This book looks at the subject of variations in a chip's operating conditions and random variations across the chip. Finding out if the chip will provide sufficient yield is paramount to business success...
Chapter 3 A pictorial primer on probabilities: Intuition on PDFs and circuits
chapter talks about probability density functions, Monte Carlo sampling
and yield estimation. Thankfully, for me, they chose to use a graphical
way to explain most of these concepts rather than equations that make
my eyes glaze over. They do eventually resort to equations for some of
them towards the end.
Chapter 4 3-sigma verification and design: Rapid design iterations with Monte Carlo accuracy
I will run an excerpt of this chapter over on EDN.
chapter deals what typical analog, RF and I/O circuits where the target
yield falls within three-sigma. It applies the general techniques and
mathematical methods introduced in the previous chapters to global and
local process variations in a statistical manner. How many Monte Carlo
samples are required? This chapter attempts to answer that question. It
starts by looking at various design flows and describes how sigma driven
corners are selected. Sigma-driven corner extraction is a crucial
element of the suggested design flow and attempts to find corners that
represent the bounds of performance. Three design examples are provided
to demonstrate the techniques. As with other chapters, useful appendices
are provided that go into more depth on some of the theoretical
Chapter 5 High-sigma verification and design: The accuracy of five billion Monte Carlo samples in minutes
blocks in a design are replicated many times over, such as memory cells
or digital standard cells. Even higher confidence is required for these
and this chapter deals with them. It starts by examining a 6 transistor
bit cell and the number of samples that would be required to get the
necessary level of confidence. Existing high-sigma approaches are
examined before outlining the High-Sigma Monte Carlo method and showing
the technique applied to five circuits.
Then it looks at applying this analysis to the system level and applying it to an SRAM memory slice
Chapter 6 Variation-aware design: Manual sizing, automated sizing and an integrated approach
previous chapters looked at a design and provided analysis tools to
assess if the design would have suitable yield under a range or
operating conditions. But the design itself can be changed to help
ensure that it will produce the desired yield, and that is the focus of
this chapter. It concentrates on device sizing and looks at manual,
automatic and an integrated approach where the user is guided towards
making the greatest-benefit design choices first.
Chapter 7 provides some conclusions.
few nits - but as you will see these are all very minor and do not get
in the way of reading this book. I wish books were written in a gender
neutral manner. It is not difficult to do and it is about time we
removed gender bias where possible. RTL has not stood for Resistor
Transistor Logic for a long time and mistakes like this show when non
industry knowledgeable people are used as editors. I wish the references
were marked as to where they were used.
So there you have it. If you are interested in variation-aware design then this book
will probably be a good one to have on your book shelf. This is
especially the case if you are working on custom logic or highly
replicated cells such as standard cells used in memories or in the
– keeping you covered
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