Interband density of states

Fig. 14. Interband density of states (IDS) of SmBj al 4K. calculated with the use of the resulting fit oscillator strength in the constant matrix element approximation the dotted line gives the uncertainty between the peak with f character and the one with d character. (After Travaglini and Wachter 1984a.)...

We can now calculate from 2 the joint density of states /cv of interband density of states (IDS) which is 2Jcv The IDS is shown in fig. 14 there exists a giant peak... 

Fig. 2.5 Experimental photoconductivity spectrum (solid line) and interband density of states (dashed line) for TiC (Lynch et al, 1980).

The two peaks at E and E2 are related to transitions (indicated by arrows in Figure 4.7) from the vicinity of specific points of high symmetry in the Brillouin zone, denoted by L and X. However, in order to explain the exact locations of these two absorption peaks, the density of states function must be also taken into account. Thus, it appears obvious that the full interpretation of interband spectra is far from simple. 

Of particular interest are the optical spectra. Chclikow.sky and Schluter calculated the Joint density of states for direct transitions (which would be proportional to C2 were the dipole matrix elements all equal). sec Section 4-A -with the result shown at the bottom of Fig. 11-12. It bears little resemblance to the experimental Cj curve (uppermost in the figure), for a number of reasons. Tlie prominent peak at 10.4 eV appears to be an cxciton peak (See Section 6-H), as had been stiggested earlier by Platzoder (1968) on the basis of observed temperature dependence. Pantelidcs and Harrison took this peak to result from interband transitions, since it lay at an enci gy above the photoconductivity threshold of 9 eV (DiStephano and Eastman, 1971b) that would rule out the possibility that the peak represents a simple exciton, but not that it represents an excitonlikc... 

The large joint density of states associated with the direct it- to ir -(interband) transition results in a very strong cross-section for stimulated emission. 

Theoretical studies were performed for Using a simple microscopic theory 2 is correlated to direct interband transitions. C2((o) can be calculated using a simple approach from the joint density of states J (to), see below. 2(0)) is then ... 

Electron energy-loss spectroscopy at low excitation energies is a surface sensitive technique to study the electronic structure by exciting collective oscillations or electrons from occupied into unoccupied states. In metals with a high density of states arising from d electrons, the excitation of plasmon losses has a relatively low probability. Therefore, the spectra are dominated by interband or intraband transitions. In rare earth metals, excitations of the partially filled/shell are observed that are assigned to be dipole-forbidden 4/4/transitions. These transitions are enhanced near the 4ii-4/threshold [56]. 

In ordinary optical absorption there are two components associated with intraband transitions (Drude component) and interband transitions, respectively. A similar situation is encountered in magneto-optical spectroscopy. Of special interest is the interband component which is related to the joint density of states. The intensity of the magneto-optical transitions is proportional to the product of spin-orbit coupling strength and net electron-spin polarization of states excited by the incident light (Erskine and Stern, 1973). 

The band structure and the DOS of the orthorhombic 3D Cgo (0-3D) polymer were calculated on the basis of the coordinates obtained by the X-ray refinement and theoretically optimized structures [68, 70, 71]. All of the calculations suggested the metallic conductivity of the 0-3D polymer with a large density of states at the Fermi level. The calculation by Yang et al. [70] suggested that the electronic band structure has steep and flat bands near the Fermi level, and possible occurrence of interband nesting which may enhance electron-phonon coupling for superconductivity. With these features it is possible that the 0-3D Cgo polymer would be a potential superconductor even without doping. The 0-3D polymer is electron... 

Fig. 3.42. Comparison of the interband optical constant with the joint density of states of Eu. The free electron model gives poor agreement with the experiment (Endriz and Spicer, 1970).

The optical band gap of a-C is determined by using a Tauc plot, a method common for amorphous material where the k selection rule is relaxed. A parabolic distribution of the density of states for both bands near the band edges is assumed, together with matrix elements for interband transitions being equal for all transitions ... 

From the preceding derivations we conclude that the dielectric function of a semiconductor or insulator will derive from interband contributions only, as given by Eqs. (5.54) and (5.55) while that of a metal with several bands will have interband contributions as well as intraband contributions, described by Eqs. (5.51) and (5.52) (see also Ref. [61]). A typical example for a multi-band rf-electron metal, Ag, is shown in Fig. 5.4. For more details the reader is referred to the review articles and books mentioned in the Further reading section. For semiconductors, it is often easy to identify the features of the band structure which are responsible for the major features of the dielectric function. The latter are typically related to transitions between occupied and unoccupied bands which happen to be parallel, that is, they have a constant energy difference over a large portion of the BZ, because this produces a large joint density of states (see problem 8). 

The band structure in real systems is more complex than the simple models we have developed in trying to understand the electronic properties of metals. This is especially true in the transition metals where the d-electrons contribute significantly to the band structure. We see that conductivity is a fimction of the Fermi surface and the density of states in the vicinity of the Fermi level. By examining the calculated or measured band structure we can obtain much more insight into interband transitions, which account for the color of metals, and why some metals are much better conductors than others. 

In oxides, excitonic transitions have been invoked to interpret the results of optical absorption and reflectivity experiments. They have also been invoked to explain discrepancies between experimental spectra and calculated joined densities of states, in quartz Si02 (Pantelides and Harrison, 1976 Chelikowsky and Schliiter, 1977 Gupta, 1985), in SrTiOs (Xu et ai, 1990), in MgO, AI2O3 and MgAl204 (Cohen et al, 1967 Bortz and French, 1989 Xu and Ching, 1991). In most cases, the absorption intensity presents an enhancement at low energy, in the interband transition continuum, rather than a well-defined peak located below this continuum. 

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