Question

If \[{N^A}\] is number density of acceptor atoms added and\[{N^D}\] is number density of donor atoms added to a semiconductor, \[{n^e}\]and \[{n^n}\] are the number density of electrons and holes in it, then
(A) \[{n^e}\]=\[{N^D}\],\[{n^n}\]=\[{N^A}\]
(B) \[{n^e}\]=\[{N^A}\],\[{n^n}\]=\[{N^D}\]
(C) \[{N^A}\]+\[{n^n}\]=\[{N^D}\]+\[{n^e}\]
(D) \[{n^e}\]+\[{N^A}\] = \[{n^n}\]+\[{N^D}\]

Answer 1

Hint: Number of electrons and that of donor atoms are related. Likewise the number of holes and the number of acceptors are related. The important aspect to be considered is the neutral nature of the lattice in the doped semiconductor, which determines the above relationship.

Complete solution: Number of electrons is given by \[{n^e}\] and number of holes is given by \[{n^n}\].
The number density of donor atoms given by \[{N^A}\] and the number density of acceptor atoms is given by \[{N^D}\].
For the crystal lattice to be neutral, the number of holes and the number density of acceptor atoms should be equal to the sum of total number of electrons and the number density of donor atoms in a semiconductor.
\[{n^e}\]+\[{N^A}\] = \[{n^n}\]+\[{N^D}\]

The correct option is D.

Note: The semiconductor is typically an intermediate between a pure conductor and insulator. The addition of impurity to the semiconductor would typically result in the reduction of the forbidden energy gap. This doping makes the materials like Silicon more conductive than before and hence the name semiconductor. The nature of impurity added to the parent material like Silicon would determine the type of semiconductor, which could be N-type or the P-type semiconductor. Of these, the N-type semiconductor has excess electrons, while the P-type has excess holes. The added impurity would form additional bonds with the parent material. This bond is important in generating the electrons or the holes in general. For instance, doping the pentavalent results in excess electrons as the fifth electron will not take part in the bonding, which becomes the donor. But doping trivalent would be deficient of an electron for binding resulting in the formation of holes termed as the acceptor. These find application in the diode that forms the basic element in the field of electronics.