Question

In a pure semiconductor, the number of conduction election 6 × 10¹⁹ per cubic metre. How many holes are there in a sample of size 1 cm × 1 mm?

Answer 1

Pure semiconductors are intrinsic semiconductors or semiconductors without any doping.
We know that for pure semiconductors, the number of conduction electrons is equal to the number of holes.
Number of electrons in volume 1 m³ = $6\times {10}^{19}$
Number of holes in volume 1 m³ = $6\times {10}^{19}$
Given volume:
V = 1 cm × 1 cm × 1 mm
$\Rightarrow$V = 1 × 10⁻² × 1 × 10⁻² × 10⁻³
$\Rightarrow$V = 10⁻⁷ m³
Now,
Number of holes in volume ${10}^{-7}{\mathrm{m}}^3$:
N = 6 × 10¹⁹ × 10⁻⁷ = 6 × 10¹²