Question

How does the energy gap of an intrinsic semiconductor vary, when doped with a trivalent impurity?

Answer 1

1. When the intrinsic semiconductor is doped with trivalent impurity that means it formed extrinsic semiconductor of a p-type.

2. In a P-type semiconductor, energy band increases.

3. Now the fermi level will have to move away from it's mid gap portion to conserve the number of particles as well as to maintain the electrical charges neutrally.

4. Fermi levels shifts closes to the valance band because, holes are the majority carriers Fermi level in P-type semiconductor is given by,

$E_F=E_V+KT\ln \frac{N_V}{N_A}$

Where,

$E_F⟶$Fermi level.

$E_V⟶$Highest energy level of valance band.

$K⟶$Boltzmann's constant.

$T⟶$Temperature.

$N_V⟶$Density of states in valance band.

$N_A⟶$Concentration of acceptors.