First-Principles Comparative Study of CuFeSe2 and CuFeS2

Abstract In this paper, on the basis of first-principles, the CASTEP module of Materials Studio is used to calculate the band structures and optical properties of CuFeSe2 and CuFeS2 under the PBE pseudopotential of the generalized gradient approximation (GGA). The calculated results show that both CuFeSe2 and CuFeS2 are direct bandgap semiconductors with forbidden band widths of 0.64 eV and 1.06 eV, respectively. In the visible light range, the highest absorption coefficient of CuFeSe2 is 1.082×105 cm-1, the average reflectivity is 0.52, the maximum conductivity is 7.23 fs-1, the electrostatic constant is 65.9; the maximum value the highest absorption coefficient of CuFeS2 is 0.872×105 cm-1, the average reflectivity is 0.44, the maximum conductivity is 4.44 fs-1, the static dielectric constant is 52.32. The calculation results in this paper show that compared with CuFeS2, CuFeSe2 has advantages in photoconductivity and carrier separation, but has disadvantages in band gap and reflectivity. It is recommended to combine the two materials to prepare tandem solar cells.


Introduction
In recent years, the consumption of energy has been increasing day by day, and traditional fossil energy, as a non-renewable resource, cannot support the sustainable development for human beings.Therefore, the utilization of renewable energy has become the general trend.Among them, solar photovoltaic power generation relies on its abundant resources, cleanliness and pollution-free, etc.It has become one of the most potential renewable energy sources 1 .Traditional solar photovoltaic cells are made of crystalline silicon and utilize p-n junctions in the silicon material to achieve carrier separation and output.However, crystalline silicon solar cells consume large raw materials, complex processes, high power consumption and high cost in the production process, and it is difficult to further improve the photoelectric conversion rate.Therefore, researchers began to study thin-film solar cells with simpler manufacturing methods, less energy consumption, and higher photoelectric conversion efficiency 2,3 .
Copper indium selenide and copper indium gallium selenide (Cu-In-Ga-Se, CIGS) thin-film solar cells have become research hot spots because of their high visible light absorption coefficient, stable performance, and long service life [4][5][6] .However, as one of the raw materials, indium is scarce, expensive and toxic 7 .Therefore, the search for new cheap and non-toxic alternative materials has become a research hot spot.As a typical chalcopyrite structure semiconductor material 8 , CuFeS 2 is a direct bandgap semiconductor 9 , with high light absorption coefficient 10, good thermal stability, no light-induced recession effect, and abundant raw material reserves, low cost, non-toxic and harmless 11 , it has the potential as a thin-film solar Absorbent layer material.However, the low conductivity of CuFeS 2 limits its photovoltaic performance.Replacing sulfur with selenium is a common modification method for sulfide semiconductor materials.The literature shows that most of the chalcogen compounds show such a law: when the oxygen in the oxide is replaced by sulfur, or the sulfur is replaced by selenium, the forbidden band width of the material usually becomes smaller, and the electrical conductivity usually becomes larger 12 .However, this law lacks systematic and theoretical research, and cannot be directly applied to CuFeS 2 materials.In order to explore the difference between the properties of CuFeSe 2 and CuFeS 2 , to find a more suitable material for the solar energy absorption layer than CuFeS 2 , this paper uses first-principles calculations to compare the energy band structure, light absorptivity and reflectivity, photoconductivity, dielectric function.The properties of CuFeSe 2 and CuFeS 2 were analyzed, and their advantages and disadvantages as absorbent layer materials for solar cells were systematically evaluated.The structure and advantages and disadvantages of the four solar cells are shown in Figure 1 [13][14][15] .

Calculation Method
According to many literatures 16,17 and the results further confirmed in the ICSD database and Findit software in this paper, the models of CuFeSe 2 and CuFeS 2 are shown in Figure 2. CuFeS 2 belongs to the I-42d space group 122 17 .CuFeSe 2 belongs to the P-42C space group 112, and this structure can be regarded as a sulfovanadate derivative structure rather than the chalcopyrite-type structure expected for typical I-III-VII semiconductor compounds 18,19 .Both systems were calculated using first-principles calculations *e-mail: liukg163@163.combased on density functional theory (DFT) 20,21 .Using the Cambridge Sequential Total Energy Package (CASTEP) module of Materials Studio, the generalized gradient approximation (GGA) and PBE pseudopotentials are used to complete the calculation 22 .The calculation content includes structure optimization, energy band calculation, density of states and optical properties (including light absorption rate, reflectivity, photoconductivity, dielectric function).The plane wave cutoff energy of both systems is set to 440.0 eV, and the k-point density of the Brillouin zone is set to 4×4×2.

