Is there a way to link the “Gain Factor in Saturation” a.k.a. "beff" to gm/Id method?

[melkord]

One of the equations that describe my circuit has the term \mu_{0}*C_{ox}*W/L.

I found out in Cadence that ID in saturation follow exactly this equation:
ID = 0.5 * beff * vgt^2.

So I assume beff = \mu_{0}*C_{ox}*W/L.

Now, I want to characterize beff of the device by using gm/Id method that I have been using.
For the device parameter extraction, I varied L and VGS.
So far, this work just fine to predict gm, rds, fT.

However, I tried to record the beff using the same method, but I got the wrong result.

What would you suggest me to do?

I appreciate any lead.

 

[deep_sea]

Be careful that changing L means moving to another family of curves. Also Vth changes with L. If your device is not not long enough, gm/ID is necessary and the square law will not give a valid approximation. To validate this, try the square law for several VGS in a short channel device and you will see it.
Also the definition of "saturation" is vague. If Vov< 0.2 V, the square law approximation is not holding true. In moderate and weak inversion, the square law becomes almost useless.
If you want to use the square law, make sure L is long enough and Vov is high enough. Then characterise the device (\[\beta\] , Vth) at a particular L. Then if you change L, calculate the new (\[\beta\] , Vth) for the new L.

 

[melkord]

Be careful that changing L means moving to another family of curves. Also Vth changes with L. If your device is not not long enough, gm/ID is necessary and the square law will not give a valid approximation. To validate this, try the square law for several VGS in a short channel device and you will see it.
Also the definition of "saturation" is vague. If Vov< 0.2 V, the square law approximation is not holding true. In moderate and weak inversion, the square law becomes almost useless.
If you want to use the square law, make sure L is long enough and Vov is high enough. Then characterise the device (\[\beta\] , Vth) at a particular L. Then if you change L, calculate the new (\[\beta\] , Vth) for the new L.

Hi, I still do not get what you mean by another family of curves.
What I did so far to characterize my device is sweeping VGS for 6 different L values.
From this, I get gm/Id, Id/W and it works to predict gm, rout, fT.

I use the same method, but the result for "beff" is not correct.

Then characterise the device (\[\beta\] , Vth) at a particular L. Then if you change L, calculate the new (\[\beta\] , Vth) for the new L.

What should I sweep at a particular L?
if you meant I should sweep VGS, I did that already. But it does not produce the correct "beff".

 

[sutapanaki]

The whole point of designing according to the gm/Id methodology is to avoid using the square law model of the transistors. beff is part of the square law and you kind of defy the purpose of using the gm/Id if you insist on knowing beff.

 

[melkord]

The whole point of designing according to the gm/Id methodology is to avoid using the square law model of the transistors. beff is part of the square law and you kind of defy the purpose of using the gm/Id if you insist on knowing beff.

Hi, yes, I am aware of that. But that particular formula has that term. do you have any other suggestion?

 

[sutapanaki]

If you insist on using the gm/Id, find a way to express that formula in terms of gm/Id.

 

[deep_sea]

I meant what sutapanaki meant. \[ \beta \] is not useful in gm/ID methodology. Your approach is correct for sweeping VGS to get gm/ID and ID/W. But \[ \beta \] is not a part of gm/ID. gm/ID methodology main point is to avoid using the square law because V*\[ \neq \] Vov.
In your circuit equation, you should know where the \[ \beta \] came from originally. If use substitute the following, you can have gm and ID instead.
\[ gm=\sqrt{2*\beta * ID } \]. or \[ \beta= \frac {gm^2} {2*ID} \]
Eventually you have ID and gm only in your equation.