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It is a simple question but I could not find a straightforward answer.

When a MOSFET enters saturation region, the channel length starts to decrease, and the channel width is the smallest near the drain (assuming conventional current flow from drain to source). This smaller channel width causes the current density to increase, and hence a strong electric field now exists between the thinner end of the channel and the drain.

This strong electric field can assist the motion of charge carriers and hence enable conduction. But is this electric field the only factor that supports conduction in the saturation region? If so, how does this conduction almost without the presence of a channel (for a small distance) not increase the on-state resistance?

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