Channel pinch-off

Channel pinch-off is the condition where the MOSFET channel thins to zero at the drain end. It is the boundary between the MOSFET triode region (channel continuous end-to-end) and the MOSFET saturation region (channel pinched at the drain). It occurs exactly when

$V_{DS}=V_{OV}$

where $V_{DS}$ is the drain-to-source voltage and $V_{OV}=V_{GS}-V_t$ the Overdrive voltage.

Why the drain end thins

What holds charge in the channel at any point is the gate-to-local-channel voltage. At the source end the channel is at (roughly) the source potential, so the gate sees the full $V_{GS}$ and the channel is at its thickest. Moving toward the drain, the channel potential climbs (current flowing through the channel’s resistance produces an IR rise), so the gate-to-channel voltage shrinks along the length. The channel is therefore tapered: fat at the source, thin at the drain.

Raise $V_{DS}$ and the drain end keeps thinning. When the drain-end channel voltage reaches $V_{OV}$, the gate-to-channel voltage there has dropped to exactly $V_t$ — the bare minimum to sustain inversion — so the channel charge at the drain end goes to zero. The channel has just pinched off. Equivalently, in terms of the gate-to-drain voltage, pinch-off is the point where $V_{GD}=V_t$, which rearranges to $V_{DS}=V_{GS}-V_t=V_{OV}$.

Pinch-off at $V_{DS}=V_{OV}$ — channel full at source, zero at drain.

What happens past pinch-off

Increasing $V_{DS}$ beyond $V_{OV}$ does not collapse the device — the channel is still fully formed near the source, where the current is set. The extra voltage $V_{DS}-V_{OV}$ drops across the narrow depletion region between the pinch-off point and the drain, and the strong field there sweeps electrons that reach the pinch-off point the rest of the way to the drain. Because the current is fixed by the still-intact source end, it becomes nearly independent of $V_{DS}$: this is the MOSFET saturation region and the MOSFET square-law.

A second-order effect: as $V_{DS}$ rises further, the pinch-off point moves slightly back toward the source, shortening the effective channel and nudging the current up a little. That is Channel-length modulation, the reason a real MOSFET has a finite output resistance in saturation rather than a perfectly flat current.