with Enhanced Optical Properties and Intrinsic Thermodynamic Stabili

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C: Energy Conversion and Storage; Energy and Charge Transport 3

Searching for Photoactive Polymorphs of CsNbQ (Q=O,S,Se,Te) with Enhanced Optical Properties and Intrinsic Thermodynamic Stabilities Heesoo Park, Fahhad H. Alharbi, Stefano Sanvito, Nouar Tabet, and Fedwa El-Mellouhi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b01787 • Publication Date (Web): 04 Apr 2018 Downloaded from http://pubs.acs.org on April 4, 2018

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The Journal of Physical Chemistry

Searching for Photoactive Polymorphs of CsNbQ3 (Q=O,S,Se,Te) with Enhanced Optical Properties and Intrinsic Thermodynamic Stabilities Heesoo Park,∗,† Fahhad H Alharbi,†,§ Stefano Sanvito,‡ Nouar Tabet,¶,§ and Fedwa El-Mellouhi∗,¶ †Qatar Environment and Energy Research Institute, Hamad Bin Khalifa University, PO BOX 34110, Doha, Qatar ‡School of Physics, AMBER and CRANN Institute, Trinity College, Dublin 2, Ireland ¶Qatar Environment and Energy Research Institute, Hamad Bin Khalifa University, Doha, Qatar §College of Science and Engineering, Hamad Bin Khalifa University, Doha, Qatar E-mail: [email protected]; [email protected]

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Nowadays materials design efforts to seek non-toxic and cost-effective photoactive semiconductors with a given chemical composition face the challenge of the coexistence of more than one configuration or crystal structure; so-called polymorphism. Polymorphs for multicomponent materials might exhibit various crystal structures by unique connectivity modes, hence creating polyhedral networks extended across the three dimensional space or restricted along specific directions. A key component in photoactive materials design consists in the assessment of the thermodynamic stability of the various polymorphs alongside with their targeted properties such as the optical band gap and the photon absorption efficiency. In this work, we conduct density functional theory (DFT) calculations on cesium-niobate and cesium-niobium-chalcogenide CsNbO3-x Qx (Q=S,Se,Te, and x=0,1,2,3) compounds aiming at identifying intrinsically stable polymorphs with high ability to absorb visible light. The connectivity between niobiumcation-centered polyhedra in the different polymorphs favors low-dimensionality due to the large radius of the Cs cation. We identify unreported compounds, CsNbS3 and CsNbSe3 in the orthorhombic phase, where the polyhedra compose networks of low-dimensional connectivity as thermodynamically stable and strong visible-light absorbers.

Introduction Lead-halide perovskites have emerged as an uprising class in the field of photovoltaics (PV), 1–4 owing to their high power conversion efficiencies (PCE) associated with a lowcost chemical processing synthesis. The methylammonium lead iodide perovskite (MAPbI3 ) has drawn significant attention as an efficient material for photovoltaic applications displaying PCE of up to 22.1%. 4 However, the pace of the conversion efficiencies has slowed down over the past few years, as the theoretical limit has been approached. We witness several modifications of MAPbI3 experiencing its intrinsic instability despite the enhancement of the

