Advances in Condensed Matter Physics

Volume 2016 (2016), Article ID 2943173, 10 pages

http://dx.doi.org/10.1155/2016/2943173

## Electronic Origin of Defect States in Fe-Doped LiNbO_{3} Ferroelectrics

^{1}Department of Applied Chemistry, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan^{2}Division of Physics, Institute of Liberal Education, School of Medicine, Nihon University, 30-1 Ooyaguchi-kamicho, Itabashi-ku, Tokyo 173-8610, Japan

Received 20 October 2015; Revised 1 March 2016; Accepted 3 March 2016

Academic Editor: Jörg Fink

Copyright © 2016 Yuji Noguchi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We investigate the role of Fe in the electronic structure of ferroelectric LiNbO_{3} by density-functional theory calculations. We show that Fe^{2+} on the Li site () features a displacement opposite to the direction of spontaneous polarization and acts as a trigger for the bulk photovoltaic (PV) effect. In contrast to Fe^{3+} on the Li site that forms the defect states (1*e*,* a*, and 2*e*) below the conduction band minimum, the reduction from Fe^{3+} to Fe^{2+} accompanied by a lattice relaxation markedly lowers only the state () owing to a strong orbital hybridization with Nb-4*d*. The state of provides the highest electron-occupied defect state in the middle of the band gap. A reduction treatment of Fe-LN is expected to increase the concentration of Fe^{2+} and therefore to enhance the PV effect under visible light illumination.

#### 1. Introduction

Spatial symmetry breaking in polar materials offers various functions including piezoelectricity, ferroelectricity, multiferroelectricity, and bulk photovoltaic (PV) effect. Because ferroelectric lithium niobate (LiNbO_{3}; LN) has a strong polar lattice arising from cooperative displacements of the constituent atoms, LN has been used in many applications including acousto-optic [1–3], electro-optic [1, 4–6], and optical-frequency conversion [1, 7–10] devices. Historically, the photorefractive effect was first discovered in LN [11, 12] and was found to be enhanced in iron-doped lithium niobate (Fe-LN) [13]. The photorefractive effect is recognized as the cause of an optical damage in the nonlinear optics, whereas it is utilized for holographic memory storages [14, 15].

Recently, the PV effect in ferroelectrics has attracted renewed interests, because the working principle can be applied to the devices that generate a high voltage beyond the limitation of present semiconductor-based solar cells [16–19]. The bulk PV effect in ferroelectrics arises from asymmetric carrier dynamics because of spatial symmetry breaking [20]. The photoinduced feature of the generation and dissociation of charge carriers in Fe-LN under visible light make it a promising candidate for the ferroelectric material used in the PV devices. Although a large number of experimental studies on Fe-LN have been conducted for several decades [21, 22], first-principles calculations of the electronic structures have been reported very recently [23–26].

Sanson et al. [25] have performed density-functional theory (DFT) calculations for Fe-LN in addition to local structure studies by an extended X-ray absorption fine structure spectroscopy. They reveal that Fe^{2+} on the Li site () produces defect states inside the band gap and that the state in the minority spin band forms the Fermi energy (). According to Inoue et al. [26], a tensile strain from substrates markedly enhances the PV effect in Fe-LN epitaxial thin films whereas their DFT calculations show that neither tensile nor compressive strain plays a minor role in the electronic structure of -LN. However, the following question remains unresolved: why the -wave states of differ in the majority and minority spin bands. In addition, the orbital interaction between and its neighbors should play an important role, but the bonding and antibonding interactions related to the -*d* states have not been understood yet. To establish the materials design for enhanced PV effect in the LN system, the electronic origin of the defect states originating from needs to be clarified.

In this paper, we report the electronic structure of -LN obtained by DFT calculations and discuss the orbital interactions of with its neighbors. We demonstrate that the mixing between Fe-3*d* and Nb-4*d* plays a crucial role in the electronic structure. Our calculations show that the state of resulting from the hybridization of Fe- and Nb-4*d* is the highest electron-occupied defect state in the middle of the band gap and acts as a trigger for the PV effect under visible light.

#### 2. Method of DFT Calculations

We performed DFT calculations within the local density approximation (LDA) [27] by the PAW (projector-augmented wave) method [28] using a plane wave basis set as implemented in the Vienna* ab initio* simulation package (VASP) [29]. A plane wave cut-off energy was set to be 520 eV, and an electronic energy was converged to less than 10^{−5 }eV in all calculations. First, the hexagonal unit cell of LN in space group* R*3*c* was structurally optimized until the Hellmann-Feynman force on each atom was less than 0.1 eV/nm. A* k*-mesh of centered on the Γ point was used in the geometrical optimization for lattice parameters and fractional coordinates. The lattice parameters of the optimized LN cell agree well with the experimental values [30] within 0.7%.

