The equation if an n-MOST with Vsb lower than 0

-Vsb on an n-MOST

Hi,
I came up with this problem and I would appreciate some guidance;

Suppose we have an n-MOST with Vgb>0, Vds>0 kai Vsb<0
Can someone decribe the equations for this n-MOST?
D.

Re: -Vsb on an n-MOST

Hi dkace
With these conditions you described, there is no difference in usual I-V equations, except that Vth should be changed with its new value (threshold voltage would be less than Vt0, i.e., the threshold voltage when vsb=0).

Vth = Vt0 + γ(sqrt(|2ΦF|+Vsb)-sqrt(|2ΦF|))
where γ is the body-effect coefficient and depends on physical parameters. It is obvious that if Vsb<0 then Vth<Vt0

Actually, that's a common method in low-voltage applications. One can bias the body terminal with a suitable voltage to reduce the Vth to the desired value. However, this reduction of Vth usually leads to more leakage current, which is not desirable in some cases especially in digital applications where there are sometimes millions of transistors on the same chip.
At last but not the least, the body terminal is very precious in low-voltage applications. There are other techniques as well which use this terminal for modulating the Vth, such as CDB (Current Driven Bulk) method.

Regards,
EZT

Re: -Vsb on an n-MOST

I new this equation and that is why I asked. If you get Vsb<0, then Vsb-φ0 <0, therefore we obtain negative square root parameter. How do we deal with this? I know - in general - the coditions for bias the body in orderto obtain better behavior ( back gate etc).
But what happens with true equations that describe it?

D.

Re: -Vsb on an n-MOST

Dear dkace
I'm not sure if we are talking about the same region of operation!
If -|2ΦF|<Vsb<0 then the value of (|2ΦF|+Vsb) would be positive while Vsb is negative and square root is valid so those previous relations are correct in this interval. But if Vsb<-|2ΦF| then the PN-junction diode of source/bulk becomes forward-biased and a large leakage current would source (in case of nMOS) from bulk to the channel. This is almost always bad! Hence, even in special applications which bulk-signaling is utilized, careful simulation should be done to make sure that the circuit never enters that region (even in worst PVT corners).
If you need the relations suitable for Vsb<-|2ΦF|, I think there's an exponential relation between Vsb and current. Since the leakage current would dominate other components of total current. But I'm not sure about the relation of Vth (threshold voltage). I'm sure you will find more information in textbooks on solid-state (semiconductor) devices, e.g. the book by Sze which is availabe in this website.

Regards,
EZT