Intrinsic semiconductors
المؤلف:
Peter Atkins, Tina Overton, Jonathan Rourke, Mark Weller, and Fraser Armstrong
المصدر:
Shriver and Atkins Inorganic Chemistry ,5th E
الجزء والصفحة:
ص104-105
2025-08-24
365
Intrinsic semiconductors
Key point: The band gap in a semiconductor controls the temperature dependence of the conductivity through an Arrhenius-like expression. In an intrinsic semiconductor, the band gap is so small that the energy of thermal motion results in some electrons from the valence band populating the empty upper band (Fig. 3.72). This occupation of the conduction band introduces positive holes, equivalent to an absence of electrons, into the lower band, and as a result the solid is conducting because both the holes and the promoted electrons can move. A semiconductor at room tempera ture generally has a much lower conductivity than a metallic conductor because only very few electrons and holes can act as charge carriers. The strong, increasing temperature dependence of the conductivity follows from the exponential Boltzmann-like temperature dependence of the electron population in the upper band. It follows from the exponential form of the population of the conduction band that the conductivity of a semiconductor should show an Arrhenius-like temperature dependence of the form
where Eg is the width of the band gap. That is, the conductivity of a semiconductor can be expected to be Arrhenius-like with an activation energy equal to half the band gap, Ea ≈ 1 2 Eg. This is found to be the case in practice.
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