We employed a simplified local spin density approximation (LSDA +* U* approach) [31] as a correction for localized and strongly correlated electrons within on-site Coulomb terms of eV for Nb-4*d* [32] and eV for Fe-3*d* [23, 30]. The details of the influence of the terms on the electronic structures are discussed later. The occupation sites of Fe in LN have been reported as Fe on the Li site () [33–40] and Fe on the Nb site () [38, 39]. Here, we adopt the model of Fe^{2+} on the Li site (), according to the reports [23, 41], because we focus our attention on the defect states arising from that absorbs visible light. To make a supercell of Fe-LN, the setting of the optimized LN cell (hexagonal) was transformed to the rhombohedral cell (Li_{16}Nb_{16}O_{48}) in space group* P*1. In this cell one Li atom was replaced by one Fe atom, leading to Li_{15}FeNb_{16}O_{48}. This rhombohedral setting was changed again to the hexagonal one in space group* R*3. This Fe-LN cell [Li_{15}FeNb_{16}O_{48} ()] was geometrically optimized (with a* k*-mesh of centered on the Γ point).

In the model of , the charge neutrality is supposed to be satisfied by the following two possible compensations: one is the formation of the small polaron, , [41, 42] and the other is the creation of Li vacancy () [23], where the prime denotes one negative charge. First, we tested the small polaron model of . In the Fe-LN cell, there are eight different kinds of the Nb sites in view of the symmetry. Prior to the geometrical optimizations, magnetic moment of +1 (where denotes Bohr magneton) or −1 was put to each of the Nb atom, and that of Fe was set to be +4 assuming the high spin configuration. After the geometrical optimizations for all of the supercells, the total magnetic moment was converged to be +4 and the was located inside the conduction band (the Nb-4*d* band). This implies that Fe-LN crystals with the polaron exhibit a metallic behavior having a low resistivity, which cannot explain the experimental result of the high resistivity of Fe-LN crystals [43]. These results force us to consider that the small polaron model of is not suitable for the charge compensation in the ground state.

Next we examined the model [23] by using the supercell containing and , that is, Li_{14}FeNb_{16}O_{48} (the cell) in space group* P*1. The Fe-LN cell has seven different kinds of Li sites. We performed the geometrical optimizations for all of the supercells with on each of the Li sites. The cells with on the first nearest neighbor (NN) and seventh NN sites with respect to exhibited a small total energy by 30–90 meV compared with the other cells. These results suggest that is not necessarily stabilized adjacent to and lead to a structural picture of the -LN lattice with a random distribution of .

In reality, -LN should have an averaged structure similar to the LN host in* R*3*c* space group. This symmetry is, however, completely lost in the model owing to the presence of on the specific site. In order to take into account the threefold rotation axis along the axis, we adopted the -LN cell without [Li_{15}FeNb_{16}O_{48} () in space group* R*3], where the valence state of Fe was controlled to be Fe^{2+}. This structural model is the same as that reported by Sanson et al. [25]. The calculations of the -LN cell were also conducted in a similar manner for comparison. The electronic band structures and density of states (DOS) of the geometrically optimized cells were calculated with a* k*-mesh of centered on the Γ point. While the calculations with a denser* k*-mesh were tested, we confirmed that the results of the electronic structures are essentially the same, as reported in [25].

#### 3. Results and Discussion

Figure 1(a) displays the crystal structure around iron in the -LN cell after the geometrical optimization. In the LN cell, Nb atoms are displaced along the axis by approximately 0.02 nm, and this cooperative displacement yields a spontaneous polarization (). In the -LN cell the bond length of Fe-O1 ( nm) is shorter by 0.02 nm than that of Fe-O2 ( nm), showing that Fe^{2+} is displaced in the direction opposite to . The bond valence sum (BVS) of is estimated to be +2.3, which is slightly larger than the nominal valence (+2). Figures 1(b)–1(d) display the electronic band structures. The total density of states (DOS) and their partial DOS (PDOS) are also shown in Figures 2(a)–2(c). For the LN (*R*3*c*) cell (Figures 1(b) and 2(a)), the is set to be 0 eV. In these figures, the valence band maximum (VBM) mainly composed of the O-2*p* band is aligned to the same level. Our calculations show that the band gap is indirect: the VBM is located at the point (1/2 1/2 1/2) and the conduction band minimum (CBM) is positioned at the Γ point. Because the maximum of the valence band at the Γ point is very close in energy to the VBM and the difference is as small as 0.02 eV, we regard the maximum of the valence band at the Γ point as the VBM. The band gap () estimated from the CBM and the VBM is 3.5 eV. This value is quantitatively in good agreement with the experimental gap of 3.8 eV [44]. In general, band gap is usually underestimated due to the well-known problem of LDA [45] while the appropriate choice of the term for Nb-4*d* with the LSDA +* U* approach enables us to obtain a reasonable comparable to the experimental gap; the influences of the terms are described later. The valence band (VB) in the energy of −5–0 eV is the O-2*p* dominant band while the conduction band (CB) in 3.4–5.5 eV consists mainly of the Nb-4*d* band (Figure 3(a)). The orbital hybridization between Nb-4*d* and O-2*p* results in the small but apparent portion of PDOS of Nb-4*d* in the VB and that of O-2*p* in the CB. The PDOS of Li is not significant in both the VB and CB, which presents the ionic character of Li^{+} in the LN lattice.