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Monte Carlo Analysis
Introduction to Uncertainty Analysis
Figure 11-2. Tail Probabilities and Yield Computation
These tasks typically enter in a manufacturing flow called “yield learning flow”. In such a flow,
yield is defined to be the proportion of the manufactured circuits that satisfy both the design
engineers’ and the process engineers’ specifications. The yield of a manufactured product
should increase from the initial design to the large-volume production. Yield is therefore related
to the cost of production. Process variations significantly impact circuit performance in nanoscale
technologies, and as process variations become relatively large beyond the 65nm
technologies, the task of yield estimation is increasingly important for circuit designers.
Yield is often interpreted as the probability of failure, rather than the probability of success. A
typical and important example is SRAM manufacturing yield, which is defined to be the
probability of a wrong operation (read, write, or retention) occurring in an SRAM circuit.
Yield may be quantitatively appreciated by considering an explicit value for the acceptable
quality limit (AQL). For example, an AQL for 1Megabit SRAM bit-cell circuits could be
100 ppm. If production of one million such circuits is targeted, the manufacturing process
cannot allow more than 100 defective bit-cells globally. This means that the probability of
failure must be at most:
A specific Monte Carlo algorithm must be used for such low probability values. Eldo provides a
a novel “rare events” Monte Carlo algorithm based on importance sampling techniques. Refer
to “Importance Sampling Monte Carlo” on page 452 for more information.
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Eldo® User's Manual, 15.3