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[SOLVED] Meaning of mac_device parameter 'Mismatch_Sigma'?

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flyingRabbit

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Hi, all. Below picture is a basic test setup of monte-carlo simulation for the PDK that I'm currently using. In order to investigate mismatch characteristics, I'm using nch_lvt_mac devices that models mismatch characteristics of low-Vt NMOS.

Is there anyone who knows the accurate meaning of 'Mismatch_Sigma' parameter in the left 'Edit Object Properties' subwindow? I guess this is some sort of factor that is multiplied to the variance of mismatch parameter because when I put 3 as 'Mismatch_Sigma', the std becomes three times larger than the case when 'Mismatch_Sigma' is 1(default).
screenshot.png
 

Yes, sigma is the same as std (standard deviation), see here.

Thanks erikl. Let me clarify a bit more. So, if I set the Mismatch_Sigma as 3, does it mean that my monte-carlo simulation will be much more rigorous? I think setting Mismatch_Sigma as 3 is too rigorous because the new standard deviation become three times larger than the default value.
 

I think setting Mismatch_Sigma as 3 is too rigorous ...
Sure, but this depends on what you need: σ=1 will cover 68.2% of all possible cases, whereas σ=3 covers 99.73% , see below.
standard-deviation.png
Standard deviation - Wikipedia said:
If a data distribution is approximately normal then about 68 percent of the data values are within one standard deviation of the mean (mathematically, μ ± σ, where μ is the arithmetic mean), about 95 percent are within two standard deviations (μ ± 2σ), and about 99.7 percent lie within three standard deviations (μ ± 3σ). This is known as the 68-95-99.7 rule, or the empirical rule.
The trustability or confidence interval is determined by the number of probes (MC runs in your case). A confidence interval (CI) means that the confidence level (CL) of a measuring (or MC run) result will be 1-(1/√N) , if N is the number of measurements (runs) - if you repeat them very often. I.e. e.g. CL=68% for 10 runs or 90% for 100 runs.

Now what does this mean in practice? If you just want a quick overview over the distribution to be expected, you'd use σ=1 and remember there could still be 32% more results outside of the number of cases you got - with 90% confidence level if you run 100 times.

If you want to buy a million chips, you'd want to see more exactly how many of them you'd have to chuck away: you'd use σ=3 and will know that there still will be 2700 bad ones to be expected in the lot - with a confidence level of 96,8% at 1000 runs.

HTH!
 
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Sure, but this depends on what you need: σ=1 will cover 68.2% of all possible cases, whereas σ=3 covers 99.73% , see below.
**broken link removed**

The trustability or confidence interval is determined by the number of probes (MC runs in your case). A confidence interval (CI) means that the confidence level (CL) of a measuring (or MC run) result will be 1-(1/√N) , if N is the number of measurements (runs) - if you repeat them very often. I.e. e.g. CL=68% for 10 runs or 90% for 100 runs.

Now what does this mean in practice? If you just want a quick overview over the distribution to be expected, you'd use σ=1 and remember there could still be 32% more results outside of the number of cases you got - with 90% confidence level if you run 100 times.

If you want to buy a million chips, you'd want to see more exactly how many of them you'd have to chuck away: you'd use σ=3 and will know that there still will be 2700 bad ones to be expected in the lot - with a confidence level of 96,8% at 1000 runs.

HTH!

Thank you for your kind reply erikl. However, I think I should clarify my question even more. My question was not about basic statistics.

Let's say our PDK defines transistor's std of threshold voltage as 5mV and average as 300mV at given size. I think if I set Mismatch_Sigma as 3, the monte-carlo simulation picks random threshold voltage values from the Gaussian distribution of N(Mean,1-Sigma)=N(300mV,15mV), not from N(300mV,5mV). That's the reason why I think setting Mismatch_Sigma as 3 is "too rigorous" since now the 99.73% of random threshold voltages will come from -255mV~345mV, not from 285mV~315mV.

I would like to know that my thinking about Mismatch_Sigma is right. Thanks again.
 

Let's say our PDK defines transistor's std of threshold voltage as 5mV and average as 300mV at given size. I think if I set Mismatch_Sigma as 3, the monte-carlo simulation picks random threshold voltage values from the Gaussian distribution of N(Mean,1-Sigma)=N(300mV,15mV), not from N(300mV,5mV).
Yes, that's what I think, too.

That's the reason why I think setting Mismatch_Sigma as 3 is "too rigorous" since now the 99.73% of random threshold voltages will come from -255mV~345mV, not from 285mV~315mV.
I would like to know that my thinking about Mismatch_Sigma is right.

No, I don't think so. I'd think 99.73% of random threshold voltages will come from mean±15mV (not ± 3*15mV).
Why? I think the Mismatch_Sigma declaration corresponds to how many sigmas of the standard deviation should be used (for the MC runs).

To get this straight - this is a contradiction to the above statement, that the std value corresponds to the Mismatch_Sigma value, but it's possible that the simulator shows this erroneously.

But I'm not sure, however. Why not try and plot a threshold voltage histogram?
 

Yes, that's what I think, too.



No, I don't think so. I'd think 99.73% of random threshold voltages will come from mean±15mV (not ± 3*15mV).
Why? I think the Mismatch_Sigma declaration corresponds to how many sigmas of the standard deviation should be used (for the MC runs).

To get this straight - this is a contradiction to the above statement, that the std value corresponds to the Mismatch_Sigma value, but it's possible that the simulator shows this erroneously.

But I'm not sure, however. Why not try and plot a threshold voltage histogram?

I found that Mismatch_Sigma is a constant that is multiplied to the random seed generated from N(0,1).
 
I found that Mismatch_Sigma is a constant that is multiplied to the random seed generated from N(0,1).

Ok, then it seems you're right (mean±3*15mV in your above case). Thanks a lot!

May be there exists an MC docu about how this Mismatch_Sigma parameter is used?
 

Unfortunately, no. That's why I post my question to this board. In order to investigate the function of Mismatch_Sigma, I tracked the equations in the library file.
 

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