OCV v/s AOCV

When I had started my career around 6 years back, we were introduced to the term called OCV. While the OCV concept was quite simple and fascinating, it didn't me long to realize that OCV can be a nightmare for every STA engineer out there. I had introduced OCV long time back while explaining the difference between OCV v/s PVT. In this post, I intend to draw a distinction between OCV (On-Chip Variation) and AOCV (Advanced On Chip Variation).

Before we discuss anything about OCVs, it would be prudent to talk about the sources and types of variations that any semiconductor chip may exhibit.

The semiconductor device manufacturing process exhibit two major types of variations:

• Systematic Variations: As the name suggests, systematic variations are deterministic in nature, and these can usually be attributed to a particular manufacturing process parameter like the manufacturing equipment used, or perhaps even the manufacturing technique used. Systematic variations can be experimentally calibrated and modeled. They also exhibit spatial correlation- meaning two transistors close to each other would exhibit similar systematic variation- which makes them easier to gauge. Example would be inter-chip process variations between two different batch of manufactured chips.
  When a certain technology is in its nascent stage (let's say 10-nm technology), the process engineers would typically be more concerned about these variations and as the technology matures, process engineers are able to calibrate and tune their manufacturing process to reduce this variation component.
• Random Variations: These are totally random, and therefore non-deterministic in nature. Random variations do not show spatial correlation and therefore very difficult to gauge and predict. Unlike systematic variations, random variations usually have a cancelling effect owing to their random nature. Examples are subtle variations in transistor threshold voltage.

As the semiconductor node shrinks, the susceptibility to the variations increase. And the effect of these variations need to be taken into account while doing timing analysis, or perhaps during the overall design planning to some extent. Shifting our focus back to OCV and AOCV. At this time one may ask themselves in what form would these variations manifest themselves? Well, these variations can manifest themselves in form of increase or decrease in the threshold voltage of devices, shift the process of the manufactured devices, perhaps vary the oxide thickness or change the doping concentration..

There might be infinite such manifestations and we engineers like to make our lives easier, don't we? ;)

Experienced folks must have guessed where am I headed. If you haven't guessed it yet, stay with me, take a step back and what does all these parameters have in common? What's that one quantifiable metric that these will impact and the answer is the delay! OCV and AOCV are essentially models which guide us on how the cell delay varies in light of the systematic and random variations.

On-Chip-Variations (OCV): OCVs are simplistic and (generally) pessimistic view of modelling process variations. Here we use that the delay of all cells can show, let's say X% variation in their delays. Now you would either model this variation as -X% to +X%, or perhaps -(X/2)% to +(X/2)%. Let's say we choose the latter. Now we would model the delay of all cells and subject them to OCVs in a manner that our timing becomes pessimistic and we can claim that in the worst case, as long as process guys can ensure that the variation would be within the bracket of -X% to +X%, we'd be safe.

• Setup Analysis under OCV: In order to make setup analysis immune to process variations on silicon, we need to model the OCVs such that setup check becomes more pessimistic. That would be the case if we increase the data path delay by X% (you can take a call whether or not to apply a derate on the net delays. One can choose to apply a net derate based on the net length, and the metal layer in which the net is routed, a separate discussion for a separate post! :)); increase the launch clock path delay by X% and decrease the capture clock path delay by X%. Here you might want to check the post on Common Path Pessimism to see what type of clock path cells need to be exempted from OCVs.

Setup Analysis under OCV

• Hold Analysis under OCV: Hold check would be the exact opposite of what we did for setup, namely decrease the data path delay by X% (you can take a call whether or not to apply a derate on the net delays. Usually, we don't apply derate on net delays); decrease the launch clock path delay by X% and increase the capture clock path delay by X%.

Hold Analysis under OCV

We talked so much about spatial correlation, then inherent cancellation of random variations but didn't use either of these concepts while explaining OCVs. This is the precise reason OCVs tend to be generally pessimistic. And as we shrink the technology node, a need arises for an intelligent methodology to perform variation aware timing analysis. And the answer is AOCV.

