First-principles insights into the electronic structure, optical and band alignment properties of earth-abundant Cu2SrSnS4 solar absorber

Cu2SrSnS4 (CSTS) is a promising alternative candidate to Cu2ZnSnS4 (CZTS) for single- or multi-junction photovoltaics (PVs) owing to its efficient light-absorbing capability, earth-abundant, nontoxic constituents, and suitable defect properties. However, as a novel absorber material, several fundamental properties need to be characterized before further progress can be made in CSTS photovoltaics. In this letter, hybrid density functional theory (DFT) calculations have been used to comprehensively characterize for the first time, the electronic structure, band alignment, and optical properties of CSTS. It is demonstrated that CSTS possesses the ideal electronic structure (direct band gap of 1.98 eV and small photocarrier effective masses) and optical properties (high extinction coefficient and wide absorption) suitable for photovoltaic applications. Simulated X-ray photoelectron spectroscopy (XPS) valence band spectra using variable excitation energies show that Cu-3d electronic state dominates the valence band maximum of CSTS. Furthermore, the vacuum-aligned band diagram between CSTS and other common absorbers (CZTS, CIGS, CdTe) and the common n-type partner materials (CdS, ZnO) was constructed, which indicate staggered type-II band alignment at the CSTS/CdS and CSTS/ZnO interfaces. Based on these results, interface band offset engineering and alternative device architectures are suggested to improve charge carrier separation and power conversion efficiencies of CSTS.

www.nature.com/scientificreports/ lattice 18 . The resulting Cu 2 BaSnS 4 (CBTS) and Cu 2 SrSnS 4 (CSTS) compounds exhibit better defect properties than kesterite Cu 2 ZnSnS 4 (CZTS) because of the larger size of Ba 2+ (1.49 Å) and Sr 2+ (1.32 Å) and the lower structural symmetry, which can suppress the formation of antisite defects 19 . CSTS compound is of considerable interest for photovoltaics owing to its sharp band edges and suitable band gap (1.78-2.1 eV) for a top absorber in tandem cells. CSTS has trigonal crystal structure [20][21][22][23] , which features CuS 4 and SnS 4 tetrahedra that share common corners, forming a 3D network analogous to kesterite. However, unlike the kesterite structure, the large electropositive cations Sr 2+ /Ba 2+ sit inside an S 8 square antiprism. The differences in size and the coordination environments around the Cu + , Sr 2+ /Ba 2+ , and Sn 4+ should discourage the formation of Cu-Sr/Ba and Sn-Sr/Ba antisite disorder. Previous theoretical studies of the optoelectronic and defect properties of Cu 2 -II-SnS 4 (II = Ba, Sr) with the P3 1 phase, predicted a direct bandgap of 1.79 (1.78) eV for CBTS (CSTS) 19 . Recent first-principles calculations of the phonon dispersion of CSTS and CBTS show that the compounds are stable at ambient pressure 24 . However, there is no systematic theoretical investigation dedicated to elucidating the structural, optoelectronic, and interface band alignment properties of these compounds, which makes this investigation timely. Herein, a comprehensive hybrid density functional theory (DFT) description of the electronic structure, energy-dependent X-ray photoelectron spectra (XPS) valence band spectra at variable excitation energies, the optical, surface, and interface properties of CSTS are presented. CSTS is demonstrated to possess a direct bandgap of 1.98 eV, a high extinction coefficient, and broad absorption, suggesting that CSTS can harvest a larger fraction of the solar spectrum when used as an active absorber layer even in ultrathin film. Analysis of the simulated valence band photoemission results provide strong evidence that Cu-3d electronic states dominate the valence band maximum of CSTS. Lastly, the structure and properties of the most stable (100) and (110) surfaces of CSTS were systematically characterized, and the fundamental energy band alignment between CSTS and other common absorbers (CZTS, CIGS, CdTe) and common n-type partner materials (CdS, ZnO) is constructed and discussed.

Material and methods
Computational details. The first-principles density functional theory calculations were carried out within the VASP -Vienna Ab initio Simulation Package 25,26 . The interactions between the valence and core electrons was described using projected augmented wave (PAW) method 27 . Geometry optimizations were performed using the generalized gradient approximation PBE (Perdew-Burke-Ernzerhof) functional 28 . The electronic structure and optical properties were predicted using the screened hybrid functional HSE06 29 with a 25% Hartree-Fock exchange. A plane-wave energy cut-off of 600 eV and Monkhorst-Pack 30 K-points mesh of 7 × 7 × 3 was used to converge the total energy of the CSTS to within 10 −6 eV and the residual forces on all relaxed atoms to 10 −3 eVÅ −1 .
The electrostatic potential of the surfaces was averaged along the c-direction, using the MacroDensity package 31,32 . A 20 Å vacuum region was added the c-direction to avoid any spurious interactions between periodic slabs. By aligning the slab vacuum level to the bulk core-level eigenvalues in the center of the slab, using S 1s core level as reference state, the ionization potential (IP) can be determined. The work function (Φ) is calculated as: Φ = E v −E F , where E v and E F are the vacuum and the Fermi level, respectively. In all calculations, dipole correction perpendicular to the surfaces was accounted for. The XPS valence band spectra were simulated using the GALORE code 33 , a materials design tool for transforming ab-initio partial density of states (PDOS) to XPS spectra by employing the Gelius method 34,35 to apply weightings to the atom PDOS using photoionization cross-sections from reference data.

