PMOS Capacitor

P-type metal-oxide-semiconductor capacitor

Since R2024b

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Libraries:
Simscape / Electrical / Semiconductors & Converters

Description

The PMOS Capacitor block represents a P-type metal-oxide-semiconductor (PMOS) capacitor. You can parameterize this block by using MOS equation parameters or parameterize the values as a function of temperature and voltage by using a tabulated capacitance lookup table.

This figure shows the elements that comprise a MOS capacitor:

The PMOS Capacitor block uses an N-type bulk semiconductor.

Equation-Based Model

When you set the Capacitor model parameter to Fundamental nonlinear equations, the PMOS Capacitor block operates in three operating modes depending on the values of the gate-bulk voltage, Vgb, the flat-band voltage, Vfb, and the threshold voltage, Vth:

• $$V_{gb}>V_{fb}$$ — Accumulation mode. The voltage on the metal plate accumulates the majority charge carriers, or the electrons, of the bulk material on the surface of the semiconductor.

• $$V_{th}<V_{gb}\le V_{fb}$$ — Depletion mode. The voltage induces the minority charge carriers, or the holes, and creates a depletion region at the surface.

• $$V_{gb}\le V_{th}$$ — Inversion mode. The majority carrier type at the surface of the semiconductor is inverted.

To calculate the flat-band voltage, the block uses this equation:

$$V_{fb}=V_{th}+\phi +\gamma \sqrt{\phi },$$

where γ is the body factor and φ is the surface potential.

The block adjusts the value of the surface potential φ by using the equation

$$\phi \left(T_{sim}\right)=\frac{k{T}_{sim}}{q}\log {\left(\frac{T_{meas}}{T_{sim}}\right)}^3+\frac{T_{sim}}{T_{meas}}\phi \left(T_{meas}\right)+EG\left(1-\frac{T_{sim}}{T_{meas}}\right),$$

where:

• T_sim is the value of the Device simulation temperature parameter, in Kelvin.

• T_meas is the value of the Measurement temperature parameter, in Kelvin.

• EG is the value of the Band-gap energy parameter, in electron-volts. The block assumes this parameter is temperature independent.

• q is the electron charge, in Coulomb, and is equal to 1.60217663e-19 C.

• k is equal to 1.380649e-23 J/K.

This equation defines the total gate charge of the capacitor, QG,

$$Q_G=-\left(Q_{acc}+Q_{dep}+Q_{inv}\right),$$

where:

• Q_acc is the accumulation charge that the majority charge carriers form.

• Q_dep is the depletion region charge within the semiconductor layer.

• Q_inv is the inversion charge that the minority charge carriers form.

Accumulation Mode

When the gate-bulk voltage is greater than the flat-band voltage, the block enters the accumulation operating mode. In accumulation mode, the majority carriers accumulate on the surface of the semiconductor. The block calculates the accumulation, depletion, and inversion charges by using these equations:

$$\begin{array}{l}{Q}_{acc}=-C_{ox}\cdot \left(V_{gb}-V_{fb}\right)\\ Q_{dep}=0\\ Q_{inv}=0\end{array}$$

where C_ox is the total oxide capacitance.

Depletion Mode

When the gate-bulk voltage is less than or equal to the flat-band voltage and greater than the threshold gate voltage, the block enters the depletion operating mode. In depletion mode, the minority carriers stack on the surface of the semiconductor. The block calculates the accumulation, depletion, and inversion charges by using these equations:

$$\begin{array}{l}{Q}_{acc}=0\\ Q_{dep}=\frac{C_{ox}{\gamma }^2}{2}\left(\sqrt{1-\frac{4\left(V_{gb}-V_{fb}\right)}{{\gamma }^2}}-1\right)\\ Q_{inv}=0\end{array}$$

where C_ox is the total oxide capacitance and γ is the body factor.

