An energy band is a range of energy levels that an electron can occupy in a solid material. These energy bands can be either filled with electrons (valence band) or empty (conduction band).
The Fermi energy is the energy level at which the probability of finding an electron in a solid material is 0.5. It is also known as the Fermi level and is a key factor in determining the electrical and thermal properties of a material.
The energy band structure of a material determines its electronic, magnetic, and thermal properties. For example, materials with a wide band gap are insulators, while materials with a narrow band gap are semiconductors. The energy band structure also affects a material's optical and mechanical properties.
The valence band is the highest energy band that is completely filled with electrons, while the conduction band is the lowest energy band that is not completely filled with electrons. Electrons in the valence band cannot move freely, while electrons in the conduction band can move and conduct electricity.
As temperature increases, the Fermi energy also increases. This is because at higher temperatures, more electrons have enough energy to move from the valence band to the conduction band, increasing the number of electrons at the Fermi level. This can result in changes in a material's electrical and thermal conductivity.