Theoretical study on the ferroelectric and light absorption properties of Li₂SbBiO₆ for harvesting visible light

Abstract

Ferroelectric oxides with large bandgaps have restricted applications in photovoltaic and photocatalytic fields. Based on recent experiments with the ferroelectric compound, LiSbO₃, the stability and optoelectronic properties of a new ferroelectric compound, namely Li₂SbBiO₆, are investigated in this study. The calculated results demonstrate that Li₂SbBiO₆ satisfies the stability conditions of the elastic coefficients and phonon dynamics. Li₂SbBiO₆ maintains the ferroelectric polarization strength of LiSbO₃ and significantly reduces the bandgap, and thus has been explored for applications in photovoltaic and photocatalytic fields. Li₂SbBiO₆ is a new potential ferroelectric oxide for harvesting visible light owing to its suitable bandgap and a large hole–electron effective mass ratio.

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1. Introduction

Polar materials with non-centrosymmetric structures have pyroelectric, piezoelectric, ferroelectric, and nonlinear optical properties and have been found to exhibit unique applications in diverse fields.^1–4 The conventional ferroelectric materials, LiNbO₃ and LiTaO₃, belong to the noncentrosymmetric R3c space group and show excellent ferroelectricity and unique features in the photovoltaic and photocatalytic decomposition of water.^5–7 LiNbO₃ and LiTaO₃ are difficult to be promoted in photovoltaic and photocatalytic applications owing to their wide bandgaps. Some rare-earth ferroelectric oxides such as LuMnO₃, YMnO₃, and TbMnO₃ do not have very strong ferroelectric polarization strengths as LiNbO₃ and BiFeO₃, but they exhibit excellent band gaps and high absorption coefficients, leading to significant interest in the ferroelectric photovoltaic field.^8,9 The ferroelectric photovoltaic material, BiFeO₃, can effectively maintain a high ferroelectric polarization strength and reduce the bandgap by doping to achieve high photovoltaic performance.¹⁰ The bandgap values of ferroelectric oxides with an LiNbO₃ structure are usually larger than 3 eV and poorly absorb visible light.^11–15 LiSbO₃ with the LiNbO₃ structure recently synthesized by Inaguma et al. showed potential ferroelectricity and a high ferroelectric Curie temperature.¹⁶ Rich structural phase transitions can appear in LiSbO₃ at different pressures with large static dielectric tensor and insulating properties.¹⁷ LiSbO₃ with a R3c structure has a large bandgap and mainly absorbs ultraviolet light according to our recent study.¹⁸ LiBiO₃ with the Pccn space group can be prepared via the hydrothermal treatment method.¹⁹ Young et al. theoretically predicted that the energy of LiBiO₃ with a R3c structure is relatively close to that of the Pccn space group and is a potentially stable ferroelectric photovoltaic material with a strong bulk photovoltaic effect.²⁰ Bi-based materials have attracted attention for splitting water to produce hydrogen under visible light.^21,22 In Bi-based compounds such as BiFeO₃, BiVO₄, Bi₂O₃, KBiO₃, LiBiO₃, and NaBiO₃ excited by visible light, the bandgap can be reduced to below 3.0 eV due to hybridization between the O 2p and Bi 6s orbitals.^23,24 The overlapping of O 2p and Bi 6s orbitals in Bi-based photocatalysts is beneficial for decreasing the bandgap to capture visible light.²⁵ The introduction of Cr ions into BiFeO₃ to form the Bi₂FeCrO₆ double perovskite with a R3 structure can also significantly reduce the bandgap and maintain a high ferroelectric polarization strength, effectively improving photovoltaic efficiency.²⁶ Considering Sb and Bi elements in the VA group and the unique 6s orbital of the Bi element and double perovskite Bi₂FeCrO₆ with the R3 structure, the introduction of Bi elements to form Li₂SbBiO₆ in the ferroelectric material LiSbO₃ can aid ferroelectric materials with the absorption of visible light. In this study, the stability and optoelectronic properties of Li₂SbBiO₆ are investigated using first-principles calculations. The calculation results show that Li₂SbBiO₆ satisfies stability conditions and maintains the ferroelectric strength of LiSbO₃, while significantly reducing the bandgap to absorb visible light.

