CESIUM-NIOBIUM-CHALCOGENIDE COMPOUNDS AND SEMICONDUCTOR

DEVICES INCLUDING THE SAME

CROSS REFERENCE TO RELATED APPLICATION

[0001] The present application claims priority to U.S. Provisional Patent Application No. 62/626,964, filed February 06, 2018 and U.S. Provisional Patent Application No. 62/627,494, filed February 07, 2018, the disclosures of which are incorporated into this specification by reference in their entirety.

BACKGROUND

[0002] Lead-halide perovskites have been used in the field of photovoltaics (PV), owing to their high power conversion efficiencies (PCE) associated with a low-cost chemical processing synthesis. Specifically, the methylammonium lead iodide perovskite (MAPbL·) has drawn attention as an efficient material for photovoltaic applications displaying PCE of up to 22.1%. However, the pace of the conversion efficiencies has slowed down over the past few years, as the theoretical limit has been approached. Several modifications of MAPbL are experiencing intrinsic instability despite the enhancement of the efficiencies. Thus, 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.

SUMMARY

[0003] According to one non-limiting aspect of the present disclosure, an example embodiment of a cesium-niobium-chalcogenide compound is selected from the group consisting of CsNbS3, CsNbSe3, and CsNbOx iQx (Q=S, Se, and x=l, 2) compounds, and comprises an edge-shared orthorhombic crystal structure.

[0004] According to another non-limiting aspect of the present disclosure, an example embodiment of a semiconductor device includes a cathode layer, an anode layer, and an active layer disposed between the cathode layer and the anode layer. The active layer includes a cesium-niobium-chalcogenide compound selected from the group consisting of CsNbS3, CsNbSe3, and CsNbOx 3Qx (Q=S, Se, and x=l, 2) compounds, and the cesium- niobium-chalcogenide compound comprises an edge-shared orthorhombic crystal structure. In addition to stability, the new cesium-niobium-chalcogenide compounds possess suitable properties to be used as photo absorbing layer associated with strong abortion properties at the visible light region.

[0005] Additional features and advantages are described herein, and will be apparent from the following Detailed Description and the figures.

BRIEF DESCRIPTION OF THE DRAWINGS

[0006] Features and advantages of the cesium-niobium-chalcogenide compounds and the semiconductor devices including the same described herein may be better understood by reference to the accompanying drawings in which:

[0007] FIGS. l(a)-l(c) are relaxed structures of different CsNb03 polymorphs. FIG. 1(a) Cubic phase with comer-sharing octahedra and Pm3m space group (ccs-CsNbCh); FIG. 1(b) tetragonal phase with comer-sharing square pyramids and P4/mm space group (fcs- CsNb03); FIG. 1(c) orthorhombic phase with edge-sharing octahedra and P2i/c space group (oES-CsNbCh), the orthorhombic structure was taken from ICSD-1266. The unit cell is marked by dashed lines.

[0008] FIGS. 2(a)-2(e) are relaxed stmctures of 2 adjacent building blocks containing MO4Q2 and MO2Q4 (Q=S,Se,Te), in fcs- and OES-CsNbCh-xQx: FIG. 2(a) fcs- CsNbChQap where Q is at the apical site, FIG. 2(b) /cs-CsNbOrQcq w here Q is at the equatorial site, FIG. 2(c) fcs-CsNbOQr, FIG. 2(d) OES-CsNbChQ, FIG. 2(e) OES-CsNbOQr. Only Nb, O, and S are depicted for clarity. /cs-CsNbOrQcq is more favorable than fcs-CsNb02Q _ap . FIG. 2(f) is a graph plotting energies above the convex hull for CsNbCh _x Qx (Q=S, Se, or Te, and x=l, 2, or 3).

[0009] FIG. 3(a) is a graph plotting band gaps calculated at the HSE06 level for CsNbCh _x Qx (Q=S, Se, or Te, and x=0, 1, 2, or 3), and FIG. 3(b) is a graph plotting site- projected density of states of OES-compounds (HSE06 calculation), showing that the valence edge is dominated by the valence states of the anions.

[0010] FIGS. 4(a)-4(b) illustrate projected charged density of OES-CsNbS3 at FIG. 4(a) the valence band maximum (VBM) and FIG. 4(b) conduction band maximum (CBM).

[0011] FIG. 5 shows the stmeture of of OES-CsNbS3.

