MOSFET regions of operation

A MOSFET operates in one of three regions of operation depending on its terminal voltages. This note is the hub that ties them together; each region has its own detailed note.

Region	Condition	Behaviour
Cut-off	$V_{GS}<V_t$	No channel, $i_D=0$. Device off.
Triode	$V_{GS}>V_t$ and $V_{DS}<V_{OV}$	Channel formed end-to-end. Gate-controlled resistor.
Saturation	$V_{GS}>V_t$ and $V_{DS}\ge V_{OV}$	Channel pinched at drain. Voltage-controlled current source — used for amplification.

Here $V_t$ is the Threshold voltage and $V_{OV}=V_{GS}-V_t$ the Overdrive voltage.

How to identify the region

Two questions, in order:

1. Is $V_{GS}>V_t$? If no, the device is in cut-off — done, $i_D=0$. If yes, a channel exists; continue.
2. Is $V_{DS}\ge V_{OV}$? If yes, the channel is pinched off at the drain (Channel pinch-off) and the device is in saturation — use the MOSFET square-law $i_D=\frac{1}{2}{k}_n{V}_{OV}^2$. If no, the channel is still continuous and the device is in triode — use $i_D=k_n[V_{OV}{V}_{DS}-V_{DS}^2/2]$.

This is also the practical DC-analysis recipe: in MOSFET DC analysis you assume saturation, solve, then check whether $V_{DS}\ge V_{OV}$ actually holds; if it does not, redo the analysis in triode.

$i_D$ vs $v_{DS}$ for one $V_{GS}$: triode below $V_{OV}$, saturation above.

Regions of the enhancement n-MOSFET: cut-off, triode, saturation.

The p-MOSFET: same three regions, via magnitudes

A p-MOSFET has the same three regions, but all the controlling voltages — $V_{GS}$, $V_{DS}$, $V_t$ — are negative. Rather than juggle signs, work in magnitudes:

• Cut-off: $|V_{GS}|<|V_{tp}|$.
• Triode: $|V_{GS}|>|V_{tp}|$ and $|V_{DS}|<|V_{OV}|$.
• Saturation: $|V_{GS}|>|V_{tp}|$ and $|V_{DS}|\ge |V_{OV}|$.

with $V_{tp}<0$ the p-MOSFET threshold and $|V_{OV}|=|V_{GS}|-|V_{tp}|$. The physics is the mirror image of the n-MOSFET: holes instead of electrons, n-substrate instead of p, and a negative gate voltage to turn it on.

p-MOSFET regions — same three, inverted polarities ($V_{GS},V_{DS},V_t$ negative).