Monte Carlo sigma value

[rspdsr]

Hi
I have basic questions related to Monte carlo simulations.
--- > What is sigma value ?
Will the variation for a parameter provided by the foundry include the sigma value for the parameters ? If so how much will it be generally?
Say in the case of TSMC 180nm spectre model file, will the sigma value be specified in the model file and what will be the value. Is it generally 1 sigma for all the parameters ? Where can I find this information?

Can someone please help here in providing this info?

 

[erikl]

--- > What is sigma value ?

See here.

The sigma value (σ) corresponds to the standard deviation of a distribution (or the square root of the variance). In Monte Carlo simulations the σ value often is abbreviated as std or stdev.

Will the variation for a parameter provided by the foundry include the sigma value for the parameters ?

Variably: Very often, ± a proportional part of the mean value is given. Sometimes it's a sigma value; if you're lucky they have stated how many of them.

If so how much will it be generally?
Say in the case of TSMC 180nm spectre model file, will the sigma value be specified in the model file and what will be the value.

Only if you get the additional mismatch files for Monte Carlo analysis. These usually include std resp. stdev values.

Is it generally 1 sigma for all the parameters ?

You can't rely on this. Very often, it is 1 sigma. But for yield analysis, in most cases it is ±3σ.

Where can I find this information?

As a good customer from the foundry.

 

[rspdsr]

Thanks for your reply.
As I understood, distribution and std deviation of the parameter is what the foundry provides (and may not explicitly specify the sigma value).

In such case, say I run and process+mismatch analysis and I want to target my design for 3 sigma, how many monte carlo iterations should i consider.

I read somewhere that when you target for 3 sigma, one needs to run for 1000 iterations, and find the mean and sample std deviation and multiply the sample std deviation by 3 if it is 3 sigma ? Is this procedure correct?

 

[D.A.(Tony)Stewart]

For large volume, you must have a Cpk of 1.33 [4 sigma] or higher to satisfy most customers.
Cost of investigating faults and scrap rises when Cpk drops towards 1 and Cpk<1 is unacceptable.

Cpk is defined by the upper and lower acceptance criteria and the mean & standard deviation.
You cant just assume 3sigma just fits within specs. the process may be asymmetrical.

Think of Cpk as a margin indicator.

Cpl = (Mean – LSL)/3*Std.dev
Cpu = (USL – Mean)/3*Std.dev
Cpk= Min (Cpl, Cpu)