(a) A frequently used empirical approximation for the yield of an IC process as a function of die size is Yws = exp (A/A0) where

(a) A frequently used empirical approximation for the yield of an IC process as a function of die size is Yws = exp (ˆ’A/A0) where A is the die area and A0 is a constant. Using Fig. 2.68, determine approximate values of A0 for each of the three processes shown. Use the point on the curve at which the yield is e ˆ’1 to determine A0. Plot the yield predicted by this expression and compare with the curves shown in Fig. 2.68.

Fig. 2.68.

(b) Use the expression derived in (a), together with the gross-die-per-wafer curves shown in Fig. 2.69, to develop an analytical expression for the cost of silicon per unit area as a function of die size, Ydf , Yft , Cp, and Cw for each of the three processes A,B, and C.

Fig. 2.69.

100 80 60 40 Process A 10 Process B 4 Process C 10 20 30 40 50 60 70 80 90 100 Die size (mil? x 10) Yws (yield, %) 2. 100,000 12" Diameter wafer 10,000 8" Diameter wafer 4" Diameter wafer 1,000 100 10 103 104 105 Die size (mil?) 106 107 Gross die/wa fer