Bulk-absorption-coefficient-a-calculated-with-the-band-gap-model-blue-dotted-line-the

In the

solid-state physics Solid-state physics is the study of rigid matter, or solids, through methods such as solid-state chemistry, quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state phy ...

semiconductor A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping level ...

s, the Urbach tail is an exponential part in the

energy spectrum In the physical sciences, the term ''spectrum'' was introduced first into optics by Isaac Newton in the 17th century, referring to the range of colors observed when white light was dispersed through a prism. Soon the term referred to a plot o ...

of the

absorption coefficient The linear attenuation coefficient, attenuation coefficient, or narrow-beam attenuation coefficient characterizes how easily a volume of material can be penetrated by a beam of light, sound, particles, or other energy or matter. A coefficient val ...

. This tail appears near the optical band edge in

amorphous In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid) is a solid that lacks the long-range order that is a characteristic of a crystal. The terms "glass" and "glassy solid" are sometimes used synonymousl ...

, disordered and

crystalline A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macrosc ...

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) found that such tails decay exponentially into the gap. Later, photoemission experiments delivered absorption models revealing temperature dependence of the tail. 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.

References

{{Sci-stub Crystallography

History

See also

References