General Problems of Electroluminescent Crystals

Abstract

The mechanism of electron transfer to the conductivity band by tunneling through the potential barrier was first considered by Zener [7], and the effect carries his name. He obtained an equation for the probability of transfer of a valence electron to the conductivity band in unit time:

$$ {P_t}\, = \frac{{eEd}}{{2\pi \hbar }}\,\exp \,\,\left\{ {\, - \frac{\pi }{{4e\hbar E}}\,\sqrt {2{m^*}} \,{\Delta ^{3{/_2}}}} \right\} $$

((I.1))

where E is the value of the electric field; e and m* are the charge and effective mass of an electron; A is the width of the forbidden band; d is the constant of the crystal lattice. However, this equation is only valid when the quasi-momentum q of an electron is the same at the bottom of the conductivity band and at the top of the valence band. This condition is often not fulfilled so that, because of the law of conservation of momentum, transitions are only possible when, although the energy level is higher at the bottom of the conductivity band, the quasi-momentum of an electron is the same there as at the top of the valence band. In this case, instead of the forbidden band width Δ in equation (I.1), it is necessary to insert the difference between this level and the top of the valence band. However, if we are dealing with a body such that it is possible to transfer the requisite momentum to an electron, then there is also a possibility of election transfer to the bottom of the conductivity band. This body can be the crystalline lattice itself (absorption or creation of phonons). Such a transition is called indirect [8] (Fig. 1).