Research Article 
Corresponding author: Evgenia V. Zabelina ( zabev@mail.ru ) © 2022 Nina S. Kozlova, Evgeniy A. Levashov, Philipp V. KiryukhantsevKorneev, Alina D. Sytchenko, Evgenia V. Zabelina.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Kozlova NS, Levashov EA, KiryukhantsevKorneev PV, Sytchenko AD, Zabelina EV (2022) Multiangle spectrophotometry as a tool for determination of film parameters on singlelayer structures. Modern Electronic Materials 8(2): 5157. https://doi.org/10.3897/j.moem.8.2.84239

Ta–Si–C–N singlelayer films have been synthesized by direct current magnetron sputtering on fused quartz substrates. The structural perfection of the films has been studied using Xray diffraction, scanning electron microscopy and glow discharge optical emission spectroscopy. The optical parameters of the films have been studied using multiangle spectrophotometry. The spectral dependences of the transmission coefficients of substrates and structures were measured for normal incidence of light in the wavelength range 200–2500 nm. We show that the transmittance spectrum of the specimen has an oscillating pattern due to interference phenomena that are typical for layered structures. The reflectance of the films and the substrates has been measured in the 200–2500 nm region for small incidence angles. The difference between the reflection coefficient at the maximum of the interference of the film and the corresponding reflection coefficient of the substrate at the same wavelength shows that the absorption in the film is low. A formula for determination of the film absorption index based on the measured parameters has been derived. The experimental and calculated data have been used for plotting the absorption spectra of the substrate, structure and film. Discrete refractive indices in the 400–1200 nm region have been calculated for reflections at two incidence angles by determining the positions of interference maxima in the reflectivity spectral responses. The results have been approximated using the Cauchy equation. The film thickness has been estimated to be d_{f} = 1046 nm ± 13%. The spectra of film extinction coefficients have been plotted with and without allowance for reflection. Obtained values of the refractive and absorption indices with and without reflection have been summarized in a table.
multiangle spectrophotometric methods, spectral transmittance, spectral reflectance, absorption index, refractive index, TaSiCN films
Thin oxide films are currently widely used in the fabrication of structures for nano and microelectronics devices, optoelectronics, acoustic electronics, microwave electronics as well as solar cells, optical and protective coatings in aircraft and space engineering etc. [
The key physical parameters that determine the properties of the films and their suitability for specific applications are [1, 2, 7–15]: film refractive index (n_{f}), film thickness (d_{f}) and film absorption, that is expressed through the absorption index (α_{f}, cm^{1}) [
where T_{f} is the spectra transmittance of the film, %; λ is the wavelength, nm.
Precision control of these parameters is of crucial importance for verifying whether synthesized films comply with the preset optical parameters of the final product [
The aim of this work is to develop nondestructive methods of multiangle spectrophotometry for determining the optical parameters and thickness of films in film/substrate singlelayer structures.
The sputtering target having the composition TaSi_{2} – 30% SiC was produced using the method of selfpropagating hightemperature synthesis. The target was magnetron sputtered in DC mode in a 99,9995% N_{2} atmosphere on a UVN2M instrument [
The spectral and angular responses of the transmittance and reflectance indices were measured at the Accredited Test Laboratory of Single Crystals and Stock on their Base of National University of Science and Technology MISiS on Agilent Technologies’ Cary 5000 spectrophotometer with a universal measurement accessory (UMA). The UMA combines a fixed light source, a 360 deg rotatable objective table and an independent detector moving through 10 to 350 deg in the horizontal plane about the objective table. This accessory allows to measure spectral and angular dependences of transmittance and reflectance in the 200–2500 nm region with a minimum step of 0.02 deg.
The test specimens can be represented by a model of a singlelayer structure consisting of a uniform film having the thickness d_{f}, the refractive index n_{f} and the absorption index α_{f} deposited onto a uniform substrate having the thickness d_{sub}, the refractive index n_{sub} and the absorption index α_{sub}. Schematic of the structure is shown in Fig.
Generally the energy interaction between the film/substrate structure and the incident light can be described by the following equation [
Ф_{0} = Ф_{T} +Ф_{A} + Ф_{S} + Ф_{R}, (2)
where Ф_{0} is the radiation flux incident upon the specimen, Ф_{T} is the radiation flux having passed through the specimen, Ф_{A} is the radiation flux absorbed by the specimen, Ф_{S} is the radiation flux scattered by the specimen and Ф_{R} is the radiation flux reflected by the specimen.
In the case considered scattering can be ignored because of its negligibility and the overall system configuration. Then Eq. (2) can be rewritten as follows:
Ф_{0} = Ф_{T} +Ф_{A} + Ф_{R}, (3)
All these parameters characterize the interaction between the material and the incident light rather than the properties of the material itself. Expressing these parameters in the form of the intensities we can proceed to the material’s parameters:
1 = Т + А + R, (4)
where Т, А, R are the spectral coefficients of transmittance, absorption and reflectance, respectively.
The transmittance spectra of a typical structure T_{str} and a typical substrate T_{sub} for normal light incidence are shown in Fig.
(1 and 3) Transmittance and (2 and 4) absorption spectra of (1 and 2) substrate and (3 and 4) typical structure.
