1.
Introduction

Oxide semiconductors generally have large band gaps, which can be widely used in thin-film transistors of the ultraviolet region, light-emitting diodes or transparent electrodes, etc.^{[1, 2]}. Most oxide semiconductors are not suitable for applications in solar cells and photocatalysis because they are almost transparent to visible light. Hexagonal ZnO and anatase TiO₂ are typical oxide semiconductor materials with band gaps of 3.37 and 3.2 eV, respectively^{[3, 4]}. However, the band gaps of Cu₂O and wurtzite-derived AgGaO₂ are approximately 2 eV, which can be used to prepare solar cells and photocatalytic materials^{[5, 6]}. In 2014, Omata et al. of Osaka University prepared β-CuGaO₂ oxide semiconductors by ion replacement of NaGaO₂ materials^[7]. β-CuGaO₂ is a direct bandgap material with a band gap of 1.47 eV, which is very beneficial for the preparation of a new type of photovoltaic material. Song et al. believe that β-CuGaO₂ also has ferroelectricity and could be potential ferroelectric photovoltaic materials by DFT research^[8]. Currently, the popular ferroelectric photovoltaic materials such as BaTiO₃ and BiFeO₃ hold relatively large band gaps, low absorption of visible light, and low current density^{[9, 10]}, while β-CuGaO₂ are expected to absorb more visible light to improve the efficiency of ferroelectric photovoltaics. Okumura et al. found that Cu vacancies as p-type intrinsic defect could be easily emerged in β-CuGaO₂, and easily formed heterojunction semiconductors with ZnO^[11]. It is necessary to introduce the Coulomb interaction parameter U into the Cu element to calculate the electronic structure for the 3d orbital of Cu ions is much localized and the traditional LDA and GGA calculated methods will underestimate the band gap^[12]. However, Suzuki et al. calculated the band gap of β-CuGaO₂ with 0.3 eV by LDA + U (U = 6 eV) method, which is much smaller than the experimental band gap value of 1.47 eV^[13]. The hybrid functional HSE and quasiparticle self-consistent GW are generally available for the accurate electronic structure relatively^[14-16]. Okumura et al. calculated the band gap of β-CuGaO₂ by HSE method, and found that the band gap of β-CuGaO₂ is 1.09, 1.21, 1.56, and 1.96 eV respectively with the variational parameter α^[11]. The band gap of 1.56 eV is the closest to the experimental value when the α parameter is 0.35^[11]. They also calculated the band gap of β-CuGaO₂ with 0.84 eV by using the GW approach, which also deviated from the experimental value^[11]. Furthermore, the computational costs of HSE and GW approach are relatively high. In this paper, the GGA + U and MBJ + U approach with low calculated cost have been employed to calculate the electronic structure of β-CuGaO₂, and found that the calculated band gap obtained by MBJ + U approach is very close to the experimental value. On the basis of electronic structure calculation by MBJ + U approach, the spectroscopic limited maximum efficiency (SLME)^[17] method was also used to calculate the photovoltaic properties of β-CuGaO₂.

2.
Theoretical model and calculated method

The calculations in this paper are carried out by the Vienna ab-initio simulation package (VASP) software package based on the density functional theory (DFT) theory^{[18, 19]}. We used the PBE functional^[20] within the generalized gradient approximation (GGA) for exchange–correlation interactions. The cut-off energy is set to 520 eV and the K-point sampling in the Brillouin zone is adopted to 6 × 5 × 6. The energy convergence standard is 10^–6 eV and the Hellmann–Feynman force convergence criterion is less than 0.01 eV/ ?. The structure of β-CuGaO₂ is shown in Fig. 1. The calculated lattice parameters (a = 5.55 ?, b = 6.69 ?, c = 5.32 ?) are closed to the experimental values (a = 5.46 ?, b = 6.61 ?, c = 5.27 ?)^[7] by GGA-PBE functional. The 2H (hexagonal) and 3R (trigonal) CuGaO₂ are usually stable structures. The space group of the 2H phase is P6₃/mmc (No. 194) and 3R phase belongs to R-3m (No. 166) space group. The calculated energy difference between 2H and 3R CuGaO₂ is in the range of 5 meV/formula by GGA calculations. The β-CuGaO₂ belongs to Pna2₁ space group (No. 33). The calculated energy of β-CuGaO₂ are higher than 2H and 3R CuGaO₂ with about 60 meV/formula. The β-CuGaO₂ could be a substable structure. To obtain more accurate electronic structure, the coulomb interaction parameter U^[21] is added to treat the 3d orbital of Cu element based on the calculated structure of GGA-PBE functional. Based on the framework of density functional calculation, the modified Becke-Johnson potential plus an on-site Coulomb U (MBJ + U)^[21-23] approach was used to calculate the band structure and electronic structure of β-CuGaO₂. Our calculated band gap of β-CuGaO₂ obtained by MBJ + U approach is much closed to the experimental value. In a similar situation, the Cu-based material Cu₂X (X = S, Se, Te) is also calculated by MBJ + U to obtain accurate band gap and electronic structure^[24].






