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Message started by Patrick on Jan 5th, 2004, 7:18am

Title: MOS Id function needed (help, urgent)
Post by Patrick on Jan 5th, 2004, 7:18am

           Who know such a formula for MOS transistor saturation mode Id to Vgs. Generally the book only show us the square term. I think there should be also higher order terms, right? So who know the full representation? Thanks a lot

Title: Re: MOS Id function needed (help, urgent)
Post by Cao-Thong on Jan 20th, 2004, 4:26am


In strong inversion, the square function is correct
under long-channel assumption. You may want
to add velocity saturation term and also mobility
reduction depending on your bias conditions. In
weak inversion the equation is exponential but
it is hardly a region you can achieve at RF frequencies.
Lots of design uses the MOST in the moderate
inversion region.

You can find all these extension on Berkley Bsim4 model equations on their website or I can recommand you Yannis Tsividis book "Operationg and modeling of the MOS transistor". Let me know if you need more precision
or help.



Title: Re: MOS Id function needed (help, urgent)
Post by naren on May 20th, 2004, 3:55am

Can you give us more information?

Title: Re: MOS Id function needed (help, urgent)
Post by City on May 24th, 2004, 10:28am


what are you specifically looking at ?

Velocity saturation is modelled with a vsat parameter that saturates the current value but SHOULD NOT be understood as the saturation region of the MOSFET device.

Mobility reduction is that used to be modelled with a theta factor but which is different in BSIM. There are 3 factor in the BSIM model that are K1,K2,K3 if I correctly remember or you can look into the BSIM manual.

About the MOSTs, it is not always operating in the strong inversion region where it is square-law. You can size it to stay in the moderate / weak inversion region to depending on the W/L ratio. Moderate and strong inversion are more attractive due to the high gm/Id value, but the load capacitor usually discourage people to do so ... especially at RF freq. if you calculate the self loading vs the gm, it will give you one interesting design


Title: Re: MOS Id function needed (help, urgent)
Post by naren on May 24th, 2004, 10:45am

ok here is the problem I am facing...

my question is simple

I want a MOSFET whose gm=20mA/V or some value like that.

How would you find the Vgs and the even more irritating Vds?

I am talking only about the short channel MOSFETs here...

Let me describe the situation I am sure all pple face........I understand that for long channel

gm= SQUAREROOT(2*Un*Cox*W/L*Id)

hence based on power constraint we can choose Id of our choice and L and Un and Cox are all fixed and we want to design for a specific gm and hence knowing
gm,L,Un,Cox,Id we can find out our W very easily to very good approximation neglecting the channel length modulation.

Thus now since we know W and gm and Un and L

we can use

gm= Un*Cox*W/L*(VGS-Vth)
to find VGS and do our beautiful biasing....


if I want a certain gm value for a 0.18um mosfet can you tell me how will you find out what is the required Vgs and the problematic Vds which I dont even understand how can one possibly hope to set!!!!!!

this is my problem!!!

I wonder what is the technique that people use?

I saw the EECS240 berkeley video fully by prof.boser but even he says that we can get gm as a function of a so called V* or actually VDSAT.....but my question again to him would be what is relation between his V* or VDAST and VGS????

anyways.....i wonder what pple do!!!!

Title: Re: MOS Id function needed (help, urgent)
Post by City on May 25th, 2004, 5:26am


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

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 = (Vg-vto) /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.


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