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Original Research

Earth-abundant photovoltaic semiconductor NaSbS2 in the rocksalt-derived structure: A first-principles study

T

Xian Zhanga,1, Menglin Huanga,1, Peng Xua,b,1, Chen-Min Daia, Zeng-Hua Caia, Dan Hana, Shiyou Chena,c,∗ a

Key Laboratory of Polar Materials and Devices (MOE) and Department of Optoelectronics, East China Normal University, Shanghai 200241, China Department of Physics, China Three Gorges University, Yichang 443002, China c Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China b

ARTICLE INFO

ABSTRACT

Keywords: NaSbS2 Photovoltaic semiconductor Optical absorption coefficients Defects First-principles calculation

NaSbS2 was recently proposed as a novel photovoltaic semiconductor with earth-abundant component elements, but its fundamental material properties have not been well studied. The systematical first-principles calculations for its electronic, optical and defect properties were carried out in the present study, and the results show that: i) NaSbS2 in the rocksalt-derived structure has a quasi-direct band gap and thus may have long minority carrier lifetime; ii) its absorption coefficients are as high as 10 4 105 cm 1 for the visible light and almost isotropic despite that the structure is distorted relative to the high-symmetry rocksalt structure; iii) the effective masses of the electron and hole carriers are anisotropic with much larger values along the z direction than in the x-y plane, and hence the orientational control of thin films should be important for enhancing the photovoltaic performance; iv) the valence and conduction band edges of NaSbS2 are close to those of CuGaSe2, so the n-CdS/pCuGaSe2 device structure can be inherited to form the n-CdS/p-NaSbS2 solar cells; v) the acceptor defects (NaSb antisites and Na vacancies) have very high concentration, making the synthesized NaSbS2 always be p-type; vi) the S-rich condition can suppress the formation of deep-level donor defects (S vacancies and SbNa antisites) and therefore should be adopted for fabricating high-efficiency NaSbS2 solar cells.

1. Introduction The search of high-efficiency, earth-abundant and environmentfriendly semiconductors as light-absorber materials in solar cells has drawn increasing attention in the past decade [1–4]. Recently, the perovskite CH3NH3PbI3 and CH(NH2)2PbI3 show remarkable photovoltaic performance and attracted intensive attention [2,5–7]. It is believed that the existence of Pb 6s2 lone-pair orbital in the top valence band plays an important role in the ideal properties of these perovskite halides, including suitable band gap size, high valence band edge position, high carrier mobility, benign defect and interface properties, because the s-p hybridization between Pb and I increases the valence band dispersion (thus decreases the hole effective masses) and pushes the valence band edge level (the antibonding states of the s-p hybridization) up, thus making many acceptor defect levels shallow [1,8]. This special role of Pb 6s2 lone-pair states in the PbeI halides is similar to that of the Cu 3d states in the chalcopyrite Cu(In,Ga)Se2 (CIGS) and

kesterite Cu2ZnSnS4 (CZTS), where the hybridization between Cu 3d and Se 4p/S 3p states also increases the valence band dispersion and pushes the valence band edge up [9–12]. As a result, the semiconductors with similar ns2 lone-pair states such as CsGeI, BiSI, Sb2Se3, Bi2S3, GeSe and SnSe [13], and even those with both ns2 lone-pair states and Cu 3d or Ag 4d states, such as CuSbS2, CuSbSe2 and AgBiS2 [14–18], have also been studied as the candidate of light-absorber semiconductors in the solar cells and very encouraging efficiency increase has been achieved [4,18]. NaSbS2 is another earth-abundant and environment-friendly semiconductor with 5s2 lone-pair states that can be derived from CuSbS2 through replacing Cu by Na. Interestingly NaSbS2 has been synthesized in 1970s [19–21] and it has a rocksalt-derived structure. In 1978, Par J. et al. [19] and Klaus et al. [20] reported two stable monoclinic structures of NaSbS2, with the C2/c and C2/m space group, respectively. One year later, Kanishcheva et al. showed that the triclinic modification with space group P1¯ is also stable at room temperature while the cubic

Corresponding author. Key Laboratory of Polar Materials and Devices (MOE) and Department of Optoelectronics, East China Normal University, Shanghai 200241, China. E-mail address: [email protected] (S. Chen). 1 These authors contributed equally. ∗

https://doi.org/10.1016/j.pnsc.2019.02.009 Received 26 February 2019; Received in revised form 28 February 2019; Accepted 28 February 2019 Available online 23 April 2019 1002-0071/ © 2019 Chinese Materials Research Society. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).

