City
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Naren,
just a few comment. Because you are looking at a particular vgs, I assume you want to fix the DC of gate of your MOS transistor, hence do a voltage polarization to control the gm, which I believe is not the correct way in a IC environnement for many reasons: even if you calculate the correct vgs, process variations will completley change your Gm value. Second temperature will also affect the Gm so the voltage polarization will not be robust enough. I suggest that you do replica biasing instead.
Do answer your question (I am doing RF analog design in a 90nm CMOS process), it is possible to calculate the required vgs for a given process case and temperature.
(I will suppose that you have all of the bsim parameter available)
First you have to determine a good approximation of Vth which will be affected by the short channel effect (we will try to neglect the polydepletion effects to) your mobility term is given by U0*f(vgs) where f(vgs)=1/(1+UA+UC*VBseff*((Vgsteff+2Vth/Toxe))+UB*((Vgsteff+2*Vth/Toxe))^2)
if you have no backgate modulation the term UC can be removed. You will see that ploting the mobility against vgsteff will give you a good guess of how much the mobility factor will be reduced. (can be around 0.8 to 0.7 for reasonnable vgsteff values)
Then velocity saturation may also occur for a 0.18um process.
You have Esat=2*Vsat/effectivemobility=2*Vsat/((f(vgs)*U0)) and an approximation you can use in S.I. is Ids=Ids0*1/(1+Vdseff/(Leff*Esat)). If you plot Ids/Ids0=1/(1+Vdseff/(Leff*Esat)) you will also have a good guess of the drain current dependance on the Vdseff.
Now you must combine both effect in the drain current expression. To obtain the Gm you have to do the derivative of Id against Vgs. If you approximate Esat as constant then Gm will be reduced by the same factor than Ids/Ids0. The only complication results in the mobility dependance with Vgs. The results explains why Gm tends to become a constant with downscaling.
Now for Vds, I believe you should not worry to much about it. If you use the square law then I believe you implicitely assumes that it is saturated i.e. Id=f(Vdssat) Vdssat is principally a function of Vgs, Vth. (EKV model uses for example Vdssat = (Vgvto) /n in S.I sat.)
But before I go deeper into all this, let me know if it this the answers you are looking for.
City
