# N-Channel LDMOS FET

N-Channel laterally diffused metal oxide semiconductor or vertically diffused metal oxide semiconductor transistors suitable for high voltage

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## Description

The N-Channel LDMOS FET block lets you model LDMOS (or VDMOS) transistors suitable for high voltage. The model is based on surface potential and includes effects due to an extended drain (drift) region:

• Nonlinear capacitive effects associated with the drift region

• Surface scattering and velocity saturation in the drift region

• Velocity saturation and channel-length modulation in the channel region

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

• The intrinsic body diode

• Reverse recovery in the body diode model

• Temperature scaling of physical parameters

• For the thermal variant (see Thermal Port), dynamic self-heating

The physical structure of the model is shown in the following figure.

The channel region is in the p+ region, from the heavily n-doped source well to the end of the p+ region. The drift region is a lightly doped drain extension. Further down, there is a p-type epi-layer, and then the entire structure is on a heavily p-doped substrate. The gate oxide is thin over the entire channel region and over part of the drift region. Further into the drift region, the gate oxide has a greater thickness in the local-oxidation-of-silicon (LOCOS) region.

The next figure shows the equivalent circuit of the model.

The modeling approach is similar to [1]. The overlaps of the gate contact with the source and drain n-wells are modeled as lumped linear capacitances. The channel (p+) region is modeled using the surface-potential-based MOSFET model. The pn-junction between the source/bulk and drain is modeled using an ideal diode, including both junction and diffusion capacitances. The drift region underneath the thin gate oxide is modeled according to a surface-potential formulation, which includes:

• The current due to the accumulation layer at the semiconductor-oxide interface

• The current due to the electrons flowing towards the drain deeper inside the drift region

The space-charge region between the epi-layer and the drift region is represented using a pinching effect on the current flowing through the bulk of the drift region. The LOCOS part of the drift region is modeled as a lumped, series resistor, and there are also series resistances added to the source and gate contacts.

For detailed description of the channel model, see the surface-potential-based model of the N-Channel MOSFET block. The drift region model is similarly derived from the surface potential using the Poisson equation. For an n-type semiconductor under the gradual-channel approximation, the defining equations are:

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

where:

• ψ is the electrostatic potential.

• q is the magnitude of the electronic charge.

• ND is the doping density of the drift region.

• ɛSi is the dielectric permittivity of the semiconductor material (for example, silicon).

• ϕB is the difference between the intrinsic Fermi level and the Fermi level deep in the drift region.

• VCB is the quasi-Fermi potential of the drift region referenced to the bulk.

• ϕT is the thermal voltage.

• kB is Boltzmann’s constant.

• T is temperature.

If we neglect inversion for the DC current model, we obtain the following current expression:

`${I}_{D}=\frac{1}{1+{\theta }_{sat}{V}_{DK}}\left[\frac{{f}_{lin}}{{R}_{D}}{V}_{DK}+\frac{\beta }{2}\cdot \frac{{V}_{GK}^{2}-{V}_{GD}^{2}}{1+\frac{{\theta }_{surf}}{2}\left({V}_{GK}+{V}_{GD}\right)}\right]$`

where:

• ID is the drain current.

• θsat is the velocity saturation.

• Vij is the voltage difference between nodes i and j, where subscripts D and K refer to the drain and to the junction of the channel and drift regions, respectively, and subscript G refers to the gate with a correction due to the flatband voltage being applied.

• flin/RD represents the conductance of the bulk of the drift region, including the effect of pinching due to depletion from the epi-drift interface.

• β is the gain of the accumulation layer at the interface between the drift region and the thin gate oxide.

• θsurf is the parameter that accounts for scattering in the accumulation layer due to the vertical electric field.

The pinching off of the bulk part of the drift region is described by

`${f}_{lin}=1-{\lambda }_{D}\frac{\sqrt{{V}_{bi}+{V}_{SB}}-\sqrt{{V}_{bi}}}{\sqrt{{V}_{bi}}}$`

where:

• λD is the parameter representing the n-side vertical depth of the space-charge region along the epi-drift interface at zero bias divided by the vertical depth of the undepleted part of the drift region at zero bias.

