Tauc plot

{{short description|Method for determining the band gap of a material}}

File:Picture Tauc.jpg

A Tauc plot

{{cite journal

|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

}} is used to determine the optical bandgap, or Tauc bandgap, of either disordered

{{cite book

|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

}} or amorphous

{{cite book

|author=Street, R. A.

|year=1991

|title=Hydrogenated amorphous silicon

|publisher=Cambridge Univ. Press, Cambridge

|isbn=0-521-37156-2

}} semiconductors.

In his original work Jan Tauc ({{IPAc-en|t|aʊ|t|s}}) 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.{{cite journal|doi=10.1002/pssb.19660150224|title=Optical Properties and Electronic Structure of Amorphous Germanium|year=1966|last1=Tauc|first1=J.|last2=Grigorovici|first2=R.|last3=Vancu|first3=A.|journal=Physica Status Solidi B|volume=15|issue=2|pages=627|bibcode = 1966PSSBR..15..627T |s2cid=121844404 |url=https://doklady.belnauka.by/jour/article/view/554|url-access=subscription}} 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.

{{cite book

|author=Yu, P. Y. & Cardona, M.

|year=1996

|title=Fundamentals of semiconductors

|publisher=Springer, Berlin

|isbn=3-540-61461-3

}} In this case, however, the ordinate is given by (α)^1/r, in which the exponent ^1/r denotes the nature of the transition:{{cite journal| doi=10.1103/PhysRev.97.1714.2 |author=MacFarlane, G. G. & Roberts, V. | pages=1714–1716 | journal=Physical Review | year=1955 | volume=97 | issue=6 | title=Infrared absorption of germanium near the lattice edge |bibcode=1955PhRv...97.1714M }}^,{{cite journal| doi=10.1103/PhysRev.111.1245 |author=MacFarlane, G. G., McLean, T. P., Quarrington, J. E. & Roberts, V. |pages =1245–1254 | journal=Physical Review | year=1958 | volume=111 | issue=5 | title=Fine structure in the absorption-edge spectrum of Si|bibcode=1958PhRv..111.1245M }}^,{{cite journal| doi=10.1080/14786437008221061|author1=Davis, E. A. |author2=Mott, N. F. |pages =903–922|journal=Philosophical Magazine A |year=1970|volume= 22|issue=179|title=Conduction in non-crystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors|bibcode=1970PMag...22..903D }}

• 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

Again, the resulting plot (quite often, incorrectly identified as a Tauc plot) has a distinct linear region that, extrapolated to the abscissa, yields the energy of the optical bandgap of the material.

{{cite journal

|author=Zanatta, A. R.

|year=2019

|title=Revisiting the optical bandgap of semiconductors and the proposal of a unified methodology to its determination

|journal=Scientific Reports

|volume=9 |issue=1

|pages=11225–12pp

|doi=10.1038/s41598-019-47670-y

|pmid=31375719

|pmc=6677798

|bibcode=2019NatSR...911225Z

|doi-access=free

}}