What is Fermi energy level? What is its position in case of an intrinsic semiconductor?

Fermi Energy Level:
The Fermi energy level (EFE_F) is defined as the energy level at which the probability of finding an electron is 50% at absolute zero temperature (T=0 KT = 0 \, \text{K}). It represents the highest occupied energy state in a material at T=0 KT = 0 \, \text{K}.
In other words, it is a reference energy level used to determine the distribution of electrons within the energy states of a material. The position of the Fermi energy depends on the type of material (metal, semiconductor, or insulator) and its electronic properties.
Fermi Energy in an Intrinsic Semiconductor:
In an intrinsic semiconductor:
1. The number of electrons in the conduction band is equal to the number of holes in the valence band because there are no impurities or doping.
2. The Fermi energy level lies midway between the conduction band (ECE_C) and the valence band (EVE_V).
Mathematically, the position of the Fermi energy level (EFE_F) for an intrinsic semiconductor is given by:
EF=EC+EV2E_F = \frac{E_C + E_V}{2}
Here:
• ECE_C: Energy level of the bottom of the conduction band.
• EVE_V: Energy level of the top of the valence band.
This midpoint position is due to the symmetric nature of the electron and hole distributions in an intrinsic semiconductor.
Key Points:
1. In intrinsic semiconductors, the Fermi level is temperature-dependent.
2. As the temperature increases, electrons are thermally excited from the valence band to the conduction band, but the Fermi level still remains at the midpoint between ECE_C and EVE_V, assuming equal effective masses of electrons and holes.
Final Answer:
The Fermi energy level is the energy level at which the probability of finding an electron is 50%. In an intrinsic semiconductor, the Fermi energy level is located midway between the conduction band and the valence band.