Electrical Engineering ⇒ Topic : Calculation of n and p in Extrinsic Semiconductor

Calculation of n and p in Extrinsic Semiconductor

In a P-type semiconductor, each acceptor atom accepts one electron and it becomes a negative ion. Similarly, in an N-type semiconductor, each donor atom donates a free electron that moves randomly in the crystal lattice and the donor atom becomes a positive ion fixed in the lattice. The hole created due to the acceptance of electron perambulates freely in the lattice. The crystal as a whole is electrically neutral. Therefore, the positive and negative charges must be equal, i.e.,

                                              N_D + p = N_A + n        ...........(1)

where n is the free electron concentration, p is the hole concentration, N_D is the concentration of donor atoms, and N_A is the concentration of acceptor atoms.

Under thermal equilibrium,

                                                      n_p = n_i²             .............(2)

where n_i is the intrinsic concentration of semiconductor.

If the material has both N- and P-type doping, the effective doping will be (N_D+ N_A). If N_D > N_A, it will behave like an N-type material. Putting N_A = 0 and p = ni Eq. (1), we have

                                     ........... (3)

If N_D is much larger than n_i, n_i can be ignored in Eq. (3). Taking +ve sign, we can write

From Eq. (2)

                                       ............ (4)

Similarly, in P-type semiconductor, p = N_A

                                ............. (5)