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Design >> Analog Design >> Some confusion about Monte Carlo simulation
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Message started by Jet_Wu on Apr 21^st, 2006, 10:42am

Title: Some confusion about Monte Carlo simulation
Post by Jet_Wu on Apr 21^st, 2006, 10:42am

In layout, we alwayse match the transistors. The matched transistors should have some correlation in the parameter variation. But in monte carlo analysis, these correlation seem not to be taken into account.
Have someone done things like this? Does Monte-carlo over-estimate?

Thanks.

Title: Re: Some confusion about Monte Carlo simulation
Post by chase.ng on Apr 21^st, 2006, 4:43pm

Hi,

As far as I know the mismatch parameter for Monte Carlo is assuming that the device is place side by side. If the transistors in the layout is being matched carefully, the Monte Carlo might over estimate the mismatch. In spectre, you can set the correlation ranging from 0 to 0.99 and it is affecting my simulation results. Did you set your Monte Carlo simulation to simulate mismatch? I was doing that to find out the offset voltage for an OPAMP and it works fine for me.

Regards,
Chase

Title: Re: Some confusion about Monte Carlo simulation
Post by Jet_Wu on Apr 21^st, 2006, 11:27pm

Thanks for the reply, I found the correlation setting (.CORREL) in eldo manual just now.
Some question further: how to choose the correlation coefficients, it seems too empirically.

Title: Re: Some confusion about Monte Carlo simulation
Post by Paul on Apr 22^nd, 2006, 5:53am

Hi,

the correlation to be set depends on the mismatch parameters in your model. In most cases, these are extracted for nearby matched devices (same orientation, shape and size etc.). In that case, the correlation effect is already taken care of in the parameters and MC would underestimate mismatch for distant or badly matched devices. If I remember correctly, correlation > 0 lowers the effectively applied mismatch between two devices, so a high correlation parameter (i.e. close to 1) may result in underestimated offset results.

The electrical parameter manual coming with the device models should contain information on the assumptions made during the mismatch parameter extraction and the use of the correlation parameter.

Paul

Title: Re: Some confusion about Monte Carlo simulation
Post by sheldon on Apr 22^nd, 2006, 8:34pm

Greetings,

The Spectre implementation of correlation is outlined in the Modeling
section of the Designer's Guide,

http://www.designers-guide.org/Modeling/montecarlo.pdf

In the past, I have not used correlation because the foundry calculated
mismatch based on the assumption of matched pairs, that is, correlation
was built into the model parameters. This approach worked except when
a design had matched devices that were not placed properly. In that case,
Monte Carlo produced results were in error. Since we had built our trim
structure based on the Monte Carlo projections for mismatch, it meant
an all-level mask spin to fix device placements.

Best Regards,

Sheldon

Title: Re: Some confusion about Monte Carlo simulation
Post by RobG on Apr 28^th, 2006, 7:39am

Jet_Wu wrote on Apr 21^st, 2006, 10:42am:

Monte Carlo doesn't overestimate. Believe it or not, poor layout techniques don't affect the variance (or standard deviation) of Vt mismatch much, at least not on a single wafer were matching parameters would be measured. I've even seen matching between devices with a 90 degree rotation and the difference is small (I think the mobility mismatch does increase, however, and different lots may produce different mean values). What happens is an unpredictable systematic offset is introduced, so it is obviously a bad idea to use "unmatched layouts."

Anyway, generally you can assume that using common centroid layouts, dummy devices, etc, won't buy you much in terms of reduced standard deviation, but it will properly center your design.

Title: Re: Some confusion about Monte Carlo simulation
Post by Paul on Apr 29^th, 2006, 5:56am

Sorry Rob, but I disagree on the form of your post. You may be correct that umatched layout introduces offsets and not variation, I believe that your post may be confusing for less experienced designers! You should not encourage them to disrespect matching guidelines, because it may introduce multiple problems in their designs.

