
The correct
Fermi distribution for most dopant levels, i.e. the probability that an
electron is occupying an energy level belonging to a dopant atom is 


f(E, E_{F},
T) =

1_{ }

½ ·
exp 
æ
è 
E_{n} –
E_{F}
kT 
ö
ø 
+ 1 




The reason for the factor 1/2 instead of the usual 1 is that there is a
spin degeneracy, i.e. the energy is the
same for different spins. 


f_{Dop}(E,T) is thus the
probability that the level is occupied by an electron of either spin. This applies to group III
acceptors, or group V donors as doping elements for group IV
semiconductors. 

There also might be cases were dopants can
accommodate two electrons (which then must
have paired spin). The Fermi distribution formulated for acceptors in this case
is 


f(E, E_{F},
T) =

1_{ }

2 · exp

æ
è 
E_{n} –
E_{F}
kT 
ö
ø 
+ 1 



If we allow also excited states of the dopant, we obtain the fully
generalized Fermi distribution 


f(E_{r}, E_{F}, T) =

1_{ }

Sg_{r} · exp 
æ
è 
E_{r} – E_{F}
kT 
ö
ø 
+ 1 




With E_{r} = energy of the
rth state; g_{r} = degeneracy/spin
factor. 

Interesting, but rather irrelevant as long as we
simply assume completely ionized donors and
acceptors. 


