Tauc plot

A Tauc plot^[1] is used to determine the optical bandgap, or Tauc bandgap, of either disordered^[2] or amorphous^[3] semiconductors.

Tauc representation illustrating the optical bandgap (E_Tauc~ 0.8 eV) of a film of amorphous Si. The insert shows their corresponding transmittance/reflectance spectra.

In his original work 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 bandgap of these crystalline-like states.^[4] 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.^[5] In this case, however, the ordinate is given by (α)^1/r, in which the exponent ^1/r denotes the nature of the transition:^[6],[7],[8]

• 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.^[9]

See also

• Band gap
• Urbach energy