Tauc plot

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Method for determining the band gap of a material

title: "Tauc plot" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["plots-(graphics)", "thin-films", "semiconductor-analysis"] description: "Method for determining the band gap of a material" topic_path: "arts" source: "https://en.wikipedia.org/wiki/Tauc_plot" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::summary Method for determining the band gap of a material ::

::figure[src="https://upload.wikimedia.org/wikipedia/commons/e/e9/Picture_Tauc.jpg" caption="Tauc representation illustrating the optical bandgap (ETauc~ 0.8 eV) of a film of amorphous Si. The insert shows their corresponding transmittance/reflectance spectra."] ::

A Tauc plot |author=Tauc, J. |year=1968 |title=Optical properties and electronic structure of amorphous Ge and Si |journal=Materials Research Bulletin |volume=3 |pages=37–46 |doi=10.1016/0025-5408(68)90023-8 |author=Mott, N. F. & Davis, E. A. |year=1979 |title=Electronic processes in non-crystalline materials |publisher=Clarendon Press, Oxford |isbn=0-19-851288-0 |author=Street, R. A. |year=1991 |title=Hydrogenated amorphous silicon |publisher=Cambridge Univ. Press, Cambridge |isbn=0-521-37156-2

In his original work Jan Tauc () 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 bandgap of these crystalline-like states. Typically, a Tauc plot shows the photon energy E (= hν) on the abscissa (x-coordinate) and the quantity (αE)1/2 on the ordinate (y-coordinate), where α is the absorption coefficient of the material. Thus, extrapolating this linear region to the abscissa yields the energy of the optical bandgap of the amorphous material.

A similar procedure is adopted to determine the optical bandgap of crystalline semiconductors. |author=Yu, P. Y. & Cardona, M. |year=1996 |title=Fundamentals of semiconductors |publisher=Springer, Berlin |isbn=3-540-61461-3

  • 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

References

References

  1. (1966). "Optical Properties and Electronic Structure of Amorphous Germanium". Physica Status Solidi B.
  2. MacFarlane, G. G. & Roberts, V.. (1955). "Infrared absorption of germanium near the lattice edge". Physical Review.
  3. MacFarlane, G. G., McLean, T. P., Quarrington, J. E. & Roberts, V.. (1958). "Fine structure in the absorption-edge spectrum of Si". Physical Review.
  4. (1970). "Conduction in non-crystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors". Philosophical Magazine A.

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plots-(graphics)thin-filmssemiconductor-analysis