N-Channel MOSFET

N-Channel metal oxide semiconductor field effect transistor using either Shichman-Hodges equation or surface-potential-based model

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Library:
Simscape / Electrical / Semiconductors & Converters

Description

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.

Threshold-Based Model

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:

$I_{D S} = 0$
In the linear region (0 < V_DS < V_GS –V_th), the drain-source current is:

$I_{D S} = K ((V_{G S} - V_{t h}) V_{D S} - V_{D S}^{2} / 2) (1 + λ | V_{D S} |)$
In the saturated region (0 < V_GS –V_th < V_DS), the drain-source current is:

$I_{D S} = (K / 2) {(V_{G S} - V_{t h})}^{2} (1 + λ | V_{D S} |)$

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. For the four terminal parameterization, V_th is obtained using these equations:

V_BS Range V_th Equation
$V_{B S} \leq 0$ $V_{t h} = V_{T 0} + γ (- \sqrt{2 ϕ_{B}}) + γ (\sqrt{2 ϕ_{B} - V_{B S}})$
$0 < V_{B S} \leq 4 ϕ_{B}$ $V_{t h} = V_{T 0} - \frac{γ V_{B S}}{\sqrt{2 ϕ_{B}}}$
$V_{B S} > 4 ϕ_{B}$ $V_{t h} = V_{T 0} + γ (- \sqrt{2 ϕ_{B}})$
λ is the channel modulation.

V_BS Range	V_th Equation
$V_{B S} \leq 0$	$V_{t h} = V_{T 0} + γ (- \sqrt{2 ϕ_{B}}) + γ (\sqrt{2 ϕ_{B} - V_{B S}})$
$0 < V_{B S} \leq 4 ϕ_{B}$	$V_{t h} = V_{T 0} - \frac{γ V_{B S}}{\sqrt{2 ϕ_{B}}}$
$V_{B S} > 4 ϕ_{B}$	$V_{t h} = V_{T 0} + γ (- \sqrt{2 ϕ_{B}})$

Charge Model for Threshold-Based Variant

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

For the four terminals parameterization, the Input capacitance, Ciss, Reverse transfer capacitance, Crss, and Output capacitance, Coss are obtained using these equations:

C_GD = Crss
C_GS + C_GB = Ciss – Crss
C_DB = Coss – Crss

A simplified Meyer's capacitance model is used to describe the gate-source capacitance, C_GS, the gate-bulk capacitance, C_GB, and the gate-drain capacitance, C_GD. These figures show how the gate-bulk and gate-source capacitances change instantaneously, while the

Gate-bulk and gate-source capacitance change instantaneously.

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 Gate-drain 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.

Surface-Potential-Based Model

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 https://briefs.techconnect.org/papers/introduction-to-psp-mosfet-model/), 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:

$\frac{\partial^{2} ψ}{\partial x^{2}} + \frac{\partial^{2} ψ}{\partial y^{2}} = \frac{q N_{A}}{ε_{S i}} [1 - \exp (\frac{- ψ}{ϕ_{T}}) + \exp (\frac{ψ - 2 ϕ_{B} - V_{C B}}{ϕ_{T}})]$

$ϕ_{T} = \frac{k_{B} T}{q}$

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:

${(V_{G B} - V_{F B} - ψ_{s})}^{2} = γ^{2} [ψ_{s} + ϕ_{T} (\exp (\frac{- ψ_{s}}{ϕ_{T}}) - 1) + ϕ_{T} \exp (- \frac{2 ϕ_{B} + V_{C B}}{ϕ_{T}}) (\exp (\frac{ψ_{s}}{ϕ_{T}}) - 1)]$

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,

$γ = \frac{\sqrt{2 q ε_{S i} N_{A}}}{C_{o x}}$

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

$I_{D} = \frac{W μ_{0}}{L G_{Δ L} G_{m o b} \sqrt{1 + {(θ_{s a t} Δ ψ)}^{2}}} [- {\bar{Q}}_{i n v} Δ ψ + ϕ_{T} (Q_{i n v L} - Q_{i n v 0})]$

where:

W is the device width.
L is the channel length.
μ₀ 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.
${\bar{Q}}_{i n v}$ 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 (Surface-Potential-Based Variant) section.
G_ΔL is the channel-length modulation.

