Energy gap measurements based on enhanced absorption coefficient calculation from transmittance and reflectance raw data

Abstract

The absorption coefficient plays an important role in studying and characterizing semiconducting materials. It is an important parameter to study the mechanism of photons absorption within the structure of the studied material. Thus, it helps to study the several types of charge carrier transport along with the energy band structure and its defects. In literature, a formula was reported to precisely calculate the absorption coefficient from raw data of transmittance and reflectance of electromagnetic radiation. However, the reported formula has several issues limiting its validity to be used i literature. In this paper, we provide a more mathematically accurate form of this equation to precisely obtain the absorption coefficient from the raw data, by considering the total internal reflection at the different interfaces. Moreover, the equation is tested by simulated data and is applied to study the optical characteristics of a single-component epoxy resin from its transmittance and reflectance raw data.

Comprehensive Analysis of E478 Single-Component Epoxy Resin and Tungsten-E478 Interface for Metallic-Polymer Composite Electron Source Applications

“…Applying the natural logarithm to both sides of eq 5 and arranging the terms yield to obtain the following linearized form: 24 = +…”

“…These results are then used to obtain the absorption coefficient function α(λ) . For a film of thickness d , α value is related to the true transmittance T = T (λ) % /100 and true reflectance R = R (λ) % /100 through the following equation: α = 1 x ln ( 2 T R 2 ( 1 − R ) 4 + 4 T 2 R 2 − ( 1 − R ) 2 ) Tauc equation is used to obtain allowed/forbidden direct and indirect optical transitions of electrons when the film is subjected to a specific radiation. Assigning A 0 as the band tailing parameter (which is an energy independent constant), E g n as transition-related optical energy gap and n as the transition type indicator, Tauc equation can then be expressed as ( α h ν ) n = A 0 ( h ν − E g n ) In eq , the values of the exponent n are assigned as n = 2 for an allowed direct transition, n = 1/2 for an allowed indirect transition, n = 2/3 for a forbidden direct transition, and n = 1/3 for a forbidden indirect transition.…”

“…Urbach band tail energy E U is a parameter to study the effects of energy band defects, and it can be measured from the first Urbach empirical rule: α = α 0 exp ( h ν − E g 2 E U ) Applying the natural logarithm to both sides of eq and arranging the terms yield to obtain the following linearized form: ln ( α ) = [ ln false( α 0 false) − E g 2 E U ] + h ν E normalU From eq , the slope S U = d(ln(α))/d( hν )of the linear part of the ln(α)vs hν plot is used to measure the band tail energy, where E U = 1/ S U . Moreover, the strength of the electron–phonon interaction E e – p is an important parameter to describe the scattering and mobility of charge carriers in semiconducting materials, where higher values of E e – p are related to a higher number of scattering and energy transfer events affecting the mobility of the electrons within the structure of the material.…”

Synthesis and Band Gap Characterization of High-Entropy Ceramic Powders

“…After obtaining F for all the samples, Tauc and Urbach plots were used to measure the allowed direct and allowed indirect energy gaps, along with the Urbach tailing energies for the tested powders [19,20]. Tauc plots have the form of (αhν) n vs. hν, where n = 2 when measuring the allowed direct energy gap, n = 1/2 when measuring the allowed indirect energy gap, and hν is the photon energy.…”

Enhancement in Sensitivity and Selectivity of Electrochemical Technique with CuO/g-C3N4 Nanocomposite Combined with Molecularly Imprinted Polymer for Melamine Detection

“…This involved determining the x-axis intercept of the straight-line equation in the reflection spectra. This allowed for the calculation of the optical band gap through the Kubelka-Munk equation [62,63]…”