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Dies Per Wafer Formula

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cherryic

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Hi all,

In Rabaey’s book <<Digital Integrated Circuits-A Design Perspective>>, he gives us a formula for evaluating the dies per warfer, which is dies per wafer = [π*(waferdiameter/2)^2]/die area – (π*waferdiameter)/sqrt(2*die area), I wanna know where is the second term (π*waferdiameter)/sqrt(2*die area) derived from? Thank you in advance.

Regards,
Cherryic
 

You have to subtract out the number of fractional dies touching the circle (on the edge of the wafer). The cirumference is \[\pi\]*wafer diameter, the width of each partial die is at most (when at a 45\[^{o}\]angle), \[\sqrt{{width}^2+{width}^2}\]. The ratio is the number that fit on the circle, on average, approximately.

Now you ask why the "most" case? Won't many of the times the dies be on top of each other, so why the longest part of the die? I guess the reason is because in the "least" case, where the width alone is the packing space on the edge of the circle, there is not much of a cut off, if you line it up correctly. (You don't want the central die necessarily at the center of the circle.) So you can beat out a random placement slightly.

Jason
 
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    erikl

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How could I *not* be on a board that allows tex in posts?

Right; your tex \[\pi\] is definitely nicer than the Unicode or UTF8 one! ;-)
Thank's a lot for your explanation!
 

Yeah, back in the day, I was the guy who procured the "TEX for the impatient" books for entire nasa gsfc theory division. I find it bizarre that html was started at cern but doesn't do equations. Bizarre. Especially because Tim Berners-Lee has a physics degree. I almost think html is an insult to technology. Probably html does do it, and I just never learned about it.
 

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