Free Carrier Concentration Spectroscopy
(FCCS) for n-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 donor
species (density
and energy level
of the
-th donor
for ), one completely ionized donor above the measurement temperatures
(density
),
and one acceptor (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 bottom (
) of the conduction band,
is
the
degeneracy factor of -th donor,
is the
compensating density expressed as
.
(4)
On
the other hand, using the effective density of states in the
conduction band,
we
can describe as
,
(5)
where
,
(6)
,
(7)
is the electron
effective mass,
is the Planck
constant, and
is the number of
equivalent
minima in the conduction band.
Substituting
Eq. (2) for one of the in Eq. (1) and
substituting Eq. (5) for the other
in
Eq. (1) give
(8)
where
.
(9)