# I Quasi Fermi level and intrinsic Fermi energy

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1. Apr 1, 2016

### yeyintkoko

Please explain me. I don't understand what is quasi fermi level f(E) and fermi energy Ef.
For example (GaAs) at the room temperature (T=300K)
Eg = 1.42 eV; (energy band gap)
mc = 0.067 me; (effective mass of electron in conduction band)
mv = 0.45 me; (effective mass of hole in valance band)
kT = 0.0259; (T=300K)
For intrinsic fermi Energy from the middle band gap can receive
using this equation
Ei = 3kT/4*ln(mv/mc);

Ei = 0.0369 eV; (intrinsic fermi Energy from the middle band gap)
Engery band gap Eg is 1.42 eV so middle band gap is 1.42/2 = 0.71 eV;
So intrinsic fermi Energy is
0.71 eV+0.0369 eV = 0.7469 eV.
Now i calculate for fermi level
using this equation
f(E) = 1/(exp(E-Ef/kT)+1);
E is the Eg? I calculate where E is value of Eg.
f(E) = 4.925 x 10-12;
This is right?

And then i understand that only one fermi level in intrinsic semiconductor at the thermal equilibrium, no bias (voltage, EM radiation, light). When semiconductor is under bias, may be quasi fermi level(2 levels) in intrinsic semiconductor or this happen only in extrinsic semiconductor? Please explain me with above example.
I need your help.
Thanks a lot

2. Apr 2, 2016

### paralleltransport

Hi Yeyintoko,

Your question is very confusing. The fermi level @ T = 0 is the energy level @ which all the lowest energies states of the band(s) are filled. In other words, the semiconductor is in its ground state, and the fermi level/energy is the energy of the state with highest energy. Now, let's say you have a semiconductor, with a valence band and a conduction band. The quasi fermi level is the (erroneous but good approximation of slightly out of equilibrium semiconductors) where we try to extend the idea of fermi level to a semiconductor out of equilibrium. Note that all the stuff about fermi-dirac statistics assumes that the semiconductor is in statistical equilibrium (hence the course where you derive this distribution is call equilibrium statistical mechanics and not non-equilibrium statistical mechanics). We say, oh why not, let's say there's an electric potential qV that causes charges to move (no more equilibrium!), into the energy value of this equilibrium distribution.

3. Apr 2, 2016

### yeyintkoko

Hi paralleltransport,