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[Motoharu Imai](https://orcid.org/0000-0002-5848-113X), [Yoshitaka Matsushita](https://orcid.org/0000-0002-4968-8905)

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[Effect of Ca substitution on crystal structure and band gap of solar cell material BaSi2](https://mdr.nims.go.jp/datasets/01e8d78e-d114-45a7-9193-3a929a0eef3c)

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1  Effect of Ca substitution on crystal structure and band gap of solar cell material BaSi2  Motoharu Imaia* and Yoshitaka Matsushitab aResearch Center for Electrical and Optical Materials, National Institute for Materials Science, Ibaraki 305-0047, Japan bResearch Network and Facility Services Division, National Institute for Materials Science, Ibaraki 305-0047, Japan  E-mail: MATSUSHITA.Yoshitaka@nims.go.jp (Y. Matsushita)  *Corresponding author Motoharu Imai National Institute for Materials Science, Ibaraki 305-0047, Japan Phone number: E-mail: IMAI.Motoharu@nims.go.jp  Abstract To ameliorate the potential of a promising solar cell material BaSi2, the effects of substituting Ba with Ca atoms on the crystal structure and band gap Eg of BaSi2, were investigated both experimentally and computationally. The solid-solution limit of the Ca atoms in BaSi2 was approximately 2.3 at.%. Single-crystal X-ray diffraction analysis of Ba1−xCaxSi2 (0.025 ≤ x ≤ 0.072) revealed that the unit cell volume decreases with Ca content x, and the Ba atoms at the A1 crystallographic site are preferentially substituted by Ca atoms. Diffuse reflectance measurements indicated that Eg decreases with x (1.24 eV at x = 0 and 1.17 eV at x = 0.07). The density functional theory calculations demonstrate that the experimentally observed decrease in Eg by Ca substitution can be explained qualitatively by the combination of the substitution of Ca atoms in the unit cell volume of BaSi2 and the volume reduction.   Keywords Silicides, Semiconductors, Crystal structure, Optical properties, Electronic structure  ORCID ID M. Imai: 0000-0002-5848-113X Y. Matsushita: 0000-0002-4968-8905   mailto:MATSUSHITA.Yoshitaka@nims.go.jp2  1. Introduction Barium disilicide (BaSi2), which is composed only of earth-abundant elements, has been investigated as a suitable candidate for next-generation thin-film solar cells [1-8] owing to its promising properties as a photoabsorber. BaSi2 has a band gap (Eg) of 1.1–1.3 eV, a large absorption coefficient at 1.5 eV (>104 cm−1), high quantum efficiency (>70%), long minority-carrier lifetime (11–14 μs), and long diffusion length for minority carriers [2, 3]. A BaSi2 homojunction diode with a thickness of 2 μm was simulated to achieve a convergent efficiency of 25% [2]. Recent experiments have demonstrated that BaSi2/n-Si solar cells have a conversion efficiency of approximately 9–10% [7, 8]. To broaden the potential of BaSi2 as a solar cell material, investigating band gap tuning by substitution is important. The effects of Sr substitution on the crystal structure and Eg of BaSi2 were examined computationally and experimentally [9-11]. BaSi2 crystallizes into a unique crystal structure with Si4 tetrahedra, the BaSi2-type, which has two crystallographic sites for the Ba atoms and three for the Si atoms [12], as shown in Fig. 1 (a). Consequently, two