Determining optical bandgap with Tauc Plot
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实验上主要采用Tauc Plot方法确定材料的光学带隙,理论计算上主要通过介电函数虚部第一个吸收峰确定材料的光学带隙。
A Tauc plot is used to determine the optical bandgap, or Tauc bandgap, of either disordered or amorphous semiconductors.
Typically, a Tauc plot shows the quantity $h\nu$ (the photon energy) on the abscissa (x-coordinate) and the quantity $(αhν)^{1/2}$ on the ordinate (y-coordinate), where $\alpha$ 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 $\alpha ^{1/r}$, 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
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.