$G_{Δ L} = 1 - \frac{Δ L}{L} = 1 - α \ln [\frac{V_{D B} - V_{D B, e f f} + \sqrt{{(V_{D B} - V_{D B, e f f})}^{2} + V_{p}^{2}}}{V_{p}}]$

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

$β = \frac{W μ_{0} C_{o x}}{L}$

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

$V_{T} = V_{F B} + 2 ϕ_{B} + 2 ϕ_{T} + γ \sqrt{2 ϕ_{B} + 2 ϕ_{T}}$

where:

2ϕ_B is the surface potential at strong inversion.

The overall three and four terminal models consist of an intrinsic MOSFET defined by the surface-potential formulation, a body diode, series resistances, and fixed overlap capacitances, as shown in the schematics.

Modeling Body Diode

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

$I_{d i o} = I_{s} [\exp (- \frac{V_{D B}}{n ϕ_{T}}) - 1]$

$C_{j} = \frac{C_{j 0}}{\sqrt{1 + \frac{V_{D B}}{V_{b i}}}}$

$C_{d i f f} = \frac{τ I_{s}}{n ϕ_{T}} \exp (- \frac{V_{D B}}{n ϕ_{T}})$

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.

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. 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:

$K_{T s} = K_{T m 1} {(\frac{T_{s}}{T_{m 1}})}^{B E X}$

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, dV_th/dT.

For the four terminals parameterization, V_th is obtained using these equations:

V_BS Range	V_th Equation
$V_{B S} \leq 0$	$\frac{d V_{t h}}{d T} = \frac{d V_{T 0}}{d T} - \frac{γ}{2 \sqrt{2 ϕ_{B}}} \frac{d 2 ϕ_{B}}{d T} + \frac{γ}{2 \sqrt{2 ϕ_{B} - V_{B S}}} \frac{d 2 ϕ_{B}}{d T}$
$0 < V_{B S} \leq 4 ϕ_{B}$	$\frac{d V_{t h}}{d T} = \frac{d V_{T 0}}{d T} - \frac{γ V_{B S}}{4} {(2 ϕ_{B})}^{- \frac{3}{2}} \frac{d 2 ϕ_{B}}{d T}$
$V_{B S} > 4 ϕ_{B}$	$\frac{d V_{t h}}{d T} = \frac{d V_{T 0}}{d T} - \frac{γ}{2 \sqrt{2 ϕ_{B}}} \frac{d 2 ϕ_{B}}{d T}$

Where:

$ϕ_{B} = \frac{k T}{q} \ln (\frac{N_{B}}{n_{i}})$ is the surface potential and $\frac{d 2 ϕ_{B}}{d T} = \frac{1}{T} [2 ϕ_{B} - (\frac{E_{g} (0)}{q} + \frac{3 k T}{q})]$ .
E_g(0) is the extrapolated zero degree band-gap, which is equal to 1.16 eV for silicon.
V_BS is the bulk-source voltage.

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 α:

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

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 (Surface-Potential-Based Variant).

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 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 exposes the Thermal Port parameters.

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 parameters, see Simulating Thermal Effects in Semiconductors.

Assumptions and Limitations

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

The block does not account for temperature-dependent effects on the junction capacitances.
When you specify R_DS(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 R_DS(on) value. Inconsistent values for R_DS(on) at the higher temperature will result in unphysical values for α and unrepresentative simulation results. Typically R_DS(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, 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_DS(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.

Ports

Conserving

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`G` — Gate terminal
electrical

Electrical conserving port associated with the transistor gate terminal

`D` — Drain terminal
electrical

Electrical conserving port associated with the transistor drain terminal

`S` — Source terminal
electrical

Electrical conserving port associated with the transistor source terminal

`B` — Body terminal
electrical

Electrical conserving port associated with the transistor body terminal

Dependencies

To enable this port, set Parameterization to Four.

Parameters

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Main (Threshold-Based Variant)

This configuration of the Main parameters 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 (Surface-Potential-Based Variant).

`Number of terminals` — Terminal parameterization
`Three` (default) | `Four`

Number of terminals of the block.

