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We know that an almost constant current flows in mosfet when it saturates and the channel is pinched off.If this happens then why doesnt the current flows in a MOSFET even when the gate voltage is below the threshold voltage?? After all both the cases seem to have the same thing i.e. no channel for electrons to flow. Also,suppose that the threshold voltage is 0.6V and the applied gate voltage is 5V and then we slowly increase the drain voltage to a value such that it saturates.Now if slowly increasing the drain voltage we suddenly put it to a value much greater than saturation, then will this case be any different from the first case?

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Take a look at how the MOSFET conducts. Essentially, as you add the gate voltage, you are accumulating more and more holes to aid in the conduction. Less voltage means less holes, but never 0. This is important in that there will always be SOME conduction, but the construction of the MOSFET plays a huge role in how much is allowed through. Subsequently, adding a large voltage all of a sudden means more holes. Assuming you haven't destroyed the device, the conduction again depends on construction.

MOSFET illustration

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