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efficiencies. Thus, immense efforts are being devoted to solve the two main challenges that stand against their deployment in the PV market namely the degradation under operating conditions and the toxicity of the lead-containing compounds. The quest for innovative ways to circumvent the obstacles has resulted in several reports proposing new photoactive materials with a robust power conversion efficiency. 5–10 Stability enhancement strategies consisted of halide mixing, replacement of anion with SCN− , and cation mixing by introduction of various organic or inorgnic cations. 7,11–21 A steady progress has been accomplished toward both stability and toxicity with the partial replacement of Pb with Sn and the complete substitution of the organic cation with Cs+ . The inorganic compound CsPb0.9 Sn0.1I Br2 led to a PCE up to 11.33% with a long-lasting thermodynamic stability. 22 Until recently, most of the focus was on three-dimensional (3D) connected networks of metal cations and anions owing to the efficient charge separation. This industrious effort targeting 3D connected networks with the perovskite structure is motivated by the proposed correlation between crystallographic network connectivity and the electronic dimensionality favoring homogeneous optical properties and charge carrier transport. 23 At the same time, efforts toward stabilizing the hybrid perovskites have led to the introduction of larger cations such as HOOC(CH2 )4 NH3 . These break the 3D connectivity of the PbI6 octahedra producing significantly more stable 2D-3D perovskite networks. Some 2D-3D perovskite networks show 11.2% efficiency and they are stable for more than 10,000 hours (1 year) with zero loss in performances measured under controlled standard conditions. 24 Recently, photo-absorbing compounds with lower-dimensional polyhedral connectivity, which is distinguished from conventional cubic perovskites, have been utilized in PV devices. 25–27 Such lower-dimensional polyhedral connectivity networks might suffer from charge transport properties inferior to those at the 3D polyhedral connectivity perovskites, 28,29 yet their successful operation in PV devices opens the door for the exploration of non-perovskite materials. Interestingly, solar cells based on 2D (CH3 NH3 )2 Pb(SCN)2 I2 perovskites have achieved decent power conver-

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sion efficiency and showed a superior defect tolerance with the tendency to exhibit p-type conductivity with a relatively long carrier lifetime. 30 Among these efforts, there has also been progress in reducing the large band gaps of perovskite oxides to match the visible light radiation spectrum. 31–33 These efforts are motivated by the fact that perovskite oxides are more thermodynamically stable than hybrid perovskite halides, despite their large band gaps, usually above the visible spectrum absorption range. 34–37 We have recently reported the efficient band-gap reduction and the stability assessment of perovskite niobates with chemical formula NaNbO3-x Qx , where Q=S,Se,Te. 38 Alkali metals such as Li, Na, K, Rb and Cs have been reported to incorporate into monovalentcation site of the M NbO3 , where M are alkali metals. They have been synthesized successfully in various crystallographic phases. The increase in atomic number and hence cationic radius, namely Rb+ > K+ > Na+ > Li+ , results in the cubic perovskite becoming less stable in favor of orthorhombic or tetragonal perovskite phases. 37,39–41 However, a further increase in the cationic radius to that of Cs, to form CsNbO3 , results in breaking into non-perovskite structures, which are experimentally reported. 42 The crystal structure features edge-sharing octahedra in CsNbO3 forming quasi-one-dimensional (quasi-1D) chain networks. Previous high-throughput density functional theory (DFT) studies to simulate the perovskite structure of CsNbO3 have reported that it has a phase obtained by deforming the cubic perovskite structure. 6,43 In this work, using DFT, we explore the polymorphism of CsNbO3 and assess the thermodynamic stability of 3D-connected network perovskite structures as well as their energetic competition with experimentally known polymorphs, where the octahedra form networks of quasi-1D connectivity. Yet, the hybrid organic-inorganic perovskites are believed to surpass the fully inorganic ones as recently demonstrated by the more rapid interfacial charge transport. 44 The final goal of this design strategy is to assess the ability of the non-toxic niobate compounds to accommodate organic cations with an ionic radius comparable to Cs+ , such as methylammonium (CH3 NH3+ ). In addition, we aim at reducing the band gap of CsNbO3 polymorphs by replacement of oxygen with chalcogen ions

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at the anion sites. 38 While comparing the chemical composition of CsNbO3-x Qx (Q=S,Se,Te, and x=1,2,3) in various polymorphs where polyhedral network are formed differently, we find that the optical absorption can be enhanced in low-dimensional compounds by introducing chalcogens. We discuss in details the origin of the strong optical absorption of the stable compounds where the octahedra NbQ6 are formed in low dimensionality proposing them as new photoactive materials.