`Parameterization` — Block parameterization
`Specify from a datasheet` (default) | `Specify using equation parameters directly`

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

`Number of terminals` — Terminal parameterization
`Three` (default) | `Four`

Number of terminals of the block.

`Gain` — MOSFET gain
`18` `A/V ²` (default) | positive scalar

The MOSFET gain, β. This parameter primarily defines the linear region of operation on an I_D–V_DS characteristic.

`Flatband voltage` — Flatband voltage
`-1.1` `V` (default)

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
`3.5` `V^1/2` (default)

Body factor, γ, in the surface-potential equation. This parameter primarily impacts the threshold voltage.

`Surface potential at strong inversion` — Surface potential at strong inversion
`1` `V` (default)

The 2ϕ_B term in the surface-potential equation. This parameter also primarily impacts the threshold voltage.

`Velocity saturation factor` — Velocity saturation factor
`0.4` `1/V` (default)

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.

`Channel-length modulation factor` — Channel-length modulation factor
`0` (default)

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` — Channel-length modulation voltage
`5e-2` `V` (default)

The voltage V_p in the G_ΔL equation. This parameter controls the drain-voltage at which channel-length modulation starts to become active

`Surface roughness scattering factor` — Surface roughness scattering factor
`0` `1/V` (default)

Indicates the strength of the mobility reduction. The mobility is μ = μ₀/G_mob, where μ₀ is the low-field mobility without the effect of surface scattering. The mobility reduction factor, G_mob, is given by $G_{m o b} = \sqrt{1 + {(θ_{s r} V_{e f f})}^{4}}$ , 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.

`Linear-to-saturation transition coefficient` — Linear-to-saturation transition coefficient
`8` (default)

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.

`Measurement temperature` — Measurement temperature
`25` `°C` (default)

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 (Surface-Potential-Based Variant).

Ohmic Resistance

`Source ohmic resistance` — Transistor source resistance
`0.0001` `Ohm` (default) | nonnegative scalar

The transistor source resistance, that is, the series resistance associated with the source contact. The default value for threshold-based variants is 1e-4 Ohm. The default value for surface-potential-based variants is 2e-3 Ohm.

`Drain ohmic resistance` — Transistor drain resistance
`0.01` `Ohm` (default) | nonnegative scalar

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

`Gate ohmic resistance` — Transistor gate resistance
`8.4` `Ohm` (default) | nonnegative scalar

The transistor gate resistance, that is, the series resistance associated with the gate contact.

Dependencies

This parameter is visible only for the surface-potential-based block variants.

`Body ohmic resistance` — Transistor body resistance
`0.001` `Ohm` (default) | nonnegative scalar

The transistor body resistance, that is, the series resistance associated with the body contact.

Dependencies

To enable this parameter, set:

Number of terminals to Four.
Threshold-potential-based block variant.

`Bulk ohmic resistance` — Transistor bulk resistance
`2e-3` `Ohm` (default) | nonnegative scalar

The transistor body resistance, that is, the series resistance associated with the bulk contact.

Dependencies

To enable this parameter, set:

Number of terminals to Four.
Surface-potential-based block variant.

Junction Capacitance

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

`Parameterization` — Capacitance parameterization
`Specify fixed input, reverse transfer and output capacitance` (default) | `Specify fixed gate-source, gate-drain and drain-source capacitance` | `Specify tabulated input, reverse transfer and output capacitance` | `Specify tabulated gate-source, gate-drain and drain-source capacitance`

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.
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` — Input Capacitance
`350` `pF` (default)

The gate-source capacitance with the drain shorted to the source:

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.

Dependencies

This parameter is visible only when the Parameterization parameter, in the Junction capacitance tab, is set to Specify fixed input, reverse transfer and output capacitance or to Specify tabulated input, reverse transfer and output capacitance.

`Reverse transfer capacitance, Crss` — Reverse transfer capacitance
`80` `pF` (default)

The drain-gate capacitance with the source connected to ground, also known as the Miller capacitance:

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.

Dependencies

`Output capacitance, Coss` — Output capacitance
`0` `pF` (default)

The drain-source capacitance with the gate and source shorted:

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.