Let's take a look at AOCV in detail:

Advanced On-Chip Variations (AOCV): AOCV methodology hinges on three major concepts:

• Cell Type: Variations should take into account the cell-type. Surely an AND gate an an OR gate can't exhibit the same variation pattern. Nor could an AND3X and an AND6X cell. The impact of variation should be calculated for each individual cell.
• Distance: As the distance in x-y coordinates increase, the systematic variations would increase and we might need to use a higher derate value to reflect the uncertainty in timing analysis to mitigate any surprises on silicon.
• Path Depth: If within a given distance, path depth is more, the impact of systematic variations would be constant, but the random variations would tend to cancel each other. Therefore as the path depth increases (within the same unit distance), the AOCV derates tend to decrease.

Bounding Box Creation for AOCV

While performing reg2reg timing analysis, AOCV methodology finds the bounding box containing the sequentials, clock buffers between two sequentials and all the data cells. Now within a unit distance, if the path depth increases, the AOCV derate decreases due to cancelling of random variations. However, if the distance increases, AOCV derates increases due to increase in the systematic variations. These variations are modeled in form of a LUT.

Sample AOCV Table for Setup Analysis

Now some final comments for OCV vs AOCV. 

• For small path depths, OCV tends to be more optimistic than AOCV. (AOCV is more accurate).
• For higher path depths, OCV tends to be more pessimistic than AOCV. (AOCV is still more accurate).

I hope you were able to draw the above inference. If not, I'd be willing to engage in discussion down in the comments section. See you all till next time! :)

Placement of Clock Gating Cells

Clock Gating Cells are indispensable components to save dynamic power. However, the backend design engineers must be prudent while placing them. In this post, I'll talk about the trade-off between timing and power that underlies the placement of clock gating cells.

Consider that your SoC has two IPs, and a single clock source. These two IPs are synchronous, and might work independently (i.e. without any interaction with the other IP) in some use-case of the chip. This entails the need of two clock gating cells. Now the question arises: where to place these clock gating cells. 

• Near the sink, i.e. the clock source, or
• Near the source, i.e. the respective IPs

Let's take up pros and cons of the two placement scenarios.

1. Clock Gating Cells placed near the source: As shown in the figure, placing the clock gating cells near the clock source, can  the increase the uncommon clock path (shown in yellow). 

Recall from the post: Common Path Pessimism that while doing timing analysis, the effect of OCV derates come into picture for the uncommon clock path because the clock tree buffers in the uncommon path can behave differently and hence an STA engineer needs to take into account that extra uncertainty or pessimism while doing timing analysis. Such a scenario is therefore hostile to the timing engineers. However, from power perspective this scheme is quite favorable. Since as soon as the clock gate is turned "Off", all the clock buffers in the fanout of that clock gate are also "off" or in other words, they do not toggle and hence do not dissipate dynamic power. Like any engineering problem, there exists a trade-off between two conflicting factors, and designers often need to prioritize.

2. Clock Gating Cells placed near the sink: While this scenario, with greater common path as compared to the first scenario and hence making the timing easier to met, is not friendly from the power perspective. 

All the clock tree buffers  in the common clock path (shown tin red) lie before the clock gate and hence would always be "on" and keep on toggling at the clock frequency, thereby dissipating dynamic power.

Solution:

The pertinence of a solution is dictated on many factors. Permissible clock latencies, power dissipation specifications, timing closure challenges and also the use-case.

Let's say we had a requirement that IP 2 will function if and only if IP 1 is on. In this case we could have placed the clock gates in series like this:

By having the two clock gates in series, we would save the dynamic power of all the clock tree buffers in the fanout of first clock gate. Moreover, the uncommon path is significantly less as compared to the scenario 1.

Again note that this solution would not work if we had the use-case where IP 1 could be "off", while IP 2 still "on".

Common Path Pessimism

Common Path Pessimism is a common source of some extra pessimism in timing analysis. Before we delve further into this, note that pessimism can be of two types: Intended and Unwanted. Intended pessimism could be like adding some extra uncertainty for clock skew before CTS stage, or some uncertainty for noise before SI (Signal Integrity) analysis. It is often prudent to have this pessimism taken upfront in your design because it will avoid any surprises when you move from one stage to another. 

Having said that, which category do you reckon should Common Path Pessimism fall? Let's define it first and then we'll take a look at it objectively.

