# P-Channel MOSFET

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

## Library

Semiconductor Devices

## Description

The P-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 a P-Channel MOSFET.

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

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

`${I}_{DS}=0$`

• In the linear region (0 < –VDS < –VGS +Vth) the drain-source current is:

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

• In the saturated region (0 < –VGS +Vth < –VDS) the drain-source current is:

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

In the preceding equations:

• K is the transistor gain.

• VDS is the negative drain-source voltage.

• VGS is the gate-source voltage.

• Vth is the threshold voltage.

• λ is the channel modulation.

### 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 iterative 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:

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 CGS and either a fixed or a nonlinear gate-drain capacitance CGD. If you select the `Gate-drain charge function is nonlinear` option for the Charge-voltage linearity parameter, then the gate-drain charge relationship is defined by the piecewise-linear function shown in the following figure.

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

### Note

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

### 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 http://nsti.org/Nanotech2005/WCM2005/WCM2005-GGildenblat.pdf), including only certain effects from the PSP model 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 surface-potential equation is derived similar to the way described on the N-Channel MOSFET block reference page, with all voltages, charges, and currents multiplied by -1.

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.

### Modeling Body Diode

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

`${I}_{dio}={I}_{s}\left[\mathrm{exp}\left(-\frac{{V}_{BD}}{n{\varphi }_{T}}\right)-1\right]$`
`${C}_{j}=\frac{{C}_{j0}}{\sqrt{1+\frac{{V}_{BD}}{{V}_{bi}}}}$`
`${C}_{diff}=\frac{\tau {I}_{s}}{n{\varphi }_{T}}\mathrm{exp}\left(-\frac{{V}_{BD}}{n{\varphi }_{T}}\right)$`

where:

• Idio is the current through the diode.

• Is is the reverse saturation current.

• VBD is the body-drain voltage.

• n is the ideality factor.

• ϕT is the thermal voltage.

• Cj is the junction capacitance of the diode.

• Cj0 is the zero-bias junction capacitance.

• Vbi is the built-in voltage.

• Cdiff 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, Vth, become a function of temperature according to the following equations:

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

Vths = Vth1 + α ( TsTm1)

where:

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

• Ts is the simulation temperature.

• KTm1 is the transistor gain at the measurement temperature.

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

• Vth1 is the threshold voltage at the measurement temperature.

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

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

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

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

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

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

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

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 Tm1 at which the other device parameters have been extracted. The Temperature Dependence tab provides the simulation temperature, Ts, and the temperature-scaling coefficients for the other device parameters. For more information, see Temperature Dependence Tab (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 adds the Thermal Port tab to the block dialog box.

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

## Basic Assumptions and Limitations

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

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

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

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

## Parameters

### Main Tab (Threshold-Based Variant)

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. RDS(on) should have a positive value. This parameter is only visible when you select ```Specify from a datasheet``` for the Parameterization parameter. The default value is `0.167` Ω.

Drain current, Ids, for R_DS(on)

The drain current the block uses to calculate the value of the drain-source resistance. IDS should have a negative value. This parameter is only visible when you select ```Specify from a datasheet``` for the Parameterization parameter. The default value is `-2.5` A.

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

The gate-source voltage the block uses to calculate the value of the drain-source resistance. VGS should have a negative value. This parameter is only visible when you select ```Specify from a datasheet``` for the Parameterization parameter. The default value is `-4.5` 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 `2` A/V2.

Gate-source threshold voltage, Vth

Gate-source threshold voltage Vth in the Shichman and Hodges equations. For an enhancement device, Vth should be negative. For a depletion mode device, Vth should be positive. The default value is `-1.4` V.

Channel modulation, L

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

Measurement temperature

Temperature Tm1 at which Drain-source on resistance, R_DS(on) is measured. The default value is `25` °C.

### Main Tab (Surface-Potential-Based Variant)

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 IDVDS characteristic. The value must be greater than 0. The default value is `18` A/V2.

Flatband voltage

The flatband voltage, VFB, 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` V1/2.

Surface potential at strong inversion

The 2ϕB 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, θsat, 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 a P-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 GΔL 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 Vp in the GΔL 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 = μ0/Gmob, where μ0 is the low-field mobility without the effect of surface scattering. The mobility reduction factor, Gmob, is given by ${G}_{mob}=\sqrt{1+{\left({\theta }_{sr}{V}_{eff}\right)}^{2}}$, where θsr is the surface roughness scattering factor and Veff is a voltage that is indicative of the effective vertical electric field strength in the channel, Eeff. For high vertical electric fields, the mobility is roughly proportional to Eeff for holes. 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 IDVDS characteristic. The expected range for this parameter value is between 2 and 8. The default value is `8`.

Measurement temperature

Temperature Tm1 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.

### Ohmic Resistance Tab

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.

### Junction Capacitance Tab

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 source-drain 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 source-drain 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 `182` pF.