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one with the space group Fm-3m is the high temperature modification [21]. In fact, all these structures can be derived from the rocksalt structures, with the Na and Sb occupying one face-centered-cubic (FCC) sublattice and S occupying the other FCC sublattice. When Na and Sb are ordered in the sublattice, the structures have C2/c, C2/m or P1¯ symmetry, and when they become disordered at high temperature, the structure becomes the exact cubic rocksalt structure with Fm-3m symmetry. In 2016, Rahayu et al. succeeded in making the semiconductorsensitized solar cells with NaSbS2 nanoparticles as the light-absorbing layer, achieving an efficiency of 3.18% [22]. In 2017, Zhe et al. synthesized NaSbS2-based thin film solar cell, yielding an efficiency of 0.13%. Later in 2018, Sun et al. fabricated NaSbS2 quantum dot-sensitized solar cells (QDSSCs) and exhibited an efficiency of 4.11% [23]. As there is little knowledge about the fundamental properties of NaSbS2, these experiments demonstrate the potential of NaSbS2 as the light-absorber material in solar cells. Sun et al. [24] also studied the crystal structure and electronic band structure using the density functional theory calculations with the modified Becke-Johnson (MBJ) potential, and theoretically predicted an indirect band gap of 1.22 eV and a direct band gap of 1.24 eV. However, the experimental measurements showed the band gaps in the range ∼1.5–1.8 eV [25], larger than the calculated values but close to the optimal band gap for the light-absorber material in single-junction solar cells. It is interesting to note that the semiconductors with the crystal structures derived from the cubic zincblende structures (CIGS and CZTS) and the cubic perovskite structures (CH3NH3PbI3) have both been well studied as the light-absorber semiconductors. However, the semiconductors with the rocksalt-derived structures have never been found to show very high photovoltaic efficiency. One important reason is that usually only very ionic compounds crystallizes in the rocksaltderived structures, but these compounds have too large band gaps so that they cannot absorb the visible light sufficiently. NaSbS2 is exceptional because the Sb 5s2 lone-pair states in the valence band pushes the valence band edge up and decreases the band gap significantly. If NaSbS2 can become a high-efficiency light-absorber, it will be of important scientific significance, opening the door to the usage of the cubic rocksalt-derived semiconductors as photovoltaic materials. Although NaSbS2 has been synthesized and tentatively studied as a light-absorber, there are still many opening questions about their material properties, e.g., what is the exact band gap, whether the carrier transport properties are good, what are the dominant defects in the lattice and whether their defect levels are as benign as those in perovskite halides? In this article, in order to answer these open questions and facilitate the application of NaSbS2 in solar cells, we performed a systematical first-principles calculation study on the electronic, optical and defect properties of NaSbS2. We calculated its band structure and found that its indirect band gap at 1.64 eV is slightly smaller than its direct band gap at 1.69 eV, which is beneficial for increasing the minority carrier lifetime. Furthermore, its optical absorption coefficient is