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Figure1.
(Color online) The structure of the β-CuGaO₂.

3.
The calculated results and discussion

3.1
The band structure and electronic structure

As shown in Fig. 2, the calculated band gap value does not exceed 1 eV by GGA + U with the values of U changing from 4 to 10 eV, which is deviated from the experimental value of 1.47 eV. However, in the calculations of MBJ + U approach, the calculated band gap value is very close to the experimental value when U takes 7 and 8 eV. Finally, we select MBJ + U (U = 7.3 eV) approach, and the calculate band gap value of β-CuGaO₂ is 1.46 eV. In the calculation of the latter electronic structure, we all take the parameters of MBJ + U (U = 7.3 eV), which ensures the reliability of our calculation.






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Figure2.
(Color online) The band gap values of β-CuGaO₂ by GGA + U and MBJ + U method.




As shown in Fig. 3, the valence-band maximum (VBM) and the conduction band bottom (CBM) of β-CuGaO₂ are both at the G point, which indicated a direct band gap material. The curve near VBM is relatively flat, indicating that the effective mass of the hole is relatively large, while the effective mass of electrons is relatively small since the curve near CBM is steep, which is consistent with the early reported results^{[11, 13]}. The valence band level of β-CuGaO₂ is mainly caused by the Cu-3d energy level and the O-2p energy level and the hybridization between Cu-3d energy level and the O-2p energy level determines the main properties of the material. The density of states (DOS) is relatively small to form a weak antibonding orbital between O-2p energy level and Ga-4s energy level near the conduction band of β-CuGaO₂. The transitions from the Cu-3d level to the O-2p energy level and the O-2p energy level to the Ga-4s energy level are prone to occur in β-CuGaO₂. These major energy level transitions will mainly affect the main optoelectronic properties of β-CuGaO₂.






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Figure3.
(Color online) The band structure and DOS of β-CuGaO₂.

3.2
Optical properties

The absorption coefficients [α(E)] of β-CuGaO₂ were obtained by the following formula:

$$alpha (E) = frac{{2omega }}{c}{left[ {frac{{sqrt {{varepsilon _{ m r}}{{(E)}^2} + {varepsilon _{ m i}}{{(E)}^2}} - {varepsilon _{ m r}}{{(E)}^2}}}{2}} ight]^{1/2}},$$

(1)

where c is the speed of light in vacuum, ω is the incident light frequency. The imaginary and real parts of the dielectric function are expressed in terms of ε_i and ε_r, respectively. Fig. 4 shows the calculated absorption coefficients spectrum of β-CuGaO₂. The AM 1.5 solar spectral irradiance in the 300–1000 nm wavelength range is also shown in Fig. 4. It can see that β-CuGaO₂ exhibit high absorption coefficient up to 10⁵ cm^–1 in the visible region. The total fractional absorption (A) of incident solar radiation can be approximately expressed as following formula with the film thickness (d) and absorption coefficient [α(E)].






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Figure4.
(Color online) The absorption coefficient of β-CuGaO₂ and AM 1.5 solar spectral irradiance in the 300–1000 nm wavelength range.

$$A({text{%}} ) = left( {1 - frac{{int_0^{{E_{ m g}}} {{S_E}} { m d}E}}{{int_0^infty {{S_E}} { m d}E}} - frac{{int_{{E_{ m g}}}^infty {{e^{ - a(E) cdot d}}} {S_E}{ m d}E}}{{int_0^infty {{S_E}} { m d}E}}} ight) times 100,$$

(2)

where E_g is the band gap and S_E is the incident solar spectral irradiance changing with incident photon energy E. As film thickness of β-CuGaO₂ changes, the calculated fraction absorption of incident solar flux is shown in Fig. 5. As the thickness of β-CuGaO₂ thin films increases from 0.1 to 1 μm, the total fractional absorption slightly increased, and then starts to saturate with thickness of 3 μm.






