Valence bands Structure, band tails

It was found that in this energy range, a follows the same behavior of the joint (valence -I- conduction) density of states. Thus, Eo, may be interpreted as a measure of the structural disorder [98], as it represents the inverse of band tail sharpness. 

Since the slope, E, of the Urbach absorption reflects the shape of the valence band tails, it follows that varies with the structural disorder. For example, one measure of the disorder is the average bond angle variation, which is measured from the width of the vibrational spectrum using Raman spectroscopy (Lannin 1984). Fig. 3.22 shows an increasing E with bonding disorder, which is caused by changes in the deposition conditions and composition (Bustarret, Vaillant and Hepp 1988 also see Fig. 3.20). The defect density is another measure of the disorder and also increases with the band tail slope (Fig. 3.22). A detailed theory for the dependence of defect density on is given in Section 6.2.4. 

The weak bond model assumes a non-equilibrium distribution of weak bonds arising from the disorder of the a-Si H network. It has been proposed that the shapes of the band tails are themselves a consequence of thermal equilibrium of the structure (Bar-Yam, Adler and Joannopoulos 1986). The formation energy of a tail state is assumed proportional to the difference in the one-electron energies, so that the energy, required to create a band tail state of energy Ey from the valence band mobility edge is... 

Another interesting comparison is with the optical absorption tail. In principle, the optical absorption coefiicient is a convolution of the valence-band density of states with the conduction-band density of states multiplied by a matrix element. However, if the band tails are exponential and one band tail is broader than the other, an elementary mathematical analysis shows that the optical absorption tail has the same energy dependence as the broader band tail, with the energy dependence of the matrix element neglected. In our picture of the electronic structure of a-Si H, the valence-band tail is broader, and hence the characteristic width of the absorption tail should be compared with the width of the valence-band tail ( 42 meV). The optical absorption tail for material prepared under conditions similar to the... 

Many important fundamental issues are unresolved. Virtually no experimental information is available about the energy dependence of the mobility in the vicinity of the mobility edge at some finite temperature. Very little is known about the nature of the electronic structure of the band-tail states or about the strength of the electron-phonon interaction for these states. Finally, it is not clear why the disorder produces exponential rather than Gaussian band tails or even why the valence-band tail is wider than the conduction-band tail, although some theoretical models have been suggested (see, for example, Yonezawa and Cohen, 1981). Much remains to be done. 

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