Solid State Physics Lecture 18 of 20

July 10, 2012 by Sandro Scandolo

S. Scandolo, ICTP

Lesson 18 (Semiconductors)

Semiconductors are insulators with a small energy gap between bands: the gap between the valence band and the conduction band is typically 2-3 eV. At room temperature this amounts to only a small number of conducting electrons as kT is roughly 25mK. The intrinsic resistance of semiconductors is large but it drops exponentially when the temperature increases as the number of conductive electrons is .

Doping semiconductors with impurities, e.g. silicon with aluminium or phosphorus, can change the conductive properties of the host crystal. Phosphorus contributes an extra electron to the conductive band (n-doping); while aluminium adds a positively charged hole to the valence band (p-doping).

Attaching together a p-type and an n-type semiconductor results in something interesting. As the extra electrons find holes, the n-side becomes positively charged, while the p-side negative. This creates a compensating electrostatic potential, which inhibits further charge build-up. Also, a layer (depletion layer) without free charge carriers between the semiconductors forms. This construction has non-linear electronic properties. It has a constant resistance if an external field cancels the effect of the aforementioned electrostatic potential. However, an opposite field would not induce any current.

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