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)