Computational Methods We performed density functional theory (DFT) calculations using the projector-augmented wave (PAW) method, 45,46 as implemented in VASP code. 47–49 The structures were fully relaxed with Perdew–Burke–Ernzerhof (PBE) 50,51 formulation of the generalized gradient approximation (GGA) of the electron exchange and correlation energy. When optimizing the structures, we conducted the relaxation in two steps in order to compare the phases within a given stoichiometry. The cell relaxation within each space group was followed by full relaxation where both the ions and cell were optimized without any structural constraint, as we optimized the volume and the shape of the cell as well as the atomic structure. The energies and forces were converged within 1.0 × 10−6 eV/atom and 1.0 × 10−2 eV/Å, respectively. The cutoff energy for the plane-waves was 520 eV. The k-points were sampled according to the Monkhorst-Pack automatic generation scheme with a 6 × 6 × 6 mesh for all unit cells. When we carried out HSE06 calculations for the band gap and the dielectric function, we sampled k-points with a Gamma-centered 4 × 4 × 4 grid. We adopted linear programming algorithm to obtain the minimum at a given chemical composition, which is represented by linear relationships. For example, as we take into account all possible decomposition reactions including the constituent elements, the energy

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above the convex hull of CsNbO2 S can be calculated as,

∆ECH (CsNbO2 S) = E(CsNbO2 S) − min {c1 E(Cs) + c2 E(Nb) ci

+ c3 E(O2 ) + c4 E(S8 ) + c5 E(Csa5 Nbb5 ) + c6 E(Csa6 Oo6 ) + c7 E(Csa7 Ss7 ) · · · + cn−1 E(Csan−1 Nbbn−1 Oon−1 ) + cn E(Csan Nbbn Ssn ) ,

where all the energies are the total energy of the corresponding stable compounds. In general, the ith compound consists of ai Cs, bi Nb, oi O, or si S atoms, and ci is its corresponding coefficient. The LP problem is solved with the constraints, X

ai ci = 1,

X

i

i

X

oi ci = 2,

X

i

bi ci = 1, s i ci = 1 ,

i

ensuring the correct stoichiometry of CsNbO2 S with ci ≥ 0. Consequently, we determined a compound to be stable by using the database available from Materials Project 52–54 and ICSD. 55 When estimating the formation energy through Pymatgen, 56–60 we took the optimized structure from Materials Project, while we relaxed the experimental structures of ICSD by carrying out DFT calculations at the PBE level. To avoid the total energy differences by the computational methods, we compared the energies in a consistent method for all the compounds, matching the computational level. We included anion corrections for oxide and sulfide compounds in order to have relative energies consistent with experimental values, since it is well known that GGA underestimates the total energies of O2 and S8 . 60–62

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Results and discussion Structural and the thermodynamic stability The structural stability of perovskite compounds strongly depends on the ionic radii of its constituents. In this work, while studying systemically cesium-niobate and cesium-niobiumchalcogenide CsNbO3-x Qx (Q=S,Se,Te, and x=0,1,2,3), we aim at exploring the possible improvements in the photoactive properties as function of the chalcogen content as well as its impact on the structural and thermodynamic stability. To the best of our knowledge, perovskites of CsNbO3 and their chalcogenized variations have not been reported experimentally. Elements in the chalcogen group have 6 valence electrons, so they share with oxygen the same chemical bonds character. The anionic radii become larger with increasing the atomic number from O, S, Se to Te. A preliminary estimation of the tolerance factor of the full chalchogen substituted oxygen cesium-niobates CsNbQ3 (Q=S,Se,Te) indicates that t decreases from 1.06 to 1.04 and 1.03 for CsNbS3 , CsNbSe3 and CsNbTe3 , respectively. Consequently, we may expect that chalcogenide perovskites are relatively more stable than perovskite oxides, as the Goldschmidt tolerance factor t approaches the ideal value of 1. Nonetheless, these reduced values of t of the perovskite chalcogenides still exceed the optimal tolerance factor to form a cubic structure, while at the same time they indicate better relative stabilities of the cubic perovskite structures compared to the full oxides. In what follows, we first explore the thermodynamic stabilities of CsNbO3-x Qx (Q=S,Se,Te, and x=0,1,2,3) polymorphs by constructing their phase diagram and by assessing their distance from the convex hull. We have considered CsNbO3 2 × 2 × 2 supercells obtained by relaxing the atomic coordinates constructed from the prototype cubic and tetragonal perovskite structure. All supercells contain 40 atoms as shown in Figure 1, with each polymorph being denoted by the structural features as discussed in the followings. The calculated lattice parameters are listed in Table S1 (supporting information). In the cubic phase, the polyhedral network

