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Why does vth vary with length?

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twlin1

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Why vth varies with length ?
Can someone provide me papers or references on it?
Thanks in advance.
 

vth vs. length

threshold does not depend on the length . This is a quite general statement given in literature but if we keep on reducing the length than it will change . This change can be observed for both length and width.

please see the ieee site
 

Re: vth vs Length

Eq (1) states that the threshold voltage is only a function of the manufacturing technology and the applied body bias VSB. The threshold can therefore be considered as a constant over all NMOS (PMOS) transistors in a design. As the device dimensions are reduced, this model becomes inaccurate, and the threshold potential becomes a function of L, W, and VDS. Two-dimensional second-order effects that were ignorable for long-channel devices suddenly become significant.
In the traditional derivation of the VTO, for instance, it is assumed that the channel depletion region is solely due to the applied gate voltage and that all depletion charge beneath the gate originates from the MOS field effects. This ignores the depletion regions of the source and reverse-biased drain junction, which become relatively more important with shrinking channel lengths. Since a part of the region below the gate is already depleted (by the source and drain fields), a smaller threshold voltage suffices to cause strong inversion. In other words, VT0 decreases with L for short-channel devices.
 
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    jdp721

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Re: vth vs Length

Threshold voltage:

It increases as Length decreases ( this is known as short channel effect )

As length further decreases, vth decreases ( reverse short-channel effect )

This is technology dependent. You can simply sweep length ( keeping w/l const. ) and check vth
 

    twlin1

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