Question

If there are 10 billion transistors (each of a square shape) uniformly (without space) distributed on a silicon chip with the squared area of 1 cm^2, what is the linear size of each unit?

Answer 1

the transistors have L=1 mm of linear size

Explanation:

For the silicon chip the area is A=1 cm² and for the transistors the area is At=L² (L=linear size) . Then since N= 10 billion transistors of area At should fit in the area A

A=N*At

A=N*L²

solving for L

L= √(A/N)

Assuming that 1 billion=10⁹ (short scale version of billion), then

L= √(A/N) = √(1 cm²/10⁹) = 1 cm / 10³ = 1 mm

then the transistors have L=1 mm of linear size