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

There are  6 × 10¹²  holes are there in a sample of size 1 cm × 1 mm

In a pure semiconductor, we know that the number of electrons is equal to the number of holes present.

So, no. of holes = no. of electrons = 6 × 10¹⁹ per 1 m³ of volume.

Given, the volume is 1cm × 1 cm ×  1 mm

= 10⁻² m × 10⁻² m × 10⁻³ m                          [1cm = 10⁻² m, 1mm = 10⁻³ m  ]

= 10⁻⁷ m³

Thus, the number of holes in the volume 10⁻⁷ m³

= Holes present per m³ × Volume

=  6 × 10¹⁹ ×  10⁻⁷

=  6 × 10¹²

Answer 2

Explanation:

• Pure semiconductors are the semiconductors that do not have doping and they are the intrinsic semiconductors.
• It is known that the number of electrons conducted is equal to the holes number.
• In volume 1 m3 , the number of electrons in volume = $6 \times 1019$
• In volume 1 m3 the number of holes = $6 \times 1019$

Given volume:

$V=1 \mathrm{cm} \times 1 \mathrm{mm} \times 1 \mathrm{cm}$

$\Rightarrow \mathrm{V}=1 \times 10^{-2} \times 10^{-3} \times 1 \times 10^{-2}$

$\Rightarrow \mathrm{V}=10^{-7} \mathrm{m}^{3}$

So, in volume $10-7 \mathrm{m} 3$, the number of holes:

$N=6 \times 10^{-7} \mathrm{x} \times 10^{19}=6 \times 10^{12}$