MOSFET Operation Formulas

NMOS

Subthreshold

\( I_D = I_0 \cdot e^{\frac{V_{GS} - V_{th}}{n \cdot V_T}} \cdot (1 - e^{-\frac{V_{DS}}{S \cdot V_T}}) \cdot (1 + \lambda \cdot V_{DS}) \)

Saturation

\( I_D = \frac{1}{2} \cdot \mu_n \cdot C_{ox} \cdot \frac{W}{L} \cdot (V_{GS} - V_{th})^2 \cdot (1 + \lambda \cdot V_{DS}) \)

Condition: \( V_{DS} \geq V_{GS} - V_{th} \)

Linear

\( I_D = \mu_n \cdot C_{ox} \cdot \frac{W}{L} \cdot ((V_{GS} - V_{th})V_{DS} - \frac{V_{DS}^2}{2}) \cdot (1 + \lambda \cdot V_{DS}) \)

Condition: \( V_{DS} < V_{GS} - V_{th} \)

PMOS

Subthreshold

\( I_D = -I_0 \cdot e^{\frac{V_{SG} - |V_{th}|}{n \cdot V_T}} \cdot (1 - e^{-\frac{V_{SD}}{S \cdot V_T}}) \cdot (1 + \lambda \cdot V_{SD}) \)

Saturation

\( I_D = -\frac{1}{2} \cdot \mu_p \cdot C_{ox} \cdot \frac{W}{L} \cdot (V_{SG} - |V_{th}|)^2 \cdot (1 + \lambda \cdot V_{SD}) \)

Condition: \( V_{SD} \geq V_{SG} - |V_{th}| \)

Linear

\( I_D = -\mu_p \cdot C_{ox} \cdot \frac{W}{L} \cdot ((V_{SG} - |V_{th}|)V_{SD} - \frac{V_{SD}^2}{2}) \cdot (1 + \lambda \cdot V_{SD}) \)

Condition: \( V_{SD} < V_{SG} - |V_{th}| \)

Parameters Definition

\( \mu_n \) and \( \mu_p \)

Electron and hole mobility, respectively. Dictate carrier speed.

\( C_{ox} \)

Oxide capacitance per unit area. Influences charge storage.

\( W \) and \( L \)

Channel width and length. Impact device characteristics.

\( V_{th} \)

Threshold voltage. Minimum \( V_{GS} \) or \( V_{SG} \) for conduction.

\( \lambda \)

Channel-length modulation parameter. Affects drain current.

\( n \) and \( S \)

Subthreshold swing coefficient and slope. Impact subthreshold current.

\( V_T \)

Thermal voltage, approx. 26mV at room temperature.

\( I_0 \)

Reverse saturation current. Sets subthreshold current scale.