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Effect of Zr substitution on structural, electronic, thermodynamic and optical properties of \((\textrm{HfO}_2)_{\text{p}}\) clusters: a DFT study of \((\textrm{HfO}_2)_{\textrm{p}}\) and \(\textrm{Hf}_{\textrm{q}} \textrm{Zr}_{\text {r}} \textrm{O}_{2(\textrm{q}+\textrm{r})}\) clusters

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Abstract

First-principles calculations have been performed on \((\text {HfO}_2)_\text{ p }\) and \(\text {Hf}_{\text{ q }} \text {Zr}_{\text{ r }} \text {O}_{2(\text {q}+\text {r})}\) clusters using DFT and TDDFT. The effect of Zr-substitution on the structural, electronic, thermodynamic, and optical properties of \((\textrm{HfO}_2)_{\text{p}}\) clusters has been investigated using B3LYP and B3PW91 functionals with LANL2DZ basis set. The calculated properties depend upon geometry, type, and number of atoms present in the clusters. Zr-substitution in \((\text {HfO}_2)_{\text{p}}\) clusters leads to the reduced molecular mass of \(\text {Hf}_{\text{q}} \text{Zr}_{\text{r}} \text {O}_{2(\text {q}+\text{r})}\) clusters so that they can be used in making light weight semiconductor devices. \(\text {Hf}_{3} \text {Zr}_{2}\text{O}_{10}\) is found to be the most reactive after Zr-substitution in \((\text {HfO}_2)_5\) because of the minimum value of HOMO-LUMO gap. Zr-substitution in \((\text {HfO}_{2})_{5}\) increases the refractive index of \(\text {Hf}_{3} \text {Zr}_{2}\text{O}_{10}\), making it suitable for multi-layer antireflecting coatings. The dielectric constant of \(\text{Hf}_{3} \text {Zr}_{2}\text{O}_{10}\) has increased after Zr-substitution finding applications in the MOSFET industry. The absorption spectra can be tuned over the ultraviolet and visible regions depending upon the Zr-substitution.

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Acknowledgements

Shilpa Kashyap is thankful to Guru Gobind Singh Indraprastha University for providing financial support under the Indraprastha Research Fellowship (IPRF) scheme (L. No. GGSIPU/DRC/ 2019/90/1797). Dr. Kriti Batra is grateful to Guru Gobind Singh Indraprastha University for the research grant under the Faculty Research Grant Scheme (FRGS) for the year 2018-19 (F. No. GGSIPU/DRC/FRGS/2018/8(1115)L) and 2019-20 (F. No. GGSIPU/DRC/FRGS/2019/1553/12).

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Shilpa Kashyap: investigation and validation of results after performing calculations, software handling, maintaining the research data, and writing the original draft. Dr. Kriti Batra: conceptualization, supervision, project administration, provision of resources and software, reviewing and editing of the draft, and funding.

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Kashyap, S., Batra, K. Effect of Zr substitution on structural, electronic, thermodynamic and optical properties of \((\textrm{HfO}_2)_{\text{p}}\) clusters: a DFT study of \((\textrm{HfO}_2)_{\textrm{p}}\) and \(\textrm{Hf}_{\textrm{q}} \textrm{Zr}_{\text {r}} \textrm{O}_{2(\textrm{q}+\textrm{r})}\) clusters. J Nanopart Res 26, 13 (2024). https://doi.org/10.1007/s11051-023-05876-2

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