On-Chip Variation (OCV)
Analysis
AOCV - Advance On-chip Variation
POCV - Parametric On-Chip Variation
Process variation can be briefly categorized into chip-to-chip (die-to-die)
variation and on-chip variation (OCV).chip-to-chip variation effect is captured by
analyzing the design in different timing corners-chip variation is captured by applying early
and late timing derating factors to timing path elements.
As the feature size of the technology nodes keeps
decreasing, on-chip variation has become more complicated. Applying a single
derating factor has become too simplistic and can either cause too much
pessimism on setup paths or bring potential risk on hold paths. In order to
overcome these problems, the Advanced OCV (AOCV) model was proposed to provide
path depth and distance-based derating factors to capture random and systematic
on-die variation effects respectively, as shown below.
Advance on-chip variation
(AOCV) :
AOCV models derating factor as a combination of
path depth and distance. PrimeTime (Timing signoff tool) models random on-die
variation and uses the derating factor as a function of path depth (stage count).
It models systematic on-die variation and uses the derating factor as a function of
distance (path bounding box). Typically, random on-die variation dominates, and
therefore the path depth-related OCV derate component tends to be the dominant
factor between the two in an AOCV model.
By modeling the derating factor as a function of path depth, depth-based AOCV captures the statistical cancellation effect of random variations. However, using path depth to determine derates for a path elements is still a simplistic approach which can add pessimism in graph-based analysis. It also makes incremental timing very challenging because of the need to update derated delays due to stage count (path depth) dependency across the fan-in and fan-out cone from the location where the cell is inserted or removed.
Parametric on chip variation (POCV) :
An advantage of parametric on-chip variation (POCV) over AOCV is that it reduces the slack pessimism between graph-based and path-based analysis. This results in less pessimistic graph-based timing results, which can reduce the amount of effort needed in ECO fixing. Furthermore, it also makes incremental timing more efficient compared with AOCV.
POCV models instance delay as a function of a random variable that is specific to the instance. That is, the instance delay is parameterized as a function of the unique delay and its variation, shown in below.
Parameterized delay of cell is calculated by
formula,
Delaynom is the delay of the cell, and Delayvar
is the one sigma value of the cell's delay distribution and P is the standard
normal random variable N(0,1).
The variation in POCV is a function of the library cell.
The value of delay variation can be easily obtained from the data used to generate depth-based AOCV tables.
There are two forms of POCV input data that you can feed into PrimeTime:
• A side file with POCV single coefficient
• A library with POCV slew-load table per timing arc
A side file with POCV single coefficient applied on a library, a cell has higher precedence than POCV slew-load table.
The variation in POCV is a function of the library cell.
The value of delay variation can be easily obtained from the data used to generate depth-based AOCV tables.
There are two forms of POCV input data that you can feed into PrimeTime:
• A side file with POCV single coefficient
• A library with POCV slew-load table per timing arc
A side file with POCV single coefficient applied on a library, a cell has higher precedence than POCV slew-load table.
POCV coefficients for a library cell can be
extracted from Monte-Carlo HSPICE simulation using the following equation.
Source: From a Friend in PDFundamentals Group---Thanking him for sharing his knowledge