Dependencies

`Gate-source junction capacitance` — Gate-source junction capacitance
`[270, 300, 290, 280, 295, 255]` `pF` (default)

The value of the capacitance placed between the gate and the source:

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.

Dependencies

This parameter is visible only when the Parameterization parameter, in the Junction capacitance tab, is set to Specify fixed gate-source, gate-drain and drain-source capacitance or to Specify tabulated gate-source, gate-drain and drain-source capacitance.

`Gate-drain junction capacitance` — Gate-drain junction capacitance
`[450, 400, 300, 190, 95, 55]` `pF` (default)

The value of the capacitance placed between the gate and the drain:

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.

Dependencies

`Drain-source junction capacitance` — Drain-source junction capacitance
`[450, 410, 390, 230, 175, 115]` `pF` (default)

The value of the capacitance placed between the drain and the source:

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.

Dependencies

`Corresponding drain-source voltages` — Corresponding drain-source voltages
`[.1, .3, 1, 3, 10, 30]` `V` (default)

The drain-source voltages corresponding to the tabulated capacitance values.

Dependencies

This parameter is visible only when the Parameterization parameter, in the Junction capacitance tab, is set to Specify tabulated input, reverse transfer and output capacitance or to Specify tabulated gate-source, gate-drain and output capacitance.

`Gate-source voltage, Vgs, for tabulated capacitances` — Gate-source voltage for tabulated capacitances
`0` `V` (default)

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.

Dependencies

`Gate-drain charge-voltage linearity` — Charge-voltage linearity
`Gate-drain capacitance is constant` (default) | `Gate-drain charge function is nonlinear`

The two fixed capacitance options 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.
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.

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.

To enable conduction through the body diode, for applications where the MOSFET current changes sign during the simulation, such as when the MOSFET is driving an inductive load, set this parameter to a non-zero value.

For applications where the MOSFET current never changes sign, such as in a small-signal amplifier, set this parameter to 0 to improve simulation speed.

`Built-in voltage` — Built-in voltage
`0.6` `V` (default)

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.

`Ideality factor` — Ideality factor
`1` (default)

The factor designated by the n symbol in the body-diode equations.

`Zero-bias junction capacitance` — Zero-bias junction capacitance
`0` `pF` (default)

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` — Transit time
`50e-9` `s` (default)

The time designated by the τ symbol in the body-diode equations.

When the Reverse saturation current and Transit time parameters are both non-zero, this block includes the reverse recovery inside the body diode model.

Temperature Dependence (Threshold-Based Variant)

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 (Surface-Potential-Based Variant)

`Parameterization` — Temperature dependance parameterization
`None — Simulate at parameter measurement temperature` (default) | `Model temperature dependence`

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_DS(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.

None — Simulate at parameter measurement temperature — Temperature dependence is not modeled.
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` — Gain temperature exponent
`1.3` (default)

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.

`Flatband voltage temperature coefficient` — Flatband voltage temperature coefficient
`5e-4` `V/K` (default)

The flatband voltage, V_FB, is assumed to scale linearly with temperature, V_FB = V_FBm1 + (T_s – T_m1)S_{T,V_FB}. V_FBm1 is the value of the Flatband voltage parameter from the Main tab and S_{T,V_FB} is the Flatband voltage temperature coefficient.

`Surface potential at strong inversion temperature coefficient` — Surface potential at strong inversion temperature coefficient
`-8.5e-4` `V/K` (default)

The surface potential at strong inversion, 2ϕ_B, is assumed to scale linearly with temperature, 2ϕ_B = 2ϕ_Bm1 + (T_s – T_m1)S_{T,ϕ_B}. 2ϕ_Bm1 is the value of the Surface potential at strong inversion parameter from the Main tab and S_{T,ϕ_B} is the Surface potential at strong inversion temperature coefficient.

`Velocity saturation temperature exponent` — Velocity saturation temperature exponent
`1.04` (default)

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.

`Surface roughness scattering temperature exponent` — Surface roughness scattering temperature exponent
`0.65` (default)

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.

`Resistance temperature exponent` — Resistance temperature exponent
`0.95` (default)

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.

