Question

1 )

a) Under what conditions would the Fermi energy be at mid-gap? b) Near the conduction band? c) Near the valence band?

2)

What are a direct and indirect bandgap semiconductors? Explain the difference between the two.

Answer 1

Fermi Level is the probability of occupancy of energy levels in conduction and valence band.

Position of Fermi level deponds upon nature of doping and quantity of doping .

Case 1: Intrinsic Type of Semi Conductor

In Intrinsic type semi conductor the number of holes in valence band is equal to the number of electrons in the conduction band and thus  the probability of occupation of energy levels in conduction band and valence band are equal.

So Fermi Level Energy

  

Case 2: N- Type

In N pentavalent impurities like Phosphorus (P) is added which will provide free electron .Hence number of free electrons will increase and thus probability of finding an electron in conduction band is more and hence probability of occupation of energy levels by the electrons in the conduction band is greater than the probability of occupation of energy levels by the holes in the valence band.

and Fermi Energy Ef

where Nc= Effective density of states in  the conduction band and Nd is concentrtion of Donar (Pentavalent) atoms.

Case 3: P Type

In p-type semiconductors, trivalent impurity like Gallium(G) is added which creates large number of  hole in valance band and hence probability of occupation of energy levels by the holes in the valence band is greater than the probability of occupation of energy levels by the electrons in the conduction band.

where

Nv is  Effective density of states in  the Valence band and Na is concentrtion of Acceptor (Trivalent) atoms.

2.

1. In direct band-gap semiconductor maximum energy level of the valence band aligns with the minimum energy level of the conduction band with respect to momentum where as in in indirect band gap maximum energy level of the valence band and the minimum energy level of the conduction band are misaligned with respect to momentum.
2. In direct band-gap probability of a radiative recombination is high where as in  indirect band-gap probability of a radiative recombination is comparatively low as compared to direct band.
3. In direct band-gap due to radioactive recombination there is emission of photons (Energy is released in form of light energy) and thats why it is well suited for making LASER and LEDS but in case of indirect band-gap energy is released in form of heat energy.
4. Examle of direct band-gap -  Gallium Arsenide and Example of  indirect band-gap is Silicon.