Model P-Channel LDMOS or VDMOS transistors suitable for high voltage

Semiconductor Devices

The P-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

For information on physical background and defining equations, see the N-Channel LDMOS FET block reference page. Both the p-type and n-type versions of the LDMOS model use the same underlying code with appropriate voltage transformations, to account for the different device types.

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.

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:

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

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

The default behavior is that dependence on temperature is not
modeled, and the device is simulated at the temperature for which
you provide block parameters. To model the dependence on temperature
during simulation, select `Model temperature dependence`

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

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 *T*_{m1} at
which the other device parameters have been extracted. The **Temperature
Dependence** tab provides the simulation temperature, *T*_{s},
and the temperature-scaling coefficients for the other device parameters.
For more information, see Temperature Dependence Tab.

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

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

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.

**Gain, [channel drift_region]**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*I*_{D}–*V*_{DS}characteristic. The values of both elements must be greater than 0. The default value is`[11.6, 0.01]`

A/V^{2}.**Flatband voltage, [channel drift_region]**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 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 2

*ϕ*_{B}is the surface potential at strong inversion and*γ*is the body factor, both at the channel region.**Body factor, [channel drift_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. The default value is`[3.4, 2.5]`

V^{1/2}.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

*N*_{A}is replaced by the doping density,*N*_{D}. 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.**Surface potential at strong inversion, [channel drift_region]**The 2

*ϕ*_{B}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 default value is`[0.95, 0.95]`

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

**Velocity saturation factor, [channel drift_region]**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. 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.**Drift region surface scattering factor**Surface scattering factor,

*θ*_{surf}, 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 default value is`0`

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

*G*_{ΔL}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.**Channel-length modulation voltage**The voltage

*V*_{p}in the*G*_{ΔL}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. The default value is`50`

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

*I*_{D}–*V*_{DS}characteristic. This parameter applies both to the channel and drift regions. The expected range for this parameter value is between 2 and 8. The default value is`8`

.**Measurement temperature**Temperature

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

°C.

**Source ohmic resistance**The transistor source resistance, that is, the series resistance associated with the source contact. The default value is

`1e-4`

Ω. The value must be greater than or equal to`0`

.**Drain ohmic resistance**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 default value is

`0.07`

Ω. The value must be greater than or equal to`0`

.**Gate ohmic resistance**The transistor gate resistance, that is, the series resistance associated with the gate contact. The default value is

`8.4`

Ω. The value must be greater than or equal to`0`

.**Drift region low-bias resistance for gated region**Resistance

*R*_{D}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. The default value is`0.1`

Ω. The value must be greater than or equal to`0`

.**Drift region depletion layer thickness factor**Parameter

*λ*_{D}in the drain-current equation. It is the ratio of vertical depths*y*_{1}and*y*_{2}at zero bias, where*y*_{1}represents the space-charge region and*y*_{2}represents the undepleted part of the drift region. See the N-Channel LDMOS FET block reference page for an illustration. The default value is`0.2`

.

**Oxide capacitance**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 default value is

`[1600.0, 1000.0]`

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

`15`

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

`15`

pF.

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

*I*_{s}symbol in the body-diode equations. The default value is`1e-13`

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

*V*_{bi}symbol in the body-diode equations. The default value is`0.6`

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

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

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

*C*_{j0}symbol in the body-diode equations. The default value is`1800`

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

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

ns.

**Parameterization**Select one of the following methods for temperature dependence parameterization:

`None — Simulate at parameter measurement temperature`

— Temperature dependence is not modeled. This is the default method.`Model temperature dependence`

— Model temperature-dependent effects. Provide a value for the device simulation temperature,*T*_{s}, and the temperature-scaling coefficients for other block parameters.

**Device simulation temperature**Temperature

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

°C.**Gain temperature exponent, [channel drift_region]**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*=*β*_{m1}(*T*_{m1}/*T*_{s})^*η*_{β}.*β*_{m1}is the value of the channel or drift region gain, as specified by the**Gain, [channel drift_region]**parameter from the**Main**tab.*η*_{β}is the corresponding element of the**Gain temperature exponent, [channel drift_region]**parameter. The default value is`[1.3, 1.3]`

.**Flatband voltage temperature coefficient, [channel drift_region]**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,

*V*_{FB}, is assumed to scale linearly with temperature,*V*_{FB}=*V*_{FBm1}+ (*T*_{s}–*T*_{m1})*S*_{T,VFB}.*V*_{FBm1}is the value of the channel or drift region flatband voltage, as specified by the**Flatband voltage, [channel drift_region]**parameter from the**Main**tab.*S*_{T,VFB}is the corresponding element of the**Flatband voltage temperature coefficient, [channel drift_region]**parameter. The default value is`[0.0005, 0.0005]`

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

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

V/K.**Velocity saturation temperature exponent, [channel drift_region]**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,

*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 channel or drift region velocity saturation factor, as specified by the**Velocity saturation factor, [channel drift_region]**parameter from the**Main**tab.*η*_{θ}is the corresponding element of the**Velocity saturation temperature exponent, [channel drift_region]**parameter. The default value is`[1.04, 1.04]`

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

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

.**Drift region low-bias resistance temperature exponent for gated portion**Resistance

*R*_{D}, 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 default value is`0.95`

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

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

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

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

The block has the following ports:

`G`

Electrical conserving port associated with the transistor gate terminal

`D`

Electrical conserving port associated with the transistor drain terminal

`S`

Electrical conserving port associated with the transistor source terminal

[1] 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.

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