Inversion Mode

When the gate-bulk voltage is less than or equal to the threshold gate voltage, the block enters the inversion operating mode. In inversion mode, the majority carrier type at the surface of the semiconductor is inverted. The block calculates the accumulation, depletion, and inversion charges by using these equations:

$$\begin{array}{l}{Q}_{acc}=0\\ Q_{dep}=\left\{\begin{array}{cc}\frac{C_{ox}{\gamma }^2}{2}\left(\sqrt{1-\frac{4\left(V_{th}-V_{fb}\right)}{{\gamma }^2}}-1\right)& \text{if you clear }Modelhigh-frequencyC-Vbehavioratstronginversion\\ \frac{C_{ox}{\gamma }^2}{2}\left(\sqrt{1-\frac{4\left(V_{th}-V_{fb}\right)}{{\gamma }^2}}-1\right)-\frac{1}{\frac{1}{C_{ox}}+\frac{1}{C_{dep}}}\left(V_{gb}-V_{th}\right)& \text{if you select }Modelhigh-frequencyC-Vbehavioratstronginversion\end{array}\right\}\\ Q_{inv}=\left\{\begin{array}{cc}-C_{ox}\cdot \left(V_{gb}-V_{th}\right)& \text{if you clear }Modelhigh-frequencyC-Vbehavioratstronginversion\\ 0& \text{if you select }Modelhigh-frequencyC-Vbehavioratstronginversion\end{array}\right\}\end{array}$$

where C_ox is the total oxide capacitance, γ is the body factor, and C_dep is the depletion capacitance.

If you select the Model high-frequency C-V behavior at strong inversion parameter, the block assumes that the minority carriers do not have enough time to react to the change in the applied voltage. Consequently, the inversion charge, Q_inv is zero and the applied voltage drops across the oxide capacitance and the depletion region capacitance.

If you clear the Model high-frequency C-V behavior at strong inversion parameter, the block instead assumes that the minority carriers have enough time to quickly respond to the change in the voltage and form the inversion layer charge beneath the oxide layer of the MOS capacitor.

Tabulated Model

When you set the Capacitor model parameter to Lookup table (2-D, temperature dependent), the PMOS Capacitor block tabulates the total gate charge of the capacitor, QG, in terms of voltage and temperature. To parameterize the block parameters as a function of temperature and voltage by using a tabulated capacitance lookup table, specify the Gate-bulk capacitance lookup table, Cgb(T,Vgb), Gate-bulk voltage, Vgb, and Temperature, T parameters.

If you specify only one value in the Temperature, T parameter, the C-V characteristics of the capacitor become temperature independent.

To ensure the gate charge conservation over one full AC cycle, the block converts the Gate-bulk capacitance lookup table, Cgb(T,Vgb) parameter to an equivalent charge lookup table. The block uses this equivalent charge table to calculate the variations in the gate charge, Q_g, with respect to the voltage by using linear interpolation and extrapolation methods.

Variables

To set the priority and initial target values for the block variables before simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Use nominal values to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources. One of these sources is the Nominal Values section in the block dialog box or Property Inspector. For more information, see System Scaling by Nominal Values.

Ports

Conserving

G — Gate terminal

electrical

Electrical conserving port associated with the gate terminal of the NMOS capacitor.

B — Bulk terminal

electrical

Electrical conserving port associated with the bulk terminal of the NMOS capacitor.

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Main

Capacitor model — Parameterization option for capacitor

Fundamental nonlinear equations (default) | Lookup table (2-D, temperature dependent)

Parameterization option for the capacitor. To specify the equation parameters directly, set this parameter to Fundamental nonlinear equations. To manually tabulate the C-V characteristics, set this parameter to Lookup table (2-D, temperature dependent).

Gate-bulk capacitance lookup table, Cgb(T,Vgb) — Lookup table for gate-bulk capacitance

[3.4574, 3.4541, 3.4407, 3.4274, 3.404, 3.374, 3.3339, 3.2938, 3.227, 3.1402, 3.0467, 2.9332, 2.8063, 2.6828, 2.5426, 2.3255, 2.0985, 1.7679, 1.5576, 1.2671, .9466, .6895, .4691, .2688, .182, .1386, .1152, .1085, .0952, .0851, .08, .0785, .0751, .0751, .0751] nF (default) | vector or matrix of positive entries

Lookup table for the gate-bulk capacitance, specified as a function of the temperature and the gate-bulk voltage. The number of rows must be equal to the number of elements of the Temperature, T parameter. The number of columns must be equal to the number of elements of the Gate-bulk voltage, Vgb parameter.

