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reverse short channel effect

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vaidhyanathan

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I read in article that
"At short channel lengths the halo doping of the source overlaps that of the drain, increasing the average channel doping concentration, and thus increasing the threshold voltage. This increased threshold voltage requires a larger gate voltage for channel inversion. However, as channel length is increased, the halo doped regions become separated and the doping mid-channel approaches a lower background level dictated by the body doping. This reduction in average channel doping concentration means Vth initially is reduced as channel length increases, but approaches a constant value independent of channel length for large enough lengths."
please explain me how the threshold value Vth varies with channel doping concentration?
 

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