Electronic energy states in crystals

This chapter first discusses the fundamentals of energy states in crystals, a subject necessary for understanding the creation and movement of electrons and holes in a solid. The properties of semiconductors are discussed next, with special emphasis given to the properties of silicon and germanium. The principle of construction and operation is accompanied by a description of the different types of detectors available in the market. Future prospects in this field are also discussed. 

Among the most important requirements in the theory of chemical bonds is the development of a unified method for the description of the chemical interaction between atoms, which would be based on the structure of the atomic electron shells and in which one would utilize the wave functions and the electron density distributions calculated for isolated (free) ions on the basis of the data contained in Mendeleev s periodic table of elements. This unified approach should make it possible to elucidate the interrelationship between the various physical properties and the relationship between the equilibrium and the excited energy states in crystals. In contrast to the study of chemical bonds in a molecule, an analysis of the atomic interaction in crystals must make allowances for the presence of many coordination spheres, the long- and short-range symmetry, the long- and short-range order, and other special features of large crystalline ensembles. As mentioned already, the band theory is intimately related to the chemi-... 

Electron occupation in the frontier bands of metal crystals varies with different metals as shown in Fig. 2-7. For metallic iron the frontier bands consist of hybridized 4s-3d-4p orbitals, in which 4s and 3d are partially occupied by electrons but 4p is vacant for electrons. Figure 2-8 shows the electron state density curve of metallic iron, where the 3d and 4s bands are partially filled with electrons. Electrons in metals occupy the energy states in a frontier band successively fix>m the lower band edge level to the Fermi level, leaving the higher levels vacant. 

Because of periodic symmetry, the electronic excitation states in a molecular crystal are also of collective nature. These are the well-studied exciton states.81 82 Their energy is close to that of discrete electronic states of isolated molecules (4-8 eV), but the excitation envelops a large group of molecules, migrating efficiently up to 100 nm along the crystal.82 In the same manner, because of efficient migration, the excitation of a fragment of a polymer chain rapidly spreads over the whole molecule.37... 

Tables of compatibility relations for the simple cubic structure have been given by Jones (1962, 1975), and similar tables can be compiled for other structures, as shown by the examples in Tables 17.2 and 17.5. Compatibility relations are extremely useful in assigning the symmetry of electronic states in band structures. Their use in correlation diagrams in crystal-field theory was emphasized in Chapters 7 and 8, although there it is not so common to use B SW notation, which was invented to help describe the symmetry of electronic states in energy bands in crystals (Bouckaert el al. (1936)).

Note that generally bands correspond to hybrids, and attributing bands to certain elements is an approximation. Unlike the electronic energy level distribution, the distribution of ionic energy levels in crystals (the meaning of which we will consider in the next section) is discrete. In the electronic case we face bands comprising a manifold of narrowly neighbored levels, so that we better speak of a continuous density of states. 

The distribution of the electrons among the allowed energy states in the semiconductor crystal at thermal equilibrium is described by the Fermi-Dirac distribution function." It is denoted by ME), which has the form... 

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