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(b) t CS -CsNbO3

(a) cCS -CsNbO3

Cs Nb

a c

O

a c

b

b

(c) oES -CsNbO3

c

b

b c

a

a

Figure 1: Relaxed structures of different CsNbO3 polymorphs. (a) Cubic phase with cornersharing octahedra and Pm¯3m space group (cCS -CsNbO3 ); (b) tetragonal phase with cornersharing square pyramids and P4/mm space group (tCS -CsNbO3 ); (c) orthorhombic phase with edge-sharing octahedra and P21 /c space group (oES -CsNbO3 ), the orthorhombic structure was taken from ICSD-1266. 42 Blue and red spheres represent Cs cation and O anions, respectively. Nb cations are located at the center of green-colored polyhedra. The unit cell is marked by dashed lines. consists of 3D-connected NbO6 octahedra, where Nb is at the center and it shares the corners with the adjacent octahedra. This polymorph adopts the cubic phase with space group Pm¯3m and the octahedra are connected by means of corner-shared (CS). This structure is denoted it as cCS -CsNbO3 . In the tetragonal phase, the polyhedral network consists of 2D connected NbO5 square pyramids exhibiting lower dimensional networks. We denote it herein as tCS -CsNbO3 , as the square pyramids show corner-shared connectivity. This polymorph results from an apical Nb−O bond having the shortest bond in an octahedron, while the opposite apical oxygen atom appears to be too far to form a Nb−O chemical bond by the distance of 4.4 Å. In tCS -CsNbO3 , the pyramidal coordination provides more room to

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accommodate the Cs cations than in the cubic phase. Hence, Nb and O form a NbO5 square pyramidal coordination, where the Nb cation is above the square plane, forming a 2D network with the P4/mm space group. In contrast, the experimentally reported polymorph of CsNbO3 with 40 atoms in an orthorhombic unit cell 42 in the P21 /c space group is composed of quasi-1D connected NbO6 octahedra, which are extended in edge-shared (ES) way along the a axis. This is denoted as oES -CsNbO3 . In order to estimate and compare the relative thermodynamic stabilities of the various polymorphs of cesium-niobates CsNbO3-x Qx (Q=S,Se,Te, and x=0,1,2,3), it is necessary to evaluate their convex hull. The convex hull in a phase diagram is constructed from the compounds having the lowest formation energy at a given chemical composition. By definition, a compound whose formation energy is on the convex hull (∆ECH = 0) is intrinsically stable. For other polymorphs with same chemical composition, the distance from the convex hull, ∆ECH , determines their stability. Consequently, it is critical to track all possible compounds in the reservoir to construct the convex hull. We have built our phase diagrams for CsNbO3-x Qx (Q=S,Se,Te, and x=0,1,2,3) by using data from the Materials Project Database. 52–54 We have complemented the missing compounds by computing additional structures taken from the Inorganic Crystal Structures Database (ICSD). 55 It turns out that the oES -CsNbO3 polymorph is the most favorable among the three phases considered and lies on the convex hull, ∆ECH = 0. Interestingly, the energy above the convex hull of the tCS -CsNbO3 polymorph is ∆ECH =45 meV/atom, classifying this compound within the scale of metastability. 63 The tCS -CsNbO3 tetragonal phase is indeed metastable, since it can accommodate large Cs cations between the corner-shared NbO5 square pyramid in the 2D-network. Furthermore, as predicted from the tolerance factor estimation, the cubic perovskite phase is unstable with ∆ECH = 250 meV/atom due to the large ionic radius of Cs that cannot be accommodated between the corner-shared NbO6 octahedra in the 3Dnetwork. We have demonstrated that the band gap of sodium niobate oxides could be tuned by O