[0012] FIG. 6 shows details of the edge-sharing octahedral (NbSe).

[0013] FIG. 7(a) is a graph plotting HSE06 computed imaginary part of the dielectric function. FIG. 7(b) is a graph plotting 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.

[0014] FIGS. 8(a)-8(c) are graphs plotting the band structures of fcs-CsNbCb (FIG. 8(a)), OES-CsNbCb (FIG. 8(b)), and OES-CsNbS3 (FIG. 8(c)). FIG. 8(d)— 8(f) are graphs plotting transition matrix elements (in arbitrary units) of fcs-CsNbCb (FIG. 8(d)), OES-CsNbCb (FIG. 8(e)) and OES-CsNbS3 (FIG. 8(f)) between the valence bands (VB) and the conduction band (CB), and between the adjacent bands near the edges. The k-points of G (0,0,0), X (½,0,0), Y (0,½,0), Z (0,0, ½), R (½,½,½), T (O. /./) in the first Brillouin zone are selected. Calculations have been performed at the HSE06 level.

[0015] FIGS. 9(a)-9(c) are graphs plotting calculated optical properties of OES- CsNbS3 by using HSE06 functional. FIG. 9(a) Real and FIG. 9(b) imaginary part of the dielectric function, and FIG. 9(c) absorption coefficient.

[0016] FIGS. 10(a)- 10(d) are graphs plotting, at the PBE level, calculated band structure of FIG. 10(a) fcs-CsNbCh, FIG. 10(b) OES-CsNbCh, FIG. 10(c) OES-CsNbS3, and FIG. 10(d) OES-CsNbSe ₃ . In the band structures G (0,0,0), X (½,0,0), Y (0,½,0), Z (0,0, ½), R (½,½,½), T (0 ,½,½), U (Z.O.Z). and V (½,½,0) points are selected in the first Brillouin zone for the path by using SeeK-path.

[0017] FIG. 11 is a cross section side view illustrating an embodiment of a semiconductor device.

[0018] The reader will appreciate the foregoing details, as well as others, upon considering the following detailed description of certain non-limiting embodiments of the of the present disclosure including cesium-niobium-chalcogenide compounds and the semiconductor devices including the same. The reader may also comprehend certain of such additional details upon using same including the cesium-niobium-chalcogenide compounds and the semiconductor devices described herein.

DETAILED DESCRIPTION

[0019] Until recently, most of the focus in searching for new photoactive materials with a robust power conversion efficiency 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. At the same time, efforts toward stabilizing the hybrid perovskites have led to the introduction of larger cations such as (HOOC(CH ₂ )4NH ₃ )2. These break the 3D connectivity of the Pbl6 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. Recently, photo-absorbing compounds with lower-dimensional polyhedral connectivity, which is distinguished from conventional cubic perovskites, have been utilized in PV devices. Such lower-dimensional polyhedral connectivity networks might suffer from charge transport properties inferior to those at the 3D polyhedral connectivity perovskites, yet their successful operation in PV devices opens the door for the exploration of non-perovskite materials. Solar cells based on 2D (CH3NH3)2Pb(SCN)2l2 perovskites have achieved decent power conversion efficiency and showed a superior defect tolerance with the tendency to exhibit p-type conductivity with a relatively long carrier lifetime.

[0020] Among these efforts, there has also been progress in reducing the large band gaps of perovskite oxides to match the visible light radiation spectrum. 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. Alkali metals such as Li, Na, K, Rb and Cs have been reported to incorporate into monovalent-cation site of the MNbCh, where M are alkali metals. They have been synthesized 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. However, a further increase in the cationic radius to that of Cs, to form CsNbCh, results in breaking into non-perovskite structures, which are experimentally reported. The crystal structure features edge-sharing octahedra in CsNbCh forming quasi-one-dimensional (quasi- 1D) chain networks.

[0021] Previous high-throughput density functional theory (DFT) studies to simulate the perovskite structure of CsNbCh have reported that it has a phase obtained by deforming the cubic perovskite structure. In the present disclosure, the polymorphism of CsNbCh and 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 are assessed using DFT. The hybrid organic- inorganic perovskites are believed to surpass the fully inorganic ones. The final goal of this design strategy is to provide non-toxic niobate compounds to accommodate organic cations with ionic radius comparable to Cs ⁺ , such as methylammonium (CH3NH3 ⁺ ). In addition, the present disclosure aims at reducing the band gap of CsNbCb polymorphs by replacement of oxygen with chalcogen ions at the anion sites. While comparing the chemical composition of CsNbCb-xQx (Q=S,Se,Te, and x=l,2,3) in various polymorphs where polyhedral network are formed differently, the present inventors found that the optical absorption can be enhanced in low-dimensional compounds by introducing chalcogens.

