Tauc-Lorentz model. The real (blue solid line) and imaginary (orange dashed line) components of relative permittivity are plotted for model with parameters 3.2 eV, 4.5 eV, 100 eV, 1 eV, and 3.5.
The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued
relative permittivity, sometimes referred to as the dielectric function. The model has been used to fit the complex
refractive index of amorphous semiconductor materials at frequencies greater than their optical
band gap. The
dispersion relation bears the names of
Jan Tauc and
Hendrik Lorentz, whose previous works[1] were combined by G. E. Jellison and F. A. Modine to create the model.[2][3] The model was inspired, in part, by shortcomings of the
Forouhi–Bloomer model, which is aphysical due to its incorrect asymptotic behavior and
non-Hermitian character. Despite the inspiration, the Tauc–Lorentz model is itself aphysical due to being non-Hermitian and
non-analytic in the
upper half-plane.
Further researchers have modified the model to address these shortcomings.[4][5][6]
The imaginary component of is formed as the product of the imaginary component of the
Lorentz oscillator model and a model developed by
Jan Tauc for the imaginary component of the relative permittivity near the bandgap of a material.[1] The real component of is obtained via the
Kramers-Kronig transform of its imaginary component. Mathematically, they are given by[2]
where
is a fitting parameter related to the strength of the Lorentzian oscillator,
is a fitting parameter related to the broadening of the Lorentzian oscillator,
is a fitting parameter related to the resonant frequency of the Lorentzian oscillator,
is a fitting parameter related to the bandgap of the material.
Tauc-Lorentz model. The real (blue solid line) and imaginary (orange dashed line) components of relative permittivity are plotted for model with parameters 3.2 eV, 4.5 eV, 100 eV, 1 eV, and 3.5.
The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued
relative permittivity, sometimes referred to as the dielectric function. The model has been used to fit the complex
refractive index of amorphous semiconductor materials at frequencies greater than their optical
band gap. The
dispersion relation bears the names of
Jan Tauc and
Hendrik Lorentz, whose previous works[1] were combined by G. E. Jellison and F. A. Modine to create the model.[2][3] The model was inspired, in part, by shortcomings of the
Forouhi–Bloomer model, which is aphysical due to its incorrect asymptotic behavior and
non-Hermitian character. Despite the inspiration, the Tauc–Lorentz model is itself aphysical due to being non-Hermitian and
non-analytic in the
upper half-plane.
Further researchers have modified the model to address these shortcomings.[4][5][6]
The imaginary component of is formed as the product of the imaginary component of the
Lorentz oscillator model and a model developed by
Jan Tauc for the imaginary component of the relative permittivity near the bandgap of a material.[1] The real component of is obtained via the
Kramers-Kronig transform of its imaginary component. Mathematically, they are given by[2]
where
is a fitting parameter related to the strength of the Lorentzian oscillator,
is a fitting parameter related to the broadening of the Lorentzian oscillator,
is a fitting parameter related to the resonant frequency of the Lorentzian oscillator,
is a fitting parameter related to the bandgap of the material.