Lesson plan
Tauc plot
A Tauc plot is used to determine the optical bandgap, or Tauc bandgap, of either disordered or amorphous semiconductors. 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. In this case, however, the ordinate is given by (α) 1/r , in which the exponent 1/r denotes the nature of the transition: , , *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
Article summary
A Tauc plot is used to determine the optical bandgap, or Tauc bandgap, of either disordered or amorphous semiconductors. 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. In this case, however, the ordinate is given by (α) 1/r , in which the exponent 1/r denotes the nature of the transition: , , *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
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Discussion questions
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