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In intrinsic semiconductors the number of excited electrons and the number of holes are equal: n = p. This may be the case even after doping the semiconductor, though only if it is doped with both donors and acceptors equally. In this case, n = p still holds, and the semiconductor remains intrinsic, though doped.
The less abundant charge carriers are called minority carriers; in n-type semiconductors they are holes, while in p-type semiconductors they are electrons. [15] In an intrinsic semiconductor, which does not contain any impurity, the concentrations of both types of carriers are ideally equal. If an intrinsic semiconductor is doped with a donor ...
An (intrinsic) semiconductor has a band gap that is smaller than that of an insulator and at room temperature, significant numbers of electrons can be excited to cross the band gap. [23] A pure semiconductor, however, is not very useful, as it is neither a very good insulator nor a very good conductor.
In a non-intrinsic semiconductor under thermal equilibrium, the relation becomes (for low doping): = where n 0 is the concentration of conducting electrons, p 0 is the conducting hole concentration, and n i is the material's intrinsic carrier concentration. The intrinsic carrier concentration varies between materials and is dependent on ...
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 ...
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:
indicates intrinsic semiconductors ... µ is the total chemical potential of electrons, or Fermi level (in semiconductor ... also called "multiple scattering theory ...
The Pauli exclusion principle limits the number of electrons in a single orbital to two, and the bands are filled beginning with the lowest energy. In solid-state physics and solid-state chemistry, a band gap, also called a bandgap or energy gap, is an energy range in a solid where no electronic states exist.