Band structure wurtzite

Alg, Zn i, 0 crystallizes in the wurtzite or in the rocksalt structure, depending on the Mg mole fraction x. The alloys remain direct-gap materials over the whole composition range. The wurtzite-structure part reflects a valence-band structure, which is similar to ZnO. For the rocksalt-structure part the... 

The data in Table 3.16 may be used to estimate the band gap energy for unstrained wurtzite-structure MgO of E = 6.9 eV and for rocksalt-structure ZnO of Ee — 7.6 eV, with stronger bowing for the rocksalt-structure than for the wurtzite-structure occurrence of the alloys. Theoretical band-structure calculations for ZnO revealed the high-pressure rocksalt-structure phase as... 

A useful approach to the wurtzite valence band structure is the quasi-cubic model of J.J. Hop field [3], In this framework, the relative energies of the valence band maxima are ... 

FIGURE 1 Electronic band structures of (a) wurtzite and (b) zincblende GaN. 

FIGURE 9 Schematic band structures in the kx-ky plane around the top of the valence bands of wurtzite GaN (a) without strain, (b) with biaxial strain, and (c) with uniaxial strain in the (0001) plane, (d) shows the direction of each strain. 

Schematic parabolic band structure for CdSe, which has a band gap of 1.75 eV. The conduction band is labeled C, and several valence bands (V,) are shown. The filled and open circle symbols indicate the position of quantized k values mr/ai allowed for the / = 1 and n = 2 states of an NC with radius a. The solid arrow shows the / = 1 transition in which an electron is excited and a hole is created (open circle). The dashed arrow shows how the position of this n = i transition would change for a nanocrystal of smaller radius 32- (Adapted from Ref. 7.) This simple diagram is for the cubic zinc blend structure the hexagonal wurtzite structure has a small gap k= 0 between the and V2 bands.

Figure 1. Energy band structure and the symmetry of the free exciton ground state in wurtzite-type semiconductors for (a) ZnO and (b) GaN, CdSe, CdS.

Fig. 7.3. The relationship between number of shared edges between cation tetra-hedra and both the electrostatic Madelung energy and the one-electron covalent band-structure energy for 2 real observed and 21 hypothetical polymorphs of BeO. The structure types plotted are the wurtzite (a-BeO) type (-I-), the p-BeO type (X), and the 21 hypothetical dipolar tetrahedral structures with (1,1) or (2,1) unit cells. The small numbers by some of the points show how many points are represented by the single symbol (after Burdett and McLarnan, 1984 reproduced with the publisher s permission).

Cardona, M., and G. Harbeke (1965). Optical properties and band structure of wurtzite-type crystals and rutile. Phys. Rev. 137, A1467-76. 

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. 

Table 3.T. Selected band structure parameters of four compounds with the wurtzite structure. The energies for ZnO and GaN are given at LHeT and at 80 K for CdSe and CdS (the effective masses are expressed in units of me)...

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]. 

Band Structures of Aluminium Compounds. Aluminium Nitride (AIN). Aluminium nitride is a direct-gap semiconductor. Since it crystallizes in the wurtzite structure, the band structure (Fig. 4.1-66) differs from that of most of the other III-V compounds. 

Fig. lr.1-132 The Brillouin zone of the wurtzite lattice Table ir.1-101 Band structures of beryllium compounds... 

The good agreement makes ns believe that the approach is accnrate and the results for finite clusters are accurate too. In addition, we also have calcnlated the band structure of bulk zinc-blende and wurtzite ZnS and are shown in Figures 12.1 and 12.2. The features in the band structures matches well with those obtained from ab initio calculations [46,47],... 

One of the most important aspects of the films and heterostructures with nonpolar and semipolar surfaces is related to the polarization dependence of their optical properties. The polarization anisotropy has been studied both theoretically and experimentally in nonpolar GaN [87, 88], as well as in InN [105]. The optical polarization anisotropy in wurtzite nitrides originates from their valence band structure, which can be significantly modified by the anisotropic in-plane strain in the films. 

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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