Lower valence band

The plot for MgO (Figure 8.5a) is typical of a main group metal oxide which fits with the classical ionic bonding model of oxide structures. The lower valence band (LVB) consists almost exclusively of 0(2s) states and the UVB of 0(2p) states. In the conduction band (CB) both Mg and O basis functions contribute to the crystal orbitals. The valence bands are completely filled and, since they have mainly O character, this corresponds to complete transfer of valence electrons from Mg to O to give the ionic species Mg and... 

For the upper valence bands (3rd and 4th bands) qA is still smaller than Qb but the differences between Qa and qe are much smaller than for the lower valence bands. For the upper valence bands the p components of the wave functions have the largest amplitudes. One thus concludes that the upper valence bands are predominantly s-p-hybrid bands formed by both the alkali and the non-alkali atoms. 

In Fig. Ila e(f) is plotted for the two upper valence bands. Distinct differences in the electron distribution for these electronic bands compared to the ones of the lower valence bands (Fig. 11b) can be found, although a gradient in the charge density from the nonalkali to the alkali sublattice still exists. For the electronic states of the upper valence bands, however, the chemical bond possesses a metallic-like component. This metallic... 

Each of Si, Ge and a-Sn is classed as an intrinsic semiconductor, the extent of occupation of the upper band increasing with increasing temperature. Electrons present in the upper conduction band act as charge carriers and result in the semiconductor being able to conduct electricity. Additionally, the removal of electrons from the lower valence band creates positive holes into which electrons can move, again leading to the ability to conduct charge. 

It is necessary to have small amounts of impurities in inorganic crystals to have luminescence. In ionic crystals in the ground state all the electrons lie in a lower valence band of energy. Excitation promotes the electrons into a higher conduction band of energy. 

The interaction along the c-direction is enhanced in y-BN as compared to a-BN. This leads to the splitting of states in y-BN which are nearly degenerate in a-BN. The band structure of y-BN shows some similarities with those of other wurtzite IIIB-VB compounds (AIN, GaN) and also wurtzite IIB-VIB compounds (CdSe, CdS, ZnS). The reported bandwidth datafory-BN are lower valence band = 6.0 eV, upper valence band =11.0 eV, full valence band = 20.3 eV [1]. 

Calculations based on the pseudopotential total energy scheme using local-density approximations (LDA) for electron-electron interactions give the following main features of the band structure of p-BN [4] lower valence band = 5.9 eV, upper valence band=10.8 eV, full valence band = 20.3 eV, minimum direct gap (r-r) = 8.6 eV, minimum indirect gap (Hg- X ) = 4.2 eV. 

Egx, indir 5.416(2) 5.409 (2) 100 Indirect exciton gap with lower valence band Indirect exciton gap with upper valence band... 

The spectrum of Fig. 5a is compared in Fig. 6 with the edge emission from a natural type Ilb diamond. Here, in addition to the free exciton peaks, we see features D, and D(, which are associated with the recombination of excitons bound to the boron acceptor. The very weak zero-phonon lines Do and Dj (not visible in Fig. 6b) occur at energies (Do) = Eg - E and (DJ) = E g - 4x where Eg and are the energies of the excitons associated with the upper and lower valence bands, and 4 and E 4 are the binding energies of the upper and lower valence band excitons to the neutral acceptors. The peaks Dj and D( are TO phonon replicas of Dq and D, and a further replica D2 is clearly visible. 

Many band calculations have been carried out on cBN. Their results mostly agree qualitatively, indicating that the minimal band gap occurs between the Xi,c conduction band and the Tis valence band (76,78,89,91,93-96,113-126). The main values related to the cBN energy band obtained from recent calculations lie in rather small ranges the band gap energies lie in the range 4.2-5.2 eV, the upper valence band width 10-11 eV, the lower valence band width 5.3-7 eV, the gap between the upper and lower valence bands 3.3-4.0 eV, and the total valence band width 20-23 eV. However, differences between the calculated and experimental values are not small the calculated band gap (4.2-5.2 eV) and the upper valence band width (10-11 eV) are smaller than the available experimental results (—6.3 eV and 14 eV, respectively see Fig. 17). 

Figure 16 shows the temperature dependence of the DC electrical conductivity of pure and of some selected examples of doped P-rhombohedral boron (see Ref 2 and references therein). In a large range of temperature the slope meets Mott s law for variable-range hopping (Fig. 17) (106,107). The striking step between 400 and 500 K is caused by the Fermi level pinned in the trap states (65). The Seebeck coefficient (Fig. 18) (see Ref 2 and references therein) is positive and indicates p-type conductivity up to the highest temperatures reached. By comparing the temperature dependences of electrical conductivity and Seebeck coefficient according to Bosman and Crevecoeur (108) it was found that the mobility of the holes has an activation energy of 0.18(1) eV (101,106), which corresponds to the distance between the split-off and the lower valence band.

Accordingly, different electronic transport mechanisms seem possible in principle a. Thermal Equilibrium at Low Temperatures Hopping at the Fermi level within the upper valence band Band-type conductivity in the lower valence band... 

When the thermal energy is sufficient, free holes are generated by exciting electrons into the upper valence band, which acts in this case like an intrinsic acceptor level. For these free holes the partly occupied upper valence band has a further meaning for the holes in the lower valence band. It acts as a trapping level of high density, hence reducing the relaxation time of the free holes considerably. This explains the p-type behavior at low temperatures. 

In particular at lower temperatures, thermal nonequilibrium can be established, for example, by optical interband excitation and subsequent trapping of electrons or by quenching from high temperatures. Compared with equilibrium, the electrical conductivity increases, and this is due to the shift of the quasi-Fermi level toward the lower valence band, which has two effects The excitation of free holes increases because the activation energy into the upper valence band is reduced, and the trapping probability of the free holes decreases because the number of occupied states in the upper valence band acting as traps for the free holes in the lower valence band becomes smaller. 

The quenched hole conductivity in the initial range is caused by reduction of the electron density in the upper valence band. This range is followed by an enhanced conductivity caused by the decreasing activation energy for free holes in the lower valence band when the Fermi level is lowered. 

At the beginning, the first electron trap for free electrons and the upper valence band for free holes in the lower valence band have similar effects on the carrier transport, because their reexcitation energies are the same. Accordingly, the shoulders in the dispersion spectra are similar. The delay of the electrons at long times is due to multitrapping in deep traps and to... 

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