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# Do you do characterization for mismatch on your technology? What is the proper way to do that?

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#### melkord

##### Full Member level 2
I have been reading about random mismatch from some sources like here, here, here, and ch4 of this book.
From what I read, I found that on device level, the matching only depends on W, L, and technology. See picture below.

So, should we characterize our technology regarding mismatch? if yes, How?

I am still checking it, but it seems that A_VT is not constant in my technology. I might be incorrect about this though.

Constant mismatch parameters are valid only if doping profile is constant as well. In most of the processes (below 0.18um) it is not met due to halo/pocket implants. Thus, mismatch parameters are geometry and bias dependent.

You validate your matching by running monte-carlo simulations and thus you will use the matching provided by you foundry models.
But to get a feel about the parameters, mainly Avt, because it is the dominant one, you can do pretty much what the formula says. Place a pair of devices in schematic with certain W and L. For example you can hook them as a current mirror but make sure the receiving side of the mirror has the same VDS as the diode connected transistor. In simulation look at the difference between the threshold voltages of the two transistors. In normal simulations this difference will be 0 but if you run monte-carlo, it will have some Gaussian statistical distribution. From the standard deviation of this distribution you can find the Avt coefficient. You can also put different amounts of current in the mirror and see if and how much the Avt changes. Place few more pair of transistors like that with 2W, 4W... and extract their Avt too. Ideally they should be the same, but in reality will come somewhat different. You may take the average of them to have just a single number. You will always validate your circuits with running MC which will give you the real mismatch.

To get the geometry dependence you need series of matched pairs padded out that cover the design space, at least out to 10x10u from min x min. Then you take a lot of data and fit the coefficients "acceptably" (which could be realism if you're a designer, or sandbagged severely if you're a modeling minion who got told to make it six sigma numbers plugged into a three sigma algorithm so the design director doesn't have to hear the product engineering director whine about random yield loss on Vio).

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