Two wafer sizes are to be compared: a 156-mm wafer with a processable area = 150mm diameter circle and a 312-mm wafer with a processable area = 300mm diameter circle. the ic chips in both cases are square with 10 mm on a side? assume the cut lines (streets) between chips are of negligible width. what is the percent increase in (a) wafer diameter, (b) processable wafer area, and (c) number of chips for the larger wafer size?

a) 100%

b) 300%

c) 301 %

Explanation:

The first wafer has a diameter of 150 mm.

The second wafer has a diameter of 300 mm.

The second wafer has an increase in diameter respect of the first of:

((300 / 150)  - 1) * 100 = 100%

The first wafers has a processable area of:

A1 = π/4 * D1^2

The scond wafer has a processable area of:

A2 = π/4 * D2^2

The seconf wafer has a increase in area respect of the first of:

(A2/A1 * - 1) * 100

((π/4 * D2^2) / (π/4 * D1^2) - 1) * 100

((D2^2) / (D1^2) - 1) * 100

((300^2) / (150^2) - 1) * 100 = 300%

The area of a chip is

Ac = Lc^2

So the chips that can be made from the first wafer are:

C1 = A1 / Ac

C1 = (π/4 * D1^2) / Lc^2

C1 = (π/4 * 150^2) / 10^2 = 176.7

Rounded down to 176

The chips that can be made from the second wafer are:

C2 = A2 / Ac

C2 = (π/4 * D2^2) / Lc^2

C2 = (π/4 * 300^2) / 10^2 = 706.8

Rounded down to 706

The second wafer has an increase of chips that can be made from it respect of the first wafer of:

(C2 / C1 - 1) * 100

(706 / 176 - 1) *100 = 301%