When any pair of launching and capturing flop have a some portion of clock path as common, the difference between the max and min delay of that common clock segment is referred to as Common Path Pessimism. We discussed the rationale behind the use of timing derates briefly in the post: OCV vs PVT. Note that the entire timing analysis revolves around this intended pessimism where the basic aim is to make the timing paths more critical to avoid seeing any surprises in the silicon. EDA tools, however, themselves have quite a fair amount of pessimism, it is always prudent for the STA engineers to augment some uncertainty/pessimism in their timing analysis.

Convince yourself that:

• Setup check would be most critical when clock reaches the launching flop late and capturing flop early; and the data path takes more delay.
• Hold check would be most critical when clock reaches the launching flop early, capturing flop late and data path takes less delay.

Consider the following example with no common clock path and note that we have just applied the above principle to add pessimism in timing analysis.

So, while doing setup analysis, the clock tree buffers in the launching path would be derated by +5% and in the capturing path would be derated by -5&. The data path would be derated by +5%.
While doing hold analysis, it would be the opposite. The clock tree buffers in the launching path would be derated by -5% and in the capturing path would be derated by +5&. The data path would be derated by -5%.

How would the situation change when there's a common clock path? Let's take a look.

Ideally speaking, for setup analysis, we would like to take the +5% derated value of the delay of these buffers while considering launching path and -5% derated value while considering the capture path. However, here lies the catch! How can the same buffer or set of buffers be derated differently for launch and capture? Recall from the definition of OCV that it is the intra-chip variation in PVT that STA engineers consider them in the first place.

However, now these buffers, they are in the same location. So at a time they would behave in a similar manner. It does not make sense to consider different delays for same buffers. And this is the origin of common path pessimism and in usually unwanted. What we can do is (or rather what EDA tools tend to do is), do the calculation considering common path to be non-existent. And in the slack, add the double derated value of the common buffers, which would be 10% of the three common buffers in this case. This is referred to as Common Path Pessimism Removal.

OCV vs PVT

In the post PVTs and How They Impact Timing, we talked about the confluence of the Process-Voltage and Temperature factors and their impact on timing. I would urge the readers to go through the post in order to grasp the difference between two key terminologies used in the VLSI industry- 

• OCV: On Chip Variation;
• PVT: Process, Voltage and Temperature

While PVTs are inter-chip variation which depend largely on external factors like: the ambient temperature; the supply voltage and the process of that particular chip at the time of manufacturing. Like PVTs, OCVs are also variations in process, voltage and temperature. But, hey, where's the difference? OCVs are intra-chip variations! To elucidate more about the OCVs, let's talk in terms of chips!

• Variation in Process: There are millions of devices (standard cells); and probably billions of transistors packed on the same chip. You can expect every single transistor to have the same process or the channel length! If we say that the chip manufactured exhibits, let's say, worst process, it means that the  channel length tends to deviate towards the higher side. This variation may be more for some transistors and less for some. It can be a ponderous task to quantify this variation between the transistors of the device, and is often modeled as a percentage deviation from the normal.
• Variation in Voltage: All the standard cells need voltage supply for their operation. And voltage is usually 'tapped' from the voltage rail via interconnects which have a finite resistance. 

In two parts of the chip, it is fairly probable for the interconnect length to be different, resulting in a finite difference in the resistance values and hence the voltage that the standard cells actually receive. As evident above, the voltage received by the standard cells on the right would be less as compared to those on the left.

This variation would be less, probably of the order of a few mili-volts, but is can be significant, is again modeled as OCV.

• Variation in Temperature: Some parts of the chip can be more densely packed or might exhibit more active switching ss compared to the other parts. In these regions, there is a high probability of the formation of localized 'HOT SPOTS' which would result in increased temperature in some localized areas of the chip. Again, this difference might be order of a few degree centigrade, but can be significant.

All the above mentioned variations are examples of On-Chip-Variations. And usually, these variations are modeled as a fixed percentage of delays. For examples, a 4% OCV derate would mean, that the delays of cells in the data path are inflated by 4% while doing setup analysis and decreased by 4% while doing hold analysis. Same methodology is applied for the clock paths. However, it would be different for launching and capture clock paths. That also gives rise to an interesting topic of Common Path Pessimism Removal which we shall take up shortly.