First-principles study of the crystal structure, electronic and optical properties of Cu2O1-xMx (M = S, Se, Te)

Cu2O has the advantages of low price, stable chemical properties, and high visible light absorption rate. It is a very promising hole transport material in solar cells. However, the pure phase Cu2O has a low hole transport rate, which can be improved it by means of doping or something else. In this paper, based on the first-principles, the performance of different amounts of S, Se, and Te doped Cu2O are calculated, it is found that the Te-doped Cu2O performance is pronounced, with the energy gap reduction (1.871 eV), there appear free electron generating, the valence band maximum enables energy level is matched (−5.463 eV), and the absorption coefficient in the ultraviolet and visible range improved, nearly 103.07% at 3.26 eV, the reflectance increased to, for the point 11.7 eV, 76%, and the loss function value is very small in the visible light region (less than 0.1).


Introduction
Perovskite solar cells (PSCs) originated from Dye-Sensitized Solar Cells (DSSCs), but they are developing rapidly. In the past ten years, its photoelectric conversion efficiency has increased from 3.8% to 25.2%, which is close to the photoelectric conversion efficiency of silicon-based solar cells [1][2][3][4]. In PSCs, the material of Spiro-OMeTAD organic small molecules is generally used as the hole transport layer (HTL). While it is expensive and difficult to prepare. It is meaningful to find some alternatives to replace it. While its excellent HTL materials need to meet the following five requirements [5]: (1) It has high hole mobility. (2) The valence band maximum (VBM) of the HTL is higher than the valence band of the perovskite layer to ensure the effective hole transport, while the conduction band minimum (CBM) should be higher than the conduction band of perovskite layer to block electron transport. (3) It has a narrow band gap and can absorb near-infrared light, and has strong absorption in the near-ultraviolet (UV) region, because the light-harvesting performance of perovskite materials in the UV region is low. (4) There is less pinhole to avoid contact between the back electrode and the perovskite layer. (5) It has good thermal stability and hydrophobicity, which helps to improve the stability of the cell. Cu 2 O is a p-type semiconductor material with a narrow bandgap (2.0 eV∼2.2 eV), which has good photoelectric effect properties, like high chemical stability, high direct absorption rate of visible (Vis) light [6][7][8][9][10][11]. Moreover, it is cheap for its abundant reserving on the Earth. So it is a good potential HTL material for the PSCs. However, the hole mobility of Cu 2 O is not high enough, and the absorption edge is only about 600 nm [12]. Among them, the same chalcogen elements (S, Se, Te) as anions doping has a good improvement on metal oxides. Zhang et al improvement on the stability and electrocatalytic activity by S-doped Cu 2 O [13]. Gu et al prepared S-doped Cu 2 O nanoparticles, the position of the valence band changed from 0.51 eV to 0.34 eV than pure Cu 2 O [14]. Sharma et al improved the charge transfer performance through Se-doped CuO and can more effectively inhibit electron-hole recombination [15]. Harb used density functional theory (DFT) to calculate Te as anion and cation doped TiO 2 respectively. TiO 2-x Te x has the most obvious increase in the absorption coefficient in the Vis range, so the bandgap of the system has a decreasing trend, and the main change comes from the upward shift of the valence band [16].
The reports on S-doped Cu 2 O are mainly related to the application of catalysis, and there are few reports on solar cells, and the reports of Se and Te-doped Cu 2 O are almost rare. then, In this paper, based on the first principles (FPs), the crystal structure, electronic and optical properties of Cu 2 O doped with S, Se, and Te were studied by analyzing microscopic mechanisms to find how the different doping types and ratios affecting the performance of solar cells, which provide ideas and references for the HTL preparation for PSCs.

Model and calculation method
2.1. Model Cu 2 O cubic crystal, whose space point group is Pn-3m. containing 6 atoms in the smallest unit cell, consists of two −2-valent O atoms and four +1-valent Cu atoms [17,18]. The doping procedure is, first, constructing a 2×2×2 Cu 2 O supercell, then, replacing the position of the O1 atom in the supercell by 2.