`Body diode reverse saturation current temperature exponent` — Body diode reverse saturation current temperature exponent
`3` (default)

$I_{s} = I_{s, m 1} {(\frac{T_{s}}{T_{m 1}})}^{η_{I s}} \cdot \exp (\frac{E_{G}}{k_{B}} \cdot (\frac{1}{T_{m 1}} - \frac{1}{T_{s}})) .$

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` — Device simulation temperature
`25` `°C` (default)

Temperature T_s at which the device is simulate.

Model Examples

MOSFET Characteristics

Generation of the characteristic curves for an N-channel MOSFET. Define the vector of gate voltages and minimum and maximum drain-source voltages by double clicking on the block labeled 'Define Conditions (Vg and Vds)'. Then click on hyperlink 'plot results' in the model.

Interactive Generation of MOSFET Characteristics

Allows the user to explore the impact of parameter choices on the I-V and C-V characteristics for a surface-potential-based MOSFET model. To open this example, in the MATLAB® Command Window, type: ee_mosfet_characteristics.

References

[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.

Documentation

N-Channel MOSFET

Description

Threshold-Based Model

Charge Model for Threshold-Based Variant

Surface-Potential-Based Model

Modeling Body Diode

Modeling Temperature Dependence

Thermal Port

Assumptions and Limitations

Ports

Conserving

G — Gate terminal electrical

D — Drain terminal electrical

S — Source terminal electrical

B — Body terminal electrical

Dependencies

Parameters

Main (Threshold-Based Variant)

Number of terminals — Terminal parameterization Three (default) | Four

Parameterization — Block parameterization Specify from a datasheet (default) | Specify using equation parameters directly

Drain-source on resistance, R_DS(on) — Drain-source on resistance 0.025 Ohm (default)

Dependencies

Drain current, Ids, for R_DS(on) — Drain current 6A (default)

Dependencies

Gate-source voltage, Vgs, for R_DS(on) — Gate-source voltage, Vgs 10 V (default)

Dependencies

Gain, K — Positive constant gain coefficient 5.0 A/V2 (default)

Dependencies

Gate-source threshold voltage, Vth — Gate-source threshold voltage 1.7 V (default)

Dependencies

Gate-source threshold voltage at zero bulk-source voltage, Vth0 — Gate-source threshold voltage at zero bulk-source voltage 1.7 V (default)

Dependencies

Channel modulation, L — Channel modulation 0 1/V (default)

Gate-source threshold voltage at first non-zero bulk-source voltage, Vth1 — Gate-source threshold voltage at first non-zero bulk-source voltage 1.9071 V (default)

Dependencies

First bulk-source voltage, Vbs1 — First bulk-source voltage -1 V (default)

Dependencies

Gate-source threshold voltage at second non-zero bulk-source voltage, Vth2 — Gate-source threshold voltage at second non-zero bulk-source voltage 2.066 V (default)

Dependencies

Second bulk-source voltage, Vbs2 — Second bulk-source voltage -2 V (default)

Dependencies

Body factor — Body factor 0.5 V^0.50000 (default)

Dependencies

Surface potential — Surface potential 0.5 V (default)

Dependencies

Measurement temperature — Measurement temperature 25 °C (default)

Main (Surface-Potential-Based Variant)

Number of terminals — Terminal parameterization Three (default) | Four

Gain — MOSFET gain 18 A/V 2 (default) | positive scalar

Flatband voltage — Flatband voltage -1.1 V (default)

Body factor — Body factor 3.5 V1/2 (default)

Surface potential at strong inversion — Surface potential at strong inversion 1 V (default)

Velocity saturation factor — Velocity saturation factor 0.4 1/V (default)

Channel-length modulation factor — Channel-length modulation factor 0 (default)

Channel-length modulation voltage — Channel-length modulation voltage 5e-2 V (default)

Surface roughness scattering factor — Surface roughness scattering factor 0 1/V (default)

Linear-to-saturation transition coefficient — Linear-to-saturation transition coefficient 8 (default)

Measurement temperature — Measurement temperature 25 °C (default)

Ohmic Resistance

Source ohmic resistance — Transistor source resistance 0.0001 Ohm (default) | nonnegative scalar

Drain ohmic resistance — Transistor drain resistance 0.01 Ohm (default) | nonnegative scalar

Gate ohmic resistance — Transistor gate resistance 8.4 Ohm (default) | nonnegative scalar

