this is my first time posting here so hopefully I'm not breaking any rules. I have a fairly simple question but I can't seem to wrap my head around it. I'm currently reading "Computer architecture: A quantitative approach" and in chapter 1 the writers mention defect rates in integrated circuit wafers. A 28nm process will have "0.016-0.047 defects per square centimeter". I'm somehow not sure if this represents a percentage or simply a quantity, but I'm guessing it's not a percentage because percentages scale with any area, i.e. they wouldn't mention an area. I want to know how this would scale to square meters. I understand that cm^2 scales to m^2 by a factor of 10^4, so does this mean that the defects per square meters is 160-470? Or are there other factors to take into account when scaling areas like this?
How does a defect rate scale with the area of a wafer
area
Related Solutions
Here is a heuristic argument.
It all started with counting how many objects of the same kind (say, barrels of wine, sacks of grains, etc), are there when they are packed in rectangular arrays. Quite early in human history - I am willing to conjecture this -- people understood that if you pile $7$ rows of barrels, and each row has, say, $6$ barrels, then you don't have to count all the $42$ barrels separately - it is sufficient to count one row, and just take the result $7$ times. Hence the word "times" we use for multiplication.
That multiplication of the lengths of the sides of a rectangle give it's area is just the realisation that if you pack your objects in an ideal manner -- you fill up the area completely, as well as the lengths of the sides.
Hint: You know the area of the square and the area of the circle, so the question is the area of the funny shapes in the lower left and right corners. In problems like these, you should look for ways to cut up the shapes into something you know. I added two lines and got this
Now your funny shapes are triangles less the bulge of a circle around the secant. That bulge is the difference between a sector of a circle and a triangle. You need to find the coordinates of the intersection of the circle and the downward lines from the top center of the square. Then find the angle the secant from there to the bottom center represents.
Best Answer
Yes, that's correct.
'$0.016 - 0.047$ defects per square centimeter' means for $1$ square centimeter, there will be between $0.016$ and $0.047$ defects.
Therefore, for $1$ square meter $=$ $10^4$ square centimeters, there will be between $0.016 \cdot 10^4 = 160$ and $0.047 \cdot 10^4 = 470$ defects.