[0022] The structural stability of perovskite compounds strongly depends on the ionic radii of its constituents. In the present disclosure, the photoactive properties of cesium- niobate and cesium-niobium-chalcogenide CsNbCb-xQx (Q=S,Se,Te, and x=0, 1,2,3) are improved as a function of the chalcogen content as well as the impact on the structural and thermodynamic stability. Perovskites of CsNbCh and their chalcogenized variations have not been reported experimentally. Elements in 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.

[0023] The tolerance factor of the full chalchogen substituted oxygen cesium- niobates CsNbQ3 (Q=S,Se,Te) indicate that t decreases from 1.06 to 1.04 and 1.03 for CsNbS3, CsNbSe3, and CsNbTe3, respectively. Consequently, the perovskite chalcogenides are expected to be 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.

[0024] The present inventors have explored the thermodynamic stabilities of CsNbCh-xQx (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. DFT calculations were performed using the projector-augmented wave (PAW) method, as it is implemented in VASP code. The structures were fully relaxed with Perdew-Burke-Emzerhof (PBE) formulation of the generalized gradient approximation (GGA) of the electron exchange and correlation energy. When optimizing the structures, the relaxation was conducted 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 the present inventors 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/A, 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 6 6 6 for all unit cells. When the present inventors carried out HSE06 calculations for the band gap and the dielectric function calculations, k-points were sampled with a Gamma-centered 4 / 4 / 4 grid.

[0025] The linear programming (LP) algorithm was adopted to obtain the minimum at a given chemical composition, which is represented by linear relationships. For example, as all possible decomposition reactions including the constituent elements are taken into account, the energy above the convex hull of CsNb02s can be calculated as,

where all the energies are the total energy of the corresponding stable compounds. In general, the rth compound consists of ai Cs, bi Nb, Oi O, or si S atoms, and Ci is its corresponding coefficient. The FP problem is solved with the constraints,

ensuring the correct stoichiometry of CsNbOiS with Ci > 0. Consequently, a compound was determined to be stable by using the database available from Materials Project and ICSD. When estimating the formation energy through Pymatgen, the optimized structure was taken from Materials Project, while the experimental structures of ICSD were relaxed by carrying out DFT calculations at the PBE level. Anion corrections for oxide and sulfide components were included in order to have relative energies consistent with experimental values, since it is known that GGA underestimates the total energies of O2 and Ss.

[0026] Referring to FIG. 1, CsNbCb 2 ^ 2 / 2 supercells were obtained by relaxing the atomic coordinates constructed from the prototype cubic and tetragonal perovskite structure. All the supercells contain 40 atoms, with each polymorph being denoted by the structural features as discussed in the followings. The calculated lattice parameters are listed in Table 1. In the cubic phase, the polyhedral network consists of 3D-connected NbCE octahedra where Nb is at the center and it shares the comers with the adjacent octahedra. This polymorph adopts the cubic phase with space group Pm3m space group and the octahedra are connected by means of comer-shared (CS). This stmcture is denoted herein as ccs-CsNbCb. In the tetragonal phase, the polyhedral network consists of 2D connected NbOs square pyramids exhibiting lower dimensional networks, and is denote herein as fcs-CsNbCh, as the square pyramids show comer-shared connectivity. This polymorph results from an apical Nb-0 bond having the shortest bond in an octahedron, while the opposite apical oxygen atom appears to be too far to form a chemical bondNb-0 by the distance of 4.4 A. In fcs-CsNbC , the pyramidal coordination provides more room to accommodate the Cs cations than in the cubic phase. Hence, Nb and O form a NbOs 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 CsNbCb with 40 atoms in an orthorhombic unit cell in the P2l/c space group is composed of quasi- 1D connected NbCE octahedra, which are extended in edge shared (ES) way along the a axis. This is denoted herein as OES-CsNbCh.

Table 1 : Lattice parameters of CsNbCb depending on the different dimensional structure.

