Chapter 1 Solutions
Case Study 1: Chip Fabrication Cost
1.1 a. Yield ¼1/(1 + (0.04 2))
14
¼0.34
b. It is fabricated in a larger technology, which is an older plant. As plants age,
their process gets tuned, and the defect rate decreases.
1.2 a. Phoenix:
Dies per wafer ¼ π 45=2ðÞ
2
=2 π 45ðÞ=sqrt 22ðÞ¼795 70:7 ¼ 724:5 ¼ 724
Yield ¼ 1= 1+ 0:04 2ðÞðÞ
14
¼ 0:340
Profit ¼ 724 0:34 30 ¼ $7384:80
b. Red Dragon:
Dies per wafer ¼ π 45=2ðÞ
2
=2 π 45ðÞ=sqrt 2 1:2ðÞ¼1325 91:25 ¼ 1234
Yield ¼ 1= 1+ 0:04 1:2ðÞðÞ
14
¼ 0:519
Profit ¼ 1234 0:519 15 ¼ $9601:71
c. Phoenix chips: 25,000/724 ¼ 34.5 wafers needed
Red Dragon chips: 50,000/1234 ¼40.5 wafers needed
Therefore, the most lucrative split is 40 Red Dragon wafers, 30 Phoenix wafers.
1.3 a. Defect-free single core ¼ Yield ¼ 1/(1 + (0.04 0.25))
14
¼0.87
Equation for the probability that N are defect free on a chip:
#combinations (0.87)
N
(1 0.87)
8N
Yield for Phoenix
4
: (0.39 + 0.21 + 0.06 + 0.01) ¼0.57
Yield for Phoenix
2
: (0.001 + 0.0001) ¼ 0.0011
Yield for Phoenix
1
: 0.000004
b. It would be worthwhile to sell Phoenix
4
. However, the other two have such a
low probability of occurring that it is not worth selling them.
# defect-free # combinations Probability
8
7
6
5
4
3
2
1
0
1
0.32821167
0.39234499
0.20519192
0.06132172
0.01145377
0.00136919
0.0001023
4.3673E-06
8.1573E-08
8
28
56
70
56
28
8
1
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