# I Fermi energy

1. Mar 16, 2016

### M.A.M.Abed

what i mean exactly what is the position of Fermi energy for semi conductor materials
1- at the highest of valance band
2- at the mid-way in energy gap like Fermi level at 0 K

Last edited: Mar 16, 2016
2. Mar 16, 2016

### DrDu

it would be helpful if you could rephrase your question in complete sentences.

3. Mar 16, 2016

### M.A.M.Abed

what i mean exactly what is the position of Fermi energy for semi conductor materials
1- at the highest of valance band
2- at the mid-way in energy gap

4. Mar 16, 2016

### ZapperZ

Staff Emeritus
You didn't..

Zz..

5. Mar 16, 2016

### M.A.M.Abed

I did

6. Mar 16, 2016

### DrDu

The precise definition of the Fermi energy is the value of the chemical potential of the electrons in the limit $T \to 0$K. This value may or may not coincide with an energy level of the system. In semiconductors it is somewhere between the upper end of the valence band and the lower end of the conduction band, not necessarily in the center.

7. Mar 16, 2016

### M.A.M.Abed

I know that it doesn't necessarily in the center.
also i know the difference between Fermi energy and Fermi level
also i know that Fermi level tends to be the same of Fermi energy at limit T=0 K
Fermi level is the level with probability 50% to occupies also represent the same electron chemical potential
Fermi energy is the difference between the max energy and the ground state energy (highest occupied level at T=0 K )
i am confused if Fermi energy highest occupied level at T=0 K which separate full levels under it and empty above it
if it in the energy gap it will be empty which contradict with definition (highest occupied level at T=0 K)

8. Mar 16, 2016

### DrDu

In the energy gap there is no level, so it makes no sense to say it is empty or not. In a semiconductor you have a well defined Fermi energy, but no Fermi level.

9. Mar 16, 2016

### M.A.M.Abed

yea the density of at it equal to zero
thank you
put what you mean by In a semiconductor you have a well defined Fermi energy
also is there any importance to define a work function for semi conductor or insulators since Fermi level in the energy gap ??

Last edited: Mar 16, 2016
10. Mar 16, 2016

### ZapperZ

Staff Emeritus
Yes, there is an "importance" to defining a work function for a semiconductor. In some cases, it is defined as the sum of the energy gap and the electron affinity. It is important because many semiconductors are being used a photocathode in an electron source, and the work function here defines the photoemission threshold.

Zz.

11. Mar 16, 2016

### M.A.M.Abed

last question sorry the Fermi energy at insulators is the top level of valance band and Fermi level for ideal case in the middle of energy gap am i right ?

12. Mar 16, 2016

### ZapperZ

Staff Emeritus
No, this is not correct. The Fermi level for insulators is somewhere in the gap.

Ideal case of what?

Zz.

13. Mar 16, 2016

### M.A.M.Abed

for pure semiconductor at T=0 K
there is a misunderstanding between fermi level and fermi energy
just tell me where fermi level and fermi energy exist at zero absolute temperature for semiconductors

14. Mar 16, 2016

### ZapperZ

Staff Emeritus
For an intrinsic semiconductor, it is located in the middle of the gap. For any other semiconductor or insulator, it is SOMEWHERE in the gap.

Zz.

15. Mar 16, 2016

### DrDu

It's called valence not valance.

16. Mar 16, 2016

### M.A.M.Abed

yea this is the Fermi level
what about Fermi energy (highest occupied energy at T=0 K)

17. Mar 16, 2016

### DrDu

No, because the density of states is usually different in the valence and conduction band. At finite temperatures, this would lead to an excess of electrons in the band with the higher DOS. Hence the chemical potential has to be further away from the band with the higher DOS. This also holds in the limit of zero temperature.

18. Mar 16, 2016

### ZapperZ

Staff Emeritus
Not according to the simplified version that is used in many textbooks at this level. And I highly doubt that the OP is dealing with the knowledge of band structure of materials to understand this issue.

Zz.

19. Mar 16, 2016

### ZapperZ

Staff Emeritus
The "Fermi level" IS the "Fermi energy", unless you are dealing with momentum space, which you're not. You are only tackling the cartoon energy band diagram, which is in "energy space", and they are the same thing, i.e. this is often mixed with the chemical potential.

Zz.

20. Mar 16, 2016

Thnx