Compounds Space group a (A) b (A) c (A) AECH Volume

_ (eV/atom) (A ³ ) _

ccs-CsNbCh (Cubic) Pm3m 8.34 8.34 8.34 250 793.9 fcs-CsNbCh (Tetragonal) 7.78 7.78 12.45 45 753.0

P4/mm

OES-CsNbCh (Orthorhombic) 5.20 9.42 16.21 0 580.4

_ P2i/c _

[0027] In order to estimate and compare the relative thermodynamic stabilities of the various polymorphs of cesium-niobates CsNb03- _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 (AECH = 0) is intrinsically stable. For other polymorphs with same chemical composition, the distance from the convex hull, AECH, determines their stability. Consequently, it is critical to trach all possible compounds in the reservoir to construct the convex hull. The present inventors have built phase diagrams for CsNbCh-xQx (Q=S,Se,Te, and x=0, 1,2,3) by using data from the Materials Project Database, and complemented the missing compounds by computing additional compounds taken from the Inorganic Crystal Structures Database (ICSD).

[0028] The OES-CsNbCh polymorph is the most favorable among the three phases considered and lies on the convex hull, AECH = 0. The energy above the convex hull of the fcs- CsNbCh polymorph is AECH=45 meV/atom, classifying this compound within the scale of metastability. The fcs-CsNbCh tetragonal phase is indeed metastable, since it can accommodate large Cs cations between the comer-shared NbCE square pyramid in the 2D-network. Furthermore, as predicted from the tolerance factor estimation, the cubic perovskite phase is unstable with AECH = 250 meV/atom due to the large ionic radius of Cs that cannot be accommodated between the comer-shared NbCE octahedra in the 3D-network.

[0029] The band gap of sodium niobate oxides could be tuned by oxygen substitution with sulfur, selenium, and tellurium, while preserving the perovskite crystal structures, despite the reduction of stability with respect to their oxide counter parts. 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 the present disclosure, as only S, Se, and Te are referred to as chalcogen, discerning from oxygen in CsNbCh for convenience, the present inventors compared the electronic structures as a function of the chalcogen contents of the anion sites in CsNbCh-xQx (Q=S,Se,Te, and x = 1; 2; 3). In addition, moving for the Q sites from oxygen to chalcogens, variations of the thermodynamic stabilities are expected.

[0030] The total energy difference between ccs- and OES-phases decreases from 250 meV/atom in CsNbCh to 136, 128, 115 meV/atom for CsNbSc CsNbSev CsNbTcv respectively, indicating a stability enhancement trend going down in the group. However, in all cases, AECH 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 CsNbfL (Q=0, S,Se,Te) compounds.

[0031] By assuming that the more stable compound has the lower formation energy above the convex hull, the present inventors were 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 2 for the lattice parameters and AECH).

Table 2: Lattice parameters of chalcogenide compounds depending on the different dimensional structure.

Compounds Space a (A) b (A) c (A) AECH Volume

ccs- P4/mmm 9.89 8.48 8.48 402 711.91

CsNb02s

cCS- P4/mmm 8.12 10.17 10.17 230 839.24

CsNbOSi

ccs-CsNbS3 Pm3m 9.92 9.92 9.92 101 976.19 tcs- P4/mm 14.60 7.79 7.79 104 885.91

CsNbOlSap

tcs- P4/mm 12.32 7.56 9.84 64 916.18

CsNbOlSeq

fcs- I4/mcm 13.20 8.98 8.97 34 1062.98

CsNbOSi

/cs-CsNbSi I4/mcm 14.75 9.01 9.01 16 1198.20

OES- P2l/c 5.13 17.91 10.89 -26 999.58

CsNbOiS

OES- P2l/c 6.22 16.64 10.69 4 1103.45

CsNbOSi

OES-CsNbS ₃ P2l/c 6.44 18.48 10.76 -35 1267.63 Compounds Space a (A) b (A) c (A) AECH Volume

