What does it mean “the channel is pinched off”?

For a MOSFET when VGS is greater than Vt, a channel is induced. As we increase VDS current starts flowing from Drain to Source (triode region). When we further increase VDS, till the voltage between gate and channel at the drain end to become Vt, i.e. VGS – VDS = Vt, the channel depth at Drain end decreases almost to zero, and the channel is said to be pinched off. This is where a MOSFET enters saturation region.

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