Suppose that you use 200-mm wafers, and also assume that you can get functional dies only within the inner 190-mm diameter (outer 5-mm margin is full of defects). On the one product that you have run so far, a chip with area 5 × 5 mm, the yield is 80%.

(a) Using the simple Poisson model, find the defect density (in the good area of the wafer) and plot the yield as a function of S, where S is the square root of the area of the die in production. Plot the total and the good die per wafer as a function of S on the same graph.

(b) Repeat the calculations and plots in (a) using the negative binomial model (α = 1.5).

(c) Suppose that an alternative explanation for the data were that some fraction f of the wafer were perfect and the rest were totally dead. This is the "black-white" model that assumes a perfect deterministic clustering of defects. What is f? Plot the "good die" per wafer for this model on the same graph as in (a)-(b).

(d) What defect density reduction would you have to achieve to yield 50% of the available die at S = 15 mm according to models (a), (b), and (c)?