Hardware Reference
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The first term is the ratio of wafer area (π r 2 ) to die area. The second compensates for the
“square peg in a round hole” problem—rectangular dies near the periphery of round wafers.
Dividing the circumference (π d ) by the diagonal of a square die is approximately the number
of dies along the edge.
Example
Find the number of dies per 300 mm (30 cm) wafer for a die that is 1.5 cm on a
side and for a die that is 1.0 cm on a side.
Answer
When die area is 2.25 cm 2 :
Since the area of the larger die is 2.25 times bigger, there are roughly 2.25 as
many smaller dies per wafer:
However, this formula only gives the maximum number of dies per wafer. The critical ques-
tion is: What is the fraction of good dies on a wafer, or the die yield ? A simple model of integ-
rated circuit yield, which assumes that defects are randomly distributed over the wafer and
that yield is inversely proportional to the complexity of the fabrication process, leads to the
following:
This Bose-Einstein formula is an empirical model developed by looking at the yield of many
manufacturing lines [Sydow 2006]. Wafer yield accounts for wafers that are completely bad and
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