Model construction and structure optimization of CuFeSe 2 and CuFeS 2
The optimization results of CuFeSe 2 and CuFeS 2 are shown in Table 1.The table data shows that the lattice constants a, b, c and the unit cell volume of CuFeSe 2 are all larger than those of CuFeS 2 .After the structure optimization, the lattice constants a, b, c and the unit cell volume of the two crystals are smaller than those before optimization.

Energy band calculation and density of states calculation of CuFeSe 2 and CuFeS 2
Figure 3a and 3b shows the energy band and density of states of CuFeSe 2 .The forbidden band width of CuFeSe 2 is 0.64 eV, and it is a straight-gap semiconductor, which is larger than that measured in the literature (~0.4 eV).The main reason for this error is that the model used in the theoretical calculation is a perfect intrinsic semiconductor with no impurities and no lattice defects.The actual CuFeSe 2 crystal has various defects, which makes the actual energy band width lower than the theoretical value.Figure 3c and 3d shows the energy band and density of states of CuFeS 2 .CuFeS 2 is also a straight-gap semiconductor with a band gap of 1.06 eV, which is also slightly larger than the measured band gap (~0.7 eV).It can be seen from Figure 3b and 3d that the slope of conduction band edge of CuFeSe 2 is smaller than that of CuFeS 2 , indicating that CuFeSe 2 has strong electron localization and is easily excited by external energy to become free electrons, which is conducive to its photoelectric conversion efficiency as the absorption layer of solar cells.
Figure 4a is the partial wave density of states map of CuFeSe 2 .It can be seen from the figure that the electron density of CuFeSe 2 in the -17.0 eV to -14.5 eV region is    conduction band of CuFeS 2 is mainly composed of the p states of Cu, Fe, and S, and the s states of these three also contribute to a certain extent.

Calculation of optical properties of CuFeSe 2
and CuFeS 2

Absorptivity and reflectivity of CuFeSe 2 and CuFeS 2
Absorption rate is the ratio of the solar energy absorbed by a material over the full range of wavelengths of sunlight to the total solar energy that reaches the surface of the material.Figure 5a presents the absorptivity map of CuFeSe 2 and CuFeS 2 .It can be seen from Figure 5a that in the visible light range, the average absorption coefficient of CuFeSe 2 is 0.911×105 cm -1 , and the highest absorption coefficient is 1.082×10 5 cm -1 .In the visible light range (1.6~3.2 eV), the average absorption coefficient of CuFeS 2 is 0.858×10 5 cm -1 , and the maximum value is 0.872×10 5 cm -1 .Reflectance is the ratio of the amount of solar energy reflected by a material over the full range of wavelengths of the sun's rays to the total amount of solar energy reaching the material's surface.Figure 5b shows the reflectivity of CuFeSe 2 and CuFeS 2 .In the visible light range, the average reflectance of CuFeSe 2 is 0.52, and the average reflectance of CuFeS 2 is 0.44.In contrast, in the visible light range, CuFeSe 2 has better light absorption properties than CuFeS 2 .But CuFeSe 2 is also more reflective in the visible range.Considering that the anti-reflection film of the solar cell can effectively reduce the reflected light on the surface of the cell, although the reflectivity of CuFeSe 2 is slightly higher, its adverse effect as the absorption layer of the solar cell can be eliminated.Comparing the absorptivity diagrams of the two substances, it can be found that the absorption coefficient of CuFeSe 2 is high in the visible light range, and the absorption peak of CuFeS 2 is blue-shifted.

