Why Is the Fermi Level Positioned in the Forbidden Gap in Semiconductors?

[ravi_nigam]

1. Fermi level is also defined as highest energy level at which electron can exist at 0K then it should be top of valence band but why is it in between conduction band and valence band ( in forbidden gap)? It should be in conduction band or valence band. How to explain this?

2. If density of state is 0 then no state should be there in semiconductor forbidden gap? So why we study of probability of occupancy of state in these conditions (semiconductor forbidden gap case).

3. How we calculate fermi level? Please suggest a very fundamental book; more basic than kittel

 

[Bill_K]

Consider the following simple example. Suppose you have just two energy levels A and B, and suppose the number of electrons present is just enough to fill the lower level A at T = 0. At some higher temperature T > 0, n electrons will be excited from A and move to B. Now where is E_F? Answer: Somewhere between A and B. In fact it is half way between A and B. In this example too, E_F is at an energy level where an electron cannot exist.

E_F is not defined, as you claim, to be the highest level occupied at T = 0. E_F is just a calculated value. It is a parameter in the Fermi distribution.