2. The calculation method and structure

First-principles calculations are based on the plane-wave basis set of the VASP software.^27,28 The generalized gradient approximation and the plane pseudopotential wave method are used to deal with the interactions between electrons and ions.²⁹ The Perdew–Burke–Ernzerhof (PBE) functional is used as the exchange–correlation function.³⁰ The cutoff energy is chosen to be 520 eV, and the K-point sample including the Γ point is selected to be 6 × 6 × 6. The lattice parameters and atomic positions are completely relaxed in the calculations. The electron self-consistency accuracy is 10⁻⁶ eV, and the atomic force is less than 0.01 eV Å⁻¹. The Heyd–Scuseria–Ernzerhof (HSE) hybrid functional is employed to calculate the bandgap and complex frequency-dependent dielectric matrix in random phase approximation (RPA) schemes with an 8 × 8 × 8 K-point sample.³¹ The elastic constants (C_ij) are calculated using the strain–stress method in the VASP package with the 8 × 8 × 8 K-point sample.³² The standard berry phase method was applied to calculate ferroelectric polarization.^33,34 A 2 × 2 × 2 supercell containing 80 atoms was used to calculate the phonon frequency for Li₂SbBiO₆, and a 4 × 4 × 4 K-point sample was used for this supercell. LiSbO₃ exhibits the R3c symmetry based on experimental reports,¹⁶ while Li₂SbBiO₆ shows the R3 symmetry by Bi substitution for Sb similar to the Bi₂FeCrO₆ double perovskite, as shown in Fig. 1. The calculated lattice parameters are shown in Table 1, where the lattice parameters of R3c-LiSbO₃ and R3c-LiBiO₃ are in good agreement with the experimental¹⁶ and theoretical values,²⁰ respectively.

Fig. 1 The structures of LiSbO₃ and Li₂SbBiO₆.

Table 1 The calculated lattice parameters (lattice constant and angle α)

	LiSbO3	LiSbO3	LiBiO3	LiBiO3	Li2SbBiO6
a (Å)	5.39 (ref. 16)	5.46	5.67 (ref. 20)	5.71	5.60
α (°)	56.4 (ref. 16)	56.6	56 (ref. 20)	56.1	56.3

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3. The stability of Li₂SbBiO₆

R3c-LiSbO₃ has six independent elasticity coefficients, while R3-Li₂SbBiO₆ has seven independent elasticity coefficients. The calculated elastic coefficients are shown in Table 2. The elastic coefficients of LiSbO₃ satisfy the inequalities of the stability conditions of the R3c structure:³⁵

C₁₁ − C₁₂ > 0,

C₁₃² < 0.5 × C₃₃ × (C₁₁ + C₁₂),

C₁₄² < 0.5 × C₄₄ × (C₁₁ − C₁₂),

C₄₄ > 0.

Table 2 The calculated elastic coefficients (GPa)

	C11	C12	C13	C14	C33	C44	C66
LiSbO3(present)	245.3	52.0	86.4	−23.4	258.6	112.9	—
LiSbO3 (ref. 18)	283.6	56.2	104.0	−28.8	308.7	135.0	—
LiSbO3(10 GPa) (ref. 18)	322.3	77.8	130.3	−32.2	336.4	150.8	—
LiSbO3(10 GPa) (ref. 17)	289.6	75.0	119.8	−28.5	304.1	135.9	—
LiSbO3(12 GPa) (ref. 17)	295.8	79.3	124.6	−28.9	309.8	138.3	—
Li2BiSbO6	196.7	50.2	68.7	−16.2	200.1	84.3	73.2

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The seven independent elastic coefficients of Li₂SbBiO₆ also satisfy the stability conditions of the R3 space group:³⁵

C₁₁ > |C₁₂|,

C₁₃² < 0.5 × C₃₃ × (C₁₁ + C₁₂),

C₁₄² + C₁₅² < 0.5 × C₄₄ × (C₁₁ − C₁₂),

C₄₄ > 0.

