Hardware Reference
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so need not be tested. For simplicity, we'll just assume the wafer yield is 100%. Defects per unit
area is a measure of the random manufacturing defects that occur. In 2010, the value was typ-
ically 0.1 to 0.3 defects per square inch, or 0.016 to 0.057 defects per square centimeter, for a 40
nm process, as it depends on the maturity of the process (recall the learning curve, mentioned
earlier). Finally, N is a parameter called the process-complexity factor, a measure of manufac-
turing difficulty. For 40 nm processes in 2010, N ranged from 11.5 to 15.5.
Example
Find the die yield for dies that are 1.5 cm on a side and 1.0 cm on a side, assum-
ing a defect density of 0.031 per cm 2 and N is 13.5.
Answer
The total die areas are 2.25 cm 2 and 1.00 cm 2 . For the larger die, the yield is
For the smaller die, the yield is
That is, less than half of all the large dies are good but two-thirds of the small
dies are good.
The botom line is the number of good dies per wafer, which comes from multiplying dies
per wafer by die yield to incorporate the effects of defects. The examples above predict about
109 good 2.25 cm 2 dies from the 300 mm wafer and 424 good 1.00 cm 2 dies. Many micropro-
cessors fall between these two sizes. Low-end embedded 32-bit processors are sometimes as
small as 0.10 cm 2 , and processors used for embedded control (in printers, microwaves, and so
on) are often less than 0.04 cm 2 .
Given the tremendous price pressures on commodity products such as DRAM and SRAM,
designers have included redundancy as a way to raise yield. For a number of years, DRAMs
have regularly included some redundant memory cells, so that a certain number of flaws can
be accommodated. Designers have used similar techniques in both standard SRAMs and in
large SRAM arrays used for caches within microprocessors. Obviously, the presence of re-
dundant entries can be used to boost the yield signiicantly.
Processing of a 300 mm (12-inch) diameter wafer in a leading-edge technology cost between
$5000 and $6000 in 2010. Assuming a processed wafer cost of $5500, the cost of the 1.00 cm 2 die
would be around $13, but the cost per die of the 2.25 cm 2 die would be about $51, or almost
four times the cost for a die that is a litle over twice as large.
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