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

First-principles calculations have been performed on \((\text {HfO}_2)_\text{ p }\) ${({\text{HfO}}_2)}_{}\text{p}$ and \(\text {Hf}_{\text{ q }} \text {Zr}_{\text{ r }} \text {O}_{2(\text {q}+\text {r})}\) ${\text{Hf}}_{\text{q}}{\text{Zr}}_{\text{r}}{\text{O}}_{2(\text{q}+\text{r})}$ clusters using DFT and TDDFT. The effect of Zr-substitution on the structural, electronic, thermodynamic, and optical properties of \((\textrm{HfO}_2)_{\text{p}}\) ${({\text{HfO}}_2)}_{\text{p}}$ 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 \((\text {HfO}_2)_{\text{p}}\) ${({\text{HfO}}_2)}_{\text{p}}$ clusters leads to the reduced molecular mass of \(\text {Hf}_{\text{q}} \text{Zr}_{\text{r}} \text {O}_{2(\text {q}+\text{r})}\) ${\text{Hf}}_{\text{q}}{\text{Zr}}_{\text{r}}{\text{O}}_{2(\text{q}+\text{r})}$ clusters so that they can be used in making light weight semiconductor devices. \(\text {Hf}_{3} \text {Zr}_{2}\text{O}_{10}\) ${\text{Hf}}_3{\text{Zr}}_2{\text{O}}_{10}$ is found to be the most reactive after Zr-substitution in \((\text {HfO}_2)_5\) ${({\text{HfO}}_2)}_5$ because of the minimum value of HOMO-LUMO gap. Zr-substitution in \((\text {HfO}_{2})_{5}\) ${({\text{HfO}}_2)}_5$ increases the refractive index of \(\text {Hf}_{3} \text {Zr}_{2}\text{O}_{10}\) ${\text{Hf}}_3{\text{Zr}}_2{\text{O}}_{10}$ , making it suitable for multi-layer antireflecting coatings. The dielectric constant of \(\text{Hf}_{3} \text {Zr}_{2}\text{O}_{10}\) ${\text{Hf}}_3{\text{Zr}}_2{\text{O}}_{10}$ 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.