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substitution with S, Se and Te, while preserving the perovskite crystal structures, despite the reduction of stability with respect to their oxide counter parts. 38 Depending on the chalcogen element, the energy level of the valence electrons and the ionic radius influence the electronic structure of the compound without severe geometry alterations. In this work, as we refer to chalcogen for only S, Se and Te, discerning from oxygen in CsNbO3 for convenience, we compare the electronic structures as a function of the chalcogen contents of the anion sites in CsNbO3-x Qx (Q=S,Se,Te, and x = 1, 2, 3). In addition, as we move for the Q sites from oxygen to chalcogens, we expect variations of the thermodynamic stabilities. The total energy difference between cCS - and oES -phases decreases from 250 meV/atom in CsNbO3 to 136, 128, 115 meV/atom for CsNbS3 , CsNbSe3 , CsNbTe3 , respectively, indicating a stability enhancement trend going down in the group. However, in all cases, ∆ECH is still over 100 meV/atom, indicating that the cCS phase (cubic perovskites) remains unstable, in agreement with the Goldsmith tolerance factor estimation. Thus, the oES phase remains the most favorable for all CsNbQ3 (Q=O, S,Se,Te) compounds. By assuming that the more stable compound has the lower formation energy above the convex hull, we are able to compare the thermodynamic stabilities at different chemical compositions as well as at the same chemical composition, by relating the DFT enthalpy with those of other elemental, binary, and ternary compounds in the external databases, while including all the possible decomposition channels. (see Table S2 for the lattice parameters and ∆ECH ) After carefully comparing to existing databases and computing phonons in the compounds, we find unreported stable phases with edge sharing configuration for oES -CsNbS3 and oES -CsNbSe3 displaying negative ∆ECH compared to existing phases reported until now. From this point on, we include these two stable compounds in the phase diagram of chalcogenides during the assessment of the thermodynamic stability of the quaternary compounds, such as CsNbO3-x Sx and CsNbO3-x Sex (x=1,2). In cCS -CsNbO3 , as we denote the O atom in the Nb−O bond parallel to the a-axis as

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(a)

(b)

(c)

(f) t o

(d)

(e)

Figure 2: Relaxed structures of 2 adjacent building blocks containing MO4 Q2 and MO2 Q4 (Q=S,Se,Te), in tCS - and oES -CsNbO3−x Qx : (a) tCS -CsNbO2 Qap where Q is at the apical site, (b) tCS -CsNbO2 Qeq where Q is at the equatorial site, (c) tCS -CsNbOQ2 , (d) oES -CsNbO2 Q, (e) oES -CsNbOQ2 . Only Nb, O, and S are depicted for clarity. Green, red and yellow spheres represent Nb, O, and Q, respectively. tCS -CsNbO2 Qeq is more favorable than tCS CsNbO2 Qap . (f) Energies above the convex hull for CsNbO3−x Qx (Q=S, Se, or Te, and x=1, 2, or 3) apical O, we replace the apical O with chalcogen atoms, so to obtain CsNbO2 Q. Furthermore, we substitute the O atoms of the Nb−O bond perpendicular to the a-axis equatorial O, in CsNbOQ2 . We found that the structure preserves the 3D network with P4/mmm space group. However, all cCS -compounds are unstable by ∆ECH > 200 meV/atom. In order to determine the preferred location of Q in tCS -CsNbO2 Q, we perform two sets of calculations, where we substitute respectively the apical O and the equatorial O atoms. The O−Nb bonds of the apical and equatorial bonds are along the a- and b-axis, respectively. For tCS -CsNbO2 Q, the equatorial-substituted structures (Figure 2b) are more favorable than the apical-substituted one (Figure 2a) for all the chalcogens. When we relaxed CsNbOQ2 , we obtain structures where all Q atoms are at the equatorial sites in I4/mcm space group by octahedra rotation. (see Figure 2c) From the quasi-1D-connected octaheda of oES -CsNbO3 , we note that the outer O atoms form the shortest Nb−O bonds, while they belong to only one octahedron and don’t participate in the edge-sharing structural feature. The Nb cations are shifted from the center of each octahedron in the outward direction from the chain of octahedra. The other O atoms

