Wurtzite selection rules

Table 3.2. Raman selection rules of the optical phonon modes of crystals with wurtzite structure21 [33]...

Infrared reflection and Raman spectroscopies have been used to derive the energies of the zone centre phonon modes in wurtzite AlxGai.xN (0 < x < 1) [1-5] (for GaN [6] and AIN [7] refer to the dedicated Datareviews). Selection rules in wurtzite allow a splitting of longitudinal and transversal modes into Ai and Ei modes and the occurrence of additional Raman active modes E2. 

Most wurtzite-type crystals are direct band-gap materials (2fP-SiC is an exception) and interband transitions can take place between these three Fils and the T7 CB minimum. These materials are anisotropic and this anisotropy reflects on the selection rules for the optical transitions and on the effective masses. The Tg (A) —> T7 (CB) transitions are only allowed for ETc while the two T7 (B. C) —> T7 (CB) transitions are allowed for both polarizations. However, the relative values of the transition matrix elements for the T7 (B, C) —> T7 (CB) transitions can vary with the material. For instance, in w-GaN, the T7 (B) —> T7 (CB) transition is predominantly allowed for ETc while the T7 (C) — I 7 (CB) transition is predominantly allowed for E//c [22]. Table 3.7 gives band structure parameters of representative materials with the wurtzite structure. 

Use of the alternative methods whose selection rules admit of spectral activity of the LO modes. One such method is polarized Raman spectroscopy, which is applicable to substances with cubic zinc blend and hexagonal wurtzite structures such as ZnS, ZnSe, CdS, ZnO, ZnTe, and the III-V compounds (see Refs. [47-49] and literature cited therein). The most direct method to measure vlo is inelastic neutron scattering (INS) since there are no selection rules for INS spectroscopy and as a result all modes are allowed [50, 51]. 

Table 1 Raman Selection Rules for Wurtzite-Type Crystallites...

Figure 3.4 Band structure and selection rules for zinc blende and wurtzite structures. Crystal-field and spin-orbit splittings are indicated schematically. Transitions that are allowed for various polarizations of photon electric field vector with respect to the c-axis are indicated. (After Ref [40].)...

To measure the spin coherence time and to estimate the spin-polarized carrier injection efficiency from the electroluminescence data, the selection rules and the valence band structure in ZnO must be understood. The valence band in wurtzite materials is split into three bands (A, B, and C) due to crystal field and spin-orbit coupling as discussed before in Chapter 3. The spin degeneracy of these three bands and the conduction band is lifted in magnetic field resulting in small symmetric Zeeman splittings as shown in Figure 5.6 near the F point [48]. The allowed transitions following the selection rules AI = 1 (for 0 polarization) are indicated... 

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