Tauc plot

A Tauc plot[1] is used to determine the optical bandgap, or Tauc gap, in semiconductors.[2] The Tauc gap is often used to characterize practical optical properties of amorphous materials.

An example of a Tauc plot for an indirect allowed transition

Jan Tauc (/taʊts/) showed that the optical absorption spectrum of amorphous germanium resembles the spectrum of the indirect transitions in crystalline germanium (plus a tail due to localized states at lower energies), and proposed an extrapolation to find the optical gap of these crystalline-like states.[3] Typically, a Tauc plot shows the quantity $hν$ (the energy of the light) on the abscissa and the quantity $(αhν) 1/r$ on the ordinate, where $α$ is the absorption coefficient of the material. The value of the exponent $r$ denotes the nature of the transition:[4]

r = 1/2 for direct allowed transitions
r = 3/2 for direct forbidden transitions.
r = 2 for indirect allowed transitions
r = 3 for indirect forbidden transitions

The resulting plot has a distinct linear regime which denotes the onset of absorption. Thus, extrapolating this linear region to the abscissa yields the energy of the optical band gap of the material.

References

Tauc, J. (1968). "Optical properties and electronic structure of amorphous Ge and Si". Materials Research Bulletin. 3: 37–46. doi:10.1016/0025-5408(68)90023-8.
Stenzel, O. (2005). The Physics of Thin Film Optical Spectra: An Introduction. Springer. p. 214. ISBN 978-3-540-27905-1.
Tauc, J.; Grigorovici, R.; Vancu, A. (1966). "Optical Properties and Electronic Structure of Amorphous Germanium". Physica Status Solidi B. 15 (2): 627. Bibcode:1966PSSBR..15..627T. doi:10.1002/pssb.19660150224.
Davis, E. A.; Mott, N. F. (1970). "Conduction in non-crystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors". Philosophical Magazine A. 22 (179): 903–922. doi:10.1080/14786437008221061.

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[1] Tauc, J. (1968). "Optical properties and electronic structure of amorphous Ge and Si". Materials Research Bulletin. 3: 37–46. doi:10.1016/0025-5408(68)90023-8.

[2] Stenzel, O. (2005). The Physics of Thin Film Optical Spectra: An Introduction. Springer. p. 214. ISBN 978-3-540-27905-1.

[Tauc,_J._et_al.-3] Tauc, J.; Grigorovici, R.; Vancu, A. (1966). "Optical Properties and Electronic Structure of Amorphous Germanium". Physica Status Solidi B. 15 (2): 627. Bibcode:1966PSSBR..15..627T. doi:10.1002/pssb.19660150224.

[4] Davis, E. A.; Mott, N. F. (1970). "Conduction in non-crystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors". Philosophical Magazine A. 22 (179): 903–922. doi:10.1080/14786437008221061.