In the figure, the top solid line is the semiconductor surface. The lower solid line is the junction between the drift region and the epi layer. The dashed lines show the extent of the space-charge region around the drift-epi interface. λD is y1/y2 at zero bias.

• Vbi is the built-in voltage for the epi-drift diode.

• VSB is the source-body voltage, used as an approximation to the bias applied across the epi-drift diode. Using this voltage instead of VKB is more numerically stable, and is justified because most of the drain-source voltage drops across the drift region in the transistor on-state.

The charge model is similar to that of the surface-potential-based MOSFET model, with additional expressions to account for the charge in the drift region. The block uses the derived equations as described in [1], which include both inversion and accumulation in the drift region.

### Modeling Body Diode

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

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

where:

• Idio is the current through the diode.

• Is is the reverse saturation current.

• VDB is the drain-body 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.

The 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 parameters provides the simulation temperature, Ts, and the temperature-scaling coefficients for the other device parameters. For more information, see Temperature Dependence.

### Thermal Port

The block has an optional thermal port, hidden by default. To expose the thermal port, right-click the block in your model, and then from the context menu select Simscape > Block choices > Show thermal port. This action displays the thermal port H on the block icon, and 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.

The thermal variant of the block includes dynamic self-heating, that is, lets you simulate the effect of self-heating on the electrical characteristics of the device.

## Ports

### Conserving

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Electrical conserving port associated with the transistor gate terminal

Electrical conserving port associated with the transistor drain terminal

Electrical conserving port associated with the transistor source terminal

## Parameters

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### Main

The gain, β, of the MOSFET regions. The parameter value is a two-element vector, with the first element corresponding to the channel, and the second — to the drift region. This parameter primarily defines the linear region of operation on an IDVDS characteristic.

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 parameter value is a two-element vector, with the first element corresponding to the channel, and the second — to the drift region. The default value is `[-1.05, -0.1]` 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.

The threshold voltage for the channel region, for a short-circuited source-bulk connection, is approximately

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

where 2ϕB is the surface potential at strong inversion and γ is the body factor, both at the channel region.

Body factor, γ, in the surface-potential equation. The parameter value is a two-element vector, with the first element corresponding to the channel, and the second — to the drift region.

For the channel region, the body factor is

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

See the N-Channel MOSFET block reference page for details on this equation. The drift region equation is similar, except that NA is replaced by the doping density, ND. The channel-region parameter value primarily impacts the threshold voltage. For the drift region, this parameter primarily affects the charge model, and also has a minor effect on the pinch-off behavior of the bulk current through the drift region.

The 2ϕB term in the surface-potential equation. The parameter value is a two-element vector, with the first element corresponding to the channel, and the second — to the drift region.

The channel-region parameter value also primarily impacts the threshold voltage. For the drift region, this parameter affects the charge model only.

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. The parameter value is a two-element vector, with the first element corresponding to the channel, and the second — to the drift region. The default value is `[0.0, 0.1]` 1/V, which means that velocity saturation in the channel region is off by default.

Surface scattering factor, θsurf, in the drain-current equation. This parameter applies to the drift region only and accounts for scattering in the accumulation layer due to the vertical electric field.

The factor, α, multiplying the logarithmic term in the GΔL equation. See the N-Channel MOSFET block reference page for details on this 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. This parameter applies to the channel region only. The default value is `0`, which means that channel-length modulation is off by default.

The voltage Vp in the GΔL equation. See the N-Channel MOSFET block reference page for details on this equation. This parameter controls the drain-voltage at which channel-length modulation starts to become active. This parameter applies to the channel region only.

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. This parameter applies both to the channel and drift regions. The expected range for this parameter value is between 2 and 8.

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.

### Ohmic Resistance

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

The transistor drain resistance, that is, the series resistance associated with the drain contact and with the LOCOS part of the drift region, which is not heavily impacted by the applied gate voltage.

