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)