<p>The accurate estimation of optical absorption coefficient (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10854_2025_15037_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>) for powdered nanomaterials to use in Tauc plot analysis remains a challenge due to the lack of explicit methodologies in the literature. This ambiguity leads to inconsistencies in bandgap determination and improper labeling of units on Tauc plot axes, particularly for nanopowdered samples without a measurable thickness. This study provides a detailed methodology for estimating <i>α</i> for nanopowders using UV–Vis-NIR spectroscopy data, and proposes alternative graphing techniques that circumvent the need for thickness measurements. Results demonstrate that, while the conventional Tauc plot <i>(</i><InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10854_2025_15037_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation><i> hν)</i><sup>n</sup> vs. <i>hν</i> can yield accurate bandgap values regardless of thickness substitution to evaluate<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10854_2025_15037_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>, the unit of <i>(</i><InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10854_2025_15037_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation><i> hν)</i><sup>n</sup> must be stated as <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10854_2025_15037_Article_IEq5.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="75" /> </InlineMediaObject> <EquationSource Format="TEX">\({(\text{eV}/\text{cm })}^{n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">(</mo> <mtext>eV</mtext> <mo stretchy="false">/</mo> <mtext>cm</mtext> <mspace width="0.333333em" /> <mo stretchy="false">)</mo> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation> if path length (thickness) was included in <i>α</i> calculation, or <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10854_2025_15037_Article_IEq6.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\({(\text{eV})}^{n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">(</mo> <mtext>eV</mtext> <mo stretchy="false">)</mo> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation> when path length was excluded. It is inappropriate to state the (arb. unit) even in the case of Tauc plot <i>[F(R)hν]</i><sup>n</sup> vs. <i>hν</i> derived from diffuse reflectance data. Furthermore, alternative methods (modified Tauc plots), such as <i>(Ahν)</i><sup><i>n</i></sup> vs<i>. hν</i> and <i>A</i><sup><i>n</i></sup> vs. <i>hν</i> with a common unit<InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10854_2025_15037_Article_IEq6.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\({(\text{eV})}^{n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">(</mo> <mtext>eV</mtext> <mo stretchy="false">)</mo> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>, which do not require thickness measurements were validated as reliable methods for bandgap estimation. Practical demonstrations using SrZrO<sub>3</sub>, TiO<sub>2</sub>: Li, Co nanopowders, and ZnO thin film confirmed the robustness of these methods and ensured consistency with literature values. It is hoped that the present work would curtail the widespread of unwarranted units on the Tauc plot. The correct unit must be stated based on how the Tauc’s equation was evaluated.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Accuracy in estimating the absorption coefficient of powdered nanomaterials: resolving misconceptions in tauc plot application for energy bandgap determination

  • P. R. Jubu,
  • O. Adedokun,
  • C. Mbakaan,
  • A. Nathan-Abutu,
  • E. Danladi,
  • J. N. Tsaviv,
  • P. I. Kyesmen,
  • B. J. Akeredolu,
  • A. T. Adepoju,
  • F. Aungwa,
  • Y. Yusof,
  • O. S. Obaseki,
  • Youssif SM Elzawiei,
  • M. Z. Pakhuruddin

摘要

The accurate estimation of optical absorption coefficient ( \(\alpha\) α ) for powdered nanomaterials to use in Tauc plot analysis remains a challenge due to the lack of explicit methodologies in the literature. This ambiguity leads to inconsistencies in bandgap determination and improper labeling of units on Tauc plot axes, particularly for nanopowdered samples without a measurable thickness. This study provides a detailed methodology for estimating α for nanopowders using UV–Vis-NIR spectroscopy data, and proposes alternative graphing techniques that circumvent the need for thickness measurements. Results demonstrate that, while the conventional Tauc plot ( \(\alpha\) α hν)n vs. can yield accurate bandgap values regardless of thickness substitution to evaluate \(\alpha\) α , the unit of ( \(\alpha\) α hν)n must be stated as \({(\text{eV}/\text{cm })}^{n}\) ( eV / cm ) n if path length (thickness) was included in α calculation, or \({(\text{eV})}^{n}\) ( eV ) n when path length was excluded. It is inappropriate to state the (arb. unit) even in the case of Tauc plot [F(R)hν]n vs. derived from diffuse reflectance data. Furthermore, alternative methods (modified Tauc plots), such as (Ahν)n vs. hν and An vs. with a common unit \({(\text{eV})}^{n}\) ( eV ) n , which do not require thickness measurements were validated as reliable methods for bandgap estimation. Practical demonstrations using SrZrO3, TiO2: Li, Co nanopowders, and ZnO thin film confirmed the robustness of these methods and ensured consistency with literature values. It is hoped that the present work would curtail the widespread of unwarranted units on the Tauc plot. The correct unit must be stated based on how the Tauc’s equation was evaluated.