Including geometric variations in Montecarlo simulation (ADEXL)

Dear NorNand,

NorNand said:

Also in the first paper the author run the Montecarlo in over process corners (SS, FF...etc), why he should include these corners when it will already covered by the Montecarlo variation ?

I'm not sure if I am overlooking something, but the link to the "first paper" does not appear to discuss the subject of Montecarlo variation - at least I could not find it. The article is titled "An Ultra-Low-Voltage Ultra-Low-Power CMOS Miller OTA With Rail-to-Rail Input/Output Swing"

In any case NorNand, an attempt to include geometric variation as well as process case variation appears to be redundant. Further, inclusion of both will likely lead to variations that are not realistic of the process. I've never had a foundry that lists the expected variation in geometries - that is the reason the foundry provides models for different process cases. I highly doubt a circuit designer can accurately assess the correlation between geometric variations for a given foundry. Hence, my thought it is best to utilize the foundry model cases as means of including expected process parameter variations.

NorNand said:

Usually for me I run with MC two other corners that are supply voltage and temperature variation but never tried to include process corners with it nor having an idea about including geometric variation

I always include process variation in Montecarlo simulations. Why? Typically, I am interested in the variation in such parameters as offset voltage, headroom, and duty cycle of a waveform. The magnitude of these variations correlates with the magnitude of the device threshold voltages. In a slow silicon process case, the threshold voltages will be larger than in a typical or fast process case. Duty cycle error can be highest in a mixed silicon process case (i.e., slow p, fast n). Hence, to estimate the maximum expected variation, performing a Montecarlo analysis with a slow silicon or mixed silicon process in addition to a typical or fast case will indicate the range in parameter variation.

I hope I understood and answered the spirit of your question NorNand.

Shawn

Thank you Shawn for your nice infiormation, 

actuallly the first paper was not about montercalo itself, but the author run the MC for his design in the way I described, 

your feedback is very helpful

thanks

Dear Andrew,

Thank you for your reply,

Nothing I can add because you made it very clear,

thank you once again

Regards

Dear Andrew,

Thank you for your reply,

Nothing I can add because you made it very clear,

thank you once again

Regards

I have noticed that I have done a mistake on the title of the first paper, it should be 

https://www.sciencedirect.com/science/article/pii/S0026269216302373

Am I allowed to attach the paper pdf file here ?

No, you are not allowed to attach the PDF here. This would be in violation of the copyright holder and I would delete the PDF as the forum moderator if you did post it here (it's a bit of a giveaway since they even charge for the PDF on the link you said; even if it was freely published I suspect they would not allow re-publishing elsewhere, and referencing their link would be enough).

Andrew