Quasi Fermi level and intrinsic Fermi energy

[yeyintkoko]

Please explain me. I don't understand what is quasi fermi level f(E) and fermi energy E_f.
For example (GaAs) at the room temperature (T=300K)
E_g = 1.42 eV; (energy band gap)
m_c = 0.067 m_e; (effective mass of electron in conduction band)
m_v = 0.45 m_e; (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
E_i = 3kT/4*ln(m_v/m_c);

E_i = 0.0369 eV; (intrinsic fermi Energy from the middle band gap)
Engery band gap E_g 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-E_f/kT)+1);
E is the E_g? I calculate where E is value of E_g.
received
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

 

[paralleltransport]

Please explain me. I don't understand what is quasi fermi level f(E) and fermi energy E_f.
For example (GaAs) at the room temperature (T=300K)
E_g = 1.42 eV; (energy band gap)
m_c = 0.067 m_e; (effective mass of electron in conduction band)
m_v = 0.45 m_e; (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
E_i = 3kT/4*ln(m_v/m_c);

E_i = 0.0369 eV; (intrinsic fermi Energy from the middle band gap)
Engery band gap E_g 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-E_f/kT)+1);
E is the E_g? I calculate where E is value of E_g.
received
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

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.

 

[yeyintkoko]

Hi paralleltransport,
Thanks for your answer
When semiconductor is no bias only one fermi level E_f in intrinsic semiconductor at the thermal equilibrium.
My question is
1.When semiconductor is under bias, may be quasi fermi level E_fc and E_fv in intrinsic semiconductor?