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The Fermi level of a solid-state body is the thermodynamic work required to add one electron to the body. It is a thermodynamic quantity usually denoted by μ or E F [1] for brevity. The Fermi level does not include the work required to remove the electron from wherever it came from.
In a Fermi gas, the lowest occupied state is taken to have zero kinetic energy, whereas in a metal, the lowest occupied state is typically taken to mean the bottom of the conduction band. The term "Fermi energy" is often used to refer to a different yet closely related concept, the Fermi level (also called electrochemical potential ).
where E F is the Fermi level, E C is the minimum energy of the conduction band, and N C is a concentration coefficient that depends on temperature. The above relationship for n e can be shown to apply for any conduction band shape (including non-parabolic, asymmetric bands), provided the doping is weak ( E C − E F ≫ kT ); this is a ...
The effect occurs when the electron carrier concentration exceeds the conduction band edge density of states, which corresponds to degenerate doping in semiconductors. In nominally doped semiconductors, the Fermi level lies between the conduction and valence bands. For example, in n-doped semiconductor, as the doping concentration is increased ...
In this system, the molecules tend to move from areas with high concentration to low concentration, until eventually, the concentration is the same everywhere. The microscopic explanation for this is based on kinetic theory and the random motion of molecules. However, it is simpler to describe the process in terms of chemical potentials: For a ...
Assuming that the concentration of fermions does not change with temperature, then the total chemical potential μ (Fermi level) of the three-dimensional ideal Fermi gas is related to the zero temperature Fermi energy E F by a Sommerfeld expansion (assuming ): = + [() +], where T is the temperature.
In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in which electrons are normally present at absolute zero temperature, while the conduction band is the lowest range of vacant electronic states.
For a large ensemble the Fermi level will be approximately equal to the chemical potential of the system, and hence every state below this energy must be occupied. Thus, particles fill up all energy levels below the Fermi level at absolute zero, which is equivalent to saying that is the energy level below which there are exactly N ...