Montecarlo simulation on matched devices

-Based on my understanding, when you click on process, all your components (FETs, Passives) will move to that specific process, say Fast-Fast, so your sample example does not seem realistic.

-Post layout has nothing to do with monte-carlo, unless in their definition they consider (mu,sigma) for layout dependent effect such as poly-effect, Metal Boundary Effect, SA, ... which I don't think that is the case, and obviously interconnects have no statistical variation.

-I believe Andrew in a post has said what you get from Monte-Carlo is with the assumption of that you have done an almost perfect work for layout matching, so if someone has not done so, then most likely would see worst results after fab. Also, I believe in your case, there is no correlation defined between FETs, so if you place them way far or other way around, to simulator, they would be the same.

I am also looking to the reply from Andrew :)

In essence, the "mismatch" variation with Monte Carlo is really modelling the residual random local variation of each device. It is not modelling systematic matching effects, but the residual random variation.

Now of course, the sensitivity of a circuit to that local residual random variation will be a good proxy for the importance of good matching of those devices, but it's not generally correct to start setting correlation coefficients between the statistical parameters of well-matched devices, because the models are not usually modelled that way. There isn't a tool which uses the physical arrangement to figure out the impact of good or poor matching strategies; it's really not Monte Carlo that does this.

In other words, even if you have arranged your layout to cancel out gradients and minimise mismatch effects by ensuring close proximity, alignment and orientation, there will still random variation and it's this that is generally what your Monte Carlo models are modelling.

Andrew

Dear Andrew.

Thank you very much for your nice explanation, I do appreciate your efforts.

As you knidly stated "here isn't a tool which uses the physical arrangement to figure out the impact of good or poor matching strategies; it's really not Monte Carlo that does this."

Which if I understood it correct, I will consider a circuit with two different layout implementation, the first one with  high matching degree , the other one with no matching at all, just simple pick and place.

I will consider DC parameter only for the post layout simulation, like the input offset voltage of op-amp, because the AC charasterictics are sensitive to parasatics and will change by anyway from layout form  to another.

Should I now expect to have the same offset voltage MC distribution of both post layout simulation?

Thank you once again

Best Regards

Senan said:

Should I now expect to have the same offset voltage MC distribution of both post layout simulation?

Yes, unless:

1. the different layout of the instances causes some difference in the layout-dependent-effects (e.g. LOD, well-proximity effect, stress parameters etc)
2. The parasitic resistance causes a change in the offset (there could be different voltages in the circuit because of the IR drop along the tracks, for example)

Andrew

Dear Senan,

Please allow me to add to Andrew's comment regarding your question about the degree to which the distributions of offset voltages of two different layouts of an op-amp are similar.

Since the amount of random variation in the vgs of a device is dependent on its absolute value, any difference in the current densities of the P and N rail input devices of the op-amp will result in an offset voltage. Hence, if there is any systematic difference in their current densities for the two layouts, a Monte-Carlo simulation result will also show a difference in the offset distributions.

Basically, the approach I might suggest is the following:

1. Perform schematic netlist based offset voltage simulations using your set of operating point, process, voltage, and temperature conditions to validate that the offset voltage variation is at a minimum (ideally zero).

2. Perform post-layout netlist based offset voltage simulations using the same set of operating point, process, voltage, and temperature conditions to compare the offset voltage variation sufficiently close to that using your schematic based netlist. Note, to identify layout features that are responsible for systematic effects in the offset voltage, you may need to perform simulations using capacitance only and full RC extracted views of your layout. A tool such as Paragon X can be extremely valuable in determining the root cause of any systematic layout effects on offset.

3. Only after you have minimized the post-layout netlist based offset voltage, perform a set of Monte-Carlo simulations to assess the resulting random variation of the offset. Consider using sets of operating point, process, voltage, and temperature conditions that will produce maximum gate-source and minimum gate-source voltage conditions to estimate the range in random variation. Use a sufficient number of simulations to verify the confidence interval of the predicted standard deviations and validate that the distributions are representative of a gaussian distribution. As an example, Figure 1 illustrates the variation in standard deviation for four time based parameters with the number of simulations chosen for a Monte-Carlo analysis.

Shawn

Figure 1

Dear Andrew,

Thank you very much for your confirmation, you made it very clear for me 

Dear Shawn,

Thanks a lot for your effort in providing the useful details.

Every thing is clear, but I want to use this chance to address you two questions in my mind, what is the number of samples of MC required for 95% confidence, may be there is is mathematical expression between both?

The second quesion, I saw two papers in which the authors nested the MC run over process corner, for example running  MC around the slow process or fast process corners. First of all, the technology I use doesn't allow to do that but I am curious to see. Because in my opinion the MC is the process profile with maximum and minimum deviation from the typical mean process and I am not sure how they did it like this way, nor if it is realistic to consider?

Senan said:

Every thing is clear, but I want to use this chance to address you two questions in my mind, what is the number of samples of MC required for 95% confidence, may be there is is mathematical expression between both?

That's complicated because it depends on the yield that you need and the distribution of the output expressions. You could pick the option on the Monte Carlo options form and specify that you want to verify the yield, then set that you want to use the basic auto-stop (the advanced auto-stop requires additional licenses and can be more efficient).

Senan said:

The second quesion, I saw two papers in which the authors nested the MC run over process corner, for example running  MC around the slow process or fast process corners.

Some technologies provide distributions about a process corner - so that means that you can simulate the local (particularly "mismatch") variation around that corner. I've always had a conceptual challenge with this approach, but it does seem to be how some technologies organise their statistical models. It's always best to understand from the foundry themselves what their statistical modelling strategy is. Put another way, even if the process is centred in a particular place, there will still be die to die variation and device to device variation, so it is still a realistic thing to consider.

Andrew

Dear Andrew,

Thank you once again for your help, the second answer is clear to me now after your explanation.

For the first part with regards to the confidence level, I usually use the fixed number of MC sample, not the auto stop.

I mostly target 3 Sigma and I do run MC with large number of samples, like 500 or 1000 some times. I always run it with Confidence level not set to value. After the MC finish and I got a yield like 100, I go to define the confidence level to 90 or 95 % and I notice drop in the estimated yield, but this drop becomes less when the MC has more number of samples. That is why I think I need to know the optimum number of fixed samples to reach certain sigma with certain confidence level.

Thank you

Regards