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are shared with the neighboring octahedra, being distinguished from the outer O. We substitute the outer and the other O atoms with Q atoms for oES -CsNbO2 Q and oES -CsNbOQ2 , respectively. Two octahedra of oES -CsNbO2 Q and oES -CsNbOQ2 are shown in Figure 2d-e, respectively. Regarding the thermodynamic stabilities as a function of the chalcogen content, we estimate the energy above the convex hull. We measure ∆ECH of tCS - and oES -compounds in Figure 2f, as we exclude cCS -compounds having ∆ECH >200 meV/atom. In tCS -CsNbO2 Q compounds, we note that the structure is more favorable when chalcogen is at the equatorial site. Hence, only tCS -CsNbO2 Q where Q is at the equatorial is marked in Figure 2f. It should be also noted that when we estimate the energy above the convex hull for oxysulfide and oxyselenide compounds, we add the computed formation energy of oES -CsNbS3 and oES -CsNbSe3 into the phase diagram. According to the ∆ECH , oxysulfide and oxyselenide compounds appear to be more stable than oxytelluride ones. Interestingly, the largest difference of formation energies between tCS and oES -compounds are 98 and 97 meV/atom for CsNbO2 S and CsNbO2 Se, respectively. tCS CsNbO2 S and tCS -CsNbO2 Se are on the boundary of the metastability criterion, ∆ECH < 100 meV/atom. 63 Having the largest ionic radius, when we substitute with tellurium as oxytelluride and telluride compounds, the stability decreases. Finally, oES -CsNbO2 Q and oES -CsNbOQ2 compounds also are stable by ∆ECH < 17 meV/atom.

Optical properties We calculated the band gaps using the HSE06 functional. Figure 3a shows the influence on the band gaps of both the content of the chalcogens and the type of polymorph. Comparing between results from PBE and PBE with spin–orbit coupling (PBE+SOC) functionals (Table S3 in supporting information), we find that the SOC effect is negligible, due to the metallic character of cCS -compounds and the low symmetry of tCS - and oES -compounds. Therefore, we have not taken account SOC effects in band gap calculations at the HSE06 level. The band 12


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(b)

(a) c t o

E-EF (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


oES-compound 4 3 2 1 0 1 2 3 4

CsNbO3

CsNbO2S

CsNbOS2

CsNbS3 Total Nb-d O-p S-p

DOS

Figure 3: (a) Band gaps calculated at the HSE06 level for CsNbO3−x Qx (Q=S, Se, or Te, and x=0, 1, 2, or 3), and (b) Site-projected density of states of oES -compounds (HSE06 calculation), showing that the valence edge is dominated by the valence states of the anions. gaps are presented as a function of their chemical composition and structure dimensionality. The band gap of tCS -CsNbO2 Q is reported for only structure where Q is at the equatorial site, because it is more stable than the structure where Q is at the apical one. Among the cCS -compounds, which are unstable according to our ∆ECH estimation, only cCS -CsNbO3 shows a finite band gap, while the other cCS -compounds are mostly metallic or their band gap approach zero, by the introduction of chalcogen atoms. We hence focus on the low dimensional compounds. In summary, low dimensionality results in finite band gaps. Figure 3b shows the site-projected DOS (density of states) of oES -compounds, as oxygen anions are substituted with sulfur anions in oES -CsNbO3 . We can see that the low-lying conduction band is localized over the d orbitals of the Nb cation. At the same time, the valence p orbitals of the anions are responsible for the valence band. The figure also shows the influence of the higher level of the p orbitals in the chalcogen atoms. It is apparent from the figure that sulfurization narrows the band gap. Thus, after full sulfurization of the oES -compound the band gap becomes 1.47 eV, decreasing by over 3 eV from the wide band gap of CsNbO3 . We can notice that there is a band gap reduction for selenium and tellurium as well: in oES -CsNbSe3 the band gap decreases down to 0.73 eV while CsNbTe3 is a metal. The partial charge densities of oES -CsNbS3 at the band edges, as shown in Figure S1 13



(suporting information), show little contribution of Cs to the states in either the valence band maximum (VBM) or conduction band maximum (CBM). This implies that Cs is still quite ionic even though the sulfur is less electronegative than oxygen. Thus, Cs cations play a considerably structural role only to form low-dimensional network of Nb and O bonds, while Nb and Q influence mainly the electronic structures.

