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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 ).
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 ...
The Fermi velocity can easily be derived from the Fermi energy via the non-relativistic kinetic energy equation. In thin films , however, the film thickness can be smaller than the predicted mean free path, making surface scattering much more noticeable, effectively increasing the resistivity .
This provides us with a method for calculating the expected values of many microscopic quantities. We add the quantity artificially to the microstate energies (or, in the language of quantum mechanics, to the Hamiltonian), calculate the new partition function and expected value, and then set λ to zero in the final
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 ...
Many environmental protection agencies have issued regulations that limit the concentration of pollutants in gaseous emissions and define the reference conditions applicable to those concentration limits. For example, such a regulation might limit the concentration of NOx to 55 ppmv in a dry combustion exhaust gas corrected to 3 volume percent O 2.
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.