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# Relation between leakage current and threshold voltage (Vt)

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##### Member level 2
Hi,

I would like to know what is the relation between leakage current and threshold voltage ?

In FinFET technology, I was reading that the gate wraps around the drain and source because of which the channel is in control, and very less leakage current flows when the device is in off state, leading to lower threshold voltage (Vt) and hence lower operating voltage.

So when the leakage current is less, why do we need a lower Vt ?

Thanks,

and drive current (IDsat). What that "best" is, is a foundry
judgment call. Lower VT makes square-law improvement in
IDsat but an exponential worsening of Ioff. There is some
range of "sweet spot" but your application might put you
to one end or the other, digital / analog / RF or drive you
to make multiple VT options.

Just to put a little more theory to this discussion -

in the subthreshold region, source/drain current in a MOSFET is described by the following functional relationship with threshold voltage Vt:

Ids ~ exp[e(Vg-Vt)/(mkT)] = exp[(Vg-Vt)/(mkT/e)]

where e is electron charge, Vg is the gate voltage, Vt is the threshold voltage, k is the Boltzmann's constant, T is the absolute temperature, and m is the body effect coefficient (dimensionless constant usually larger than 1.0, more specifically - m=1+Cdm/Cox; devices with m value below 1.0, also called as having a steep sub-threshold slope, are a subject of intense research in the recent and coming years).

"Better electrostatic control" of the gate over the channel means smaller value of m.
For smaller value of m (a derivative of this parameter - S=2.3*(kT/e)*m - is called subthreshold slope), you can allow for a lower Vt by keeping the leakage current (Ids) the same. And lower Vt will allow you a higher saturation current (current at high Vg, above Vt).

Hope this explanation helps to understand the relationship between Vt, subthreshold slope, and leakage current - from the theory / physics viewpoint...

All these formulas, and more, can be found in any textbook on MOSFET or semiconductor device physics - Sze, Taur and Ning, etc.

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