(a)

(b)

oES oES

oES oES

oES tCS

Figure 4: HSE06 computed (a) imaginary part of the dielectric function and (b) absorption coefficient of the selected compounds. The dielectric functions are taken from the tensor elements xx and yy for tCS - and oES -compounds, respectively. This direction shows the onset of the absorption in an energy lower than for other directions. Figure 4 shows the dielectric function of the selected compounds. The fully chalcogenized compounds, such as oES -CsNbS3 and oES -CsNbSe3 , show a relatively high ability to absorb photons at much lower region than oES -CsNbO3 . The absorption onset might occur between the valence band and the conduction band at the X point in the first Brillouin zone, as we can see in the band structure of oES -CsNbS3 in Figure 5c. The VBM and CBM are contributed mainly by the S 3p and Nb 4d states, respectively. Since the dielectric function of oES -CsNbS3 depends on the direction, as shown in Figure S3 (supporting information), we conclude that the compounds are optically anisotropic. This is the result of the electronic structure, which displays connectivities between the adjacent NbS6 octahedra being formed in quasi-1 dimensionality. As the octahedra are repeated along 14


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tCS-CsNbO3

(d) VB VB VB VB-1 VB-1 VB-1 VB-2 VB-2 VB-2

Transit ion

(a)

0.5 CB CB+1 CB+2 CB CB+1 CB+2 CB CB+1 CB+2

0.4 0.3 0.2 0.1 --- X R2---

(b)

oES-CsNbO3

--- T2 Y ---

--- Z

(e) 0.5 CB CB+1 CB+2 CB CB+1 CB+2 CB CB+1 CB+2

0.4 0.3 0.2

(c)

oES-CsNbS3

|P| 2 (a.u.)

Transit ion

VB VB VB VB-1 VB-1 VB-1 VB-2 VB-2 VB-2

0.1 --- X R ---

--- T Y ---

--- Z

(f) 0.5 VB VB VB VB-1 VB-1 VB-1 VB-2 VB-2 VB-2

CB CB+1 CB+2 CB CB+1 CB+2 CB CB+1 CB+2

0.4 0.3 0.2

|P| 2 (a.u.)

Transit ion

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


|P| 2 (a.u.)

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0.1 --- X R ---

--- T Y ---

--- Z

Figure 5: The band structures of (a) tCS -CsNbO3 , (b) oES -CsNbO3 , and (c) oES -CsNbS3 . Transition matrix elements (in arbitrary units) of (d) tCS -CsNbO3 , (e) oES -CsNbO3 , and (f) oES -CsNbS3 , between the valence bands (VB) and the conduction band (CB), and between the adjcent bands near the edges. In this plot, we present the computed transition matrix elements by selecting the k-points of Γ (0,0,0), X ( 12 ,0,0), Y (0, 21 ,0), Z (0,0, 12 ), R ( 12 , 12 , 12 ), T (0, 21 , 21 ) in the first Brillouin zone. We used SeeK-path 64 to select the k-points. Calculations have been performed at the HSE06 level.

15



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Table 1: Computed effective masses of holes, m∗h (m0 ), and electrons, m∗e (m0 ), at the band edges of oES -CsNbO3 , oES -CsNbS3 , and oES -CsNbSe3 . m0 is the free electron mass. Compound oES -CsNbO3

oES -CsNbS3

oES -CsNbSe3

Direction (1 0 0) (0 1 0) (0 0 1) (1 0 0) (0 1 0) (0 0 1) (1 0 0) (0 1 0) (0 0 1)

