Hole random semiconductors

Light is generated in semiconductors in the process of radiative recombination. In a direct semiconductor, minority carrier population created by injection in a forward biased p-n junction can recombine radiatively, generating photons with energy about equal to E. The recombination process is spontaneous, individual electron-hole recombination events are random and not related to each other. This process is the basis of LEDs [36]. 

Two theories have been proposed to explain the Hall effect in amorphous semiconductors. Both treat the strong scattering by expressing the result in terms of a transfer integral J between specific sites. Friedman s calculation is based on the random phase approximation in which there is assumed to be no phase correlation between the electron or hole wavefunction on adjacent sites (Friedman 1971). The calculation yields... 

This always holds when the semiconductor is clean, without any added impurities. Such semiconductors are called intrinsic. The balance (4.126) can be changed by adding impurities that can selectively ionize to release electrons into the conduction band or holes into the valence band. Consider, for example, an arsenic impurity (with five valence electrons) in gennanium (four valence electrons). The arsenic impurity acts as an electron donor and tends to release an electron into the system conduction band. Similarly, a gallium impurity (three valence electrons) acts as an acceptor, and tends to take an electron out of the valence band. The overall system remains neutral, however now n p and the difference is balanced by the immobile ionized impurity centers that are randomly distributed in the system. We refer to the resulting systems as doped or extrinsic semiconductors and to the added impurities as dopants. Extrinsic semiconductors with excess electrons are called n-type. In these systems the negatively charged electrons constitute the majority carrier. Semiconductors in which holes are the majority carriers are calledp-type. 

Let us consider the Frenkel reaction in an ideally pure crystal. If we gradually reduce the temperature, the interstitial ion will eventually fall back into the vacancy (cf. Kp —> 0 for T- 0). In the same way, the semiconductor s conduction electrons will, via annihilation of holes, become valence electrons (Kb —> 0). In a similar sense, in strongly Cd-doped AgCl, there is a Coulomb attraction between Cd g and the counterdefect V g leading to a mutual trapping and thus to a deviation from random distribution at low temperatures. This can be described approximately by an exothermal production of associates [203,204] of the form... 

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