Urbach tail explained

In the solid-state physics of semiconductors, 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.

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

• Tauc plot

Notes and References

1. https://www.oeaw.ac.at/gedenkbuch/personen/q-z/franz-urbach Franz Urbach
2. Urbach. Franz. 1953. The Long-Wavelength Edge of Photographic Sensitivity and of the Electronic Absorption of Solids. Physical Review. 92. 5. 1324. 10.1103/physrev.92.1324. 1953PhRv...92.1324U.
3. 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. 10.1103/physrevlett.64.2811. 10041817. 1990PhRvL..64.2811A.
4. 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. 10.1103/physrevb.37.2714. 9944833. 1988PhRvB..37.2714B.
5. 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. 10.1147/rd.321.0082.