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

Resistance RD in the drain-current equation. It represents the resistance of the bulk part of the drift region in the absence of depletion from the top and bottom interfaces.

Parameter λD in the drain-current equation. It is the ratio of vertical depths y1 and y2 at zero bias, where y1 represents the space-charge region and y2 represents the undepleted part of the drift region.

### Capacitances

The parallel plate gate-channel and gate-drift-region capacitance. The parameter value is a two-element vector, with the first element corresponding to the channel, and the second — to the drift region.

The fixed, linear capacitance associated with the overlap of the gate electrode with the source well.

The fixed, linear capacitance associated with the overlap of the gate electrode with the drain well.

### Body Diode

The current designated by the Is symbol in the body-diode equations.

The built-in voltage of the diode, designated by the Vbi symbol in the body-diode equations.

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

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

### 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 the device simulation temperature, Ts, and the temperature-scaling coefficients for other block parameters.

Temperature Ts at which the device is simulated

The parameter value is a two-element vector, with the first element corresponding to the channel, and the second — to the drift region. Both in the channel and the drift region, the MOSFET gain, β, is assumed to scale exponentially with temperature, β = βm1 (Tm1/Ts)^ηβ. βm1 is the value of the channel or drift region gain, as specified by the Gain, [channel drift_region] parameter from the Main tab. ηβ is the corresponding element of the Gain temperature exponent, [channel drift_region] parameter.

The parameter value is a two-element vector, with the first element corresponding to the channel, and the second — to the drift region. The flatband voltage, VFB, is assumed to scale linearly with temperature, VFB = V FBm1 + (TsTm1)ST,VFB. VFBm1 is the value of the channel or drift region flatband voltage, as specified by the Flatband voltage, [channel drift_region] parameter from the Main tab. ST,VFB is the corresponding element of the Flatband voltage temperature coefficient, [channel drift_region] parameter.

The surface potential at strong inversion, 2ϕB, is assumed to scale linearly with temperature, B = 2ϕBm1 + (TsTm1)ST,ϕB. 2ϕBm1 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 parameter value is a two-element vector, with the first element corresponding to the channel, and the second — to the drift region. The velocity saturation, θsat, is assumed to scale exponentially with temperature, θsat = θsat,m1 (Tm1/Ts)^ηθ. θsat,m1 is the value of the channel or drift region velocity saturation factor, as specified by the Velocity saturation factor, [channel drift_region] parameter from the Main tab. ηθ is the corresponding element of the Velocity saturation temperature exponent, [channel drift_region] parameter.

The series resistances are assumed to correspond to semiconductor resistances. Therefore, they decrease exponentially with increasing temperature. Ri = Ri,m1 (T/Ts)^ηR, where i is Sm1, D, or G, for the source, drain, or gate series resistance, respectively. Ri,m1 is the value of the corresponding series resistance parameter from the Ohmic Resistance tab and ηR is the Ohmic resistance temperature exponent.

Resistance RD, the low-bias resistance of the bulk part of the drift region, scales similarly to the other series resistances. A separate value of the temperature exponent for this resistance provides an extra degree of freedom.

The reverse saturation current for the body diode is assumed to be proportional to the square of the intrinsic carrier concentration, ni = NC exp(–EG/2kBT). NC 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

`${I}_{s}={I}_{s,m1}{\left(\frac{{T}_{s}}{{T}_{m1}}\right)}^{{\eta }_{Is}}\cdot \mathrm{exp}\left(\frac{{E}_{G}}{{k}_{B}}\cdot \left(\frac{1}{{T}_{m1}}-\frac{1}{{T}_{s}}\right)\right).$`

Is,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.

## Compatibility Considerations

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Behavior changed in R2019b

## References

[1] Aarts, A., N. D’Halleweyn, and R. Van Langevelde. “A Surface-Potential-Based High-Voltage Compact LDMOS Transistor Model.” IEEE Transactions on Electron Devices. 52(5):999 - 1007. June 2005.

[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.