<p>A special design, based on the Bridgman technique, was used in our laboratory for preparing single crystals of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {TlInTe}_2\)</EquationSource> </InlineEquation>. The structure of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {TlInTe}_2\)</EquationSource> </InlineEquation> in powder form was examined using X-ray diffraction. <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {TlInTe}_2\)</EquationSource> </InlineEquation> at room temperature was found to be a tetragonal system with lattice parameters of <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq6.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="69" /> </InlineMediaObject> <EquationSource Format="TEX">\(a = 8.494\)</EquationSource> </InlineEquation> Å and <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq7.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="67" /> </InlineMediaObject> <EquationSource Format="TEX">\(c = 7.181\)</EquationSource> </InlineEquation> Å. The structural parameters, such as crystallite size <i>D</i>, micro strain <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq8.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(\epsilon\)</EquationSource> </InlineEquation>, dislocation density <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq9.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta\)</EquationSource> </InlineEquation>, and unit cell parameters were determined from XRD spectra. Thermo gravimetric analysis (TGA) was employed to study the thermal behavior of <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq10.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {TlInTe}_2\)</EquationSource> </InlineEquation>, showcasing its significance in solid state physics. The TGA curve of <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq11.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {TlInTe}_2\)</EquationSource> </InlineEquation> exhibited distinct weight loss events corresponding to thermal decomposition processes. The frequency and temperature dependence of Ac-conductivity in a <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq12.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {TlInTe}_2\)</EquationSource> </InlineEquation> single crystal was studied by assessing the permittivity (<InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq13.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\epsilon _r\)</EquationSource> </InlineEquation>) and dielectric loss (<InlineEquation ID="IEq14"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq14.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tan \delta\)</EquationSource> </InlineEquation>) over a broad frequency range. The dependence of AC conductivity and dielectric properties on the frequency and temperature for <InlineEquation ID="IEq15"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq15.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {TlInTe}_2\)</EquationSource> </InlineEquation> in pellet form obtained from <InlineEquation ID="IEq16"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq16.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {TlInTe}_2\)</EquationSource> </InlineEquation> single crystal were studied in the frequency range of (40 Hz–3 MHz) and temperature range of <InlineEquation ID="IEq17"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq17.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="82" /> </InlineMediaObject> <EquationSource Format="TEX">\((290{-}395)^{\circ }\)</EquationSource> </InlineEquation>K. The AC conductivity of the <InlineEquation ID="IEq18"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq18.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {TlInTe}_2\)</EquationSource> </InlineEquation> was found to obey the power law, i.e., <InlineEquation ID="IEq19"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq19.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="99" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sigma _{ac} (\omega ) = A \omega ^s\)</EquationSource> </InlineEquation>. AC conductivity of <InlineEquation ID="IEq20"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq20.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {TlInTe}_2\)</EquationSource> </InlineEquation> was dominated by the correlated barrier hopping (CBH) model. The obtained activation energy values of the AC conductivity have confirmed that the hopping conduction is the dominant one. A decrease in these values has noticed with the increase in frequency. The density of localized states <InlineEquation ID="IEq21"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq21.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(N (E_F)\)</EquationSource> </InlineEquation> close to Fermi level for <InlineEquation ID="IEq22"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq22.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {TlInTe}_2\)</EquationSource> </InlineEquation> was obtained in the range of <InlineEquation ID="IEq23"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq23.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="158" /> </InlineMediaObject> <EquationSource Format="TEX">\((1.02{-}2.8 \times 10^{19}\ \text {eV}^{-1}\)</EquationSource> </InlineEquation> cm<InlineEquation ID="IEq24"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq24.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{-3}\)</EquationSource> </InlineEquation>) for various temperatures and frequency. The frequencies corresponding to maxima of the imaginary electric modulus at different temperatures were found to satisfy an Arrhenius law with activation energy <InlineEquation ID="IEq25"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq25.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(E_R\)</EquationSource> </InlineEquation> of 0.32 eV. A decrease in the relaxation time <InlineEquation ID="IEq26"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq26.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau\)</EquationSource> </InlineEquation> was observed with the increase in temperature. The average hopping distance <i>R</i> and the average time of charge carrier hoping between localized states <i>t</i> were found in the range of 6.10–11.95 nm and <InlineEquation ID="IEq27"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq27.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="148" /> </InlineMediaObject> <EquationSource Format="TEX">\(2 \times 10^{-7} {-} 2.4 \times 10^{-2}\)</EquationSource> </InlineEquation> s respectively, for the investigated range of frequency and the value of the binding energy <InlineEquation ID="IEq28"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq28.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\(W_m\)</EquationSource> </InlineEquation> was 0.52 eV. We report on the preparation, characterization, and analysis of <InlineEquation ID="IEq29"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq29.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {TlInTe}_2\)</EquationSource> </InlineEquation> semiconductor single crystals, focusing on the influence of frequency and temperature on AC conductivity. Utilizing X-ray diffraction, thermo gravimetric analysis, and dielectric property measurements, we delineate the material’s structural and electrical properties. Complementing our experimental findings, Machine Learning (ML) models, including Random Forest and Gradient Boosting, were employed to predict AC conductivity, revealing significant predictors and corroborating the experimental insights with high accuracy. This interdisciplinary approach enhances our understanding of <InlineEquation ID="IEq30"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_87788_Article_IEq30.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {TlInTe}_2\)</EquationSource> </InlineEquation>’s properties and demonstrates the potential of ML in materials science research.</p>

