# Electrons with in the forbidden gap

1. Oct 1, 2008

### GAGS

Hi all, on one side we say that probability of finding electron with in the forbidden gap is zero, on other side we define fermi level as highest filled energy level(at absolute zero) lying in the mid of forbidden gap.Also for(T>0) probability of finding electron is 1/2 upto fermi level. So what's that dilemma???
Electrons are lying with in the forbidden gap!!! or some-thing is mis-understood here.

2. Oct 2, 2008

### Cthugha

Strictly speaking the Fermi level in the meaning as you use it, is a concept, which is just valid for metals, which do not have a band gap. In metals the Fermi level equals the electron chemical potential (the energy you need to bring into the system to add another particle.) at 0K.

Now some textbooks are a bit sloppy and identify the chemical potential with the Fermi energy even for semiconductors, where the chemical potential can of course be equal to an energy inside the band gap, but the Fermi level in its strictest meaning of course can't.

3. Oct 2, 2008

### ZapperZ

Staff Emeritus

Are you sure you're not the same person?

Zz.

4. Oct 2, 2008

### Defennder

Wow, Zz you sure have a good memory. That thread was dated 2 years ago! Anyway it isn't surprising that this question has been asked multiple times. I myself had similar doubts about this when I first learned semiconductor physics.

5. Oct 2, 2008

### ZapperZ

Staff Emeritus
True. This is a rather common question. In fact, I can recall of at least another thread asking almost the same thing.

Like an elephant, I never forget. Now where are my keys?

Zz.

6. Oct 2, 2008

### GAGS

Thank you so much to all of you.Yes no doubt Zapper Z has very sharp memory. No sir i am not the same person to ask question.

7. Apr 5, 2011

### xw0927

i also confused about it when i m studying the semiconductor now....i had doubt like the statement/question post by GAGS

8. Apr 8, 2011

### raul_l

The Fermi level comes from Fermi-Dirac statistics. But it's not the only distribution function. You also have to think about the density of states. And while the Fermi-Dirac function F(E) (E - energy) might be non-zero in the forbidden gap the density of states g(E) is zero. The number of electrons with a specific energy N(E) is given by N(E) = F(E)g(E).

9. Apr 8, 2011