AdvancedQuestion 41 of 63Source: Synopsys PrimeTime User Guide: Parametric On-Chip Variation (POCV)

How does distance-based POCV derating differ from single-parameter POCV, and can the two combine?

From PDVerse STA Mentor Guide · pdVerse Mentor Guide

By Tabish Iqbal · 9+ Years VLSI Physical Design Experience

Short Answer

Single-parameter POCV models each cell's own random variation independently, as a statistical distribution built from that cell's own sigma data. Distance-based POCV instead models systematic variation across a timing path as a function of the physical distance the path spans on the die, computing one scalar derate factor from a lookup table and applying it to shift the mean of the path's timing - never the standard deviation - and the two can be combined in the same analysis, since PrimeTime computes and applies each contribution independently.

Two identical 6-stage buffer chains drawn on a chip floorplan, one confined to a small 200 by 200 micron block and one stretching 3mm across the die; both show the same single-parameter sigma per stage, but the long chain's bounding-box diagonal produces a larger mean-shifting derate factor than the short chain's — Technical Reference DiagramHow does distance-based POCV derating differ from single-parameter POCV, and can the two combine?

Technical Explanation

Single-parameter variation treats each cell instance as independently random. Both the cell's own behavior and how that randomness propagates through the logic are modeled as statistical distributions, one per cell instance.
Distance-based variation is about systematic drift across the die, not per-cell randomness. It assumes two points far apart on the chip are more likely to see different process conditions than two points close together, and it derates based on that physical separation.
The distance used is the diagonal of a bounding box around the path's objects. PrimeTime computes a bounding box that contains every object on the timing path, then uses the diagonal - the largest possible distance between any two of those objects - to look up a derate factor from a table.
Graph-based and path-based analysis compute that distance differently. In graph-based analysis, each cell gets a distance-derived factor computed from every path that passes through it; in path-based analysis, one path gets a single distance factor computed just for that specific path.
A distance-based factor only shifts the mean, never the sigma. When distance-based derating is layered onto a single-parameter statistical distribution, it moves where the distribution is centered - it does not widen or narrow the spread that the single-parameter sigma already describes.
Both can be provided in the library and used together. LVF single-parameter sigma tables and LVF distance-based derate tables can coexist in the same library, with PrimeTime computing each contribution on its own and combining them for the final timing result.

Common Mistake

Assuming a distance-based derate factor works the same way as a single-parameter sigma, and that applying both means "adding two sources of spread" to a path's timing distribution.
Distance-based derating only shifts the mean of the distribution; it leaves the standard deviation exactly as the single-parameter data set it, so the two effects are not both widening the same uncertainty in the same way.
Cost: a manual sanity check that expects the combined variance to grow proportionally with both effects finds a smaller-than-expected spread and incorrectly assumes the distance-based data is not actually being applied.

Follow-up Question & Model Response

If two functionally identical paths have very different bounding-box diagonals - one entirely within a small block, one crossing most of the die - what should you expect to differ between their POCV-derated timing, and what should stay the same?

Candidate Model Response: The mean of the longer path's timing distribution should shift by a larger distance-based derate factor than the shorter path's, since the derate is looked up directly from the bounding-box diagonal and a larger diagonal typically maps to a larger systematic-variation assumption in the table. What should stay comparable, all else equal, is each path's standard deviation contribution from single-parameter variation, since that part of the model is computed per cell instance and does not depend on how far apart those instances happen to sit on the die. In practice this means two paths with identical logic can end up with different derated means but very similar spreads, which is a useful check that the two variation mechanisms are being applied independently rather than conflated into one.

Practical Example

A 5nm design has two structurally identical 6-stage buffer chains: one entirely inside a small 200 x 200 micron IP block, the other stretching across a 3mm reticle from a memory controller to a far-corner PHY. Both get the same single-parameter sigma contribution per stage from the library's LVF tables. The short chain's bounding-box diagonal looks up a late derate factor of about 1.1 in the aocvm_distance_template table; the long chain's much larger diagonal looks up a late derate factor of about 1.4 from the same table. The result is that the long chain's mean delay is derated roughly 27% more heavily than the short chain's, even though both chains have the identical per-stage standard deviation from single-parameter POCV.

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