Conductivity of Extrinsic Semiconductor

       In an extrinsic semiconductors, there are two types of materials n type and p type. Let us obtain the expressions for the conductivity of n type and p type materials.

1.1 Conductivity of n Type Material

       It is known that in n type material, the free electrons are majority carriers while the holes are minority carriers.

       Let              n_n = Concentration of free electrons in n type

                          p_n = Concentration of holes in n type

                          N_D = Concentration of donor atoms

Note : In the symbol, main letter n or p indicates concentration of type of charge carrier electron or whole while the suffix indicates the type of material i.e. n type or p type. Thus n_n indicates electron concentration in n type material while n_p indicates electron concentration in p type material and so on.

From the basic equation of conductivity, the conductivity of n type material can be expressed as,

                     σ_n = (n_n μ_n + p_n μ_p) e                        ............(1)

But p_n << n_n   as holes are in minority hence,

                      σ_n ≈ n_n μ_n e                                 ................. (2)

       The number of free electrons is dominantly controlled by donor atoms added than the thermal generation at room temperature. Hence concentration of donor atoms N_D added can be approximately assumed to be equal to the concentration of free electrons n_n in n type materials.

Thus as N_D >> n_i we can write,

                               n_n  ≈ N_D                       ................ (3)

.^..                             σ_n ≈ N_D μ_n e                  ..................(4)

1.2 Conductivity of p Type Material

       For a type material, holes are in majority and electrons are in minority.

       Let      n_p = Concentration of free electrons in p type

                 p_p = Concentration of holes in p type

                 N_A = Concentration of acceptor atoms

       Thus the conductivity of p type material can be expressed as,

                    σ_p = (n_p μ_n + p_p μ_p) e                   ................ (5)

       But n_p << p_p as free electrons are in minority hence,

                     σ_p  ≈ p_p μ_p e                                     ........... (6)

       The number of holes is dominantly controlled by added acceptor impurity than the thermal generation. Each added impurity atom creats a hole hence N_A >> n_i. Thus all the holes generated p_p can be approximately assumed to be equal to the concentration of acceptor N_A. Thus,

                       p_p  ≈ N_A                                             ............... (7)

.^..                    σ_p ≈ N_A μ_p e                                        ............. (8)

Sponsored links :