Dependencies

To enable this parameter, set Capacitor model to Lookup table (2-D, temperature dependent).

Temperature, T — Temperature for gate-bulk capacitance lookup table

25 degC (default) | scalar | vector

Temperature for the gate-bulk capacitance lookup table.

Dependencies

To enable this parameter, set Capacitor model to Lookup table (2-D, temperature dependent).

Gate-bulk voltage, Vgb — Gate-bulk voltage

[.9897, .7165, .3995, .201, .0851, -.0309, -.134, -.2216, -.3015, -.4021, -.5, -.6082, -.6804, -.7268, -.7706, -.8093, -.8428, -.8686, -.9149, -.9536, -1.0077, -1.0567, -1.1031, -1.1624, -1.2526, -1.3608, -1.4948, -1.6701, -1.8402, -2.0464, -2.2887, -2.5052, -2.7216, -2.8711, -2.9897] V (default) | vector

Gate-bulk voltage. The elements of this vector must be in strictly descending order.

Dependencies

To enable this parameter, set Capacitor model to Lookup table (2-D, temperature dependent).

Semiconductor Material Parameters

Oxide capacitance, Cox — Total oxide capacitance of capacitor

345.31 nF (default) | positive scalar

Total oxide capacitance of the capacitor.

Dependencies

To enable this parameter, set Capacitor model to Fundamental nonlinear equations.

Band-gap energy, EG — Energy of band gap

1.12 eV (default) | scalar

Energy of the band gap. Set this parameter to a value appropriate for the material of the semiconductor in the capacitor.

Dependencies

To enable this parameter, set Capacitor model to Fundamental nonlinear equations.

Threshold voltage, Vth — Threshold gate voltage for inversion mode

-1.0222 V (default) | scalar

Threshold gate voltage. If the gate-to-bulk voltage is less than or equal to the value of this parameter, the PMOS capacitor enters inversion mode.

Dependencies

To enable this parameter, set Capacitor model to Fundamental nonlinear equations.

Surface potential, phib — Surface potential

0.9115 V (default) | positive scalar

Semiconductor surface potential at which the surface minority carrier concentration is equal to the bulk majority carrier concentration. The block transitions between the depletion and inversion modes at this value.

Dependencies

To enable this parameter, set Capacitor model to Fundamental nonlinear equations.

Body factor, gamma — Body effect parameter

1.1798 V^(1/2) (default) | positive scalar

Body effect parameter, which relates the threshold voltage, Vth, to the flat-band voltage.

Dependencies

To enable this parameter, set Capacitor model to Fundamental nonlinear equations.

Model high-frequency C-V behavior for strong inversion — Option to model high-frequency C-V behavior for strong inversion mode

off (default) | on

Option to model the high-frequency C-V behavior for strong inversion mode. If you clear this parameter, the block assumes that the minority carriers can quickly respond to the change in voltage and an inversion layer charge forms beneath the oxide. Otherwise, the block assumes that the minority carriers do not have enough time to quickly respond to the change in the voltage and form the inversion layer charge beneath the oxide layer of the MOS capacitor.

Dependencies

To enable this parameter, set Capacitor model to Fundamental nonlinear equations.

Measurement temperature — Temperature at which block quotes parameters

25 degC (default) | positive scalar

Temperature at which the block quotes the parameters.

Dependencies

To enable this parameter, set Capacitor model to Fundamental nonlinear equations.

Temperature Dependence

Parameterization — Option to specify simulation temperature of device

None - Simulate at parameter measurement temperature (default) | Model temperature dependence

Option to specify the simulation temperature of the device.

If you set this parameter to None - Simulate at parameter measurement temperature and Capacitor model to Lookup table (2-D, temperature dependent), the block uses a simulation temperature of 25 degC.

Device simulation temperature — Temperature at which to simulate device

25 degC (default) | positive scalar

Temperature at which to simulate the device.

Dependencies

To enable this parameter, set one of these options:

• Capacitor model to Fundamental nonlinear equations and Parameterization to Model temperature dependence.

• Capacitor model to Lookup table (2-D, temperature dependent).

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2024b