Hybrid density functional theory study of vanadium doping in stoichiometric and congruent $\mathrm{LiNb}{\mathrm{O}}_3$

The basic features of vanadium (V)-doped $\mathrm{LiNb}{\mathrm{O}}_3$, such as V doping sites, local lattice distortions, and electronic structures are investigated via hybrid density functional theory. The interaction between V and the intrinsic point defects is also studied in this work. V is found to prefer to substitute Li (${\mathrm{V}}_{\mathrm{Li}}$) at its highest charge state of +4 in most $\mathrm{LiNb}{\mathrm{O}}_3$ samples, and begins to substitute Nb to form a neutral ${\mathrm{V}}_{\mathrm{Nb}}$ defect as the Fermi level is increased. Furthermore, ${\mathrm{V}}_{\mathrm{Li}}$ exhibits different polaronic behaviors in stoichiometric and congruent $\mathrm{LiNb}{\mathrm{O}}_3$. The most stable ${\mathrm{V}}_{\mathrm{Li}}^{4+}$ tend to form a ${\mathrm{V}}_{\mathrm{Li}}^{2+}$ small bound polaron by simultaneously capturing two electrons in stoichiometric $\mathrm{LiNb}{\mathrm{O}}_3$, and form a bound bipolaron along the nonpolarization axis in the congruent samples. Moreover, both bound bipolarons along the polarization and nonpolarization axes are found in congruent $\mathrm{LiNb}{\mathrm{O}}_3$ by capturing two more electrons.

Figure 1

Stability range of the chemical potentials (in eV) of the $\mathrm{LiNb}{\mathrm{O}}_3$ constituents within DFT-PBE (a) and HSE06 (b) functionals respectively. The colored region is the intersection between them and represents the thermodynamically allowed range of the chemical potentials. The arrows point to the black dots that indicate the chemical potentials we used in this work.

Figure 2

Defect formation energies of ${\mathrm{V}}_{\mathrm{Li}}$ and ${\mathrm{V}}_{\mathrm{Nb}}$, as well as the intrinsic defects $\mathrm{N}{\mathrm{b}}_{\mathrm{Li}}$ and $\mathrm{Va}{\mathrm{c}}_{\mathrm{Li}}$ as a function of the Fermi energy. The Fermi energy range corresponds to the calculated fundamental band gap of $\mathrm{LiNb}{\mathrm{O}}_3$, which is 5.21 eV. Li-deficient conditions suitable for congruent $\mathrm{LiNb}{\mathrm{O}}_3$ are chosen.

Figure 3

Comparison between the local lattice distortions of ${\mathrm{V}}_{\mathrm{Li}}$ (b)–(d) and $\mathrm{N}{\mathrm{b}}_{\mathrm{Li}}$ (b′)–(d′) and the bulk $\mathrm{LiNb}{\mathrm{O}}_3$ (a), (a′) calculated by spin-polarized HSE06. The distances between the defect and its neighboring O and Nb ions are shown (in units of Å).

Figure 4

Spin-polarized PDOSs and charge density differences of the bulk $\mathrm{LiNb}{\mathrm{O}}_3$ (a) and the materials with ${\mathrm{V}}_{\mathrm{Li}}$ (b)-(d) and ${\mathrm{V}}_{\mathrm{Nb}}$ (e)-(f) dopants within HSE06. The shadowed and blank regions represent the occupied and unoccupied states of the electron respectively. The total spins $S$ are indicated for all the charge states. The yellow and blue regions in the charge density difference maps represent the electron accumulation and depletion, respectively.

Figure 5

Spin-polarized density of the $d$ electronic states of ${\mathrm{V}}_{\mathrm{Li}}$ and their neighboring Nb atoms in stoichiometric $\mathrm{LiNb}{\mathrm{O}}_3$ calculated by HSE06. The shaded and blank regions represent the occupied and unoccupied states of the electron, respectively.

Figure 6

Calculated binding energies of defect pairs within DFT-PBE as a function of the distance. The Fermi energy is assumed to be the VBM. The range of 1NN to 5NN corresponds to the first- to fifth-next-neighboring sites of the highly charged defect.

Figure 7

Local structures and charge density difference maps of ${\mathrm{V}}_{\mathrm{Li}}^{4+}+{\mathrm{Nb}}_{\mathrm{Li}}^{4+}$(a), ${\mathrm{V}}_{\mathrm{Li}}^{2+}+{\mathrm{Nb}}_{\mathrm{Li}}^{4+}$(b) and ${\mathrm{V}}_{\mathrm{Li}}^0+{\mathrm{Nb}}_{\mathrm{Li}}^{4+}$(c) defect pairs within HSE06. The yellow and blue regions represent the electron accumulation and depletion, respectively. The distances labeled in the figures are in units of Å.

Figure 8

Density of the $d$ electronic states of charged ${\mathrm{V}}_{\mathrm{Li}}$ and $\mathrm{N}{\mathrm{b}}_{\mathrm{Li}}$ defects and their neighboring Nb ($\mathrm{N}{\mathrm{b}}_{\mathrm{A}}$ and $\mathrm{N}{\mathrm{b}}_{\mathrm{s}}$) atoms in (a) V-doped congruent $\mathrm{LiNb}{\mathrm{O}}_3$ (V:CLN) and (b) undoped congruent $\mathrm{LiNb}{\mathrm{O}}_3$ (CLN) within HSE06. The shaded region represents the occupied states of the electron.

Figure 9

Side view of the configurations of the three most stable charge-compensated defect clusters: (a) ${\mathrm{V}}_{\mathrm{Li}}^{4+}+{\mathrm{Nb}}_{\mathrm{Li}}^{4+}+8{\mathrm{Vac}}_{\mathrm{Li}}^{-}$, (b) ${\mathrm{V}}_{\mathrm{Li}}^{4+}+4{\mathrm{Vac}}_{\mathrm{Li}}^{-}$, and (c) ${\mathrm{V}}_{\mathrm{Li}}^{4+}+4{\mathrm{Vac}}_{\mathrm{Li}}^{-}+{\mathrm{V}}_{\mathrm{Nb}}^0$. The white dotted circles represent lithium vacancies.

Figure 10

PDOSs of ${\mathrm{V}}_{\mathrm{Li}}^{4+}$ calculated by HSE06 (a) and DFT-PBE (b), respectively, and the ${\mathrm{V}}_{\mathrm{Li}}^{4+}+{\mathrm{Nb}}_{\mathrm{Li}}^{4+}+8{\mathrm{Vac}}_{\mathrm{Li}}$ (c), ${\mathrm{V}}_{\mathrm{Li}}^{4+}+4{\mathrm{Vac}}_{\mathrm{Li}}$ (d), ${\mathrm{V}}_{\mathrm{Li}}^{4+}+4{\mathrm{Vac}}_{\mathrm{Li}}+{\mathrm{V}}_{\mathrm{Nb}}^0$ (e) defect clusters calculated by DFT-PBE.