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The influence of frequency and temperature on the AC-conductivity in \(\text {TlInTe}_2\) semiconductor single crystal

  • Mohamed M. Fangary,
  • Muhammad A. O. Ahmed

摘要

A special design, based on the Bridgman technique, was used in our laboratory for preparing single crystals of \(\text {TlInTe}_2\) . The structure of \(\text {TlInTe}_2\) in powder form was examined using X-ray diffraction. \(\text {TlInTe}_2\) at room temperature was found to be a tetragonal system with lattice parameters of \(a = 8.494\) Å and \(c = 7.181\) Å. The structural parameters, such as crystallite size D, micro strain \(\epsilon\) , dislocation density \(\delta\) , and unit cell parameters were determined from XRD spectra. Thermo gravimetric analysis (TGA) was employed to study the thermal behavior of \(\text {TlInTe}_2\) , showcasing its significance in solid state physics. The TGA curve of \(\text {TlInTe}_2\) exhibited distinct weight loss events corresponding to thermal decomposition processes. The frequency and temperature dependence of Ac-conductivity in a \(\text {TlInTe}_2\) single crystal was studied by assessing the permittivity ( \(\epsilon _r\) ) and dielectric loss ( \(\tan \delta\) ) over a broad frequency range. The dependence of AC conductivity and dielectric properties on the frequency and temperature for \(\text {TlInTe}_2\) in pellet form obtained from \(\text {TlInTe}_2\) single crystal were studied in the frequency range of (40 Hz–3 MHz) and temperature range of \((290{-}395)^{\circ }\) K. The AC conductivity of the \(\text {TlInTe}_2\) was found to obey the power law, i.e., \(\sigma _{ac} (\omega ) = A \omega ^s\) . AC conductivity of \(\text {TlInTe}_2\) was dominated by the correlated barrier hopping (CBH) model. The obtained activation energy values of the AC conductivity have confirmed that the hopping conduction is the dominant one. A decrease in these values has noticed with the increase in frequency. The density of localized states \(N (E_F)\) close to Fermi level for \(\text {TlInTe}_2\) was obtained in the range of \((1.02{-}2.8 \times 10^{19}\ \text {eV}^{-1}\) cm \(^{-3}\) ) for various temperatures and frequency. The frequencies corresponding to maxima of the imaginary electric modulus at different temperatures were found to satisfy an Arrhenius law with activation energy \(E_R\) of 0.32 eV. A decrease in the relaxation time \(\tau\) was observed with the increase in temperature. The average hopping distance R and the average time of charge carrier hoping between localized states t were found in the range of 6.10–11.95 nm and \(2 \times 10^{-7} {-} 2.4 \times 10^{-2}\) s respectively, for the investigated range of frequency and the value of the binding energy \(W_m\) was 0.52 eV. We report on the preparation, characterization, and analysis of \(\text {TlInTe}_2\) semiconductor single crystals, focusing on the influence of frequency and temperature on AC conductivity. Utilizing X-ray diffraction, thermo gravimetric analysis, and dielectric property measurements, we delineate the material’s structural and electrical properties. Complementing our experimental findings, Machine Learning (ML) models, including Random Forest and Gradient Boosting, were employed to predict AC conductivity, revealing significant predictors and corroborating the experimental insights with high accuracy. This interdisciplinary approach enhances our understanding of \(\text {TlInTe}_2\) ’s properties and demonstrates the potential of ML in materials science research.