TY - JOUR
T1 - Application of the Holomorphic Tauc-Lorentz-Urbach Function to Extract the Optical Constants of Amorphous Semiconductor Thin Films
AU - Ballester, Manuel
AU - García, Marcos
AU - Márquez, Almudena P.
AU - Blanco, Eduardo
AU - Fernández, Susana M.
AU - Minkov, Dorian
AU - Katsaggelos, Aggelos K.
AU - Cossairt, Oliver
AU - Willomitzer, Florian
AU - Márquez, Emilio
N1 - Publisher Copyright:
© 2022 by the authors.
PY - 2022/10
Y1 - 2022/10
N2 - The Tauc–Lorentz–Urbach (TLU) dispersion model allows us to build a dielectric function from only a few parameters. However, this dielectric function is non-analytic and presents some mathematical drawbacks. As a consequence of this issue, the model becomes inaccurate. In the present work, we will adopt a procedure to conveniently transform the TLU model into a self-consistent dispersion model. The transformation involves the integration of the original TLU imaginary dielectric function (Formula presented.) by using a Lorentzian-type function of semi-width, (Formula presented.). This novel model is analytic and obeys the other necessary mathematical requirements of the optical constants of solid-state materials. The main difference with the non-analytic TLU model occurs at values of the photon energy near or lower than that of the bandgap energy (within the Urbach absorption region). In particular, this new model allows us to reliably extend the optical characterization of amorphous-semiconductor thin films within the limit to zero photon energy. To the best of our knowledge, this is the first time that the analytic TLU model has been successfully used to accurately determine the optical constants of unhydrogenated a-Si films using only their normal-incidence transmission spectra.
AB - The Tauc–Lorentz–Urbach (TLU) dispersion model allows us to build a dielectric function from only a few parameters. However, this dielectric function is non-analytic and presents some mathematical drawbacks. As a consequence of this issue, the model becomes inaccurate. In the present work, we will adopt a procedure to conveniently transform the TLU model into a self-consistent dispersion model. The transformation involves the integration of the original TLU imaginary dielectric function (Formula presented.) by using a Lorentzian-type function of semi-width, (Formula presented.). This novel model is analytic and obeys the other necessary mathematical requirements of the optical constants of solid-state materials. The main difference with the non-analytic TLU model occurs at values of the photon energy near or lower than that of the bandgap energy (within the Urbach absorption region). In particular, this new model allows us to reliably extend the optical characterization of amorphous-semiconductor thin films within the limit to zero photon energy. To the best of our knowledge, this is the first time that the analytic TLU model has been successfully used to accurately determine the optical constants of unhydrogenated a-Si films using only their normal-incidence transmission spectra.
KW - amorphous semiconductors
KW - dielectric function
KW - optical properties
KW - Tauc–Lorentz model
KW - Tauc–Lorentz–Urbach model
KW - thin-film characterization
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U2 - 10.3390/coatings12101549
DO - 10.3390/coatings12101549
M3 - Article
AN - SCOPUS:85140761901
SN - 2079-6412
VL - 12
JO - Coatings
JF - Coatings
IS - 10
M1 - 1549
ER -