Urbach tail

• Comment: User:Bkissin - Yes.
  It's a physics thing, and every physics thing is a math thing. Robert McClenon (talk) 22:16, 13 July 2021 (UTC)

---

Band-gap model (blue dotted line), the Urbach-tail extension (red dotted line), and the band-gap model with Urbach tail (black solid line).

Urbach Tail is an exponential part in the absorbtion coefficient curve. This tail appears near the optical band edge, in the amorphous, disordered and crystaline materials.

History

Researchers were questioning the nature of the disordered semiconductors' tale states since the nineteen-fifties. It has been found that such tails arise from the strains sufficient to push local states past the band edges. In 1953 F.Urbach identified that such tails decay exponentially into the gap. Later photoemission experiments delivered absorbtion models displaying temperature dependence of the tail. Variety amorphous and imperfect crystalline solids reveal exponential band edges via optical absorption. The surprising universality of this feature suggested the possibility of a common cause. Several attempts to explain the phenomenon were limited, and could not connect specific topological units to the electronic structure

Recent studies showed that topological filaments (structural patterns that resemble hydrodynamic flow fields) can be a structure underlying the Urbach edge. However, TF might be not unique in producing the Urbach tail