Carrier Concentrations in Extrinsic Semiconductors

        We can obtain the concentration of minority and majority carriers in n-type and p-type materials using law of mass action.

n-type material :

For n-type material it is seen that, n_n = N_D.

At any fixed temperature, according to law of mass action,

                    n_n x p_n = n_i²         

       where n_n is electrons i.e. majority carriers concentration while p_n is hole i.e. minority carriers concentration. Using n_n  ≈   N_D, we can write minority carrier concentration as,

                       N_D p_n = n_i²         

.^..                     p_n   = n_i²/N_D                                         .....................(1)

Note : Knowing n_i and N_D, the number of holes in n-type material i.e. minority carrier concentration can be obtained.

p-type material :

       For p-type material it is seen that, p_p  = N_A.

According to law of mass action,

              n_p x p_p = n_i²

       where n_p is electrons i.e. minority carrier concentration while is holes i.e. majority carrier concentration. Using p_p ≈ N_A we can write.

.^..             n_p = n_i²/N_A                               ............... (2)

Note : Knowing n_i and N_A, the number of electrons in p-type material i.e. minority carrier concentration can be obtained.

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