• If you select ```Specify tabulated input, reverse transfer and output capacitance```, the default value is `[225 210 200 185 175 170]` pF.

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

• If you select ```Specify fixed input, reverse transfer and output capacitance```, the default value is `24` pF.

• If you select ```Specify tabulated input, reverse transfer and output capacitance```, the default value is `[75 60 50 35 25 20]` 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 `[180 160 125 80 60 45]` 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 `158` pF.

• If you select ```Specify tabulated gate-source, gate-drain and drain-source capacitance```, the default value is `[150 150 150 150 150 150]` 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 `24` pF.

• If you select ```Specify tabulated gate-source, gate-drain and drain-source capacitance```, the default value is `[75 60 50 35 25 20]` 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 `[105 100 75 45 35 25]` pF.

Corresponding source-drain voltages

The source-drain 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 negative of the values specified for the Corresponding source-drain voltages parameter (Vdg = –VsdVgs). 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 CGS and either a fixed or a nonlinear gate-drain capacitance CGD. 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 only visible when you select `Gate-drain charge function is nonlinear` for the Charge-voltage linearity parameter. The default value is `200` pF.

Drain-gate voltage at which oxide capacitance becomes active

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

### Channel Capacitances Tab

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.

### Body Diode Tab

Reverse saturation current

The current designated by the Is 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 Vbi 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 Cj0 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.

### Temperature Dependence Tab (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 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, Ts, a value for BEX, and a value for the measurement temperature Tm1 (using the Measurement temperature parameter on the Main tab). You also have to provide a value for α using one of two methods, depending on the value of the Parameterization parameter on the Main tab. If you parameterize the block from a datasheet, you have to provide RDS(on) at a second measurement temperature, and the block will calculate α based on that. If you parameterize by specifying equation parameters, you have to provide the value for α directly.

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

The ratio of the drain-source voltage to the drain current for specified values of drain current and gate-source voltage at second measurement temperature. This parameter is only visible when you select ```Specify from a datasheet``` for the Parameterization parameter on the Main tab. It must be quoted for the same working point (drain current and gate-source voltage) as the Drain-source on resistance, R_DS(on) parameter on the Main tab. The default value is `0.25` Ω.

Second measurement temperature

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

Gate threshold voltage temperature coefficient, dVth/dT

The rate of change of gate threshold voltage with temperature. This parameter is only visible when you select ```Specify using equation parameters directly``` for the Parameterization parameter on the Main tab. The default value is `2` 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, ni = N Cexp(–EG/2kBT). N C is the temperature-dependent effective density of states and EG 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, kB is Boltzmann’s constant (8.617x10-5eV/K), and ηIs is the Body diode reverse saturation current temperature exponent. The default value is `3`, because NC for silicon is roughly proportional to T3/2. You can remedy the effect of neglecting the temperature-dependence of the bandgap by a pragmatic choice of ηIs.

Device simulation temperature

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

### Temperature Dependence Tab (Surface-Potential-Based Variant)

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, Ts, 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(Tm1/Ts)^ηβ. β m1 is the value of the Gain parameter from the Main tab and ηβ is the Gain temperature exponent. The default value is `1.3`.

Flatband voltage temperature coefficient

The flatband voltage, VFB, is assumed to scale linearly with temperature, VFB = V FBm1 + (TsTm1)ST,VFB. V FBm1 is the value of the Flatband voltage parameter from the Main tab and ST,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, 2ϕB, is assumed to scale linearly with temperature, B = 2ϕ Bm1 + (TsTm1)ST,ϕB. 2ϕ Bm1 is the value of the Surface potential at strong inversion parameter from the Main tab and ST,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, θsat, is assumed to scale exponentially with temperature, θsat = θ sat,m1(Tm1/Ts)^ηθ. θ sat,m1 is the value of the Velocity saturation factor parameter from the Main tab and ηθ 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, θsr, is assumed to scale exponentially with temperature, θsr = θ sr,m1(Tm1/Ts)^ηsr. θ sr,m1 is the value of the Surface roughness scattering factor parameter from the Main tab and ηsr 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. Ri = R i,m1(Tm1/Ts)^ηR, 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 ηR 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, ni = N Cexp(–EG/2kBT). N C is the temperature-dependent effective density of states and EG 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, kB is Boltzmann’s constant (8.617x10-5eV/K), and ηIs is the Body diode reverse saturation current temperature exponent. The default value is `3`, because NC for silicon is roughly proportional to T3/2. You can remedy the effect of neglecting the temperature-dependence of the bandgap by a pragmatic choice of ηIs.

Device simulation temperature

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

## Ports

The block has the following ports:

`G`

Electrical conserving port associated with the transistor gate terminal

`D`

Electrical conserving port associated with the transistor drain terminal

`S`

Electrical conserving port associated with the transistor source terminal

## References

[1] 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.