why does fermi level vary with temperature
The Fermi level is the highest energy level occupied by an electron at absolute zero temperature in a material. It represents the boundary between the filled and unfilled electron energy levels in a material, and is important in understanding the electrical and thermal properties of materials.
The Fermi level can vary with temperature due to two main factors:
1. Thermal excitation: As temperature increases, the thermal energy of the electrons also increases. This can cause electrons to move from lower energy levels to higher energy levels, thereby increasing the number of electrons in the higher energy states. This leads to a shift in the Fermi level towards higher energy levels.
2. Band structure changes: The orbital energy levels in a material determine its electronic band structure. In some materials, the band structure can change with temperature due to thermal expansion effects or temperature-dependent lattice vibrations. These changes can alter the position of the energy band edges, which in turn affects the position of the Fermi level.
Overall, the variation of the Fermi level with temperature is a result of the interplay between these factors and depends on the material's electronic structure and temperature-dependent properties.