Optical Characterization of H-Free a-Si Layers Grown by rf-Magnetron Sputtering by Inverse Synthesis Using Matlab: Tauc–Lorentz–Urbach Parameterization

Abstract

Several, nearly-1-µm-thick, pure, unhydrogenated amorphous-silicon (a-Si) thin layers were grown at high rates by non-equilibrium rf-magnetron Ar-plasma sputtering (RFMS) onto room-temperature low-cost glass substrates. A new approach is employed for the optical characterization of the thin-layer samples, which is based on some new formulae for the normal-incidence transmission of such a samples and on the adoption of the inverse-synthesis method, by using a devised Matlab GUI environment. The so-far existing limiting value of the thickness-non-uniformity parameter, Δd, when optically characterizing wedge-shaped layers, has been suppressed with the introduction of the appropriate corrections in the expression of transmittance. The optical responses of the H-free RFMS-a-Si thin films investigated, were successfully parameterized using a single, Kramers–Krönig (KK)-consistent, Tauc–Lorentz oscillator model, with the inclusion in the model of the Urbach tail (TLUC), in the present case of non-hydrogenated a-Si films. We have also employed the Wemple–DiDomenico (WDD) single-oscillator model to calculate the two WDD dispersion parameters, dispersion energy, Ed, and oscillator energy, Eso. The amorphous-to-crystalline mass-density ratio in the expression for Ed suggested by Wemple and DiDomenico is the key factor in understanding the refractive index behavior of the a-Si layers under study. The value of the porosity for the specific rf-magnetron sputtering deposition conditions employed in this work, with an Ar-pressure of ~4.4 Pa, is found to be approximately 21%. Additionally, it must be concluded that the adopted TLUC parameterization is highly accurate for the evaluation of the UV/visible/NIR transmittance measurements, on the H-free a-Si investigated. Finally, the performed experiments are needed to have more confidence of quick and accurate optical-characterizations techniques, in order to find new applications of a-Si layers in optics and optoelectronics.

Fabrication of Li-Doped NiO Thin Films by Ultrasonic Spray Pyrolysis and Its Application in Light-Emitting Diodes

“…The accurate calculation of the thickness and optical constant of a thin layer deposited on a transparent substrate, from the experimental transmittance spectrum is a very challenging problem. Some of the most accurate methods for the determination of the thickness and optical parameters of a thin film have been developed for amorphous silicon films, and these are based on the rigorous expression for the optical transmission of the system of a thin absorbing film on a thick finite transparent substrate [ 49 , 50 ]. In our case, the thickness and optical constants of the NiO:Li films were calculated using a similar rigorous method recently applied for transparent conducting coatings of ZnO:Al deposited on glass substrates by ultrasonic spray pyrolysis [ 51 ].…”

“…The term with the factor, , where , and the real part of the refractive index of the film, gives rise to the maxima and minima of interference. The dependence of the refractive index with wavelength is obtained from a given model, through the well know interrelationships between the respective real and imaginary parts of the complex index of refraction and the real and imaginary parts of the complex dielectric function [ 50 ]. The details of the fitting process between the theoretical transmittance and the experimental transmittance spectra are out of the scope of this work and will be published elsewhere.…”

Hybrid Dispersion Model Characterization of PAZO Azopolymer Thin Films over the Entire Transmittance Spectrum Measured in the UV/VIS/NIR Spectral Region

“…In Table 1 , f i is the strength of the “i”-th oscillator, E i is its central energy and B i is its energy broadening, as the subscript “1” refers to the lower energy oscillator and the subscript “2” to the higher energy oscillator. Moreover, E g0 is the fitted bandgap, which can differ from the optical bandgap E g , as discussed for rf-magnetron-sputtered a-Si in [ 34 ], and ε r (∞) = real[ ( E → ∞)] = n 2 ( E → ∞).…”

“…Therefore, Tauc plots for p = 2 and p = 3/2, prepared by utilizing k ( E ) from Figure 2 b, are presented in Figure 5 . As per Equation (4), the optical bandgap E g equals the photon energy E corresponding to the interception point of the straight line approximation of (α E ) 1/2 , from the Tauc plot in Figure 5 a, and the E -axis [ 34 , 42 ].…”

“…However, DMs are based on assumptions which can be inaccurate for some thin films. Arguably, the most popular DMs of amorphous materials in the UV/VIS/NIR range are: the Tauc–Lorentz model (TL) [ 29 , 30 ], the new amorphous dispersion formula (NADF) [ 31 , 32 ], the Tauc–Lorentz–Urbach model of Foldyna (TLUF) [ 33 , 34 ], and the Taucv–Lorentz–Urbach model of Rodriguez (TLUR) [ 35 , 36 ]. Importantly, TL and NADF assume k ( λ ) = 0 for E < E g , where E (eV) = 1239.8/λ(nm) is the photon energy and E g is the optical bandgap, which can lead to inaccurate characterization of amorphous films in the range E < E g .…”