Calculation method
The Cambridge Sequential Total Energy Package (CASTEP) module based on DFT was used for calculation in this study. The exchange-correlation energy was determined by the Perdew-Burke-Ernzerhof-solid method for Generalized Gradient Approximation (GGA-PBEsol) in the calculation process [19]. The electron wave function was expanded in the plane-wave basis set with a cutoff energy of 440 eV, and a Monkhorst-Pack grid with parameters of 2×2×2 k-point was used for an irreducible Brillouin zone sampling. All atoms were geometrically optimized using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method until the energy change of per atom was less than 5.0×10 -6 eV, the force on the atoms were less than 0.01 eV Å −1 , the stress on the atoms were less than 0.02 GPa, and the atomic displacement was less than 5.0×10 -4 Å [20]. The valence electrons of the atoms are described by the ultrasoft pseudopotential, which proportions were set as Cu 3d 10 4s 1 , O 2s 2 2p 4 , S 3s 2 3p 4 , Se 4s 2 4p 4 , and Te 5s 2 5p 4 .
is the energy of the pure Cu 2 O, E O and E M are the energy of a single O atom and a single M atom respectively, and n is the number of substitutions. As shown in table 1, the formation energies of all the six doping systems are greater than 0, which indicates that the doping processes need to absorb energy from the outside to form a stable structure [22]. As the electronegativity of O atoms is greater than that of M atoms, the M atoms are not easily doped into the cell. It can also be known from the atomic radius that O is 0.66 Å, which is smaller than that of S (1.04 Å), Se (1.60 Å), and Te (1.70 Å) [23]. The radius of the M atom differs much from that of the O atom, and it is difficult for the M atoms to occupy the position of the O atoms. When the M atoms replaces the O atoms, the generated Cu-M bond is larger than its own Cu-O bond, which will cause the M atoms to deviate from the position of the O atoms itself, which is also one of the reasons for the lattice distortion. The M atoms can react with more surface-dangling Cu atoms, but there will be a small portion of M atoms that may be doped into the interior of the Cu 2 O cell later with the temperature rising or the holding time prolongs. The M-doped Cu 2 O cell is metastable, and may eventually generate a Cu 2 O@Cu x M y compound, in which Cu 2 O acts as the main phase and a small amount of Cu x M y coexists.
In order to explore whether the crystal structure of M-doped Cu 2 O is finally stable, the mechanical properties were calculated. The mechanical properties of pure Cu 2 O and Cu 2 O 1-x M x are shown in table 2. The bulk modulus (B H ), shear modulus (G H ), Young's modulus (E H ), Poisson's ratio (v) are obtained by calculating the elastic constants C ij [23][24][25]. For the cubic crystal, the criteria for judging the mechanical stability are: The elastic constants in table 2 are taken into equation (2) to calculate, all systems satisfy the judgment of mechanical stability, so the crystal structure of M-doped Cu 2 O is mechanically stable, while the mechanical properties need to further analyze. After doping, the B H of Cu 2 O basically tends to increase, indicating that the resistance to volume deformation increases under the action of external force. The G H of M-doped Cu 2 O also showed an increasing trend, indicating that the hardness of the material also increased. According to Pugh criterion: G H /B H <0.57, it belongs to ductile material, otherwise it belongs to brittle material. It can be seen that all systems are ductile materials with good ductility, which is also in line with their properties as nanomaterials. E H is also used to characterize the ductility of the material, and the change trend is the same as the ratio of G H /B H . v can also be used to characterize the ductility of the material. If v>0.26, the material is a ductile material, otherwise it is a brittle material, and the change trend is consistent with that of E H and G H /B H .  Figure 2 shows the DOS of pure Cu 2 O from the two methods and different proportions of S, Se, and Te doped Cu 2 O.
As shown in figure 2(a), the value between the VBM and the CBM of pure Cu 2 O from the PBEsol method is 0.583 eV, which is the energy gap (Eg) value. The result is similar to those calculated in the literature [22,26]. Because of the overestimation of the Cu 3d states, the bandgap calculation is inaccurate, so the Eg value of singlecell Cu 2 O is calculated more accurately based on the Heyd-Scuseria-Ernzerhof (HSE06) method, and the result is 2.247 eV, which is consistent with the experimental value [6,27]. By comparison, it can be seen that the main difference between PBEsol and HSE06 method is the upward shift of the conduction band. Because the conclusions are based on the trends, in order to save the cost of calculation, the scissors operator is used under the PBEsol method and a correction value of 1.417 eV is given, and the experimental value of pure Cu 2 O is 2.0 eV [28], and the Eg values of the Cu 2 O 1-x M x are shown in table 1. Pure Cu 2 O is mainly contributed by Cu 3d, Cu 4s and O 2p states near VBM, and Cu 3p, Cu 3d, O 2p and a small part of Cu 4s and O 2s states near CBM [29]. The holes transport process are mainly completed near the VBM, so it is necessary to reduce the bandgap, to increase the DOS near the VBM, to enhance the carrier concentration, and to improve the localization of electrons by doping.
For the doping of same group elements, the total number of valence electrons in the system remains the same, and their s and p states distributions are similar, there will be no impurity level in the bandgap [30,31]. It can be seen from figure 2(b) that due to the doping of S, the VBM is unchanged, and the CBM multiple hybridization makes a small move to the high-energy end and the Eg value increases to 2.062 eV, and the whole system does not change much. With the S doping content increasing, the VBM remains unchanged, the CBM continues to move to the high-energy end, and the optical bandgap blue-shift increases. As can be seen from figure 2(c) that the DOS of Se-doped Cu 2 O is similar to that of S-doped Cu 2 O, the difference is that the doping of Se will aggravate the shift of O 2p states to the high-energy end. The Eg does not change with the Se doping content increasing. From figure 2(d), it can be seen similar phenomenon with previous, when doping 2.08% Te. When doping 4.17% Te, the Te 5p states of the valence band moves to the high-energy end to the Fermi level, which improves the localization of electrons, the Te 5p states and the O 2p states of the conduction band move to the lower-energy end, which makes the Eg reduce to 1.871 eV and the optical red-shift is enhanced.
Mulliken population is a method to study the charge transfer between positive and negative ions [26]. As shown in figure 3, M at the positions 1 and 2, the Cu atom at the position 3 and its next O atom at the position 4, the interaction between the doping atom and their neighboring atoms is studied.
The valence electron distributions of intrinsic Cu 2 O and Cu 2 O 1-x M x are shown in table 3. It can be seen that in pure Cu 2 O, each Cu loses 0.32 e, O gets 0.63 e, and the population of O-Cu is 0.41, which indicates the existence of a strong covalent bond. When S-doped Cu 2 O, S performs electron gaining state, S-Cu population and bond length are larger than that of O-Cu, covalency is enhanced, Cu-Cu bond length becomes shorter, and such trends are enhanced with S doping quantity increasing. When Se-doped Cu 2 O, the Se atoms loses more than 1 e, which indicates that there are free electrons, and the neighboring Cu atom also appears losing electrons, making it metallized. Compared with Se atoms, Te atoms performs stronger electron-loss characteristics, which can more effectively improve the inherent Cu 2 O carrier transport ability and its conductivity. Compared with Se atoms, Te atoms performs stronger electron-loss properties, which can more effectively improve the weak  The VBM of pure Cu 2 O is roughly the same as the data of other documents, and the results from PWC method are closer to the experimental value −5.4 eV [14,32]. The VBM of Cu 2 O 0.94 Te 0.06 has a slight decrease, but higher than the VBM (−5.5 eV) of the perovskite layer (CH 3 NH 3 PbI 3 ) [2], which is an excellent energy level matching status and helps the hole transport. Figure 4 shows the HTM energy level matching of the PSCs from the above conclusion, and the CBM of Cu 2 O 0.94 M 0.06 (around −3.4 eV) is still higher than the CBM of CH 3 NH 3 PbI 3 (−3.7 eV) when combined with the Eg value, which can effectively prevent the electron transport to the hole layer in the excited state.