Indeed, matching rules are not only targeting Vt mismatches. In differential pairs, which you would usually bias in moderate or weak inversion, mobility mismatch is the dominant contribution to the overall device mismatch. Further more, orientation shall provide robustness agains thermal gradients, possibly also against residual substrate currents (in case you have vertical bipolar devices in your design). Obviously these factors may vary over time and appear as a time-dependent offset component.

In this sense, please don't overstress the fact that poor matching results in offset only, it may be misleading.

Best,

Paul

Title: Re: Some confusion about Monte Carlo simulation
Post by RobG on Apr 30^th, 2006, 11:58am

Paul, I think yer bored and needed something to post :-). I was worried that people might get the idea that common centroids weren't needed so I mentioned that they were useful not once, but twice. I was going to mention thermal gradients, but it just seemed to be getting more off topic to give yet another reason. By the way, you forgot temperature dependent stess, esp. in plastic packages. ;)

The main point was to answer the question, and to give the reason why. Monte Carlo isn't pessimistic; you shouldn't expect common centroid to decrease the random offsets caused by device mismatch - that is just an oft repeated myth.

Anyway, are you sure you didn't mean V_T mismatch in the post below? The effect of mobility mismatch in a diff pair is minimized by biasing in weak inversion, whereas the effects of V_T mismatch is bias independent (for a diff pair).

Paul wrote on Apr 29^th, 2006, 5:56am:

Indeed, matching rules are not only targeting Vt mismatches. In differential pairs, which you would usually bias in moderate or weak inversion, mobility mismatch is the dominant contribution to the overall device mismatch.

Title: Re: Some confusion about Monte Carlo simulation
Post by Paul on May 1^st, 2006, 12:15pm

Hi Rob,

I have seen people misinterpreting statements like the one in your post and claiming that matched layout was not important. I couldn't simply leave this statement without comment...

Nevertheless, you are right correcting me on the diff pair. Obviously I messed up my post, a diff pair is sensitive to Vt mismatch while a strong inversion current mirror is mostly sensitive to mobility mismatch. Sorry for the confusion, I must have been tired :-[

Best
Paul

Title: Re: Some confusion about Monte Carlo simulation
Post by vivkr on May 2^nd, 2006, 12:11am

Hi Paul, Rob,

I would like to add one comment to the discussion:

While it is true that current mirror mismatch in strong inversion depends on mobility mismatch,
the level of inversion required to attain the state where mobility mismatch dominates over VT
mismatch may be quite high, high enough that one never encounters it.

Perhaps this is a process dependent thing, but I remember doing a calculation long ago with one of
the processes I was using, and with information about VT mismatch and mobility mismatch based
on measurements of well-matched devices, I found that the (VGS-VT) level needed to be about 2x
the maximum operating VGS allowed in the process.

So for all practical purposes, mobility mismatch was negligible. I would advice everyone to
first write out a simple equation for estimating the sensitivity (dI/I) based on VT and mobility
mismatch values, and to plug in the numbers from their respective process docs to see the dominant
source of mismatch.

I typically allow >= 1V (VGS-VT) and use long channel devices in a 3.3V process for realizing current
mirrors, wherever possible.

Regards
Vivek

Title: Re: Some confusion about Monte Carlo simulation
Post by RobG on May 2^nd, 2006, 7:38am

vivkr wrote on May 2^nd, 2006, 12:11am:

Vivkr... that is a good comment of which I agree. Someone confused the issue by saying mobility mismatch was important for diff pairs ;D

Supposedly, as processes get smaller, it will take less overdrive (i.e. Vgs-Vt) for the mobility mismatch to dominate over mismatch. At the same time, supplies will go down (so max Vgs-Vt will also go down), so I don't know if mobility mismatch will ever dominate...

On the other hand, stresses, such as those found in plastic packaging, increase mobility mismatch. At one time I needed a 10 fold increase in σ(Δμ/μ) to explain the temperature drift I saw when moving a chip into a plastic package. So, under some conditions it can be very important, especially in explaining temperature drift.

rg