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

I agree with Shawn - the first paper doesn't mention monte carlo, and I couldn't access the second paper as it requires a login that I don't have...

Anyway, typically the monte carlo models provided by foundries are capturing the process-based random variation (die to die) and mismatch-based (which would probably be better called "local") variation. These are capturing the renaming random variation of the device, not the systematic variation caused by poor layout (e.g. lack of proximity, alignment or orientation). A design sensitive to the effects of this random variation per device is more likely to require good layout to match similar devices, but that's not strictly what you're measuring.

Also, the model variation is not normally in terms of physical dimensions (nor are the process corners). I see no reason to try to vary those statistically as well (for a start, where are you getting the data about how they vary?). Some foundries do provide models which do local variation about a process corner, but many provide statistics models that vary across the entire process (and local mismatch variation too), and in that case it would make no sense to simulate over PVT corners. Over VT corners, yet, but not PVT.

So the best thing is to consult the documentation for the specific PDK/models you're using. Understanding what the models are capturing is the best way to know how to use them.

Regards,

Andrew.

I agree with Shawn - the first paper doesn't mention monte carlo, and I couldn't access the second paper as it requires a login that I don't have...

Anyway, typically the monte carlo models provided by foundries are capturing the process-based random variation (die to die) and mismatch-based (which would probably be better called "local") variation. These are capturing the renaming random variation of the device, not the systematic variation caused by poor layout (e.g. lack of proximity, alignment or orientation). A design sensitive to the effects of this random variation per device is more likely to require good layout to match similar devices, but that's not strictly what you're measuring.

Also, the model variation is not normally in terms of physical dimensions (nor are the process corners). I see no reason to try to vary those statistically as well (for a start, where are you getting the data about how they vary?). Some foundries do provide models which do local variation about a process corner, but many provide statistics models that vary across the entire process (and local mismatch variation too), and in that case it would make no sense to simulate over PVT corners. Over VT corners, yet, but not PVT.

So the best thing is to consult the documentation for the specific PDK/models you're using. Understanding what the models are capturing is the best way to know how to use them.

Regards,

Andrew.

hi andrew,

"These are capturing the renaming random variation of the device, not the systematic variation caused by poor layout (e.g. lack of proximity, alignment or orientation)."

Do you mean i will get different monte carlo results with two layout: the first one have key device with common centriod layout and the second have no matching technique?

Irenexox said:

Do you mean i will get different monte carlo results with two layout: the first one have key device with common centriod layout and the second have no matching technique?

No, if the design netlist is the same, you would see no difference. Monte Carlo knows nothing about the layout positioning, and what you are talking about is a systematic variation not a random variation - there's nothing to capture that, nor model it.

Now of course, if you did a monte carlo mismatch simulation of two extracted netlists of the different layouts, you would likely see a difference - but that's more likely just to be because the random numbers are different caused by the differing parasitics and order of the devices in the netlists.

Monte Carlo "mismatch" variation would likely tell you which devices in your design have more impact to the variation of the output measurements (particularly if you're using mismatch contribution analysis), but it is not going to tell you whether one layout arrangement is any better than another in terms of reducing systematic variation.

Andrew. 

Thanks a lot for your clarification.