ccs- P4/mmm 10.34 8.57 8.57 511 758.66

CsNbChSe

CCS- P4/mmm 8.06 10.74 10.74 233 930.69

CsNbOSd

CCS- Pm3m 10.41 10.41 10.41 96 1129.02

CsNbSe3

tc s- P4/mm 15.10 7.80 7.89 132 928.97

CsNbChSeap

tc s- P4/mm 12.87 7.63 10.17 72 999.63

CsNbChSeeq

fcs- I4/mcm 13.60 9.35 9.35 25 1188.42

CsNbOSd

tc s- I4/mcm 15.30 9.41 9.41 6 1356.35

CsNbSe3

OES- P2i/c 5.13 18.37 11.29 -14 1063.32

CsNbOiSe

OES- P2i/c 6.50 17.24 10.94 17 1222.42

CsNbOSe2

OES- P2i/c 6.87 18.83 11.10 -32 1412.35

CeCsNbSe ₃

CCS- P4/mmm 11.05 8.76 8.76 788 848.22

CsNb0 ₂ Te

ccs- P4/mmm 8.00 11.71 11.71 285 1097.29

CsNbOTe ₂

CCS- Pm3m 11.19 11.19 11.19 194 1402.53

CsNbTe ₃

tc s- P4/mm 15.96 7.88 8.01 216 1007.22

CsNb02Teap

tc s- P4/mm 13.85 7.68 10.70 113 1138.96

CsNb0 ₂ Teeq

tcs- I4/mcm 14.29 9.98 9.98 58 1423.79

CsNbOTe ₂

fcs- I4/mcm 15.29 10.19 10.19 88 1588.11

CsNbTe ₃

OES- P2i/c 5.16 19.84 11.71 28 1198.72

CsNb0 ₂ Te

OES- P2i/c 7.02 17.28 12.14 94 1471.76

CsNbOTe ₂

OES- P2i/c 7.31 19.89 11.75 79 1674.50

CsNbTe ₃

[0032] After careful comparison to existing databases, the present inventors found unreported stable phases with edge sharing configuration for OES-CsNbS3 and OES-CsNbSe3 displaying negative AECH compared to existing phases. From this point on, the present inventors included these two stable compounds in the phase diagram of chalcogenides during the assessment of the thermodynamic stability of the quaternary compounds, such as CsNbC - xSx and CsNbC -xSex (x=l,2).

[0033] In the ccs-CsNbCh, as the O atom in the Nb-0 bond parallel to the a-axis is denoted as apical O, the apical O atoms are replaced with chalcogen atoms, so as to obtain CsNbOiQ. Furthermore, the present inventors substituted the O atoms of the Nb-0 bond perpendicular to a-axis equatorial O, in CsNbOQ2. The present inventors found that the structure preserves the 3D network with P4/mmm space group. However, all ccs-compounds are unstable by AECH > 200 meV/atom.

[0034] To determine the preferred location of Q in /cs-CsNbOiQ. two sets of calculations were performed, where the apical O atoms and the equatorial O atoms were substituted. The O-Nb bonds of the apical and equatorial bonds are along the a- and b-axis, respectively. For /cs-CsNbOiQ. the equatorial-substituted structures (Figure 2b) were more favorable than the apical-substituted one (Figure 2a) for all the chalcogens. When the present inventors relaxed CsNbOQ2, structures could be obtained where all Q atoms are at the equatorial sites in I4/mcm space group by octahedra rotation (see Figure 2c). From the quasi- lD-connected octahedra of OES-CsNbCh, the outer O atoms form the shortest Nb-0 bonds, while they belong to only one octahedron and do not 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 are shared with the neighboring octahedra, being distinguished from the outer O. The outer and the other O atoms are substituted with Q atoms for OES-CsNbC Q and OES-CsNbOQ2, respectively. Two octahedra of OES-CsNbC Q and OES-CsNbOQ2 are shown in Figure 2d-e, respectively.

[0035] Regarding the thermodynamic stabilities as a function of the chalcogen content, the present inventors estimated the energy above the convex hull. AECH of tcs- and OES-compounds are measured in Figure 2f, as ccs-compounds having AECH > 200 meV/atom are excluded. In fcs-CsNbChQ compounds, the present inventors noted that the structure is more favorable when chalcogen is at the equatorial site. Hence, only fcs-CsNbChQ where Q is at the equatorial is marked in Figure 2f. It should also be noted that when the present inventors estimated the energy above the convex hull for oxysulfide and oxyselenide compounds, the computed formation energy of OES-CsNbS3 and OES-CsNbSe3 was added into the phase diagram.

[0036] According to the AECH, the oxysulfide and oxyselenide compounds appear to be more stable than oxytelluride ones. The largest difference of formation energies between tcs- and OES-compounds are 98 and 97 meV/atom for CsNbOiS and CsNbOiSc. respectively. tc s- CsNbOiS and fcs-CsNbC Se are on the border of the criterion, AECH < 100 meV/atom. Having the largest ionic radius, when tellurium is substituted as oxytelluride and telluride compounds, the stability decreases. OES-CsNbC Q and OES-CsNbOQ2 compounds also are stable by AECH < 17 meV/atom.