Results and discussion
Crystal structure. CSTS adopts the trigonal space group P3 1 20 , with lattice parameters a = 6.25 Å, c = 15.57 Å (Fig. 1a). The trigonal structure features CuS 4 and SnS 4 tetrahedra that share common corners, forming a 3D network analogous to kesterite. But unlike the kesterite structure, the Sr 2+ cation sits inside an S 8 square antiprism. The primitive unit cell contains 24 atoms (3 Sr, 6 Cu, 3 Sn, and 12 S atoms). A full unit cell relaxation yielded a strain-free CSTS with lattice parameters a = 6.300 Å, and c = 15.495 Å, which compares closely with experimental 20 and previous theoretical 19,36,37 results. The average Sr-S, Cu-S, and Sn-S relaxed bond distances are predicted at 2.309, 3.092, and 2.427 Å, respectively. Based on the optimized structure, the powder diffraction pattern of CSTS is simulated using the VESTA Crystallographic software 38 as shown in Fig. 1b. All assigned peaks in the simulated DFT spectrum match very closely with the experimental X-ray Diffraction (XRD) patterns of Crovetto et al. 23 .
Electronic band structure and related properties. The band structure (Fig. 2a) shows that CSTS is a direct bandgap material at the Brillouin zone's gamma-point. The bandgap is predicted at 1.98 eV, which is in good agreement with known experimental (1.78-2.1 eV) [21][22][23] and previous DFT predictions 19,37,38 . From the predicted band structure, the effective masses of electrons ( m * e ) and holes ( m * h ) were calculated by fitting the energy of the conduction band minimum and valence band maximum, respectively, to a quadratic polynomial in the The effective masses are intricately linked to the diffusion coefficient ( D = k B T e µ ) and mobility ( µ = e τ m * ) of the charge carriers in a semiconductor. Generally, small effective masses give rise to higher charge carrier mobility and diffusion 39 . Summarized in Table 1   Simulated XPS valence band spectra. The XPS valence band spectra of a semiconductor are interpreted by direct comparison with DFT calculated projected density of states (PDOS) weighted by the photoionization cross-sections, and good agreement is generally observed [43][44][45][46][47] . The non-weighted of PDOS of CSTS (Fig. 2b) shows that the valence band maximum (VBM) is dominated by Cu-3d and S-2p states, whereas the conduction band minimum (CBM) is dominated by S-3p and Sn-5s, with small contributions from Cu-3d and S-1s states. The photoionization cross-section depends on the probe radiation, the orbital shapes, and their energies. To account for this, the GALORE software 33 employs the Gelius method 34,35 to apply weightings to the atom projected PDOS using the photoionization cross-sections formulated by Scofield 48 . The simulated valence band photoelectron spectrum of CSTS at Kα1 (1486 eV), as well as at 4068 eV and 8133 eV photon energies (i.e., soft to hard X-ray ionization photon energy (hν)) are shown in Fig. 3. The main valence band has a spectral onset from 0.0 eV and expands up to 7 eV in binding energy. Besides, broad peaks are found on the high-bindingenergy side of the main valence band, centered at 8 eV and 14 eV binding energy. Three spectral features can be assigned: I for the main valence band region and II and III for the broad satellite features at 8 eV and 14 eV. The intensity of I relative to II and III continuously increases while moving from soft to hard X-ray ionization photon energy (hν), resulting in a change in the valence band spectrum's shape. At the same time, switching from soft to hard X-ray hν leads to a marked increase in the broad satellite features' relative intensity at 8 eV and 14 eV high binding energy sides. The observed changes in the valence band spectral feature originate from the hν-dependence of the photoionization cross-section of the atomic orbitals contributing to the valence levels. Due to their higher photoionization cross-section (Fig. 3d), Cu-3d photoelectrons dominate the main valence band region (I) for CSTS. The high binding energy satellite broad feature at 8 eV can be assigned mainly to the contribution from Sn-5s, whereas the broad feature at 14 eV can be assigned to contributions mainly from S-3s. The Cu-3d photoionization cross-section decreases much rapidly than Cu-3p and S-3p with photon energy, so at higher photon energies, its contribution becomes less significant (Fig. 3a-c). Although there are no available experimental XPS data to directly compare with the simulated XPS spectra, the simulated XPS spectra at different excitation energies may help clarify future experiments. The results can also help assign the atomic orbital contributions to various features (peaks) observed in X-ray photoelectron spectroscopy measurements.