high and almost isotropic, but its effective masses of carriers are highly anisotropic, so the orientation control is important for enhancing the photovoltaic performance of NaSbS2. Through calculating the band offsets between NaSbS2 and CdS as well as other light-absorber semiconductors, we found that NaSbS2 has high valence and conduction band edge levels, as high as those of CuGaSe2, so it is difficult to dope NaSbS2 to n-type and easy to dope NaSbS2 to p-type. This is supported by the calculated defect properties, which shows that the easy formation of acceptor defects with shallow levels makes NaSbS2 always ptype. Since the S-rich condition can lead to higher p-type conductivity (high hole concentration) and less deep-level recombination-center donor defects, we propose that the S-rich condition should be adopted for fabricating NaSbS2 solar cells. 2. Calculation methods All the calculations are performed within the density functional theory [26] (DFT) framework as implemented in Vienna ab initio simulation package [27] (VASP) code. The projector-augmented wave (PAW) pseudopotentials are used with a cutoff energy of 400 eV for the plane-wave basis. An 8 × 8 × 8 Monkhorst-Pack k-point mesh has been shown to give converged results for the primitive cell calculations, and equivalent k-point meshes have been used for the supercell calculations. For the exchange-correlation functional, we used the generalized gradient approximation in the Perdew Burke Ernzerhof [28] (PBE) form for all the structural relaxation of supercells and slabs. However, it is known that PBE generally underestimates the band gap, so we also used the Heyd Scuseria Ernzerhof [29,30] hybrid functional with a mixing parameter of 25% (HSE06) for all the band structure and total energy calculations based on the PBE-relaxed structures. The results have been shown to agree well with those from the complete HSE06 calculations in both the structural relaxations and static calculations. 3. Results and discussions 3.1. Crystal structure The structure of NaSbS2 has been refined into three rocksalt-like structures with the space groups, C2/c, C2/m and P1¯. As depicted in Ref. [31], the C2/c and P1¯ structures were found to have very little difference, and the energy of P1¯ structure is 0.005 eV/f. u. lower than that of C2/c, so in this study we focus on the properties of the ground state monoclinic P1¯ structure. Fig. 1(a) shows the rocksalt-derived P1¯ crystal structure of NaSbS2 with Na and Sb occupying one FCC sublattice and S occupying another FCC sublattice. There are two sodium atoms, two antimony atoms and four sulfur atoms per unit cell. Our HSE06 relaxed lattice parameters are a = 5.874 Å , b = 5.874 Å , c = 6.84 Å , = 113.18°, = 113.18°, = 90.87°, in agreement with the results reported in Ref. [31]. Compared to the ideal rocksalt structure, the fully relaxed structure

Fig. 1. (a) Rocksalt-derived P1¯ crystal structure of NaSbS2 with Na (green) and Sb (red) occupying one FCC sublattice and S (blue) occupying the other FCC sublattice. (b) Lengths of the NaeS and SbeS bonds around one S anion. (c) Structure viewed along the b axis. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 323

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Fig. 2. (a) HSE06 calculated band structure of NaSbS2 with a quasi-direct band gap. The VBM is located at the point Y (0.5 0.5 0) and the CBM is at the point M (0.5 0.5 0.5). (b) High symmetry k points in the Brillouin zone. (c) Calculated optical absorption coefficient along three directions and the shaded area denotes the energy range of the visible sunlight.

of NaSbS2 has a distortion deviated from the ideal rocksalt structure, in which the bond lengths between Sb and four neighboring S (2.4–2.8 Å ) are distinctly shorter than those between Sb and the other two neighboring S (3.4–3.5 Å ). In contrast, all the NaeS bond lengths are similar (∼2.9 Å ). In Fig. 1(b), we show the bond lengths of the three SbeS bonds and three NaeS bonds around one S anion. Obviously, the S anion is bonded strongly with three Na and two Sb, while the other Sb is far from the S anion with a distance around 3.45 Å , so the anion S is actually bonded with only five cations in the distorted rocksalt-derived structure.

3.3. Carrier effective masses As we know, the carrier mobility is critical to the photovoltaic performance of semiconductors because the carrier mobility influences the diffusion length of the carriers directly. For defect-free semiconductor crystals, the carrier mobility is mainly determined by the effective masses, which depends on the band dispersion near the valence (for hole carriers) and conduction (for electron carriers) band edges, i.e., a flat valance band near the valence band maximum (VBM) state leads to a large hole effective mass, while a flat conduction band near the conduction band minimum (CBM) state leads to a large electron effective mass. Since the crystal structure of NaSbS2 is distorted from the high-symmetry rocksalt structure, it is not clear whether the lower symmetry will cause the anisotropy in the carrier transport and thus influence the device design. In Table 1, we calculated the effective masses of the hole (mh) and electron (me) carriers along the x, y and z directions. Because of the large dispersion of the valance band edge which is composed mainly of the antibonding states of the Sb 5s and S 3p hybridization, the effective masses of holes are only 0.298m0 and 0.296m0 along the x and y direction, respectively. In contrast, the effective mass of holes along the z direction is much larger, 0.931m0, almost three times larger than those along the x and y directions, showing that the hole transport is anisotropic in the rocksalt-derived NaSbS2. The calculated effective masses of the electron carriers are generally larger than those of the holes along all the three directions. Along the x and y directions, the difference is small, however, the difference is very large along the z direction, 3.639m0 versa 0.931m0. The large difference between the x-y and the z effective masses of electron carriers indicates that the anisotropy is very serious for the electron transport in the rocksalt-derived NaSbS2, especially the electron transport along the z direction is very poor. Based on this, we can predict that the oriental control of the synthesized NaSbS2 samples is very important for

