Polaron optical absorption in congruent lithium niobate from time-dependent density-functional theory

Michael Friedrich, W. G. Schmidt, Arno Schindlmayr, and Simone Sanna

Phys. Rev. Materials 1, 054406 – Published 11 October 2017

Abstract

The optical properties of congruent lithium niobate are analyzed from first principles. The dielectric function of the material is calculated within time-dependent density-functional theory. The effects of isolated intrinsic defects and defect pairs, including the ${Nb}_{Li}^{4 +}$ antisite and the ${Nb}_{Li}^{4 +} - {Nb}_{Nb}^{4 +}$ pair, commonly addressed as a bound polaron and bipolaron, respectively, are discussed in detail. In addition, we present further possible realizations of polaronic and bipolaronic systems. The absorption feature around 1.64 eV, ascribed to small bound polarons [O. F. Schirmer et al., J. Phys. Condens. Matter 21, 123201 (2009)], is nicely reproduced within these models. Among the investigated defects, we find that the presence of bipolarons at bound interstitial-vacancy pairs ${Nb}_{V} - V_{Li}$ can best explain the experimentally observed broad absorption band at 2.5 eV. Our results provide a microscopic model for the observed optical spectra and suggest that, besides ${Nb}_{Li}$ antisites and Nb and Li vacancies, Nb interstitials are also formed in congruent lithium-niobate samples.

Received 24 July 2017

DOI:https://doi.org/10.1103/PhysRevMaterials.1.054406

Physics Subject Headings (PhySH)

Dielectric properties Electronic structure Point defects Polarons

DFT+U Hybrid functionals Time-dependent DFT

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Michael Friedrich^*, W. G. Schmidt, and Arno Schindlmayr

Department Physik, Universität Paderborn, 33095 Paderborn, Germany

Simone Sanna

Institut für Theoretische Physik, Justus-Liebig-Universität Gießen, Heinrich-Buff-Ring 16, 35392 Gießen, Germany

^*michael.friedrich@uni-paderborn.de

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Vol. 1, Iss. 5 — October 2017

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Images

Figure 1
(a) Defect-free stoichiometric lithium niobate is characterized by the Nb-vacancy-Li stacking (from bottom to top) of the cations inside the oxygen octahedra. Intrinsic defects include (b) isolated ${Nb}_{Li}$ antisites and (c) ${Nb}_{V}$ interstitials at structural vacancies inside empty oxygen octahedra as well as (d) interstitial niobium atoms paired with Li vacancies ( ${Nb}_{V} - V_{Li}$ ). (e) The ilmenite structure is equivalent to the lithium-niobate structure but has a slightly different cationic stacking sequence. (f) In this structure, we also consider ${Nb}_{Li}$ antisites. The atoms referenced as $X$ in Tables 1, 2, and 3 are marked with arrows.
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Figure 2
Calculated electronic band structure of stoichiometric lithium niobate. The HSE06 hybrid exchange-correlation functional widens the fundamental band gap with respect to PBEsol but yields an almost identical dispersion.
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Figure 3
Electronic structure resulting from the presence of a polaron in the material. Left: The electronic charge density associated with the ${Nb}_{Li}^{4 +}$ ( $4 d^{1}$ ) polaron level in SLN is localized at the Nb atom. This is true for all defect types. Right: Electronic band structures for all considered defects. Only the spin-up channel is shown, as the spin-down channel has no defect state inside the band gap. The black, gray, and green curves refer to DFT+ $U$ calculations with the PBEsol functional. The HSE06 hybrid functional raises the conduction bands (red dashed lines) and shifts the position of the polaron level (blue). To facilitate reading, the arrows indicating the energy separation between the occupied polaron level and the unoccupied conduction bands are not added to all panels.
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Figure 4
Imaginary part of the dielectric function from TDDFT. Polaron absorption occurs around 1.7 eV. H denotes a high defect concentration with Li:Nb = 88%, and L denotes a low defect concentration with Li:Nb = 96%. The different cell sizes and defect concentrations explain the different oscillator strengths of the curves. The dotted vertical line marks the experimentally observed peak maximum at 1.64 eV.
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Figure 5
Left: The electronic charge density associated with the bipolaron at the ${Nb}_{Li}$ (SLN) antisite is not localized at one lattice site but extends to the nearest ${Nb}_{Nb}$ atom, forming a hybridized $4 d^{1} - 4 d^{1}$ orbital. This is true for all defect types. Right: Electronic band structures for all considered defects. The color scheme is the same as in Fig. 3. The energy separation from the bipolaron levels to the conduction bands is indicated by yellow (PBEsol) and red (HSE06) arrows. The two structures containing interstitial ${Nb}_{V}$ atoms exhibit the largest separation from the conduction bands and are therefore the best models to explain the experimentally observed absorption peak at 2.5 eV.
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Figure 6
Imaginary part of the dielectric function from TDDFT. The bipolaron absorption peaks for ${Nb}_{Li}$ and ${Nb}_{V} - V_{Li}$ are clearly positioned at distinct energies. H denotes a high defect concentration with Li:Nb $= 88 %$ , and L denotes a low defect concentration with Li:Nb $= 96 %$ . The different cell sizes and defect concentrations explain the different oscillator strengths of the curves. The dotted vertical line marks the experimentally observed peak maximum at 2.5 eV.
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