Calculation of photoconductivity of CuFeSe 2 and CuFeS 2
Photoconductivity determines the electrical conductivity of optoelectronic materials under illumination, and has a direct impact on the performance of solar cell materials.Light absorption makes the semiconductor form non-equilibrium carriers, and the increase of carrier concentration must increase the conductivity of the sample.This phenomenon of increasing the conductivity of the semiconductor caused by light is called photoconductance effect, and the corresponding conductivity is called photoconductivity. Figure 6a and 6b are the real and imaginary parts of the theoretically calculated photoconductivity of CuFeSe 2 and CuFeS 2 , respectively.In the visible light range, the photoconductivity of CuFeSe 2 is significantly higher than  that of CuFeS 2 .The photoconductivity of CuFeSe 2 reaches the maximum value of 7.23 fs -1 at the incident photon energy of 0.689 eV, and the average photoconductivity is 3.02 fs -1 .The CuFeS 2 photoconductivity peaks at 4.44 fs -1 at 0.926 eV, and the average photoconductivity is 2.32 fs -1 .The photoconductivity of CuFeSe 2 is about 30% higher than that of CuFeS 2 , and it is more suitable as an absorbent layer material for solar cells.
In this paper, the electron density of CuFeS 2 and CuFeSe 2 is simulated, and the physical models are constructed to explain the photoconductivity of them.As can be seen from the Figure 7, the volume of electron cloud overlapping between atoms in CuFeSe 2 crystal is larger, which is to electron transfer, and thus its electrical conductivity is higher, making CuFeSe 2 a potential material for solar cell absorption layer.

Complex dielectric functions of CuFeSe 2 and CuFeS 2
The dielectric function is a bridge connecting the microphysical process of the interband transition and the electronic structure of the solid, which reflects the band structure of the solid and various other kinds of spectral information.In the linear response range, the solid macroscopic optical response function is described by the complex dielectric function 23 .The complex dielectric function ε(ω) consists of a real part ε 1 (ω) and an imaginary part ε 2 (ω).The real part of the dielectric function represents the ability of the dielectric to bind charges under the action of an external electric field, and the imaginary part can reflect the transition process of electrons between energy bands 24,25 .The formula is as follows: ( ) ( ) ( ) Both CuFeSe 2 and CuFeS 2 are direct band gap semiconductor materials, and their spectra are generated by electronic transitions between energy levels, and each dielectric peak can be explained by the energy band structure and density of states.Figure 8 is a graph of the theoretically calculated complex permittivity function of CuFeSe 2 and CuFeS 2 as a function of photon energy.When there is no incident light, it corresponds to the static permittivity.Permittivity is a physical quantity that describes a material put into a capacitor to increase its ability to store charge.The electrostatic permittivity of CuFeSe 2 is 65.9 and that of CuFeS 2 is 52.3, indicating that the CuFeSe 2 system has a higher photogenerated electric field intensity and higher carrier separation efficiency, laying the foundation for highefficiency solar power generation.The imaginary parts of the dielectric functions of CuFeSe 2 and CuFeS 2 increase sharply in the range of 0-6 eV, and each has a main peak.The secondary peaks of CuFeSe 2 at 7.3 eV and 10.3 eV, and the secondary peaks of CuFeS 2 at 6.9 eV and 10.4 eV, respectively, are caused by electronic transitions, which can be analyzed from the density of states diagram 25 .

Conclusion
In this paper, first-principles calculations are performed on the band structures and optical properties of CuFeSe 2 and CuFeS 2 .The calculation results show that CuFeSe 2 has two disadvantages as a light-absorbing layer for solar cells: the band gap of 0.64 eV is smaller than that of CuFeS 2 , which is 1.06 eV, and the reflectivity in the visible light range is larger than that of CuFeS 2 .However, CuFeSe 2 has unique  advantages.In the visible light range, CuFeSe 2 has higher absorption rate and higher electrical conductivity, which is beneficial to its performance as an absorption layered material for solar cells.
From what has been said, a conclusion is drawn.Due to its narrow band gap and high reflectivity, CuFeSe 2 is not suitable for use as a light-absorbing layer material alone, and the stacking with CuFeS 2 happens to make up for the defects of CuFeSe 2 .It is recommended to use the two in combination to form a CuFeS 2 /CuFeSe stacked battery, using CuFeS 2 as a wide-bandgap absorption layer and anti-reflection layer, CuFeSe 2 acts as a narrow bandgap absorption layer to achieve full utilization of solar radiation.

Figure 1 .
Figure 1.Schematic diagram of the structure of crystalline silicon, CIGS, CuFeS 2 cells and CuFeSe 2 solar cells and the comparison of possible advantages and disadvantages.

Figure 3 .
Figure 3. (a) (b) Energy band diagram and density diagram of states of CuFeSe 2 ; (c)(d) Energy band diagram and density diagram of states of CuFeS 2 .

Figure 8 .
Figure 8.The real and imaginary parts of the complex dielectric functions of (a) CuFeSe 2 and (b) CuFeS 2 .