Valence band spin-orbit splitting

Valence band spectra for Au 5d (Figure 11) show a slight shift to higher energy compared with bulk gold, and decrease in spin-orbit splitting. These features are characteristic of crystalline AuSn alloys. 

Here ji are the Luttinger parameters, and is a spin-orbit splitting energy. L and a denote orbital and spin angular momentum operators, respectively. [Lj,Lj] is defined as [Lj,Lj] = (LjLj + LjLj)/2. The summation of i,j runs through x,y,z. In the analysis of wurtzite (WZ) compounds, the Bir-Pikus Hamiltonian for the valence band states is used. The Hamiltonian is given by [3]... 

Spin-orbit splittings of the valence-band maximum, in eV. 

Among the theoretical papers, the most interesting results are found by Wei, et al. and Lambrecht et al." Wei, et al. show that interaction of oxygen p-levels with zinc d-levels, i.e. p - d repulsion and hybridization, reduces the spin-orbital splitting and alters the sign of the crystal-field splitting p - d coupling mixes d-character into the wave function at the valence-band maxima ... 

Fig. 2.11. The one-electron energy ( ) vs momentum (/c) diagram for GaAs near k = 0 showing the band gap Eg and the spin—orbit splitting of 0.34 eV in the valence P band. Transitions with cr" and cr light from the Py2 band are indicated by solid and dashed lines respectively. The circled numbers represent the relative transition probabilities.

The broadening of both valence and conduction band due to spin-orbit splitting of levels, and the net upward shift and broadening of the W 5d component of the VB are largely responsible for the differences seen in comparing NR and R DOS in Fig. 12. 

In describing the magneto-optical properties one has to take account of the spin-orbit splitting, which was not included in the band-structure calculations of de Groot et al. These authors note that no orbital quenching occurs at the F point in the Brillouin zone so that here one may expect the spin-orbit interaction to be a maximum. It follows from the magneto-optical spectra that the onset of the Kerr peak at about 2 eV is located near 1 eV (see fig. 37). From these considerations it follows that the transition responsible for the large Kerr intensity involves initial electron states located rather close to the top of the valence band (at F in the lower... 

As mentioned in Section 4.2.2, no free carrier absorption is usually observed in amorphous semiconductors. Another effect of free carriers is transitions between various branches of the valence band split by spin-orbit interaction. This absorption which is observable in p-type crystalline semiconductors (p-bands) was reported also in a-Se (Kessler and Sutter (1963)) and in a-Ge (Tauc et al (1966)). However, in the case of a-Se the energy difference between the corresponding bands deduced from experiment is much higher than the spin-orbit splitting observed in the emission spectra of c-Se and predicted theoretically. In the case of a-Ge, the results of more accurate experiments on thicker films could not be interpreted as p-bands (Tauc et al. (1970a)). The suggested explanation of the observed infrared bands in a-Ge was discussed in connection with Figure 4.2 in this Section and in Sections 4.2.1 and 4.2.3. There is therefore no evidence of p-bands in amorphous semiconductors. 

Diamond is an indirect-gap semiconductor, the lowest minima of the conduction band being located along the A axes. The valence band has the structure common to all group IV semiconductors, namely three bands degenerate at F. The spin-orbit splitting of these bands is negligible. 

The valence band has its maximum at the P point (symmetry Pg), the light- and heavy-hole bands being degenerate at this point. Both bands are warped. The third, spin-orbit spUt-off band has P symmetry. In contrast to silicon the spin-orbit splitting energies are considerable. Thus, the symmetry notation of the double group of the diamond lattice is mostly used for Ge. 

The spin-orbit splitting of the top of the valence band is negligible compared with most other energy separations in the band structure. Therefore, Fig. 4.1-86 shows the band structure calculated without inclusion of spin-orbit splitting the symmetry symbols of the high-symmetry band states are symbols of the single group of the zinc blende structure. 

Indium Arsenide (InAs). Indium arsenide resembles InSb in its band structure, having only a slightly larger energy gap and a smaller spin-orbit splitting of the top of the valence band. The conduction band minimum (Fg) is situated in the center of the Brillouin zone. Near the minimum, E(k) is isotropic but nonparabolic. The valence band shows the usual structure common to all zinc blende-type III-V compounds (Fig. 4.1-116). 

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