On-Chip Variation (OCV) Kunal Ghosh

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Transcription:

On-Chip Variation (OCV) Kunal Ghosh

Ever thought what s an interviewer s favorite questions to rip you off all my previous ebooks. And On-Chip Variation (OCV) is one of them, specifically for Static Timing Analysis interview. This analysis is coming from people who got interviewed and recruited into leading VLSI industries. Most importantly, my posts and videos have helped most of them and I really feel proud about it. Nice feeling. Coming back to analyze OCV, the first task is to find all possible sources variation, and find out how these can affect a delay of a cell and hence, timing. First things first Sources of variation 1) Etching Look into the below layout of an inverter (which also shows the Width (W) and Length (L) parameters of an inverter) And, a chain of inverters (this is mostly the case of clock path, be with me for upcoming posts and I will exactly let you know, why OCV is mainly applied on clock paths, 50% should be clear from the term chain of inverters ) VLSISYSTEMDESIGN.COM 1

We use photo-lithography fabrication technique to build the inverters on Silicon wafer, and this is a non-ideal process, where the edges will not exactly be straight lines, but there will be disturbances. And why so, because the above technique needs photo-masks which are created using etching, which is again non-ideal. Below is how the ideal mask and real mask looking like VLSISYSTEMDESIGN.COM 2

Now these variations on the sides, is also dependent on what logic cell is present on either side of this inverter, if its surrounded by chain of inverters on either side, the variation on the sides will be less as the process parameters to build mask for a chain of similar size inverter, is almost the same. But, if the inverters are surrounded by other gates, like flip-flops, then the variation will be more. With that said, the below inverters in the middle will have a similar and less variations and the inverters on the boundaries will have different and more variations. (observe the difference in actual mask, in below and above image) VLSISYSTEMDESIGN.COM 3

And guess what. this directly impacts the drain current below, as it is proportional to (W/L) ratio You feel, we are almost there. not yet. we need to identify other sources of variation, find out how the current changes, and eventually, find out a range on what should be the value of OCV. VLSISYSTEMDESIGN.COM 4

After this, do you feel, we are done. not yet. :), we need to use these OCV values, plug it in STA analysis and see its (+ve or -ve) impact. Do you now feel, we are done? We were identifying sources of variations, and below is the second one 2) Oxide Thickness Let s go back to the inverter layout and look which part are we talking about Here, we are talking about gate oxide thickness variation Below is the section from inverter chain, which we are worried about VLSISYSTEMDESIGN.COM 5

If we go by ideal fabrication process, below is what you will achieve, a perfectly cubic shape (below is the 2D image, so it looks rectangle) oxide layer, and perfectly deposited metal gate or poly-silicon gate VLSISYSTEMDESIGN.COM 6

But, if we go by actual oxidation process, it s very difficult or almost impossible to achieve the above perfect oxide thickness. And I can confidently say that, as I have worked on fabrication for a brief period during my Masters at IIT Bombay. Below is what you will get VLSISYSTEMDESIGN.COM 7

So, what s wrong having above oxide thickness. Again, it s the drain current (which is a function of oxide thickness, shown in below image) that will get varied for the complete chain of inverter, especially, the one s on the sides. The variations in middle inverters will still be uniform. We discussed the reason for this in last post Imagine a chain of, if, 40 inverters or buffers. the variation is HUGE. And this needs to be accounted for, in STA. VLSISYSTEMDESIGN.COM 8

So, the challenge is, how to we find the range and effectively model it in STA. Are we scared? Of course, Not. The below image models low-to-high waveform condition at input of CMOS inverter, in terms of resistances and capacitance. So, overall, it s the RC time constant that decides the delay of a cell VLSISYSTEMDESIGN.COM 9

With above, we can safely say, the propagation delay tpd is a function of R Now, from previous posts, we seen variation in drain current Id due to variation in W/L and oxide thickness variations, and above we see, how propagation delay is function of R. The question is now, what next? If I am, somehow, able to prove, that drain current Id strongly depends on R, then I can directly relate (W/L) and oxide thickness variation to R, and below images will exactly do that VLSISYSTEMDESIGN.COM 10

Hence, every inverter in the below chain, will have delay which is different than the immediate next one, something like below VLSISYSTEMDESIGN.COM 11

If we plot a Gaussian Curve with delays on x-axis and no. of inverters on y-axis, it will give us a clue, about the peak variation in inverter delays, the minimum and maximum variation in inverter delays like below Now, we know the percentage variation in delays of inverter compared to 100ps, because that s where the inverter delay (with used W/L ratio) is expected to be, and most number of inverters on chip with that W/L ratio have a delay of 100ps VLSISYSTEMDESIGN.COM 12

OCV variation is +8% and -9% and one of them will be used for launch and other for capture in setup/hold timing calculations. For e.g. for setup calculation, the launch clock will have OCV of +8% and capture clock path will have OCV of -9%. That means, if the original clock cell delay is x in launch clock, with OCV into account, the same clock cell delay will be ( x + 0.08x). This calculation in setup considers the On-Chip Variation, and that s where the name comes from, as shown below VLSISYSTEMDESIGN.COM 13

the images in above post and the previous one s makes this concept so simple. Isn t it? But, keeping things simple is the most difficult job. I took around 3 weeks, just to make these images. And, finally, we have a video on what we posted on this topic. Below is the snippet of the same. https://youtu.be/oi2ehpgqpqy VLSISYSTEMDESIGN.COM 14

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