[0037] The present inventors 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 3), it was found that the SOC effect is negligible, due to the metallic character of ccs-compounds and the low symmetry tcs- and OES-compounds. Therefore, the SOC effect was not taken into account in band gap calculations at the HSE06 level. The band gaps are presented as a function of their chemical composition and structure dimensionality. The band gap of /cs-CsNbOiQ 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.

Table 3 : Computed band gaps (E _g ) at the PBE, PBE with spin-orbit coupling (SOC), and HSE06 functional level.

Compounds _ Band Gaps (eV)

_ PBE PBE+SOC HSE06

ccs-CsNbCb 1.39 1.26 2.20

ccs-CsNbC S 0.0 0.0

ccs-CsNbC Se 0.0 0.13

ccs-CsNbOiTe 0.0 0.0

ccs-CsNbOS2 0.0 0.0

ccs-CsNbOSe2 0.0 0.0

ccs-CsNbOTe2 0.0 0.0

ccs-CsNbS3 0.0 0.0

ccs-CsNbSe3 0.0 0.0

ccs-CsNbTe3 _ 0.0 OO _

fcs-CsNb0 ₃ 1.62 1.61 2.66

fcs-CsNbC S 1.19 1.18 1.93

ics-CsNb02Se 0.72 0.68 0.88

ics-CsNb0 ₂ Te 0.53 0.52 0.67

fcs-CsNbOSr 0.35 0.35 0.22

ics-CsNbOSe2 0.20 0.24 0.39

As-CsNbOTer 0.27 0.19 0.26

fcs-CsNbS ₃ 0.08 0.32

ics-CsNbSe3 0.0 0.26

/cs-CsNbTc3 _ 0 0 OO _

OES-CsNb0 ₃ 3.34 3.32 4.60

OES-CsNb02S 2.58 2.56 3.45

OES-CsNb02Se 2.21 2.17 2.96

OES-CsNbC Te 1.55 1.46 2.09

OES-CsNbOS ₂ 1.37 1.47 2.07

OES-CsNbOSe2 0.94 0.99 1.50

OES-CsNbOTe2 0.31 0.34 0.65

OES-CsNbS ₃ 0.92 1.47

OES-CsNbSe3 0.33 0.80

OES-CsNbTe3 0.0 0.0

[0038] Among the ccs-compounds, which are unstable according to the AECH estimation, only ccs-CsNbCb 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. The present inventors hence focused on the low dimensional compounds. In summary, a low dimensionality results in finite band gaps.

[0039] Figure 3b shows the site-projected DOS (density of states) of OES- compounds, as oxygen anions are substituted with sulfur anions in OES-CsNb03. It can be seen that 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 sulf irization 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 CsNbCb. The band gap reduction for selenium and tellurium can be noticed as well; in OES- CsNbSe3 the band gap decreases down to 0.73 eV, while CsNbTe3 is a metal.

[0040] As shown in Figure 4, the partial charge densities of oES-CsNbS3 at the band edges 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 the Nb and Q influence mainly the electronic structures. The structure of OES-CsNbS3 is shown in Figure 5 and the details of the edge-sharing octahedral (NbSe) are shown in Figure 6.

[0041] Figure 7 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-CsNbCb. The absorption onset might occur between the valence band and the conduction band at the X point in the first Brillouin zone, as seen in the band structure of OES-CsNbS3 in Figure 8c. The valence band maximum (VBM) and conduction band maximum (CBM) are contributed mainly by the S 3p and Nb 4d states, respectively.

[0042] Since the dielectric function of oES-CsNbS3 depends on the direction, as shown in Figure 9, the present inventors concluded that the compounds are optically anisotropic. This is the result of the electronic structure, which displays the connectivities between the adjacent NbS6 octahedra being formed in quasi- 1 dimensionality. As the octahedra are repeating along the [1 0 0] direction sharing the edges, the onset of the absorption is mostly along this direction.

