Answer:
1. yield_1=0.959 and yield_2=0.909
2. Cost_1=0.148 and Cost_2=0.165
3. New area per die=1.912 cm^2 and yield_1=0.957
New area per die=2.85 cm^2 and yield_2=0.905
4. defects=0.042 per cm^2 and defects=0.026 per cm^2
Step-by-step explanation:
1. Find the yield for both wafers.
yield= 1/(1+(defects per unit area*dies per unit area/2))^2
Wafer 1:
Radius=Diameter/2=15/2=7.5 cm
Total Area=pi*r^2=pi(7.5)^2=176.71 cm^2
Area per die= 176.71/84=2.1 cm^2
yield_1= 1/(1+(0.020*2.1/2))^2
yield_1=1/1.04244=0.959
Wafer 2:
Radius=Diameter/2=20/2=10 cm
Total Area=pi*r^2=pi(10)^2=314.159 cm^2
Area per die= 314.159/100=3.14 cm^2
yield_2= 1/(1+(0.031*3.14/2))^2
yield_2=1/1.0997=0.909
2. Find the cost per die for both wafers.
Cost per die= cost per wafer/Dies per wafer*yield
Wafer 1:
Cost_1=12/84*0.959=0.148
Wafer 2:
Cost_2=15/100*0.909=0.165
3. If the number of dies per wafer is increased by 10% and the defects per area unit increases by 15%, find the die area and yield.
Wafer 1:
There is a 10% increase in the number of dies
10% of 84 =8.4
New number of dies=84.4+8=92.4
There is a 15% increase in the defects per cm^2
15% of 0.020=0.003
New defects per area= 0.020 + 0.003=0.023 defects per cm^2
New area per die= 176.71/92.4=1.912 cm^2
yield_1= 1/(1+(0.023*1.912/2))^2=0.957
Wafer 2:
There is a 10% increase in the number of dies
10% of 100=10
New number of dies=100+10=110
There is a 15% increase in the defects per cm^2
15% of 0.031=0.0046
New defects per area= 0.031 + 0.00465=0.0356 defects per cm^2
New area per die= 314.159/110=2.85 cm^2
yield_2= 1/(1+(0.0356*2.85/2))^2=0.905
4. Assume a fabrication process improves the yield from 0.92 to 0.95. Find the defects per area unit for each version of the technology given a die area of
Assuming a die area of 2cm^2
We have to find the defects per unit area for a yield of 0.92 and 0.95
Rearranging the yield equation,
yield= 1/(1+(defects*die area/2))^2
defects=2*(1/sqrt(yield) - 1)/die area
For 0.92 technology
defects=2*(1/sqrt(0.92) - 1)/2
defects=0.042 per cm^2
For 0.95 technology
defects=2*(1/sqrt(0.95) - 1)/2
defects=0.026 per cm^2