Optical properties. The optical properties, including dielectric function, optical absorption and conductivity, reflectivity, refractive index, and the extinction coefficient for CSTS have been characterized for the photon energy from 0 to 10 eV. The calculated real (dispersive, ε 1 ) and imaginary (absorptive, ε 2 ) parts of the dielectric function for CSTS are shown in Fig. 4a. The results show that CSTS has a higher dielectric constant at low energy region (from 0 to 2 eV) with the onset dielectric constant predicted at 8.25 (Fig. 4a), which compares closely to that of Cu 2 ZnSnSe 4 reported at 8.64. A high dielectric constant is a desired property for potential photovoltaic materials as it indicates an increased ability to screen charge and decrease charge carrier recombination rates [49][50][51][52][53][54] . Therefore, the high dielectric constant predicted for CSTS makes it an attractive candidate to achieve enhanced photovoltaic performance. The combination of large dielectric constants and low effective masses calculated from the electronic band structure is expected to promote effective ionization of defect states 55 , leading to fewer deep trap states in CSTS. It can be seen from the absorption spectra (Fig. 4b) that the absorption starts at around 1.98 eV, which corresponds to the fundamental bandgap. CSTS exhibits a high absorption coefficient in the order of 10 4 cm −1 in the visible light region, which makes it a suitable material for the photovoltaic application. For completeness of the optical properties, the optical conductivity (Fig. 4c), extinction coefficient (Fig. 4d), reflectivity (Fig. 4e), and refractive index (Fig. 4f) for CSTS are calculated. The optical conductivity is a good gauge of photoconductivity that could shed light on the electrical conductivity of the material 56,57 . The features of the optical conductivity are quite identical with that of the absorption spectra, with the highest absorption and optical conductivity predicted at 2.1 eV. The low reflectivity (~ 25%) and high extinction coefficient (~ 3.7) for CSTS also show that this material is ideal for photovoltaic and optoelectronic applications. The high extinction coefficient and wide absorption for CSTS indicate that it can harvest a larger fraction of the solar spectrum when  58 and CdTe (~ 3.0 at 600 nm) 59 , is also ideal for photovoltaic application. When compared with perovskite materials, the refractive index of CSTS if higher than that of CH 3 NH 3 PbI 3 (2.61 at 633 nm) 60 and CsPbBr 3 (1.85-2.30 at 400-530 nm) 61 .
Surface and interface properties. As a new solar absorber material, studies dedicated to the characterisation of the surface structure, composition, and relative stabilities of the major surfaces of CSTS are limited. Evaluation of the surface and interfacial properties of CSTS would ultimately dictate its suitability as a thin film solar absorber material. Therefore, the structure and properties of the two most stable (100) and (110) surfaces of CSTS have been systematically characterized. Each surface has two non-dipolar terminations (denoted as termination A and B), both of which were characterized to determine the most stable one. Shown in Fig. 5 are the relaxed structures of the (100) and (110) surfaces of CSTS, with the surface energy of the most stable termination-A calculated at 0.48 and 0.67 Jm −2 , respectively, (see Table 2). These results suggest that the (100) is thermodynamically more stable than the (110) surface. The work function (Φ) of termination A (B) of the CSTS (100) is calculated at 4.76 (4.38 eV) vs. vacuum as shown in Fig. 6a,b. For the CSTS (110) surface, the Φ of termination A (B) is 4.02 (4.63 eV), as shown in Fig. 6c,d.
Using the most stable CSTS (100) surface, the band alignment of CSTS is shown in Fig. 7. The valence band energy (ionization potential, IP) of CSTS (100) was found to be 5.50 eV below the vacuum level, and is noticeably very similar to other commonly used solar absorbers [CZTS (5.80 eV) 62 , CIGS (5.67) 63 , and CdTe (5.69 eV) 64 ]. The band alignments for common n-type partner materials (CdS and ZnO) is also shown in Fig. 7. Considering that the magnitude of the band offset at the absorber/buffer interface controls transport phenomena and characteristics of fabricated devices, an accurate determination of band offsets at semiconductor heterojunctions interfaces is also of great interest. From Fig. 7, a staggered type-II band alignment is predicted to exist between the valence and conduction bands at the CSTS/CdS and CSTS/ZnO interfaces. The conduction band offset (CBO) and the valence band offset (VBO) at the CSTS/CdS interface are calculated at 0.76 and 1.20 eV. At the CSTS/ZnO, the CBO and VBO are estimated at 0.92 and 2.18 eV, respectively. These results suggest that CdS would be a more appropriate choice of partner material for CSTS from an electronic point of view, because of the smaller CBO between CSTS and CdS, which is also often the first successful choice as the n-type partner material

Summary and conclusions
In summary, the electronic structure, optical properties, and energy band alignment of CSTS have been systematically characterized for the first time employing hybrid density functional theory calculations. It is demonstrated CSTS possesses appropriate electronic structures and optical properties for solar energy applications. Analysis of the simulated valence band photoemission results provides strong evidence that Cu-3d electronic states dominate the valence band maximum of CSTS. A staggered type-II band alignment is predicted at the CSTS/CdS and CSTS/ZnO interfaces, with CdS giving a smaller conduction band offset than ZnO. These results suggest that CSTS is a suitable earth-abundant and low-cost absorber material for efficient solar device fabrication although further investigations of interface and band offset engineering to improve charge carrier separation will be needed in the near future.  www.nature.com/scientificreports/   www.nature.com/scientificreports/ Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/.