The elasticity coefficient of R3c-LiSbO₃ calculated using the PBE function is smaller than that of the SCAN function (Table 2),¹⁸ and the elasticity coefficient becomes larger under high pressure conditions according to reports in the literature.^17,18 All elasticity coefficients of R3c-LiSbO₃ and R3-Li₂SbBiO₆ in Table 2 meet the stability conditions. The eigenvalue matrices of the elastic coefficients of LiSbO₃ and Li₂SbBiO₆ in Table 3 are greater than 0 and satisfy the mechanical stability condition. The phonon frequencies and phonon density of states were calculated to verify the stability of LiSbO₃ and Li₂SbBiO₆ (Fig. 2). The results show that they are potentially stable structures with no imaginary frequencies throughout the Brillouin zone. Li₂SbBiO₆ has a smaller elasticity coefficient than LiSbO₃, which implies that mechanical properties, such as Young's modulus, bulk modulus, and hardness, may be modulated by the mutual doping of Sb and Bi. The calculated phonon density of state shows that the phonon frequency of Li₂SbBiO₆ shifts toward lower frequencies as compared to that of LiSbO₃, which is in line with the trend of the reduced elasticity coefficient.

Table 3 The calculated eigenvalue matrices of elastic coefficients (GPa)

	λ1	λ2	λ3	λ4	λ5	λ6
LiSbO3	79.7	100.7	131.1	156.2	207.6	396.7
Li2BiSbO6	61.6	78.3	101.0	124.2	159.1	318.7

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Fig. 2 The calculated phonon frequency and phonon density of states.

4. Ferroelectricity analysis

The ferroelectric polarization strengths of LiSbO₃ and Li₂SbBiO₆ are calculated using the berry phase method. As shown in Fig. 3, the energy curves and ferroelectric polarization strengths are calculated by the linear interpolation of the atomic positions between the centrosymmetric and polarized structures. The centrosymmetric and polarized structures for LiSbO₃ are R3̄c and R3c, respectively, while R3̄ and R3 structures are chosen for Li₂SbBiO₆. Displacement-type ferroelectric materials can form energy double potential well curves between the ferroelectric (polar) and paraelectric (centrosymmetric) states. The calculated energies of LiSbO₃ and Li₂SbBiO₆ show significant ferroelectric double potential wells. Interestingly, the calculated ferroelectric polarization values of LiSbO₃ and Li₂SbBiO₆ are 34 μc cm⁻² and 39 μc cm⁻², respectively. Thus, the ferroelectric polarization strength of Li₂SbBiO₆ is slightly greater than that of LiSbO₃. According to our previous study, Li–O atomic interactions play a significant role in the ferroelectricity of LiSbO₃.¹⁸ We further calculated the effect of the ionic movement on the ferroelectricity of Li₂SbBiO₆ (Fig. 4). The movement of Li–O atoms induces the double potential well shift and promotes the ferroelectric stability in Li₂SbBiO₆. This is consistent with the results of the phonon density of states calculations (Fig. 2), where evidently the Li–O phonon coupling effect is stronger in the high phonon frequency area.

Fig. 3 The calculated energy and polarization as the position of the atom changes.

Fig. 4 The calculated energy as the position changes with the movement of different atoms.