possible substitution sites for the Ba atoms (A1 and A2) and three sites for the Si atoms (Si1, Si2, and Si3) exist. The local environments of the A1 and A2 sites are different; the Ba atoms at the A1 site have 9 Si atoms as neighbors, whereas the A2 site has 11 Si atoms as nearest neighbors. Single-crystal X-ray diffraction (XRD) and diffuse reflectance measurements of Ba1−xSrxSi2 (0.0 ≤ x ≤ 0.8) revealed that the Ba atoms at the A1 site are preferentially substituted by Sr atoms, and Eg decreases with x (1.24 eV at x = 0 and 1.15 eV at x = 0.65) [11]. The preferential occupation of the A1 site by Sr atoms is consistent with the computational result for Ba0.5Sr0.5Si2, wherein, Ba atoms at the A1 site substituted with Sr are more stable than those in which Ba atoms at the A2 site substituted with Sr [10,11]. However, the effects of substitution with other elements have not yet been investigated. Although the pseudo-binary system of BaSi2 and CaSi2 has been reported to exhibit a eutectic phase diagram [13], no other experimental studies on ternary Ba–Ca silicides have been reported. In this study, we investigated the effect of Ca substitution on the crystal structure and band gap of BaSi2. We synthesized Ca-substituted BaSi2, Ba1−xCaxSi2, determined their crystal structures, and estimated their band gaps using diffuse reflectance measurements. In addition, we determined the band structure of Ba7Ca1Si16 using density functional theory (DFT) calculations. Finally, the experimental and computational results are compared and discussed. 3   Fig. 1. (a) Crystal structure of BaSi2 [11]. Green, red, blue, sky-blue, and gray spheres represent atoms at A1, A2, Si1, Si2, and Si3 sites, respectively. The arrow indicates a Ba atom replaced by a Ca atom in the electronic structure calculation of Ba7Ca1Si16. Coordination polyhedra at (b) the A1 and (c) A2 sites.     (a)(b) (c)A1Si2A2Si1Si34  2. Experimental and computational methods BaSi2 and CaSi2 were synthesized by Ar-arc melting a 1.03:2 molar mixture of Ba (or Ca) and Si. The Ba1−xCaxSi2 samples were prepared in two steps: Ar-arc melting of a mixture of BaSi2 and CaSi2, followed by remelting and slow cooling of arc-melted Ba1−xCaxSi2 and subsequent annealing. A (1−xs):xs molar mixture of BaSi2 and CaSi2 (xs = 0.05, 0.10, 0.15, 0.16, and 0.20) was Ar-arc melted. The resultant ingot loaded into a BN crucible was melted in an Ar atmosphere by heating at 1470 K for 2 h, cooling to 1140 K at 5 K/h, and maintaining at 1140 K for 24 h. The detailed synthesis procedure is described in a previous study [11]. Prior to this melting step, the melting temperature of the arc-melted ingots was confirmed to be less than 1470 K using differential thermal analysis. The chemical composition of the samples was evaluated by electron probe microanalysis (EPMA). The details of the preparation method for the EPMA samples are described in a previous study [14]. The structures of single crystals isolated from the samples were determined using the XRD technique, which was performed using a four-axes goniometer equipped with a charge-coupled device area detector (Rigaku, AFC11 and Saturn 724+, graphite-monochromated Mo-Kα radiation, λ = 0.71073 Å) at room temperature. The following software programs were used for the XRD analysis: CrystalClear [15] for data