How does fermi level vary with temperature. Explain
The Fermi level (also known as the Fermi energy) is a fundamental concept in quantum mechanics that describes the highest energy state occupied by an electron at absolute zero temperature. It can be thought of as the energy level dividing the filled electron states from the empty ones in a solid.
The position of the Fermi level determines the electrical and thermal conductivity of a material and plays a crucial role in various electronic and thermoelectric phenomena. Its variation with temperature can be explained by considering the effects of thermal energy on the electron distribution.
At absolute zero temperature (0 Kelvin), the Fermi level lies at the top of the filled electron states, and all energy levels below it are occupied by electrons. As the temperature increases, electrons gain thermal energy and start to occupy higher energy levels due to their increased mobility. This causes a small shift in the Fermi level towards higher energies.
The exact behavior of the Fermi level as temperature increases depends on whether the material is a metal, an insulator, or a semiconductor.
1. Metals: In metals, the Fermi level shifts very little with temperature, especially at low temperatures. This is because metals have a high density of states near the Fermi level, allowing electrons to rapidly fill the available energy levels. Any additional thermal energy is almost immediately absorbed by the electrons, causing very little change in the Fermi level position.
2. Insulators: In insulators, there is a large energy gap between the filled and empty states, and the Fermi level lies inside this gap. As the temperature increases, a few electrons gain enough thermal energy to cross the energy gap and occupy higher energy levels. This leads to a small shift of the Fermi level towards the conduction band, creating additional charge carriers and increasing electrical conductivity.
3. Semiconductors: Semiconductors have a smaller energy gap between the valence and conduction bands compared to insulators, allowing thermal excitation of electrons across the gap. As the temperature rises, more electrons gain enough energy to move from the valence band to the conduction band, resulting in a significant increase in the number of charge carriers. Consequently, the Fermi level moves towards the conduction band, enabling higher electrical conductivity.
In summary, the Fermi level generally exhibits a slight shift towards higher energies as the temperature increases. The magnitude of this shift depends on the material's properties, such as its density of states and energy band structure, and determines its electrical conductivity behavior.