverse saturation current temperature exponent**The reverse saturation current for the body diode is assumed to be proportional to the square of the intrinsic carrier concentration,

*n*_{i}=*N*_{C}exp(–*E*_{G}/2*k*_{B}*T*).*N*_{C}is the temperature-dependent effective density of states and*E*_{G}is the temperature-dependent bandgap for the semiconductor material. To avoid introducing another temperature-scaling parameter, the block neglects the temperature dependence of the bandgap and uses the bandgap of silicon at 300K (1.12eV) for all device types. Therefore, the temperature-scaled reverse saturation current is given by$${I}_{s}={I}_{s,m1}{\left(\frac{{T}_{s}}{{T}_{m1}}\right)}^{{\eta}_{Is}}\cdot \mathrm{exp}\left(\frac{{E}_{G}}{{k}_{B}}\cdot \left(\frac{1}{{T}_{m1}}-\frac{1}{{T}_{s}}\right)\right).$$

*I*_{s,m1}is the value of the**Reverse saturation current**parameter from the**Body Diode**tab,*k*_{B}is Boltzmann’s constant (8.617x10-5eV/K), and*η*_{Is}is the**Body diode reverse saturation current temperature exponent**. The default value is`3`

, because*N*_{C}for silicon is roughly proportional to T^{3/2}. You can remedy the effect of neglecting the temperature-dependence of the bandgap by a pragmatic choice of*η*_{Is}.**Device simulation temperature**Temperature

*T*_{s}at which the device is simulated. The default value is`25`

°C.

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

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

[2] Van Langevelde, R., A. J. Scholten, and
D. B .M. Klaassen. "Physical Background of MOS Model 11. Level 1101."* Nat.Lab.
Unclassified Report 2003/00239*. April 2003.

[3] Oh, S-Y., D. E. Ward, and R. W. Dutton.
“Transient analysis of MOS transistors.” *IEEE
J. Solid State Circuits*. SC-15, pp. 636-643, 1980.

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