2022
DOI: 10.1088/1402-4896/ac670a
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Effects of Nb concentration on Nb-doped anatase TiO2: DFT + U calculations

Abstract: The crystal structure, formation energy, electronic structure, electrical properties and optical properties of anatase TiO2 with various Nb concentrations were studied by first-principles calculations based on density functional theory (DFT) and the Hubbard U correction. Firstly, the crystal structures of TiO2 with various Nb concentrations were optimized successfully. The higher concentrations of Nb facilitate the synthesis of Nb-doped TiO2 systems in an O-rich environment. Furthermore, the band structures an… Show more

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Cited by 3 publications
(4 citation statements)
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“…From equation (3), the electron effective masses along the [100] ( ma* ${{m}_{a}^{{^\ast}}}$ ) and [001] ( mc* ${{m}_{{\rm c}}^{{^\ast}}}$ ) direction of the pure titanium dioxide and titanium dioxide doped with high‐valence transition metals are calculated, Table 3. The calculated results of niobium‐doped titanium dioxide are consistent with values reported in the literatures [37, 43]. To simplifying the comparison, we defined mn* ${{m}_{n}^{{^\ast}}}$ as the average effective mass of ma* ${{m}_{a}^{{^\ast}}}$ and mc* ${{m}_{{\rm c}}^{{^\ast}}}$ by the following equation [45]. 3mn*=2ma*+1mc* $\vcenter{\openup.5em\halign{$\displaystyle{#}$\cr {{3}\over{{m}_{n}^{{\rm {^\ast}}}}}={{2}\over{{m}_{a}^{{\rm {^\ast}}}}}+{{1}\over{{m}_{c}^{{\rm {^\ast}}}}}\hfill\cr}}$ …”
Section: Resultssupporting
confidence: 79%
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“…From equation (3), the electron effective masses along the [100] ( ma* ${{m}_{a}^{{^\ast}}}$ ) and [001] ( mc* ${{m}_{{\rm c}}^{{^\ast}}}$ ) direction of the pure titanium dioxide and titanium dioxide doped with high‐valence transition metals are calculated, Table 3. The calculated results of niobium‐doped titanium dioxide are consistent with values reported in the literatures [37, 43]. To simplifying the comparison, we defined mn* ${{m}_{n}^{{^\ast}}}$ as the average effective mass of ma* ${{m}_{a}^{{^\ast}}}$ and mc* ${{m}_{{\rm c}}^{{^\ast}}}$ by the following equation [45]. 3mn*=2ma*+1mc* $\vcenter{\openup.5em\halign{$\displaystyle{#}$\cr {{3}\over{{m}_{n}^{{\rm {^\ast}}}}}={{2}\over{{m}_{a}^{{\rm {^\ast}}}}}+{{1}\over{{m}_{c}^{{\rm {^\ast}}}}}\hfill\cr}}$ …”
Section: Resultssupporting
confidence: 79%
“…The exchange and correlation potential are modeled by generalized gradient approximation Perdew‐Becke‐Erzenhof function [36]. The settings of the plane‐wave cutoff energy, K ‐points grid sampling size, convergence threshold for self‐consistent iterations, maximum force, maximum stress, and maximum displacement are the same as the previous theoretical work [37].…”
Section: Calculation Models and Methodsmentioning
confidence: 99%
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