By Th. Wolkenstein
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Extra info for Electrons and Crystals (Science For Everyone)
Let us consider an electron in the conduction band. Suppose its state is characterized by a set of three integer quantum numbers n,, n,, n, and a spin that can have either of two values. 3. 29). Let us write this formula once again: 2n W = ~ . + c r - 2 ~(cos T n z + c o s 2n 7nu where N is the number of atoms along the edge of the cube (we assume, as in the preceding chapter, t h a t the crystal is cubic). 1), we obtain + a - 6P. 3. e. if the electron is ascribed an effective mass m* instead of its true mass m.
This case is illustrated in Fig. 18c where the whole range of n, is doublehatched. I t is also essential in the case under consideration to know whether the filled band is adjacent to the vacant band lying above i t or separated from i t by a forbidden band. (a) If the band occupied by electrons is in contact with or overlaps the vacant band, then the vacant band can be considered to be an extension of the filled one. This is the case when the velocity redistribution of the electrons can be carried out a t the expense of this overlying band.
An exciton cannot live forever and sooner or later i t is extinguished. There are two ways for this to happen. e. the electron recombines with the hole. 5. Electrons and Quanta 97 into a pocket leaving neither a free electron nor a free hole. This sort of disappearance is accompanied by a release of energy. The other way is for the exciton to dissociate into a free electron and a free hole. The electron and the hole making up the exciton move far enough apart for the electrostatic attraction binding the exciton together to fall practically to zero.
Electrons and Crystals (Science For Everyone) by Th. Wolkenstein