Dependencies

Body ohmic resistance — Transistor body resistance 0.001 Ohm (default) | nonnegative scalar

Dependencies

Bulk ohmic resistance — Transistor bulk resistance 2e-3 Ohm (default) | nonnegative scalar

Dependencies

Junction Capacitance

Input capacitance, Ciss — Input Capacitance 350 pF (default)

Dependencies

Reverse transfer capacitance, Crss — Reverse transfer capacitance 80 pF (default)

Dependencies

Output capacitance, Coss — Output capacitance 0 pF (default)

Dependencies

Gate-source junction capacitance — Gate-source junction capacitance [270, 300, 290, 280, 295, 255] pF (default)

Dependencies

Gate-drain junction capacitance — Gate-drain junction capacitance [450, 400, 300, 190, 95, 55] pF (default)

Dependencies

Drain-source junction capacitance — Drain-source junction capacitance [450, 410, 390, 230, 175, 115] pF (default)

`G` — Gate terminal
electrical

`D` — Drain terminal
electrical

`S` — Source terminal
electrical

`B` — Body terminal
electrical

`Number of terminals` — Terminal parameterization
`Three` (default) | `Four`

`Parameterization` — Block parameterization
`Specify from a datasheet` (default) | `Specify using equation parameters directly`

`Drain-source on resistance, R_DS(on)` — Drain-source on resistance
`0.025` `Ohm` (default)

`Drain current, Ids, for R_DS(on)` — Drain current
`6A` (default)

`Gate-source voltage, Vgs, for R_DS(on)` — Gate-source voltage, Vgs
`10` `V` (default)

`Gain, K` — Positive constant gain coefficient
`5.0` `A/V²` (default)

`Gate-source threshold voltage, Vth` — Gate-source threshold voltage
`1.7` `V` (default)

`Gate-source threshold voltage at zero bulk-source voltage, Vth0` — Gate-source threshold voltage at zero bulk-source voltage
`1.7` `V` (default)

`Channel modulation, L` — Channel modulation
`0` `1/V` (default)

`Gate-source threshold voltage at first non-zero bulk-source voltage, Vth1` — Gate-source threshold voltage at first non-zero bulk-source voltage
`1.9071` `V` (default)

`First bulk-source voltage, Vbs1` — First bulk-source voltage
`-1` `V` (default)

`Gate-source threshold voltage at second non-zero bulk-source voltage, Vth2` — Gate-source threshold voltage at second non-zero bulk-source voltage
`2.066` `V` (default)

`Second bulk-source voltage, Vbs2` — Second bulk-source voltage
`-2` `V` (default)

`Body factor` — Body factor
`0.5` `V^0.50000` (default)

`Surface potential` — Surface potential
`0.5` `V` (default)

`Measurement temperature` — Measurement temperature
`25` `°C` (default)

`Number of terminals` — Terminal parameterization
`Three` (default) | `Four`

`Gain` — MOSFET gain
`18` `A/V ²` (default) | positive scalar

`Flatband voltage` — Flatband voltage
`-1.1` `V` (default)

`Body factor` — Body factor
`3.5` `V^1/2` (default)

`Surface potential at strong inversion` — Surface potential at strong inversion
`1` `V` (default)

`Velocity saturation factor` — Velocity saturation factor
`0.4` `1/V` (default)

`Channel-length modulation factor` — Channel-length modulation factor
`0` (default)

`Channel-length modulation voltage` — Channel-length modulation voltage
`5e-2` `V` (default)

`Surface roughness scattering factor` — Surface roughness scattering factor
`0` `1/V` (default)

`Linear-to-saturation transition coefficient` — Linear-to-saturation transition coefficient
`8` (default)

`Measurement temperature` — Measurement temperature
`25` `°C` (default)

`Source ohmic resistance` — Transistor source resistance
`0.0001` `Ohm` (default) | nonnegative scalar

`Drain ohmic resistance` — Transistor drain resistance
`0.01` `Ohm` (default) | nonnegative scalar

`Gate ohmic resistance` — Transistor gate resistance
`8.4` `Ohm` (default) | nonnegative scalar