collection, cell refinement, and data reduction, and SHELXL-97 [16] for structure refinement. Diffuse reflectance spectra were recorded in the range of 190–2000 nm using a spectrometer (JASCO Co. V-570) equipped with an integrating sphere attachment. Optical absorbance spectra were obtained by converting the diffuse reflectance spectra using the Kubelka–Munk equation: α/S = (1−R)2/2R, where α, R, and S are the optical absorption coefficient, relative diffuse reflectance of a sample to the standard material, and scattering coefficient, respectively [17]. The band structure was calculated within the generalized gradient approximation of Perdew, Burke, and Ernzerhof (GGA- PBE) [18] using the Advance/PHASE program package [19]. A norm-conserving pseudopotential was employed for the Si atoms and an ultrasoft pseudopotential was utilized for the Ca and Ba atoms. The cut-off energies for plane waves and charge densities were 16.25 and 146.25 Hartree, respectively. A 4 × 4 × 2 Monkhorst–Pack k-point grid was adopted for convergence.  3. Results and discussion 3.1 Phase identification 5  Figure 2 shows backscattered electron images of the samples with xs = 0.05, 0.10, and 0.15. The sample with xs = 0.05 consists of a single phase (light gray area), while those with xs = 0.10 and 0.15 consist of two phases (light and dark gray areas). The EPMA revealed that the light gray area corresponds to Ba1−xCaxSi2 (x = 0.04 and 0.05), and the dark gray area corresponds to Ca1−yBaySi2 (y = 0.006 and 0.01). Figure 3 shows the Ca content of the light gray area determined by EPMA (x) as a function of xs. x increases with xs; however, x is smaller than xs. x reaches 0.07 approximately at xs = 0.20. x of 0.07 corresponds to 2.3 at.%. These results suggest that the BaSi2–CaSi2 pseudo-binary diagram has a eutectic phase, as suggested in a previous study [13], and the solid-solution limit of Ca in BaSi2 is approximately 2.3 at.%, and that of Ba in CaSi2 is approximately 0.4 at.%.   Fig. 2 Backscattered electron images of samples Ba1-xsCaxsSi2 with (a) xs = 0.05, (b) xs = 0.10, and (c) xs = 0.15.    (a) xs=0.05100 µm(c) xs=0.15100 µm(b) xs=0.10100 µm6   Fig. 3. (a) Ca content of Ba1-xsCaxsSi2 determined by EPMA (x) as a function of Ca content in the starting material (xs). (b) Ca content of Ba1-xCaxSi2 determined by single-crystal XRD (xXRD) as a function of x.  3.2 Crystal structure Table 1 lists lattice parameters, atomic coordinates, and temperature factors of Ba1−xCaxSi2 determined by the single-crystal XRD measurements. Figure 4 (a) shows the lattice parameters normalized with those of BaSi2 [20] as functions of the Ca content, x. The lattice parameters decrease monotonically with x, with the a/a0 parameter decreasing slightly more than the other two, b/b0 and c/c0. The normalized lattice parameters of Ba1−xCaxSi2 are smaller than those of Ba1−xSrxSi2 for all the substitution element content. The XRD analysis revealed that Ca atoms preferentially occupied only the A1 site for all x values. As shown in Fig. 4 (b), the occupancy of the A1 site increases with x. The x dependence of the Ca occupancy at the A1 site in Ba1−xCaxSi2 is almost the same as that of the Sr occupancy at the A1 site in Ba1−xSrxSi2. The preferential occupation of the A1 site by Ca atoms is consistent with the previously reported