[0043] Unexpectedly, fcs-compounds show much weaker absorption and the absorption onset is even higher than the band gap. For example, although the band gap of tcs- CsNbCh 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 fcs-CsNbCb-xSx compounds (see Figure lOa). However, there is no noticeable absorption below 3.5 eV. Only a weak transition between the valence band (VB) and the conduction band (CB) can be seen, as the dipole transition matrix is shown in Figure 8d. This indicates that the absorption around the edges is forbidden in fcs-compounds. Furthermore, the onset of the absorption occurs between the VB and the CB+l, and between the VB-l (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 8f. It should be noted that OES-CsNbS3 and OES-CsNbSe3 are found stable, namely AECH < 0. Thus, OES-CsNbS3 and OES-CsNbSe3 are proposed as new semiconducting materials for applications in solar cells, photocatalysts, photoelectrodes, and light-emitting diodes.

[0044] In summary, although niobate perovskites had been suggested as ferroelectric and photoactive compounds, there has not been any report on the experimental synthesis of CsNbCh perovskite. The tolerance factor of CsNbCh indicates that the ionic radius of Cs cation is too large to be accommodated in the cavity of the NbCE networks. In the present disclosure, the inventors quantified and explained the thermodynamic stabilities of different polymorphs of CsNbCh in polyhedral networks extended across the three dimensional space or restricted along specific directions. The present inventors found that CsNbCh in the cubic perovskite structure is unstable. However, the tetragonal phase where 2D connected NbCri square pyramids are formed by comer-shared networks is metastable. Nonetheless, the optical absorption of CsNbCh in the tetragonal phase is weak in the visible light region. In an attempt to stabilize the perovskite structure and reduce the band gaps, the chemical composition of the structures was altered by introducing chalcogen atoms, such as S, Se, and Te at the O anion sites. The present inventors 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 comers (quasi- 1D), are possibly new stable materials, according to the computed convex hull energies. In addition, the quasi-lD 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, the present disclosure highlights an alternative approach to the discovery of lead-free semiconducting materials with enhanced optical properties.

[0045] Figure 11 illustrates one implementation of the structure and operating principle of a semiconductor device 100. In implementations, an semiconductor device 100 can include, but are not limited to, optoelectronic devices such as solar cells, photocatalysts, photoelectrodes, light-emitting diodes, photoelectrodes, and so forth. As shown in Figure 11, the semiconductor device 100 may include a cathode layer 101, an anode layer 103, and an active layer 102 disposed between the cathode layer 101 and the anode layer 103. The cathode layer 101 functions as a cathode electrode. The anode layer 103 can include an anode electrode. [0046] In some specific embodiments, the cathode layer 101 can include an Al layer and/or a Ag layer that functions as a cathode, and the anode layer 103 can include an indium- tin oxide (ITO) layer that functions as an anode. In other specific embodiments, the cathode layer 101 can include an indium-tin oxide (ITO) layer that functions as a cathode, and the anode layer 103 can include an aluminum layer that functions as an anode. Other materials may also be used to form the cathode layer 101, such as calcium, magnesium, lithium, sodium, potassium, strontium, cesium, barium, iron, cobalt, nickel, copper, silver, zinc, tin, samarium, ytterbium, chromium, gold, graphene, an alkali metal fluoride, an alkaline-earth metal fluoride, an alkali metal chloride, an alkaline-earth metal chloride, an alkali metal oxide, an alkaline- earth metal oxide, a metal carbonate, a metal acetate, and/or a combination of two or more of the above materials. Further, other materials may be used to form the anode layer 103 (or a transparent electrode), such as fluorine-doped tin oxide (FTO), aluminum-doped zinc oxide (AZO), antimony -tin mixed oxide (ATO), a conductive polymer, a network of metal nanowire, a network of carbon nanowire, nanotube, nanosheet, nanorod, carbon nanotube, silver nanowire, or graphene.

[0047] The active layer 102 can include a cesium-niobium-chalcogenide compound selected from the group consisting of CsNbS3, CsNbSe3, and CsNbOx iQx (Q=S, Se, and x=l, 2) compounds, wherein the cesium-niobium-chalcogenide compound comprises an edge- shared orthorhombic crystal structure. The band gaps of the cesium-niobium-chalcogenide compounds are suitable for absorption of the visible light, expanding their applicability in various semiconductor applications including photovoltaics where the thermodynamic stability is strongly required.

[0048] It should be understood that various changes and modifications to the presently preferred embodiments described herein will be apparent to those skilled in the art. Such changes and modifications can be made without departing from the spirit and scope of the present subject matter and without diminishing its intended advantages. It is therefore intended that such changes and modifications be covered by the appended claims.