Answer:
We are given:
- Increase in dies per wafer = 10%
- Increase in defects per area unit = 15%
Let's assume the original number of dies per wafer was D, and the original die area was A. Then the new number of dies per wafer is 1.1D, and the new defect density is 1.15 times the original defect density.
The yield Y is defined as the number of good dies per wafer divided by the total number of dies per wafer. So:
Y = (number of good dies per wafer) / (total number of dies per wafer)
To find the die area, we can use the fact that the total wafer area is constant, so:
total wafer area = original number of dies per wafer x original die area
total wafer area = (1.1D) x A
The new die area can be found by dividing the total wafer area by the new number of dies per wafer:
new die area = (total wafer area) / (new number of dies per wafer)
new die area = [(1.1D) x A] / (1.1D)
new die area = A
So the die area is unchanged by the increase in dies per wafer.
To find the new yield, we need to calculate the number of good dies per wafer. Let's assume the original defect density was D0 defects per unit area, and the original yield was Y0. Then the new defect density is 1.15D0 defects per unit area, and the new yield is:
Y = (number of good dies per wafer) / (1.1D)
The number of bad dies per wafer is:
number of bad dies per wafer = (total number of dies per wafer) x (new defect density)
number of bad dies per wafer = (1.1D) x (0.15D0 x A)
number of bad dies per wafer = 0.165D0A
So the number of good dies per wafer is:
number of good dies per wafer = total number of dies per wafer - number of bad dies per wafer
number of good dies per wafer = 1.1D - 0.165D0A
Substituting this into the yield equation, we get:
Y = (1.1D - 0.165D0A) / (1.1D)
Y = 1 - 0.15(D0A/D)
So the new yield is 1 - 0.15(D0A/D) times the original yield.