5. Discussion of photoelectric properties

As shown in Fig. 5, LiSbO₃ and Li₂SbBiO₆ present the characteristics of an indirect bandgap material with 3.2 and 1.9 eV bandgap values, respectively. The calculated bandgap of LiSbO₃ using the HSE06 functional is close to the value (3.4 eV) of the MBJ functional as-obtained in our earlier report.¹⁸ The energy band of Li₂SbBiO₆ has been calculated using the HSE06 + SOC (spin orbit coupling) approach due to the heavy Bi element. The calculation results from Fig. 6 show that the energy band structure of Li₂SbBiO₆ remains basically unchanged by the SOC effect, and the bandgap increases slightly to 2.1 eV. Considering the calculation of HSE06 + SOC is relatively expensive and HSE06 calculations can usually give accurate results in general, the HSE06 approach is mainly used to calculate the optical properties and electronic density of states of Li₂SbBiO₆. The bandgap of Li₂SbBiO₆ maintains the nature of the indirect bandgap of LiSbO₃, which is unfavorable for photovoltaic performance, but the introduction of Bi ions can significantly reduce the bandgap to absorb visible light. From the density of states calculations (Fig. 5), the valence charges of both LiSbO₃ and Li₂SbBiO₆ mainly comprise O-2p orbitals. It is also found that the antibonding states formed by O-2p and Bi-6s orbitals significantly reduce the bandgap of Li₂SbBiO₆. The absorption coefficients (α(ω)) of Li₂SbBiO₆ were acquired using the frequency-dependent dielectric matrix:
where ω is the incident light frequency, and c is the speed of light in a vacuum. The imaginary and real parts of the dielectric function are denoted by ε_i and ε_r, respectively. The calculated absorption coefficient of Li₂SbBiO₆ is shown in Fig. 7. LiSbO₃ does not absorb visible light because of its large bandgap. Li₂SbBiO₆ can significantly absorb visible light and is a potential ferroelectric photovoltaic material. The bandgap of Li₂SbBiO₆ using the HSE06 calculation is 1.9 eV, which is close to that of the photocatalytic materials BiOI³⁶ and LiBiO₃ (ref. 37) with applications in photocatalytic water splitting. The bandgap value of Li₂SbBiO₆ is not as favorable as that of rare-earth ferroelectric oxides for absorbing visible light,^8,9 but the ferroelectric polarization strength of Li₂SbBiO₆ is relatively large, which could be favorable for driving carrier separation by the depolarization field. A ferroelectric material with an internal electric field can reduce the probability of carrier recombination and improve the efficiency of photogenerated carriers. We calculated the effective mass to investigate the photoelectric properties. The expression for effective mass is m*(k) = ±ℏ²[∂²E(k)∕∂²k]⁻¹. The calculation results of the effective mass and ferroelectric polarization strength are shown in Table 4. The calculated electron effective mass of LiSbO₃ and Li₂SbBiO₆ is close to 0.5m₀, and the electron carrier mobility could be larger due to the small effective mass. The ratio of m_h/m_e was calculated to further explore the response to photoelectric performance. A lower recombination rate and higher transfer rate of photogenerated carriers could be induced for a larger ratio of m_h/m_e. The m_h/m_e ratios of Li₂SbBiO₆ are 7.414 and 5.934 without and with the SOC effect, respectively, which are greater than those of LiSbO₃ polarized structures. The m_h/m_e ratio of the ferroelectric material BiFeO₃ is 4.589,³⁸ and the ferroelectric polarization strength is higher than that of Li₂SbBiO₆, but the bandgap of BiFeO₃ is relatively large and absorbs only a small amount of visible light for photocatalytic properties.^39,40 The high degradation efficiency could arise from the strong visible light absorption, depolarization field of ferroelectrics, intrinsic small carrier effective mass, and large m_h/m_e ratio in Li₂SbBiO₆, which contribute to the photoinduced carrier separation in the photocatalytic process.

Fig. 5 The calculated energy band structure and density of states.

Fig. 6 The calculated energy band of Li₂SbBiO₆ with and without the SOC effect.

Fig. 7 The calculated light absorption coefficient.

Table 4 The calculated effective mass of holes (m_h) and electrons (m_e), the ratio of m_h/m_e, and ferroelectric polarization strength (P_s)

Compounds	mh (m0)	me (m0)	mh/me	Ps (μc cm^−2)
LiSbO3	1.484	0.433	3.424	34
LiBiO3	1.651	0.504	3.272	47 (50 (ref. 20))
Li2SbBiO6	3.618(3.258-soc)	0.488(0.549-soc)	7.414(5.934-soc)	39
BiFeO3	3.171 (ref. 38)	0.691 (ref. 38)	4.589	90

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6. Conclusions

The stability and photoelectric properties of the Li₂SbBiO₆ ferroelectric compound have been investigated using density functional theory. The calculation results as well as the elastic coefficient and phonon dynamics analyses show that Li₂SbBiO₆ is a potentially stable ferroelectric material. The ferroelectric stability of Li₂SbBiO₆ and LiSbO₃ is related to the strong effect of the Li–O bond. Li₂SbBiO₆ slightly improves the ferroelectric polarization of LiSbO₃ and significantly reduces the bandgap to expand its applications in photovoltaic and photocatalysis with visible light. The larger m_h/m_e ratio of Li₂SbBiO₆ accompanied by a suitable bandgap and ferroelectric properties is more favorable for the separation of carriers and absorption of visible light.

Conflicts of interest

The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

Acknowledgements

This work was supported by the Natural Science Foundation of Guangdong Province, China (Grant No. 2019A1515011914, 2018A030307028, and 2019A1515010916), Maoming Natural Science Foundation of Guangdong, China (Grant No. 2019018001), Guangdong University Student Climbing Project, China (Grant No. pdjh2021a0331), and Natural Science Foundation of Guangdong University of Petrochemical Technology (no. 2017rc19).

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