Free Carrier Concentration Spectroscopy
(FCCS) for p-type semiconductor
A function to be
evaluated is defined as
,
(1)
where is the Boltzmann
constant,
is the
measurement temperature, and
is
a parameter which can shift peak
temperatures of .
We consider different
acceptor species (density
and energy level
of the
-th
acceptor for ), one completely ionized acceptor above the measurement temperatures
(density ), and one donor (density
). From the
charge neutrality condition, the free electron
concentration can be derived
as
,
(2)
where is the
Fermi-Dirac distribution function given by
,
(3)
is the Fermi
Level measured from the top (
) of the valence band,
is the
degeneracy
factor
of -th acceptor,
is the
compensating density expressed as
.
(4)
On
the other hand, using the effective density of states in the Valence band,
we can describe
as
,
(5)
where
,
(6)
,
(7)
is the electron
effective mass and
is the Planck
constant.
Substituting
Eq. (2) for one of the in Eq. (1) and
substituting Eq. (5) for the other
in
Eq. (1) give
(8)
where
.
(9)