3.2. Electronic band structure and optical absorption The calculated band structure of NaSbS2 is shown in Fig. 2 (a), and the corresponding high-symmetry k points in the Brillouin zone are shown in Fig. 2(b). From Fig. 2(a), we can find that the valence band maximum (VBM) state is located at the k-point Y (0.5 0.5 0), while the conduction band minimum (CBM) is at the k-point M (0.5 0.5 0.5), leading to an indirect band gap of 1.64 eV which agrees with the previous experimental results of 1.5–1.8 eV [22,25]. Notably, the direct band gap at the Y point is only 1.69 eV, only slightly larger than the indirect band gap, showing a quasi-direct band gap which may impede the carrier recombination and thus increase the lifetime of minority carriers as pointed out in Ref. [31]. As the band gap is close to the optimal band gap (1.4–1.5 eV) for single-junction solar cells [32], NaSbS2 may be a potential high-efficiency light-absorber semiconductor. In order to evaluate the optical absorption of the visible light, we also calculated the absorption coefficient as shown in Fig. 2(c). The calculated absorption coefficient in the energy region (about 1.7–3.2 eV) can be as high as 104-105 cm−1, consistent with the experimentally measured value [25]. The large absorption coefficient indicates that the optical transition is symmetry-allowed across the direct band gap at the Y point (1.69 eV). Furthermore, the absorption edges along the x, y and z directions (calculated from the xx, yy and zz diagonal elements of the dielectric constant matrix) almost overlap, showing that the optical absorption coefficients are isotropic. Therefore, the absorption of the visible light is not sensitive to the orientation of the synthesized samples.

Table 1 Calculated effective masses (in the unit of the electron mass m0) of electron and hole carriers along the x, y and z directions.

324

Direction

me/m0

mh/m0

x [100] y [010] z [001]

0.342 0.335 3.639

0.298 0.296 0.931

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Fig. 3. Plot of the squared wavefunction of the VBM state: (a) viewed along the a axis and (c) viewed along the c axis, and the plot of the squared wavefunction of the CBM state: (b) viewed along the a axis and (d) viewed along the c axis.

achieving high photovoltaic performance, i.e., the NaSbS2 samples should have its a or b axis perpendicular to the p-n junction interface so that the carrier transport is mainly along the x or y directions. To understand the origin of the large anisotropy in the calculated effectives masses, we calculated the squared wavefunction of the VBM and CBM states in Fig. 3. Obviously the VBM wavefunction is weakly connected along the z direction (shown in Fig. 3(a)), but closely connected in the x-y plane (shown in Fig. 3(c)), so the transport of hole carriers is difficult along the z direction but easy in the x-y plane. The CBM wavefunction has the similar character with weak connection between different x-y layers, i.e., the CBM wavefunction is closely connected and becomes even layered in different x-y planes (shown in Fig. 3(b) and (d)), so the x and y effective masses of the electrons are small and the z effective mass is very large. 3.4. Band alignment

Fig. 4. Band alignment of NaSbS2, CdS and other high-efficiency photovoltaic semiconductors.

