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The current which will flow in an intrinsic semiconductor consists of both electron and hole current. That is, the electrons which have been freed from their lattice positions into the conduction band can move through the material. In addition, other electrons can hop between lattice positions to fill the vacancies left by the freed electrons.
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.
In a metal, semimetal or degenerate semiconductor, μ lies within a delocalized band. A large number of states nearby μ are thermally active and readily carry current. In an intrinsic or lightly doped semiconductor, μ is close enough to a band edge that there are a dilute number of thermally excited carriers residing near that band edge.
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.
In n-type semiconductors, electrons in the conduction band move through the crystal, resulting in an electric current. In some conductors, such as ionic solutions and plasmas, positive and negative charge carriers coexist, so in these cases an electric current consists of the two types of carrier moving in opposite directions.
That applies for intrinsic (undoped) semiconductors. This means that at absolute zero temperature, there would be no free conduction electrons, and the resistance is infinite. However, the resistance decreases as the charge carrier density (i.e., without introducing further complications, the density of electrons) in the conduction band increases.
Importantly, an insulator can be made to conduct by increasing its temperature: heating provides energy to promote some electrons across the band gap, inducing partially filled states in both the band of states beneath the band gap (valence band) and the band of states above the band gap (conduction band). An (intrinsic) semiconductor has a ...
As an application example, the steady-state space-charge-limited current across a piece of intrinsic silicon with a charge-carrier mobility of 1500 cm 2 /V-s, a relative dielectric constant of 11.9, an area of 10 −8 cm 2 and a thickness of 10 −4 cm can be calculated by an online calculator to be 126.4 μA at 3 V. Note that in order for this ...