Question

The value indicated by Fermi energy level in an intrinsic semiconductor is
(A) The average energy of electrons and holes.
(B) The energy of electrons in the conduction band.
(C) The energy of holes in the valence band.
(D) The energy of the forbidden region.

Answer 1

Hint: To solve this question, we must be clear with the concepts of Fermi energy and intrinsic semiconductor. The energy difference between the highest and lowest occupied single-particle state at an absolute zero temperature in a quantum system of non-interacting fermions, is known as the Fermi energy. An undoped semiconductor is also known as an intrinsic semiconductor which signifies that holes in the valence bands are vacancies created by electrons that have been thermally excited to the conduction band as is opposed to doped semiconductors in which the electrons or holes are generally supplied by a foreign atom denoting an impurity.

Complete step by step answer
Let n be the number of electrons in intrinsic semiconductors. Let p be the number of holes in intrinsic semiconductor.
We know, This means that we have an equal chance of finding a hole at the valence band edge as there is of finding an electron at the valence band edge. Hence, we can determine that the average energy level of holes and electrons in an intrinsic semiconductor, is half the energy of its bandgap. Also, we need to keep in mind that the Fermi energy level in intrinsic semiconductors lie exactly in the middle of the energy band gap. Therefore, the value indicated by Fermi energy level is the average energy of electrons and holes in an intrinsic semiconductor.

Therefore, the correct answer is option A.

Note: We must know that semiconductors are of two types, namely intrinsic and extrinsic semiconductors. Intrinsic semiconductors are those in pure form or undoped while extrinsic semiconductors are doped, hence impure.