Band offset (band alignment) between two semiconductors is a very important parameter for designing the heterojunction devices. Since CdS has a suitable band alignment relative to CdTe, CuInSe2 and CuGaSe2, it is used as the n-type buffer layer in both the CdTe and Cu (In,Ga)Se2 solar cells. Here we calculated the band offset between NaSbS2 and CdS, as shown in Fig. 4 where the band offsets relative to other high-efficiency light-absorber semiconductors such as CdTe, CuGaSe2, CuGaSe2 and MAPbI3 are also shown [33–37]. When calculating the band offset between NaSbS2 and CdS, we used the slab model with the VBM levels of these semiconductors referenced to the vacuum level. As we can see, the VBM of NaSbS2 (−5.21 eV) is slightly lower than those of CdTe (−5.12 eV), CuInSe2 (−5.15 eV) and CuGaSe2 (−5.12 eV), but significantly higher than that of MAPbI3 (−5.92 eV). It was well known that the high valence band edge of CuInSe2 and CuGaSe2 results from the hybridization between Cu 3d and Se 4p states, whose antibonding state composes the VBM state and pushes the VBM level up. Similarly, the VBM state of NaSbS2 is composed of the antibonding state of the hybridization between the Sb 5s and S 3p orbitals, which increases the dispersion of the top valence band and pushes the VBM level up too. In this way, we can understand why the valence band edge of NaSbS2 is almost as high as those of CuInSe2 and CuGaSe. Owing to the relatively large band gap of 1.64 eV, the CBM level of NaSbS2 is also high compared to other photovoltaic semiconductors. According to the doping limit rule [38], it is difficult to dope a

semiconductor to n-type if its CBM level is high, and it is easier to dope a semiconductor to p-type if its VBM level is high. Because of the high CBM and VBM levels of NaSbS2, we predict that it should be hard to dope NaSbS2 to n-type but easier to dope NaSbS2 to p-type. Furthermore, considering that the NaSbS2/CdS band alignment is similar to those of CdTe/CdS and CuGaSe2/CdS, we propose that CdS can also be used as a potential buffer layer in the NaSbS2 solar cells, forming a pNaSbS2/n-CdS junction. 3.5. Intrinsic point defects Besides the band gap and band structure, the properties of the point defects in semiconductors are also critical to the photovoltaic performance since they can produce electron or hole carriers, thus increasing the electrical conductivity, and also induce the non-radiative recombination of electron and hole pairs, thus limiting the lifetime of minority carriers. Therefore, we also calculated the properties of the point defects in NaSbS2. A 96-atom supercell and single k-point in the Brillouin zone are used for the calculation of defect properties. The convergence test shows that the formation energy difference is only 0.01 eV between the calculations with the cutoff energy of 300 eV and 325

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400 eV, so the cutoff energy is set to 300 eV for saving the computational cost. The formation energy Hf ( , q) of a point defect is a function of elemental chemical potentials as well as the electronic Fermi level, following [39,40].

Hf ( , q) = E ( , q)

E (host ) +

ni [µi + E (i)] + q (EF + EVBM ) (1)

where E ( , q) is the total energy of the supercell with a defect in the charge state q, E (host ) is the total energy of the host supercell without any defects. ni is the number of atoms added into (ni = 1) or removed from (ni = +1) the supercell for the element i during the formation of the defect. µi is the elemental chemical potential referenced to the total energy E (i) of the elemental solid or gas phase. EF is the Fermi energy referenced to the VBM level, ranging from 0 to the value of the band gap, and EVBM is the eigenenergy of the VBM level. According to Eq. (1), the defect formation energy depends on the elemental chemical potentials, so the range of the chemical potentials should be determined first. The range can be determined through considering a series of thermodynamic limits to the chemical potentials. If the compound NaSbS2 is stable at the equilibrium state, the chemical potentials of all the component elements must satisfy,

µNa + µSb + 2µS = Hf (NaSbS2) =

2.953 eV

Fig. 5. Stable chemical potential region of NaSbS2. The shaded area shows the chemical potentials where NaSbS2 is thermodynamically stable against all the secondary phase compounds. Points A, B and C denote the S-rich, moderate and S-poor conditions in order.