Measuring the reflectance of the structure R_{str} at the film side we can evaluate the absorption coefficient of the structure A_{str} using the formula [
A _{str} = 1 – Т_{str} – R_{str}. (5)
The results are shown in Fig.
In the simplest case without allowance for scattering and reflection Eq. (4) can be written as follows:
1 = А_{str} + T_{str}. (6)
Then the absorption coefficient of the structure can be expressed as follows:
А _{str} = А_{f} + А_{sub}. (7)
where А_{f} and А_{sub} are the absorption coefficients of the film and the substrate, respectively.
А _{str} = 1 – Т_{str}; А_{f}= 1 – Т_{f}; А_{sub} = 1 – Т_{sub}. (8)
where T_{f} and T_{sub} are the transmittances of the film and the substrate, respectively.
The transmittance of the film can be derived from Eqs. (6)–(8):
Т _{f} = 1 – Т_{sub} + Т_{str}. (9)
The absorption coefficient of the film is determined using Eq. (1) which taking into account Eq. (9) can be transformed, and the following expression can be written for absorption without allowance for reflection:
The absorption index α with allowance for reflection is written as follows [
Thus with allowance for reflection Eq. (10) can be transformed as follows:
The transmittances of the substrate and the structure and the reflectance of the structure at the film side can be measured with a spectrophotometer. Our measurement results are shown in Fig.
The thicknesses and the refractive indices of the films can be calculated using the spectrophotometric method of reflection at two angles of incidence [
(1, 3 and 5) Transmittance and (2 and 4) reflectance spectra of (3 and 4) typical structure, (1 and 2) substrate and (5) film.
Light reflection measurement data for 10 deg incidence angle on specimen taken at (1) fused quartz substrate side and (2) film side.
The reflectance spectra of the specimens (Fig.
To evaluate the refractive index of the deposited layer we used the reflectance spectra for two nonpolarized light incidence angles, i.e., φ_{1} = 10 deg and φ_{2} = 20 deg.
First of all refractive indices are measured. To do this, the wavelengths λφ_{1} and λφ_{2} corresponding to the same interference extremum for each interference extremum are selected on the obtained spectra. Then the film refractive index for the narrow wavelength range λφ_{1} – λφ_{2} was determined using the formula
where b is the coefficient determined as follows:
The final value of the film refractive index is calculated using the following equation:
As a result of the calculations we obtain a discrete array of refractive indices. The dispersion dependence of the refractive index is determined by approximating the calculated data using e.g. the Cauchy equation as follows:
where A, B and C are material constants.
The optical thickness of the film (d_{f}∙n_{f}) is determined using the following formula:
where λ_{1}, λ_{2} are the wavelengths of adjacent interference extrema in the interference response taken at one incidence angle, nm; and k is a coefficient which takes on 2 if two adjacent maxima are taken or 4 if adjacent maximum and minimum are taken.
With allowance for the film refractive index obtained using Eq. (15) the film thickness can be calculated as follows:
The refractive index evaluation results obtained using the reflection spectrophotometric method for two incidence angles and their approximation results obtained using the Cauchy equation (Eq. (16)) are shown in Fig.
Dispersion dependence of refractive index of typical specimen: (1) data obtained by calculation using Eq. (16) and (2) Cauchy approximation.
Refractive and absorption indices with and without allowance for reflection for a typical specimen in the 450–1200 nm region
λ (nm)  n  Α _{f} (μm^{–1})  
With allowance for reflection  Without allowance for reflection  
450  2.153  0.603  0.959 
500  2.075  0.367  0.744 
550  2.018  0.192  0.391 
600  1.974  0.222  0.553 
650  1.940  0.157  0.471 
700  1.913  0.191  0.580 
750  1.891  0.057  0.221 
800  1.873  0.160  0.591 
850  1.858  0.161  0.578 
900  1.846  0.054  0.244 
950  1.835  0.041  0.237 
1000  1.826  0.116  0.495 
1050  1.818  0.160  0.629 
1100  1.812  0.138  0.544 
1150  1.806  0.075  0.345 
1200  1.801  0.022  0.188 
Ta–Si–C–N singlelayer films were synthesized by magnetron sputtering on fused quartz substrates. The structural perfection of the films was studied using Xray diffraction, scanning electron microscopy and glow discharge optical emission spectroscopy.
The 200–2500 nm transmittance spectra of the structures and the fused quartz substrates for normal light incidence and the reflectance spectra at 10 and 20 deg incidence angles were measured using multiangle spectrophotometry.
A formula for determination of the film absorption coefficient based on the measured parameters was derived. The experimental and calculated data were used for plotting the absorption spectra of the substrate, structure and film, with and without allowance for reflection.
Using experimental methods based on the measurement of interference extrema in the reflectance spectra, the film thickness was estimated to be d_{f.} = 1046 nm ± 13 %, and discrete film refractive indices were obtained. The results were approximated using the Cauchy equation.
The studies were carried out with financial support within State Assignment FSME20200031 (071820200031) at the Accredited Test Laboratory of Single Crystals and Stock on their Base of National University of Science and Technology MISiS.