`Body ohmic resistance` — Transistor body resistance
`0.001` `Ohm` (default) | nonnegative scalar

`Bulk ohmic resistance` — Transistor bulk resistance
`2e-3` `Ohm` (default) | nonnegative scalar

`Input capacitance, Ciss` — Input Capacitance
`350` `pF` (default)

`Reverse transfer capacitance, Crss` — Reverse transfer capacitance
`80` `pF` (default)

`Output capacitance, Coss` — Output capacitance
`0` `pF` (default)

`Gate-source junction capacitance` — Gate-source junction capacitance
`[270, 300, 290, 280, 295, 255]` `pF` (default)

`Gate-drain junction capacitance` — Gate-drain junction capacitance
`[450, 400, 300, 190, 95, 55]` `pF` (default)

`Drain-source junction capacitance` — Drain-source junction capacitance
`[450, 410, 390, 230, 175, 115]` `pF` (default)

`Corresponding drain-source voltages` — Corresponding drain-source voltages
`[.1, .3, 1, 3, 10, 30]` `V` (default)

`Gate-source voltage, Vgs, for tabulated capacitances` — Gate-source voltage for tabulated capacitances
`0` `V` (default)

`Gate-drain charge-voltage linearity` — Charge-voltage linearity
`Gate-drain capacitance is constant` (default) | `Gate-drain charge function is nonlinear`

`Gate-drain oxide capacitance` — Gate-drain oxide capacitance
`200` `pF` (default)

`Drain-gate voltage at which oxide capacitance becomes active` — Drain-gate voltage at which oxide capacitance becomes active
`-0.5` `V` (default)

`Gate-bulk and gate-source charge-voltage linearity` — Gate-bulk and gate-source charge-voltage linearity
`Gate-bulk and gate-source capacitance change instantly` (default) | `Gate-bulk and gate-source capacitance change gradually`

`Oxide capacitance` — Oxide capacitance
`1500` `pF` (default)

`Gate-source overlap capacitance` — Gate-source overlap capacitance
`100` `pF` (default)

`Gate-drain overlap capacitance` — Gate-drain overlap capacitance
`14` `pF` (default)

`Reverse saturation current` — Reverse saturation current
`0` `A` (default)

`Built-in voltage` — Built-in voltage
`0.6` `V` (default)

`Ideality factor` — Ideality factor
`1` (default)

`Zero-bias junction capacitance` — Zero-bias junction capacitance
`0` `pF` (default)

`Transit time` — Transit time
`50e-9` `s` (default)

`Parameterization` — Temperature dependance parameterization
`None — Simulate at parameter measurement temperature` (default) | `Model temperature dependence`

`Drain-source on resistance, R_DS(on), at second measurement temperature` — Drain-source on resistance at second measurement temperature
`0.037` `Ohm` (default)

`Second measurement temperature` — Second temperature
`125` `°C` (default)

`Gate threshold voltage temperature coefficient, dVth/dT` — Gate-source voltage, Vgs
`-6` `mV/K` (default)

`Mobility temperature exponent, BEX` — Mobility temperature exponent
`-1.5` (default)

`Body diode reverse saturation current temperature exponent` — Body diode reverse saturation current temperature exponent
`3` (default)

`Device simulation temperature` — Device simulation temperature
`25` `°C` (default)

`Parameterization` — Temperature dependence parameterization
`None — Simulate at parameter measurement temperature` (default) | `Model temperature dependence`

`Gain temperature exponent` — Gain temperature exponent
`1.3` (default)

`Flatband voltage temperature coefficient` — Flatband voltage temperature coefficient
`5e-4` `V/K` (default)

`Surface potential at strong inversion temperature coefficient` — Surface potential at strong inversion temperature coefficient
`-8.5e-4` `V/K` (default)

`Velocity saturation temperature exponent` — Velocity saturation temperature exponent
`1.04` (default)

`Surface roughness scattering temperature exponent` — Surface roughness scattering temperature exponent
`0.65` (default)

`Resistance temperature exponent` — Resistance temperature exponent
`0.95` (default)

`Body diode reverse saturation current temperature exponent` — Body diode reverse saturation current temperature exponent
`3` (default)

`Device simulation temperature` — Device simulation temperature
`25` `°C` (default)

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