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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 .
The mass action law defines a quantity called the intrinsic carrier concentration, which for undoped materials: n i = n 0 = p 0 {\displaystyle n_{i}=n_{0}=p_{0}} The following table lists a few values of the intrinsic carrier concentration for intrinsic semiconductors , in order of increasing band gap.
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 ...
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 band. The valence band, immediately below the forbidden band, is normally very nearly completely occupied. The conduction band, above the Fermi level, is normally nearly completely empty.
The Fermi energy is only defined at absolute zero, while the Fermi level is defined for any temperature. The Fermi energy is an energy difference (usually corresponding to a kinetic energy), whereas the Fermi level is a total energy level including kinetic energy and potential energy.
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.
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 ...