(2)

where Hf (NaSbS2) is the formation enthalpy of NaSbS2. If the compound NaSbS2 is synthesized without the coexistence of any secondary compounds such as NaS, Na2S, NaS2, Na2S5, NaSb, Na3Sb, Sb2S3 and Na3SbS4, the chemical potentials must be limited by the following relations,

µNa + µS < Hf (NaS) =

1.804 eV

2µNa + µS < Hf (Na2S) =

3.437 eV

µNa + 2µS < Hf (NaS2) =

1.964 eV

2µNa + 5µS < Hf (Na2S5) = µNa + µSb < Hf (NaSb) =

contribution to the p-type conductivity is small. The formation energies of the neutral donor defects are generally higher than those of the neutral acceptors. Among all the donors, Si has the lowest formation energy, however, Si prefers the neutral charge state in a very wide range of the Fermi energy (0.1–1.6 eV), so it will not produce any electron carriers and do not increase the n-type conductivity when the Fermi energy is higher than 0.1 eV. Other donor defects such as VS and Nai have higher formation energies in the neutral state and the values are lower than 1 eV only when the Fermi energy is below 0.3 eV. Therefore, the competition of these acceptor and donor defects makes the Fermi level limited to below 0.3 eV and the synthesized NaSbS2 samples under the S-rich condition should always be p-type, otherwise the acceptor NaSb will form spontaneously. When the chemical potential is changed to the point B (moderate condition), the formation energies of all the acceptors except VNa increase significantly, and VNa keeps almost the same formation energy as that under the S-rich condition. Thus, VNa have the lowest formation energy among the acceptors when the Fermi energy is below 0.8 eV. For the donors, the formation energies of VS and SbNa are decreased significantly and have the lowest formation energies. VS is a deep-level donor defect with its (2+/0) transition energy level at 0.55 eV, so it may act as a detrimental non-radiative recombination center. SbNa acts a deep-level donor when the Fermi energy is close to the VBM level, but it becomes a deep-level acceptor when the Fermi energy is high and closer to the CBM level. Under this moderate condition (point B), the Fermi level should be higher and the hole concentration should be lower than that under the S-rich condition (point A). Meanwhile, the concentration of the deep-level donors is higher, which is detrimental to the minority carrier lifetime and the photovoltaic performance. Therefore, this condition is not as good as the S-rich condition for fabricating solar cells. Finally, when the condition becomes S-poor, NaSb predominates among all the acceptor defects and VS and Nai predominate among all the donor defects. The charge-compensation effect between the acceptor and donor defects makes Fermi level located at 0.4 eV above the VBM level. Therefore, the NaSbS2 sample synthesized under the S-poor condition still shows p-type conductivity. Compared to NaSb, VS and Nai, other defects have much higher formation energies, so NaSb, VS and Nai will form at a very high concentration but the concentration of

3.818 eV 0.799 eV

3µNa + µSb < Hf (Na3Sb) =

2.005 eV

2µSb + 3µS < Hf (Sb2 S3) =

1.418 eV

3µNa + µSb + 4µS < Hf (Na3SbS4) =

6.796 eV

(3)

If the compound NaSbS2 is synthesized without the coexistence of any elemental phases of Na, Sb and S, the chemical potentials must be limited by,

µNa < 0, µSb < 0, µS < 0

(4)

Considering these limits (2), (3) and (4), the chemical potential range can be determined, as shown in Fig. 5 (shaded area surrounded by the A, B, C points). The point A ( µNa = 1.963 eV , µSb = 0.99 eV , µS = 0 ) denotes the S-rich condition, B (µNa = 2.007 eV , µSb = 0, µS = 0.473 eV ) denotes a moderate condition, while C ( µNa = 1.307 eV , µSb = 0, µS = 0.823 eV ) denotes the S-poor condition. In the following, we will discuss the defect properties of the NaSbS2 samples synthesized under the three different conditions A, B and C. The calculated formation energies of a series of intrinsic point defects as a function of Fermi level are plotted in Fig. 6. For the ionized donor defects, the dependence of their formation energies has a positive slope while for the ionized acceptor defects, the dependence has a positive slope. The turning points of the lines in Fig. 6 denote the transition energy levels of defects at which the formation energies of the defects in different charge states are equal. Under the chemical potential condition A (S-rich condition), NaSb has the lowest formation energy (0.5 eV) among all the acceptor defects at the neutral state and the formation energy decreases to a negative value when the Fermi energy is higher than 0.3 eV. Four other acceptors, VSb, VNa, SSb and SNa have higher formation energies, so their 326

