One Donor and One Acceptor for n-type semiconductor

 

Since the electron concentration  is described as

,                                     (1)

the following relation is obtained:

                             (2)

On the other hand, since

,                                            (3)

the following relation is obtained:

.                                                 (4)

Therefore, substituting Eq. (4) to Eq. (2) gives

.                                  (5)

Since

,                                            (6)

we obtain the following relationship:

.                  (7)