Indium antimonide has a band gap of 0.23 eV between the valence and the conduction band. Find the temperature at which kT equals the band gap.

Calculate the number of states per cubic metre of sodium is 3s band. The density of sodium is 1013 kg m^–3. How many of them are empty?

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

The band gap for silicon is 1.1 eV.

(a) Find the ratio of the band gap to kT for silicon at room temperature 300 K.

(b) At what temperature does this ratio become one tenth of the value of 300 K? (Silicon will not retain its structure at these high temperatures)

When a semiconducting material is doped with an impurity, new acceptor levels are created. In a particular thermal collision, a valence electron revives an energy equal to 2kT and just reaches one of the acceptor levels. Assuming that the energy of the electron was at the topo edge of the valence band and that the temperature T is equal to 300 K, find the energy of the acceptor levels above the valence band.