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Fig. 6. Calculated formation energies of intrinsic defects in NaSbS2 as a function of the Fermi level at three different chemical potential points A，B and C.

other defects can be neglected. Comparing the formation energies of the defects under the S-rich, moderate or S-poor conditions, we can see that the undoped NaSbS2 always shows p-type conductivity due to the formation of these intrinsic point defects, and it is difficult to dope it to n-type because of the thermodynamic limit of the acceptor defects, consistent with the prediction according to the dope limiting rule and the high valence and conduction band edge levels. The transition energy levels of the low-energy acceptors such as NaSb, VNa, SNa and SSb are all shallow in the band gap, so they only increase the hole carrier concentration and do not limit the minority carrier lifetime, i.e., they are benign to the photovoltaic performance of the NaSbS2 solar cells. However, most of the donors except Nai produce very deep levels in the band gap. Such a large discrepancy between the acceptor and donor defects results from the character of the VBM and CBM states, i.e., NaSbS2 has a VBM state with the antibonding character of the hybridization between Sb-5s and S-3p states, which pushes the VBM level up and makes the acceptor levels shallow; whereas the CBM state is an antibonding state of the Sb-5p and S-3p hybridization, which pushes the CBM level up and makes the donor level deep (the formation of donor defects weakens the hybridization dramatically, so the donor level is much lower than the CBM level). The deep-level donors (VS and SbNa) have higher concentration under the S-poor and moderate conditions, but much lower concentration under the S-rich conditions. Since the p-type conductivity (hole carrier concentration) is higher and the concentration of deep-level donor defects is lower under the S-rich condition, we propose that the S-rich condition should be adopted for fabricating high-efficiency NaSbS2 solar cells.

high-symmetry cubic rocksalt structure, so the VBM and CBM wavefunctions tend to be distributed in different x-y layers and weakly connected between different layers, so the effective masses of the electron and hole carriers (thus the carrier transport properties) are highly anisotropic with much larger effective masses along the z direction than in the x-y plane. Therefore, the orientational control of the NaSbS2 thin films should be important for enhancing the photovoltaic performance. Through calculating the band offsets between NaSbS2 and CdS as well as other light-absorber semiconductors, we found that the valence and conduction band edges of NaSbS2 are both close to those of CuGaSe2, so the n-CdS/p-CuGaSe2 device structure can be inherited to form the n-CdS/p-NaSbS2 solar cells. Because the valence band edge state of NaSbS2 is the antibonding state of the Sb 5s and S 3p hybridization, the valence band edge level is high, which makes the acceptor defects (NaSb antisites and Na vacancies) have very high concentration and shallow transition energy levels, so the synthesized NaSbS2 are always self-doped to p-type. In contrast, the donor defects (S vacancies and SbNa antisites) have deeper levels than the acceptor defects, so they are possible recombination-center defects and detrimental to the photovoltaic performance. Fortunately, their concentration is low under the S-rich condition and meanwhile the concentration of the shallow acceptor defects and hole carriers is high, so we propose that the S-rich condition should be adopted for fabricating high-efficiency NaSbS2 solar cells. Acknowledgements This work was supported by National Natural Science Foundation of China (NSFC) under grant Nos. 61574059, 61722402, 61704097 and 91833302, Science Challenge Project (TZ2018004), National Key Research and Development Program of China (2016YFB0700700), ShuGuang program (15SG20), Fok Ying Tung Education Foundation (161060) and CC of ECNU.

4. Conclusions In summary, we performed a systematical first-principles calculation study on the electronic, optical and defect properties of the novel earth-abundant photovoltaic semiconductor NaSbS2. We found that NaSbS2 in the rocksalt-derived ground-state structure has a quasi-direct band gap (the direct band gap of 1.69 eV is slightly larger than the indirect band gap of 1.64 eV) as well as very strong and isotropic optical absorption of the visible light, so it should be a good light-absorber semiconductor with a long minority carrier lifetime. However, its structure has a lower symmetry and is highly distorted relative to the

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