Evaluation of the Thickness in Nanolayers Using the Transfer Matrix Method for Modeling the Spectral Reflectivity

Abstract

The reflectivity spectra have been traditionally used to determine the thicknesses in semiconductor films. However, thicknesses of nanofilms are not easy to evaluate because the interference fringes are not visible in the transparent region. In this paper, we present a computed method based on the transfer matrix (TM) which is used to match the calculated and experimental room temperature reflectivity spectra of the ZnTe/GaAs films and to determine its thickness film values afterwards. The TM method needs only to know refraction indices and absorption coefficients as a function of wavelength for the film and the substrate. The thickness nanofilms evaluated by our method are in agreement with the values measured by ellipsometry, Rutherford backscattering spectroscopy and transmission electron microscopy techniques. The present procedure extends the application of the standard spectral reflectance technique to determine semiconductor nanolayer thicknesses.

The Ellipsometrical Analysis of External Reflection of Light on Superficial Films on Solid Substrates

“…For example, for ∆=186.37 0 and Ψ=51.317 0 , the film thickness with n f =1.4 For films with thicknesses greater than d min , further measurements are needed to determine the thickness, due to the periodicity of the functions ∆=f(d f ) and Ψ=f(d f ). Usually, interferometer measurements are used to determine the order of magnitude of d f , with a precision of 0.1 µm [4,5,6]. Typically, the thickness d min value is on the order of 0.3÷0.5 µm.…”

Optical Properties of Three-Dimensional Photonic Crystal with Face-Centered-Cubic Structure

“…In this paper, the interaction of dielectric layer and the light waves is determined by transfer matrix method (TMM) [8]. Taking into account the boundary conditions for electric (E) and magnetic (H) fields, a matrix equation will be obtained which relates the fields at two adjacent boundaries:…”

Thickness evaluation of AlOx barrier layers for encapsulation of flexible PV modules in industrial environments by normal reflectance and machine learning

“…The reduced thickness of nanocoatings commonly requires the use of very specific characterization techniques like those based on X‐ray photoelectron spectroscopy, 19,20 atomic force and electron microscopy, 21,22 Rutherford backscattering spectroscopy, 23 ellipsometry, 4,13,15,16,18,24–26 or transmittance‐reflectance spectroscopy, 8,27,28 among others. These techniques require long acquisition times, sample destruction, and/or high‐energy (deep UV or X‐ray) excitation wavelengths.…”