computational result for Ba0.5Ca0.5Si2, wherein, the Ba atoms substituted with Ca at the A1 site are more stable than those of the Ba atoms substituted with Ca at the A2 site [10]. Figure 3 (b) shows the Ca content calculated based on the Ca occupancy determined from single-crystal XRD data (xXRD) as a function of x. The xXRD value is consistent with that of x, although the xXRD value is slightly larger than that of x. Figure 4 (c) shows the volumes of the coordination polyhedra at the A1 and A2 sites, Si4 tetrahedron, and unit cell of Ba1−xCaxSi2 normalized with respect to those of BaSi2 [20] as functions of x. The coordination polyhedra at the A1 and A2 sites are denoted as CP-A1 and CP-A2, respectively. The volume of CP-A2 (89.013 Å3 for BaSi2) is larger than that of CP-A1 (75.311 Å3 for BaSi2). All normalized volumes decreased 7  with increasing x, although the decrease in the Si4 tetrahedron was smaller than that of the other three, unit cell, CP-A1, and CP-A2. The small decrease in the Si4 volume is attributed to the covalent bonds forming the Si4 tetrahedron [21,22]. For any given Ca content, the normalized volume of CP-A2 was larger than that of the unit cell, whereas that of CP-A1 was smaller than that of the unit cell. This result suggests that the volume of CP-A1 decreased more rapidly with an increase in Ca content than that of CP-A2.    8  Table. 1. Lattice parameters, atomic coordinates, and temperature factors (in Å2) of Ba1−xCaxSi2 (orthorhombic, space group: Pnma, No. 62, Z = 8). Ueq and Uij (i, j = 1, 2, and 3) are the isotropic and anisotropic temperature factors, respectively. The values in the parenthesis are standard deviations. (a) x = 0.025 Lattice parameters: a = 8.9070(2) Å, b = 6.7136(2) Å, c = 11.5147(2) Å, V = 688.56(3) Å3. Final R indexes: Rint = 0.0301, R [F2 > 2σ(F2)] = 0.0230, wR(F2) = 0.0517, S = 1.193.   Atomic site Wyckoff position x y z Occupancy Ueq A1 4c 0.01435(2) 1/4 0.69337(2) 0.9533(12) Ba 0.01332(3)              0.0467(12) Ca       A2 4c 0.83853(2) 1/4 0.09466(2) 1 Ba 0.01479(3) Si1 4c 0.41738(6) 1/4 0.08966(5) 1 0.01756(10) Si2 4c 0.19714(6) 1/4 0.96526(4) 1 0.01487(9) Si3 8d 0.19434(4) 0.42822(6) 0.14504(3) 1 0.01587(7)  Atomic site U11 U22 U33 U12 U13 U23 A1 0.01255(4) 0.01422(6) 0.01319(4) 0.0000 -0.00033(2) 0.0000 A2 0.01715(5) 0.01312(6) 0.01411(4) 0.0000 0.00023(3) 0.0000 Si1 0.01277(18) 0.0227(3) 0.0172(2) 0.0000 0.00016(15) 0.0000 Si2 0.01696(19) 0.0163(2) 0.01136(16) 0.0000 -0.00123(14) 0.0000 Si3 0.01844(14) 0.01342(17) 0.01574(13) 0.00133(12) -0.00028(11) -0.00269(11)  (b) x = 0.037 Lattice parameters: a = 8.8737(2) Å, b = 6.70000(10) Å, c = 11.4855(3) Å, V = 682.86(3) Å3. Final R indexes: Rint = 0.0272, R [F2 > 2σ(F2)] = 0.0244, wR(F2) = 0.0542, S = 1.315.   Atomic site Wyckoff position x y z Occ. Ueq A1 4c 0.01386(2) 1/4 0.69391(2) 0.8727(10) Ba 0.01312(3)      0.1273(10) Ca  A2 4c 0.83836(2) 1/4 0.09458(2) 1 Ba 0.01450(3) Si1 4c 0.41913(6) 1/4 0.08909(4) 1 0.01853(8) Si2 4c 0.19738(5) 1/4 0.96483(4) 1 0.01500(7) Si3 8d 0.19530(4) 0.42875(5) 0.14504(3) 1 0.01637(6)  9  Atomic site U11 U22 U33 U12 U13 U23 A1 0.01236(4) 0.01385(4) 0.01313(4) 0.0000 -0.00051(2) 0.0000 A2 0.01710(5) 0.01259(4) 0.01379(4) 0.0000 0.00026(2) 0.0000 Si1 0.01348(18) 0.0232(2) 0.01887(19) 0.0000 -0.00098(13) 0.0000 Si2 0.01732(17) 0.01567(16) 0.01201(15) 0.0000 -0.00175(13) 0.0000 Si3 0.01969(13) 0.01335(11) 0.01606(13) 0.00155(9) -0.00103(10) -0.00263(9)  (c) x = 0.062 Lattice parameters: a = 8.8563(2) Å, b = 6.6895(2) Å, c = 11.4728(3) Å, V = 679.70(3) Å3. Final R indexes : Rint = 0.0341 R [F2 > 2σ(F2)] = 0.0284, wR(F2) = 0.0609, S = 1.369.   