Hybrid polar energy

For polar covalent solids, sp hybrids of the form of Eq. (3-1) can be constructed on each of the atom types present and oriented in the directions of its nearest neighbors. The hybrid energies will be different we call the lesser energy and the greater energy i-, and, in direct analogy with Eq. (1-32), define a hybrid polar energy proportional to their difference ... 

For any compound, the hybrid polar energy can be estimated by using the term values given in Table 2-2 or the Solid State Table. 

Consider hexagonal boron nitride, shown in Fig. 3-10. Define a hybrid covalent and hybrid polar energy for this structure, in analogy with the corresponding definitions for tetrahedral solids in Eqs. (3-4) and (3-6). Compare the polarity obtained from these values with that of tetrahedral BN, listed in Table 7-2. Take d = 1.42 A as in graphite. Notice that many values arc modified by having sp hybrids rather than sp hybrids. 

Hybrid covalent and hybrid polar energies, in eV. The hybrid polarity a can be compared with the polarity a, based upon p states and used to describe dielectric properties. 

Within the framework of the bond polarization the shift components of the unpolarized bond and the parameter Aai giving the polarization influence on the chemical shift are determined empirically from solving a set of linear equations 1 for a number of substances where both the chemical shift tensor and the molecular structure are known. The bond polarization energies Vai are calculated as effect of surrounding net atomic charges qx on atomic hybrids %. With the bond polarity parameter the polarization energy can be calculated. 

Bond orbitals are constructed ft om s/r hybrids for the simple covalent tetrahedral structure energies are written in terms of a eovalent energy V2 and a polar energy K3. There are matrix elements between bond orbitals that broaden the electron levels into bands. In a preliminary study of the bands for perfect crystals, the energies for all bands at k = 0 arc written in terms of matrix elements from the Solid State Tabic. For calculation of other properties, a Bond Orbital Approximation eliminates the need to find the bands themselves and permits the description of bonds in imperfect and noncrystalline solids. Errors in the Bond Orbital Approximation can be corrected by using perturbation theory to construct extended bond orbitals. Two major trends in covalent bonds over the periodic table, polarity and metallicity, arc both defined in terms of parameters from the Solid State Table. This representation of the electronic structure extends to covalent planar and filamentary structures. 

We must now make a sharp distinction between the concepts we are using and the parameters of the theory. The V l and defined in the preceding paragraphs for the hybrid bond are the direct counterparts of covalent and polar energies... 

Here, as in the discussion of simple molecules, we consider the two hybrids that make up the bond to be orthogonal, that is, = 0, so that there is no term in u, U2 in the denominator. We shall see in Appendix B that this is permissible since the two effects that nonorthogonality has can be absorbed in a redefinition of the covalent and polar energies and in a contribution to the overlap interaction between atoms, which is discussed in Chapter 7. Similarly, we have neglected the more complicated aspects of electron-electron interaction, treating it instead in terms of an average potential associated with each electron. The neglect of... 

The last form is obtained by using the expressions for the interatomic matrix elements from the Solid State Table. For polar semiconductors the splitting becomes 2(Vl+ with the polar energy- m contrast to the hybrid polar... 

F2m/(polar energy represents the difference in hybrid energy on the two atom types and cannot show a change proportional to the displacement (by symmetry, since the change for reversed displacements must be the same). Thus the polarity change is... 

This mcclianism is not so efrcctivc in polar semiconductors. The conversion of empty hybrids to doubly occupied hybrids on a GaAs surface would require the double occupation of a gallium hybrid, which is unfavorable because of the polar energy. Indeed, recent experiments (Chye, Babalola, Sukegawa, and Spicer, 1975) indicate that the I crmi level is not pinned on surfaces of GaP at the vacuum. Nonetheless, Schottky barriers can arise at GaP- metal interfaces. Metal-induced surface states" have been proposed as a mechanism (discussed in Section 18-1 ) but the barriers could well arise simply from incorporation of metal atoms in the semiconductor or vice versa. 

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