Optical properties
Semiconductor materials can be regarded as continuous media in the range of wavelengths from UV to Vis. In the linear response range, the macroscopic optical response function is usually described by the complex dielectric function, and the expression is: ( ) ( ) ( ) i 1 2 e w e w e w = + [33,34]. Properties such as absorption coefficient ( ), a w reflectance ( ) R w and loss function ( ) L w can be derived from the real part ( )  13, and 6.92, which is in upward trend. It indicates that the polarization ability of the M-doped Cu 2 O becomes stronger, the intensity of the photo-generated electric field becomes larger, and the light-excited carriers migrate faster in the crystal. For the first main peak, it is mainly formed by the transition from Cu 3d to O 2p. The peak gradually grows with different doping elements, which is corresponding to the gradual increase of VBM energy in DOS. As the photon energy increases, the real part value ( ) 1 e w decreases rapidly and the light absorption of transition electrons within the band increases. Figure 5(b) shows the absorption coefficient before and after Cu 2 O doping, the red-shift becomes more pronounced with different doping elements. In the Vis range (1.55 eV∼3.26 eV), Te-doped Cu 2 O has a significant improvement compared with pure Cu 2 O and the the other two elements doping, nearly 103.07% at 3.26 eV. In the UV range (3.26 eV∼12 eV), the first absorption peak is enhanced, especially the absorption coefficient of Te-doped Cu 2 O is as high as 1.75×10 5  cm −1 at 4.91 eV, and the second absorption peak is reduced, and the overall performance of Te-doped Cu 2 O is improved relatively best in light absorption capacity. Figure 5(c) shows the reflectance before and after Cu 2 O doping. In the UV-vis range, Te-doped Cu 2 O increase obviously in reflectance than the pure Cu 2 O, which is 52% at 5.5 eV and 76% at 11.7 eV. The increase in reflectivity is beneficial to reflect back the light lost when the perovskite layer absorbs to increase the light utilization rate. According to the law of conservation of energy A R T 1, + + = where A is the absorptance, R is the reflectance, and T is the transmittance, the transmittance reduction can avoid energy loss through the material in the form of thermal energy, which is very beneficial for being used as HTL. Figure 5(d) is energy loss when electrons pass through the medium quickly before and after Cu 2 O doping, which peak is related to the plasma oscillation. The energy loss in the visible light region is extremely small (less than 0.1), most of which at the location of 12 eV, small at 6.9 eV, corresponding to the energy of the plasma edge.

Conclusions
As HTL materials in PSCs, the crystal structure, electronic and optical properties of the pure Cu 2 O and Cu 2 O 1-x M x in a total of 7 systems were studied based on the FPs.
(1) Compared with the pure Cu 2 O, M-doped Cu 2 O has different degrees of lattice distortion, and the formation energy are greater than 0, which indicates that the doping processes need to absorb energy from the outside to form a stable structure. And calculated the mechanical properties, all the systems meet the judgment of mechanical stability, in line with good ductility as nanomaterials.