When doing statistical characterization,
excellent nominal characterization accuracy
is essential. Nominal correlation for path
delays of within 2% of Spice reduces the
uncertainty that must be accounted for
through statistical distributions.
Keeping the runtime under control with
acceptable throughput is very important, especially
for random variations. That's because
they have to be modeled on a per-transistor
(intra-cell) basis. In addition, a given transistor
may be significantly affected by random variations
of a number of parameters in terms of the
measurable electrical impact seen on the cell
as a whole.
The brute-force approach to characterization
is to take measurements for every transistor
over the entire range of variation of
every parameter. But what's really of interest
is reducing the number of needed circuit
measurements, which requires considerable
intelligence and sophistication. The techniques
applied should efficiently determine
how to prune out measurements that do not
add to the overall cell's statistical distributions
of electrical properties, preserving accuracy
while reducing runtime.
An acceptable result of such measurement
optimization is that statistical characterization
takes less than 10 times the time required for a
single PVT-point (process, voltage, and temperature)
characterization.
Systematic variations are characterized by
capturing the sensitivity of overall cell electrical
behavior to these variations. Because these
variations are not random, their use allows for a
reduction in the range of statistical variation
that must be modeled, or, in other words, a
reduction in uncertainty. These variations also
require fewer measurements for characterization.
As a result, they provide far better runtime
than statistical characterization.
With chip designers utilizing multi-vendor
solutions, it becomes imperative for characterization
to support all major statistical model
formats, such as s-ECSM and CCS-VA, and
formats for statistical timing-analysis tools,
such as Magma's Quartz SSTA and Extreme
Design Automation's GoldTime. Finally, SSTA
characterization must be automated to
ensure ease of use comparable to traditional
characterization.
Khalid Islam is the senior product manager
with the Custom Design Business Unit at Magma
Design Automation, San Jose, Calif.
