Physics:Urbach tail
The Urbach tail is an exponential part in the energy spectrum of the absorption coefficient. This tail appears near the optical band edge in amorphous, disordered and crystalline materials.
History
Researchers began questioning the nature of "tail states" in disordered semiconductors in the 1950s. It was found that such tails arise from the strains sufficient to push local states past the band edges.[citation needed]
In 1953, the Austrian-American physicist Franz Urbach (1902–1969)[1] found that such tails decay exponentially into the gap.[2] Later, photoemission experiments delivered absorption models revealing temperature dependence of the tail.[3]
A variety of amorphous crystalline solids expose exponential band edges via optical absorption. The universality of this feature suggested a common cause. Several attempts were made to explain the phenomenon, but these could not connect specific topological units to the electronic structure.[4][5]
See also
References
- ↑ Franz Urbach. Austrian Academy of Sciences
- ↑ Urbach, Franz (1953). "The Long-Wavelength Edge of Photographic Sensitivity and of the Electronic Absorption of Solids". Physical Review 92 (5): 1324. doi:10.1103/physrev.92.1324. Bibcode: 1953PhRv...92.1324U.
- ↑ Aljishi, Samer; Cohen, J. David; Jin, Shu; Ley, Lothar (1990-06-04). "Band tails in hydrogenated amorphous silicon and silicon-germanium alloys". Physical Review Letters 64 (23): 2811–2814. doi:10.1103/physrevlett.64.2811. PMID 10041817. Bibcode: 1990PhRvL..64.2811A.
- ↑ Bacalis, N.; Economou, E. N.; Cohen, M. H. (1988). "Simple derivation of exponential tails in the density of states". Physical Review B 37 (5): 2714–2717. doi:10.1103/physrevb.37.2714. PMID 9944833. Bibcode: 1988PhRvB..37.2714B.
- ↑ Cohen, M. H.; Chou, M.-Y.; Economou, E. N.; John, S.; Soukoulis, C. M. (1988). "Band tails, path integrals, instantons, polarons, and all that". IBM Journal of Research and Development 32 (1): 82–92. doi:10.1147/rd.321.0082.
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