Charge Densities in a Semiconductor

• In intrinsic semiconductor, the electron density is equal to hole density.
• In extrinsic semiconductor the electron and hole densities are related by n_i² = N⋅P                                    …….(1)
• The law of charge neutrality also relate the densities of free electron and holes in an extrinsic semiconductor.
• The law of charge neutrality states that the total positive charge density is equal to the total negative charge density.

         i.e.    N_D + P = N_A + N                     ………(2)

Where N_D is the number of donor atom

N_A is the number of acceptor atoms

N is the density of electrons and

P is the density of holes.

Case 1: In N-type semiconductor, there is no acceptor doping atoms. i.e., N_A = 0. and also the majority carriers are electrons. The number of electrons is greater than the number of holes. i.e., N>>> P.

∴         Equation (2) becomes N_D = N

Thus in N-type material, the free electron concentration equals to the density of donor atoms.

Case 2: In P-type semiconductor, there is no donor doping atoms. i.e., N_D = 0. and also the majority carriers are holes. The number of holes is greater than the number of electrons. i.e., P >>> N,

∴  N  can be neglected.

∴  Equation (2) becomes    N_A = P

Thus in P-type material, the hole concentration equals to the density of acceptor atoms.

N   = n_i² / N_A  and  P = n_i² / N_D