m∗h at VBM 2.67 20.62 2.34 0.73 6.04 12.66 0.35 48.27 2.44

m∗e at CBM 2.40 6.54 5.17 0.94 9.01 16.85 0.70 111.68 8.42

the (1 0 0) direction sharing the edges, the onset of the absorption is mostly along to this direction. And, this electronic dimensionality results in the anisotropic effective masses of charge carriers, as shown in Table 1. The effective masses along the (1 0 0) direction are smaller than those in any other direction. In addition, the chalcogens reduce the effective masses in (1 0 0) direction. Unexpectedly, tCS -compounds show much weaker absorption and the absorption onset is even higher than the band gap. For example, although the band gap of tCS -CsNbO3 is 2.66 eV, the onset for the absorption is located at over 3.5 eV. The band structure shows the direct optical transition for tCS -CsNbO3−x Sx compounds. (see Figure S4a in supporting information) However, there is no noticeable absorption below 3.5 eV. We can see only a weak transition between the valence band and the conductin band, as the dipole transition matrix is shown in Figure 5d. This indicates that the absorption around the edges is forbidden in tCS -compounds. Furthermore, the onset of the absorption occurs between the VB and the CB+1, and between the VB-1 (VB-2) and the CB along the path of the k-points T –R. On the other hand, the band edges of oES -CsNbS3 contribute to the strong transition at the X and R point, as shown in Figure 5f. It should be noted that oES -CsNbS3 and oES -CsNbSe3 are found stable, namely ∆ECH < 0. Thus, we propose oES -CsNbS3 and oES -CsNbSe3 as new semiconducting materials for applications in solar cells, photocatalysts, photoelectrodes, and 16


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light-emitting diodes.

Conclusions Although niobate perovskites had been suggested as ferroelectric and photoactive compounds, there has not been any report on the experimental synthesis of CsNbO3 perovskite. The tolerance factor of CsNbO3 indicates that the ionic radius of Cs cation is too large to be accommodated in the cavity of the NbO6 networks. In this work, we quantified and explained the thermodynamic stabilities of different polymorphs of CsNbO3 in polyhedral networks extended across the three dimensional space or restricted along specific directions. We found that CsNbO3 in the cubic perovskite structure is unstable. However, the tetragonal phase where 2D connected NbO5 square pyramids are formed by means of corner-shared networks is metastable. Nonetheless, the optical absorption of CsNbO3 in the tetragonal phase is weak in the visible light region. In an attempt to stabilize the perovskite struture and reduce the band gaps, we altered the chemical composition of the structures by introducing chalcogen atoms, such as S, Se and Te at the O anion sites. We found, by comparison with thermochemistry databases, that CsNbS3 and CsNbSe3 in the orthorhombic phase where the octahedra are connected with the adjacent by sharing the corners (quasi-1D), are possibly new stable materials, according to the computed convex hull energies. In addition, the quasi-1D compounds in the orthorhombic phase have lower band gap with strong absorption peak. Taking into account polymorphism, thermodynamic stability and strong absorption in the visible light region, this work highlights an alternative approach to the discovery of lead-free semiconducting materials with enhanced optical properties.

Supporting Information Available The following files are available free of charge.

17



• CsNbOxQy-SI.pdf: Details of the relaxed structures; band gap at various levels, additional band structures; dielectric function along the different directions; list of stable compounds in the phase diagram.

Acknowledgement This work is sponsored by the Qatar Environment and Energy Research Institute (FE, FHA and NT ). Computational resources have been provided by the research computing group at Texas A&M University at Qatar. This work is supported by the Qatar National Research Fund (QNRF) through the National Priorities Research Program (NPRP8-090-2-047).

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25



Graphical TOC Entry Cs

Cs

Cs 2 S

CsS

4

21

S

8

Nb

b

Cs 2 S

N

N

S

N b S N 3 b b S 25 2 S N 48 b N 3 S5 b 3S

Cs 3 N b 2 S 11

+C sN

CsN b S 3

CsS

bS 3

b

21

S

8

4

26

Nb

N

S

N b S N 3 b b S 25 2 S N 48 b N 3 S5 b 3S

CsN b S 3

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


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with Enhanced Optical Properties and Intrinsic Thermodynamic Stabili

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