# Fermi level

#### logearav

Joined Aug 19, 2011
243
Revered Members,
Can i know what is meant by fermi level? I googled this, but i could not understand. One site says Fermi level as top of collection of electron energy levels at absolute zero. As far as my knowledge I know electron energy levels as K, L,M, N etc with energy values -13.6eV, -3.4eV etc. Top of collection means, is it O eV?

#### BillO

Joined Nov 24, 2008
990
Are you asking in reference to semi-conductors?

#### logearav

Joined Aug 19, 2011
243

#### Papabravo

Joined Feb 24, 2006
13,962
If you have some background in statistics and know what a distribution function is that will be helpful. Try the following article which has a reasonable explanation of the FD distribution function.

http://en.wikipedia.org/wiki/Fermi-Dirac_statistics

#### BillO

Joined Nov 24, 2008
990
Yes, BillO
Not really my strongest area, but here is my understanding of it.

The significance with respect to creating/designing a practical semi-conductor has to do with knowing the required doping agent necessary to give the semi-conductor the desired characteristics. The Fermi level represents the energy level of the valence electrons, those closest to the conduction band energy. The key here is the gap between the Fermi level energy and the conduction band energy. Once you know that, you can select doping agents that will adjust the gap such that the semi-conductor material behaves as you would like it to.

If anyone has more details on this, I'm sure they'll chime in, but this is real gritty stuff. Not for a leisurely Saturday evening read.

• logearav

#### Papabravo

Joined Feb 24, 2006
13,962
If a certain variable, x, follows a particular distribution function, you can answer questions like the following:

1. What is the probability that x > X
2. What is the probability that x < X
where lowercase x is the variable and uppercase X is a particular value. In the case of our electrons there is some nonzero probability that a given electron will be in the conduction band. The more doping applied to an intrinsic semi-conductor the greater the probability of finding an electron(hole) with sufficient energy to conduct. It is hard to grasp that holes can move the same as electrons.

• logearav

#### logearav

Joined Aug 19, 2011
243
Mr. BillO,
Materials teaching semiconductors,(N and P type) show both fermi level as well as Acceptor or Donor level. This is where i get confusion. Do Fermi level is the energy level of parent atom(Si or Ge) rather than dopant impurity?

#### Wendy

Joined Mar 24, 2008
22,146
I am very weak on this subject. I wonder where graphine fits in?

#### Papabravo

Joined Feb 24, 2006
13,962
The Fermi Level is what happens when the potential energy is equal to the chemical potential. The exponential equals 1 (because the exponent is 0) and the value of the distribution function is 1/2 == 0.5

From the wikipedia article:
http://en.wikipedia.org/wiki/Fermi_level

"...the Fermi level as a state with 50% chance of being occupied by an electron for the given temperature of the solid."

Does that clear things up a bit?