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Figure5.
(Color online) The optical absorption properties of β-CuGaO₂.

3.3
Photovoltaic properties

The Shockley-Queisser limit indicates an absorber with bandgap nearby 1.4 eV has higher photovoltaic conversion efficiency^[25]. The calculated bandgap of β-CuGaO₂ is 1.47 eV, showing that this material has the potential to an efficiency solar cell absorber. However, the thickness of the absorber layer, visible light absorption coefficient and carrier recombination are also important factors to the real cells’ efficiency. Therefore, the photovoltaic properties of β-CuGaO₂ are estimated by the spectroscopic limited maximum efficiency (SLME) metric proposed by Yu and Zunger^[17]. The SLME efficiency for β-CuGaO₂ thin films is shown in Fig. 6 with a function of thickness. We find that the SLME efficiency first increases rapidly with increasing film thickness. This mainly attribute to the increasing of film absorption. The SLME efficiency achieves maximum value as high as 32% at large film thickness. A layer thickness L = 3.0 μm is considered for the SLME calculation since beyond that value the efficiency is not noticeably changed whereas below that value. The typical current density–voltage (J–V) curves for the β-CuGaO₂ are shown in Fig. 7. The photovoltaic parameters can be derived from Fig. 7, as shown in Table 1. For comparison, the photovoltaic parameters of theoretically and experimentally CdTe solar cells are also given in Table 1. Even though the open circuit voltage (V_oc) of β-CuGaO₂ based photovoltaics cells is lower than the value of CdTe, but the conversion efficiency (η) and short circuit current density (J_sc) are much higher. These calculated results indicate that β-CuGaO₂ is a candidate for use as a highly efficient photovoltaic absorber material.

Absorber	Voc (V)	Jsc (mA/cm2)	η (%)
β-CuGaO2 (SLME)	1.20	30.2	32.4
CdTe (SLME)[26]	1.30	23.0	27.0
CdTe (EXP)[27]	0.87	26.0	20.4

Table1.
The photovoltaic parameters of β-CuGaO₂ and CdTe solar cells obtained by SLME method, the experimentally parameters for CdTe solar cells are also included for comparison.



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Absorber	Voc (V)	Jsc (mA/cm2)	η (%)
β-CuGaO2 (SLME)	1.20	30.2	32.4
CdTe (SLME)[26]	1.30	23.0	27.0
CdTe (EXP)[27]	0.87	26.0	20.4

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Figure6.
(Color online) The SLME η as a function of film thickness for ideal β-CuGaO₂ solar cell.






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Figure7.
(Color online) The current density–voltage (J–V) curves of the ideal β-CuGaO₂ solar cell with a thickness of 3 μm.

4.
Conclusions

In summary, GGA + U and MBJ + U approach with lower calculated costs are employed to calculate the electronic structure of β-CuGaO₂ in this paper. It is found that the calculated band gap value obtained by MBJ + U (U = 7.3 eV) approach is closer to the experimental value. Near the top of the valence band of β-CuGaO₂ is mainly composed of the Cu-3d energy level and the O-2p energy level. The bond formed by the hybridization between Cu-3d energy level and the O-2p energy level determines the main properties of the material. When the thickness of β-CuGaO₂ film is increased from 0.1 to 1 μm, the total absorption of the film increases sharply. The total absorption becomes to saturation when the film thickness is about 3 μm. The photovoltaic performance parameters of idea β-CuGaO₂ solar cells are calculated by the SLME method, which indicated that it could reach 32.4% energy conversion efficiency. By comparison with photovoltaic parameters of CdTe thin film solar cells, it was found that β-CuGaO₂ could be a potential high-efficiency photovoltaic material.

Acknowledgements

This work was supported by the NSFC (Grant No. 11547201), Natural Science Foundation of Guangdong Province, China (Grant No. 2017A030307008), Natural Science Basic Research Program of Shaanxi (Program No. 2019JQ-380), and Natural Science Foundation of Guangdong Petrochemical University of Technology, China (Grant No. 2017rc20).