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The Fermi level does not necessarily correspond to an actual energy level (in an insulator the Fermi level lies in the band gap), nor does it require the existence of a band structure. Nonetheless, the Fermi level is a precisely defined thermodynamic quantity, and differences in Fermi level can be measured simply with a voltmeter.
At absolute zero temperature, all of the electrons have energy below the Fermi level; but at non-zero temperatures the energy levels are filled following a Fermi-Dirac distribution. In undoped semiconductors the Fermi level lies in the middle of a forbidden band or band gap between two allowed bands called the valence band and the conduction ...
µ is the total chemical potential of electrons, or Fermi level (in semiconductor physics, this quantity is more often denoted E F). The Fermi level of a solid is directly related to the voltage on that solid, as measured with a voltmeter. Conventionally, in band structure plots the Fermi level is taken to be the zero of energy (an arbitrary ...
Similarly, when a metal is deposited onto a semiconductor (by thermal evaporation, for example), the wavefunction of an electron in the semiconductor must match that of an electron in the metal at the interface. Since the Fermi levels of the two materials must match at the interface, there exists gap states that decay deeper into the semiconductor.
E i: The intrinsic Fermi level may be included in a semiconductor, to show where the Fermi level would have to be for the material to be neutrally doped (i.e., an equal number of mobile electrons and holes). E imp: Impurity energy level. Many defects and dopants add states inside the band gap of a semiconductor or insulator. It can be useful to ...
For intrinsic semiconductors (undoped), the valence band is fully filled with electrons, whilst the conduction band is completely empty. The Fermi level is thus located in the middle of the band gap, the same as that of the surface states, and hence there is no charge transfer between the bulk and the surface. As a result no band bending occurs.
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.
The carrier concentration can be calculated by treating electrons moving back and forth across the bandgap just like the equilibrium of a reversible reaction from chemistry, leading to an electronic mass action law. The mass action law defines a quantity called the intrinsic carrier concentration, which for undoped materials: