Tetrahedral semiconductors

The origin of this hybridization gap in tetrahedral semiconductors can best be understood by taking the four sp3 hybrid orbitals as our starting basis rather than the four free atomic orbitals s, p, p , and pz. As is well known (see, for example, McWeeny (1979)), the former are linear... 

Table 7.2 The bond order for tetrahedral semiconductors. (From Alinaghian et a/. 1994).)...

A. A. Levin, Introduction to the Quantum Theory of Solids. Chemical Bonding and Structure of Energy Bands in Tetrahedral Semiconductors, Khimiya, Moscow, 1974. 

The formation of bands in a liomopolar tetrahedral semiconductor as the atoms are brought together. Intcrnuclear distance decreases to the right. 

Energy bands are accurately known for most tetrahedral semiconductors Chapter 6 contains a discussion of the details of these bands as obtained by more accurate methods than will be discu.ssed here. In this section we shall continue the construction of electron states in terms of the bond orbitals introduced in the... 

Boron nitride forms the same structure that graphite does, as indicated in Fig. 3-10. The sp -hybrid energy-difference may be evaluated by using the Solid State Table and used to estimate the corresponding. It is possible to treat the counterparts of all the properties of polar tetrahedral semiconductors also for the... 

The largest peak in Fig. 4-3, labelled 2. can be easily identified with the fairly parallel bands separated by between 4 and 6 eV over most of the region shown in Fig. 4-4. (A careful study of this was made recently by Kondo and Moritani, 1977.) These bands arise from the Jones Zone, which will be discussed in detail in the treatment of tetrahedral semiconductors with pseudopotentials in Chapter 18. The energy at which this peak occurs was used earlier as a basis for obtaining experimental values for the covalent energy Fj (Harrison and Ciraci, 1974). 

The picture that emerges is remarkable and applies to all tetrahedral semiconductors. The principal peak in the optical absorption comes at an energy determined by matrix elements between p orbitals, rather than between hybrids. To be sure, the s orbitals are necessary for any reasonable description of the energy bands or for calculating the full absorption spectrum, but the strongest features in X2(< ) and, by Eq. (4-4), in Xi(w), and perhaps in all dielectric properties, are dominated by p orbitals. 

Parameters for tetrahedral semiconductors, and predicted and experimental dielectric constants. A compilation for other classes of solids has been recently made by Wcmple (1977). 

Elastic constants (in 10" erg/cm ) and force constants (in eV) for tetrahedral semiconductors. 

It will help here to mention the structure of polar counterparts to SiC)2. These are constructed exactly as aluminum phosphide is constructed from silicon in the simple tetrahedral solid. The process is illustrated for the simple molecular lattice in I ig. 11-5, which shows how the structure for SiOj can be transformed to the structure for aluminum phosphate. Transferring an additional proton leads to magnesium sulphate. Indeed, the counterpart of each AB tetrahedral semiconductor, ABO4, is po.ssible in principle. The structures may be obtained from Wyck-hoff (1963), and if the structure has twofold-fourfold coordination, it can be analyzed by the methods outlined here. 

Covalent random networks conform to the (8- ) rule. In these structures, a number of bonds are strained, either bent or over-stretched. Therefore, occasionally they get broken . These broken bonds correspond to single electron carrying orbitals and are described as dangling bonds. In the case of a tetrahedral semiconductor, the nature of such states can be understood with the help of simple molecular orbital diagrams as shown in Figure 8.14. The bonding orbitals are the sp ... 

These bands arise from the Jones Zone, which will be discussed in detail in the treatment of tetrahedral semiconductors with pseudopotentials in Chapter 18. The energy at which this peak occurs was used earlier as a basis for obtaining experimental values for the covalent energy V2 (Harrison and Ciraci, 1974). 

Data are presented in five tables. Table 1 lists the main crystallographic and semiconducting properties of a large number of semiconducting materials in three main categories Tetrahedral Semiconductors in which every atom is tetrahedraUy coordinated to four nearest neighbor atoms (or atomic sites) as for example in the diamond structure Octahedral Semiconductors in which every atom is octahedrally coordinated to six nearest neighbor atoms—as for example the halite structure and Other Semiconductors. ... 

This approach has been successful in rationalizing the melting points, heats of formation and mixing, and various optical and electrical phenomena of tetrahedral semiconductor crystals (e.g., see Ref. 173). It is not clear how far it may be extended to other types of materials in the light of the complexities of bonding which many experiments demonstrate—also few experimental results may be related directly to a fractional ionicity for comparison. Levine, however, has generalized the dielectric model in terms of individual bond properties to several different structures. The critical ionicity ft = 0.785) between octahedral and tetrahedral coordination is not always appropriate for example PbS, PbSe, and PbTe (with rock-salt structures) have ft 0.6, and for LiH (also rock-salt)yi 0.1. This latter value would seem to be in... 

Stuke (1970) noticed that the intensity of the E2 peak in the spectra of ZnS depends on the crystallographic modification (zincblende or wurzite) much more than the Ei peak. He suggested that the E2 peak which dominates the spectra of crystalUne tetrahedral semiconductors is much more sensitive to the long-range order than the Ej peak. In his interpretation, this effect is the reason of the shift of the maximum of the absorption band towards the Ei peak observed in the amorphous forms. Ortenburger et al (1972) calculated the band state densities and 2 for a hypothetical hexagonal structure of Ge, and observed a shift of E2 towards smaller energies. 

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