Modified Tauc–Lorentz dispersion model leading to a more accurate representation of absorption features below the bandgap

Likhachev, Dmitriy; Malkova, Natalia; Poslavsky, Leonid

doi:10.1016/j.tsf.2015.07.035

Cited by 63 publications

(35 citation statements)

References 90 publications

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“…The PZT refractive index (n) and extinction coefficient (k) were first estimated using a B-spline function for the PZT before these constants were used as starting values with a Tauc-Lorentz oscillator for further refinement of the fit. [57][58][59][60] A second EMA-coupled layer was used at the PZT surface with both void (air) and PZT, to account for the surface roughness. For calculation of relative thickness values, all fit parameters other than the PZT film thickness were held constant during the fitting process, to ensure a consistent optical model was applied.…”

Section: Experimental Methodsmentioning

confidence: 99%

Thickness distribution of sputtered films on curved substrates for adjustable x-ray optics

Bishop

Walker

DeRoo

et al. 2019

J. Astron. Telesc. Instrum. Syst.

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McKinstry, "Thickness distribution of sputtered films on curved substrates for adjustable x-ray optics," J.Abstract. Piezoelectric adjustable x-ray optics use magnetron sputtered thin film coatings on both sides of a thin curved glass substrate. To produce an optic suitable for a mission requiring high-angular resolution like "Lynx," the integrated stresses (stress × thickness) of films on both sides of the optic must be approximately equal. Thus, understanding how sputtered film thickness distributions change for convex and concave curved substrates is necessary. To address this, thickness distributions of piezoelectric Pb 0.995 ðZr 0.52 Ti 0.48 Þ 0.99 Nb 0.01 O 3 films are studied on flat, convex, and concave cylindrical substrates with a 220-mm radius of curvature. A mathematical model of the film thickness distribution is derived based on the geometric properties of the sputter tool and the substrate, and film thicknesses deposited with a commercially available sputtering tool are measured with spectroscopic ellipsometry. Experiment and modeled results for flat and convex curved substrates demonstrate good agreement, with average relative thickness distribution difference of 0.19% and −0.10% respectively, and a higher average difference of 1.4% for concave substrates. The calculated relative thickness distributions are applied to the convex and concave sides of a finite-element analysis (FEA) model of an adjustable x-ray optic prototype. The FEA model shows that, left uncorrected, the relative film thickness variation will yield an optic with an optical performance of 2.6 arc sec half power diameter (HPD) at 1 keV. However, the mirror figure can be corrected to diffraction-limited performance (0.3 arc sec HPD) using the piezoelectric adjusters, suggesting that the tolerances for applying a balanced integrated stress on both sides of a mirror are alleviated for adjustable x-ray optics as compared to traditional static x-ray mirrors. Furthermore, the piezoelectric adjusters will also allow changes in mirror figure over the telescope lifetime due to drift in the stress states of the x-ray surfaces to be corrected on orbit.

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Section: Experimental Methodsmentioning

confidence: 99%

Thickness distribution of sputtered films on curved substrates for adjustable x-ray optics

Bishop

Walker

DeRoo

et al. 2019

J. Astron. Telesc. Instrum. Syst.

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“…The TaucLorentz approximation can be considered an accurate way of modelling light absorption in amorphous semiconductor thin films. On the basis of this model, the imaginary part of dielectric function e 2 is given by the following expression: [25][26][27] …”

Section: -2mentioning

confidence: 99%

Optical bandgap of semiconductor nanostructures: Methods for experimental data analysis

Raciti

Bahariqushchi

Summonte³

et al. 2017

Journal of Applied Physics

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Determination of the optical bandgap (Eg) in semiconductor nanostructures is a key issue in understanding the extent of quantum confinement effects (QCE) on electronic properties and it usually involves some analytical approximation in experimental data reduction and modeling of the light absorption processes. Here, we compare some of the analytical procedures frequently used to evaluate the optical bandgap from reflectance (R) and transmittance (T) spectra. Ge quantum wells and quantum dots embedded in SiO2 were produced by plasma enhanced chemical vapor deposition, and light absorption was characterized by UV-Vis/NIR spectrophotometry. R&T elaboration to extract the absorption spectra was conducted by two approximated methods (single or double pass approximation, single pass analysis, and double pass analysis, respectively) followed by Eg evaluation through linear fit of Tauc or Cody plots. Direct fitting of R&T spectra through a Tauc-Lorentz oscillator model is used as comparison. Methods and data are discussed also in terms of the light absorption process in the presence of QCE. The reported data show that, despite the approximation, the DPA approach joined with Tauc plot gives reliable results, with clear advantages in terms of computational efforts and understanding of QCE.

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“…The ellipsometric analysis was carried out by fitting the experimental data with a model using the Tauc-Lorentz dispersion equation, which is one of the most suitable model to describe the amorphous carbon films. 17,18 The final result was evaluated in the fitting error (v 2 ) to be the smallest (generally v Figs. 1(c) and 1(d), the hydrogen content was obtained from the fitting of RBS/ERDA spectra. The C and Si peaks in RBS spectra attributable to the film and the substrate, respectively, are identified using an RBS fitting calculation package (NHV-ERNIE ver.…”

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confidence: 99%

Structural analysis of amorphous carbon films by spectroscopic ellipsometry, RBS/ERDA, and NEXAFS

Zhou

Suzuki

Nakajima

et al. 2017

Applied Physics Letters

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The structural analysis of amorphous carbon films is not only the premise of their unique properties applied in the industrial fields but also the indispensable element on their classification. In this letter, we refurbished the classification of amorphous carbon films based on the optical constants in terms of the refractive index (n) and the extinction coefficient (k). In the selected photon energy range, we defined the maximum of n (En-max) and k at a value more than 10−4 (Ek) to explore the relationship between different classification schemes for amorphous carbon films deposited by different techniques. We found that Ek and En-max of the deposited amorphous carbon films have an exponential relationship with the hydrogen contents. Thus, the spectroscopic ellipsometry analysis can also be used as one of the effective methods for the structural evaluation of the amorphous carbon films.

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Modified Tauc–Lorentz dispersion model leading to a more accurate representation of absorption features below the bandgap

Cited by 63 publications

References 90 publications

Thickness distribution of sputtered films on curved substrates for adjustable x-ray optics

Thickness distribution of sputtered films on curved substrates for adjustable x-ray optics

Optical bandgap of semiconductor nanostructures: Methods for experimental data analysis

Structural analysis of amorphous carbon films by spectroscopic ellipsometry, RBS/ERDA, and NEXAFS

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