I have a rather fundamental question regarding Monte-Carlo simulation using Spectre. And I would like to use a Band-gap circuit as a reference design, as it would include a Bjt, resistor and MOS elements in the same design, and maybe designers have different experiences with those elements. The models support simulation of process and mismatch (globalmc_localmc) and the simulated variation (with sufficient no. of samples) in the band-gap voltage should cover 3-Sigma variation seen at the foundry.
(Also, this is common with designers from a lot of big semicon companies; no one I came across uses the correlation parameter between devices for simulation as described by Don O’Riordan in "Recommended Spectre Monte Carlo Modeling Methodology".)
Now, my question is with so much variation covered under-the-hood by the same model(globalmc_localmc), what kind of process variation/mismatch is getting simulated and are different devices correlated to each other? For example, can there be a case where the differential pair of op-amp in BGR have the two devices at extreme process corners with x%-mismatch on top (should be an impossible event even with lot/wafer/die/intra-die variations)? Is there any correlation between a fast MOS corner and fast BJT/min resistor corner.
I know this has a lot to do with foundry data but would appreciate if someone could shed some light here?

Thanks,
Aman

Rfidea Thanks!! for the explanation. I have few follow-up questions from your answer
and would appreciate some more guidance.

1) Break-down of the local/global variation on a qualitative basis?
How much variation would be accounted in local mismatch vs global mismatch.
Example (intra-die+ die-die, same wafer) = local mismatch
             (lot + wafer) = global mismatch
               (1 wafer) = 1 process corner, all dies
Is there any such correlation or just an aggregate distribution?
2) Approach of running Monte-Carlo's?
This comes from the newer sub-nano models where process corner comes with its own
3-sigma variation, compared to older models with 3-sigma around typical corner.
Example, (tt+3-sigma1) compared to (tt/ss/ff/fs/sf+3-sigma2) assuming no particular
bias in the latter, where obviously (sigma1 > sigma2). What is your strategy to simulate
say a BGR in this case for the worst-case? (If my understanding is correct you would
take the process corner with least margin and run a local mismatch to simulate this, please
do correct me.)

Thanks,
Aman

Thanks!!