The Fermi level

Using The Fermi Function

The Fermi function is a probability distribution function.  It can only be used under

equilibrium conditions.  The Fermi function determines the probability that an energy

state (E) is filled with an electron when the material we are working with is under

equilibrium conditions.  The Fermi level (E_F) helps determine carrier distributions. 

To a first approximation, all the energy states above the Fermi level have a low

probability of being filled with electrons and all the energy states below the Fermi

level have a high probability of being filled with electrons.  For an electronic state

with energy the same as E_F, the probability of that state being filled is 1/2, or 50%.

Some of the properties of the Fermi function are:

The probability an energy state is occupied:
The probability an energy state is empty:
The Fermi function at E = EF:	f (EF) = 1/2
The Fermi function is simply a mathematical  function and has no units:	0 < f (E) < 1

 
In a band diagram, the position of the Fermi level determines which carrier dominates. 

 If the semiconductor contains more electrons than holes, n-type material, the Fermi

 level is positioned above mid gap.  If holes are more abundant than electrons, p-type

 material, E_F is positioned below mid gap.  When the electron and hole concentrations

 are approximately equal, intrinsic material, E_F is positioned at mid gap.  The Fermi

function, or level, also varies with temperature and carrier concentration.

Anderson Jose Mariño Ortega

C.I. 17.456.750

E.E.S.

http://www.ece.utep.edu/courses/ee3329/ee3329/Studyguide/ToC/Fundamentals/Carriers/fermi.html