Question

Let ΔE denote the energy gap between the valence band and the conduction band. The population of conduction electrons (and of the holes) is roughly proportional to e−ΔE/2kT. Find the ratio of the concentration of conduction electrons in diamond to the in silicon at room temperature 300 K. ΔE for silicon is 1.1 eV and for diamond is 6.1 eV. How many conduction electrons are likely to be in one cubic metre of diamond?

Answer 1

Explanation:

It is given in the question that

In the conduction band, the no. of electrons, $n=e^{-\Delta R / 2 k T}$

Diamond’s band gap, ΔE1 = 6 eV

Silicon’s band gap, ΔE2 = 1.1 eV

Now,

ndiamond = $e-\Delta E 12 \mathrm{kT}$nsilicon = $\mathrm{e}-\Delta \mathrm{E} 22 \mathrm{kT}$

Therefore, ndiamondnsilicon = $e-12 k T(\Delta E 1-\Delta E 2)$

⇒ndiamondnsilicon = $7.15 \times 10-42$

In diamond, the electrons of conduction per cubic metre is very less when it is compared to that of in silicon. It can also be said that it is almost zero.