Corner Simulation Question

If we refer to model file, there is a sigma value to represent the process variation. From this sigma we will have SS, SF, TT, FS and FF corner case.... My question is how the foundry get the sigma value and why they are using 3 sigma value instead of 1 sigma only.... 3 sigma will lead to circuit overdesign isn't it?

1. How fundry gets the 3-sigma value?

Its a pure statistical data. After a process/technogy file is being finalised, they go for fabrication at individual device level and even some small block level. From different lots of fabrication, they measure the parameters etc. and gets the statistical value for the particular process. There may be some theoritical predictions (may be at device characteristaion level/ modeling level). But the final value is dependent on measurement. Once these measurement is done enough in numbers and the statistical values comes reliable, the process could be called matured.

2. Why 3-sigma instead of 1-sigma?

The variation is taken, as a thumb of rule, as normal distribution. For this distribution pattern 1-sigma ~68.3% and 3-sigma~99.7%. Now the matter is if your design is dependent on 1-sigma value of variation of process, then the block level/system level yield may drop a lot. For 3-sigma it is ok. Thus this thing is totally related with the yirld of the product u r designing. U even can design depending on absolute matching ( no variation at all). But whether the design, after fabrication, would be functional or not can not be guarented.

There is a good writing , 3-sigma Vs. sisx-sigma....
https://www.qualityamerica.com/knowledgecente/articles/SixSig_pg140-2.html

sankudey

sankudey said:

1. How fundry gets the 3-sigma value?

Its a pure statistical data. After a process/technogy file is being finalised, they go for fabrication at individual device level and even some small block level. From different lots of fabrication, they measure the parameters etc. and gets the statistical value for the particular process. There may be some theoritical predictions (may be at device characteristaion level/ modeling level). But the final value is dependent on measurement. Once these measurement is done enough in numbers and the statistical values comes reliable, the process could be called matured.

2. Why 3-sigma instead of 1-sigma?

The variation is taken, as a thumb of rule, as normal distribution. For this distribution pattern 1-sigma ~66% and 3-sigma~99%. Now the matter is if your design is dependent on 1-sigma value of variation of process, then the block level/system level yield may drop a lot. For 3-sigma it is ok. Thus this thing is totally related with the yirld of the product u r designing. U even can design depending on absolute matching ( no variation at all). But whether the design, after fabrication, would be functional or not can not be guarented.

There is a good writing , 3-sigma Vs. sisx-sigma....
h**p://www.qualityamerica.com/knowledgecente/articles/SixSig_pg140-2.html

sankudey

Click to expand...

Actually the statistical value from question 1 is 3 sigma or 1 sigma? If we refer to the model, that value will be multiplied by 3 to become 3 sigma I think.....
Another thing that I don't understand is that, with 3 sigma, the design is become loosen..... This will lead designer to overdesign the circuit.... Maybe I don't understand statistic..... Is there any simple reference for statistic....

pbs681 said:

Actually the statistical value from question 1 is 3 sigma or 1 sigma? If we refer to the model, that value will be multiplied by 3 to become 3 sigma I think.....
Another thing that I don't understand is that, with 3 sigma, the design is become loosen..... This will lead designer to overdesign the circuit.... Maybe I don't understand statistic..... Is there any simple reference for statistic....

Click to expand...

Hi,
I guess some more elaboration will be helpful to understand the matter.

1. On Corner:
Suppose u want a BJT with ft=100MHz and beta=100. For the time being take these two parameters only. Now u have ur fab-facility for that and that matches with ur requirement. But when a these BJTs go under fabrication process, they face a variation : that may be at doping level, geometry level. It is not at all achievable that all the BJTs will face identical environment. Some BJTs are at middle at the die and some are at the edge etc. So after fabrication u may see that the ft of different BJTs varies from , say, 90MHz to 110MHz and beta say 90 to 110. Now these variation in parameters is found to be following a normal/gaussian distribution curve, which is very common. Now suppose if u wanna design a diff-amp with these BJTs. What will happen? As the BJTs are not perfectly matched, they vary in their paramaters, the ideal equations for diff-amp will not be followed by the diff-amp. They will give rise to offset and other things. Now this shift of paramaters (say from 90 to 110) are called corner variations.

2. On Sigma Value:
Now if ur design is based on 1-sigma (68.3%) value variation of paramaters, say , when two BJTs cascaded, the ultimate yield will be (68.3% * 68.3%) ~ 46.6%. That means out of 100 parts (final product) only ~46 are going to work and others will be found faulty. This is a simple arithmatic and nothing to do with much complex mathematics. Now suppose u design in such a way (WHAT U CALL OVER DESIGN) that ur design is robust to any change in the device parameters (take it for granted for the time being). Now , u can see out of 100 parts 100 are going to work as the change in device parameter does not hamper ur system performance. But it is not possible to design in this way , as like, ignoring device parametrs. It may cost a huge over design and may be in-feasible too. So here comes a point where u need to make a trade-off kind of thing such that u don't go for too-much over design while ensuring a good yield or a large % of final parts are going to work. Other wise the business cannot run.

Now it is being well accepted as 3-sigma be the optimum value. Like the above case, two BJTs in cascade, (99.7% * 99.7) ~99.4%. It is still acceptable. Now see for more devices and blocks and small systems integrated in one big system, the above percentage may drop to a significance value. But this is not always true. As every blcok will be having some tolerance. Thus 3-sigma is well accepted to be fruitful.

3. General:
As u wrote u are not very much familiar with statistics, I guess u need not too. But still u can find the very basics of Gaussian Distribution (a probability distribution function) in Google/any coomunication book/mathematics books etc. To understand it from circuit perspective u may go thru The analog Book by Gray-Meyer. The book is avaialble in this board (in e-book forums). U go thru chapter - 3 . Particularly the appendix A.3.1 (4ed). I guess u can have a realisation regarding this.

The link given in above post describes it lucidly such that u can percept the matter and even this reccomends to adhere to 6-sigma (where the spread of variation is much more).

Hope it would help u to resolve the issue...
sankudey[/u]