domingo, 14 de febrero de 2010

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 (EF) 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 EF, 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, EF is positioned below mid gap.  When the electron and hole concentrations
 are approximately equal, intrinsic material, EF 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 

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