NMOS Capacitor

N-type metal-oxide-semiconductor capacitor

Since R2024b

Libraries:
Simscape / Electrical / Semiconductors & Converters

Description

The NMOS Capacitor block represents an N-type metal-oxide-semiconductor (NMOS) 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:

Schematic of a MOS capacitor. The top element is the gate, the middle element is the oxide component, the bottom element is the semiconductor.

The NMOS Capacitor block uses a P-type bulk semiconductor.

Equation-Based Model

When you set the Capacitor model parameter to Fundamental nonlinear equations, the NMOS Capacitor block operates in three operating modes depending on the gate-bulk voltage, V_gb, the flat-band voltage, V_fb, and the threshold voltage, V_th:

$V_{g b} < V_{f b}$ — Accumulation mode. The voltage on the metal plate accumulates the majority charge carriers, or the holes, of the bulk material on the surface of the semiconductor.
$V_{f b} \leq V_{g b} < V_{t h}$ — Depletion mode. The applied voltage induces the minority charge carriers, or the electrons, and creates a depletion region at the surface.
$V_{g b} \geq V_{t h}$ — 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:

$V_{f b} = V_{t h} - φ - γ \sqrt{φ},$

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

$φ (T_{s i m}) = \frac{k T_{s i m}}{q} \log {(\frac{T_{m e a s}}{T_{s i m}})}^{3} + \frac{T_{s i m}}{T_{m e a s}} φ (T_{m e a s}) + E G (1 - \frac{T_{s i m}}{T_{m e a s}}),$

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, Q_G,

$Q_{G} = - (Q_{a c c} + Q_{d e p} + Q_{i n v}),$

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 less 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:

$\begin{array}{l} Q_{a c c} = - C_{o x} \cdot (V_{g b} - V_{f b}) \\ Q_{d e p} = 0 \\ Q_{i n v} = 0 \end{array}$

where C_ox is the total oxide capacitance.

Depletion Mode

When the gate-bulk voltage is less than the threshold gate voltage and greater than or equal to the flat-band 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:

$\begin{array}{l} Q_{a c c} = 0 \\ Q_{d e p} = \frac{C_{o x} γ^{2}}{2} (1 - \sqrt{1 + \frac{4 (V_{g b} - V_{f b})}{γ^{2}}}) \\ Q_{i n v} = 0 \end{array}$

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

Inversion Mode

When the gate-bulk voltage is greater 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:

$\begin{array}{l} Q_{a c c} = 0 \\ Q_{d e p} = {\begin{matrix} \frac{C_{o x} γ^{2}}{2} (1 - \sqrt{1 + \frac{4 (V_{t h} - V_{f b})}{γ^{2}}}) & i f y o u c l e a r M o d e l h i g h - f r e q u e n c y C - V b e h a v i o r a t s t r o n g i n v e r s i o n \\ \frac{C_{o x} γ^{2}}{2} (1 - \sqrt{1 + \frac{4 (V_{t h} - V_{f b})}{γ^{2}}}) - C_{G B, t h} \cdot (V_{g b} - V_{t h}) & if you select M o d e l h i g h - f r e q u e n c y C - V b e h a v i o r a t s t r o n g i n v e r s i o n \end{matrix}} \\ Q_{i n v} = {\begin{matrix} - C_{o x} \cdot (V_{g b} - V_{t h}) & if you clear M o d e l h i g h - f r e q u e n c y C - V b e h a v i o r a t s t r o n g i n v e r s i o n \\ 0 & if you select M o d e l h i g h - f r e q u e n c y C - V b e h a v i o r a t s t r o n g i n v e r s i o n \end{matrix}} \end{array}$

where C_ox is the total oxide capacitance, γ is the body factor, and $C_{G B, t h} = \frac{C_{o x}}{1 + \frac{C_{o x}}{C_{d e p}}} = \frac{C_{o x} C_{d e p}}{C_{o x} + C_{d e p}}$ is the gate-bulk capacitance at the inversion threshold, which is equivalent to C_ox and C_dep in series. C_dep is the depletion layer 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 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 NMOS Capacitor block tabulates the total gate charge of the capacitor, Q_G, 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

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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

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

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

Dependencies

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