Atomic site Wyckoff position x y z Occ. Ueq A1 4c 0.01362(2) 1/4 0.69413(2) 0.8381(12) Ba 0.01295(4)      0.1619(12) Ca  A2 4c 0.83832(2) 1/4 0.09456(2) 1 Ba 0.01425(3) Si1 4c 0.41976(6) 1/4 0.08876(5) 1 0.01900(10) Si2 4c 0.19752(6) 1/4 0.96470(4) 1 0.01511(8) Si3 8d 0.19571(4) 0.42896(6) 0.14504(3) 1 0.01653(6)  Atomic site U11 U22 U33 U12 U13 U23 A1 0.01215(5) 0.01369(5) 0.01301(5) 0.0000 -0.00054(2) 0.0000 A2 0.01689(5) 0.01232(5) 0.01355(5) 0.0000 0.00031(2) 0.0000 Si1 0.01412(18) 0.0236(3) 0.0192(2) 0.0000 -0.00154(15) 0.0000 Si2 0.01755(18) 0.0155(2) 0.01225(16) 0.0000 -0.00218(14) 0.0000 Si3 0.02002(14) 0.01340(14) 0.01619(14) 0.00148(10) -0.00119(11) -0.0261(10)  (d) x = 0.064 Lattice parameters: a = 8.8529(2) Å, b = 6.6874(2) Å, c = 11.4654(3) Å, V = 678.78(3) Å3. Final R indexes: Rint = 0.0355 R [F2 > 2σ(F2)] = 0.0389, wR(F2) = 0.0725, S = 1.288.   Atomic site Wyckoff position x y z Occ. Ueq A1 4c 0.01353(2) 1/4 0.69423(2) 0.831(2) Ba 0.01285(5)      0.169(2) Ca  A2 4c 0.83830(2) 1/4 0.09455(2) 1 Ba 0.01421(5) Si1 4c 0.41989(11) 1/4 0.08856(9) 1 0.01905(18) Si2 4c 0.19763(11) 1/4 0.96453(8) 1 0.01501(15) 10  Si3 8d 0.19595(8) 0.42895(10) 0.14507(6) 1 0.01669(12)  Atomic site U11 U22 U33 U12 U13 U23 A1 0.01191(7) 0.01361(9) 0.01303(8) 0.0000 -0.00055(5) 0.0000 A2 0.01678(8) 0.01226(8) 0.01360(8) 0.0000 0.00035(5) 0.0000 Si1 0.0139(3) 0.0237(5) 0.0195(4) 0.0000 -0.0017(3) 0.0000 Si2 0.0175(3) 0.0152(4) 0.0124(3) 0.0000 -0.0019(3) 0.0000 Si3 0.0200(3) 0.0135(3) 0.0166(3) 0.0015(2) -0.0015(2) -0.0027(2)  (e) x = 0.072 Lattice parameters: a = 8.8624(4) Å, b = 6.6934(3) Å, c = 11.4723(6) Å, V = 680.53(6) Å3. Final R indexes: Rint = 0.0365, R [F2 > 2σ(F2)] = 0.0224, wR(F2) = 0.0527, S = 1.159.   Atomic site Wyckoff position x y z Occ. Ueq A1 4c 0.01366(2) 1/4 0.69411(2) 0.8406(10) Ba 0.01374(3)      0.1594(10) Ca  A2 4c 0.83834(2) 1/4 0.09455(2) 1 Ba 0.01509(3) Si1 4c 0.41975(6) 1/4 0.08875(5) 1 0.01973(9) Si2 4c 0.19748(6) 1/4 0.96465(4) 1 0.01590(8) Si3 8d 0.19572(4) 0.42896(5) 0.14503(3) 1 0.01740(6)  Atomic site U11 U22 U33 U12 U13 U23 A1 0.01323(5) 0.01413(4) 0.01385(5) 0.0000 -0.00053(3) 0.0000 A2 0.01803(5) 0.01286(4) 0.01439(5) 0.0000 0.00029(2) 0.0000 Si1 0.01497(19) 0.0240(2) 0.0202(2) 0.0000 -0.00128(15) 0.0000 Si2 0.01847(19) 0.01585(16) 0.01337(17) 0.0000 -0.00202(15) 0.0000 Si3 0.02123(14) 0.01396(12) 0.01701(14) 0.00143(10) -0.00145(11) -0.00253(9)     11   Fig. 4. (a) Lattice parameters normalized with respect to those of BaSi2 [20] as functions of substitution element content (x). (b) Site occupancy of substitution atoms at A1 and A2 sites as a function of x. (c) Volumes of CP-A1, CP-A2, Si4 tetrahedron, and unit cell normalized with respect to those of BaSi2 [20], as functions of x. Solid and empty symbols represent data of Ba1−xCaxSi2 (BCS) and Ba1−xSrxSi2 (BSS), respectively.    12  3.3 Band gap Figure 5 (a) shows the plot of the optical absorbance(α/S) of Ba1−xSrxSi2 as a function of the photon energy (hν), where α and S are the optical absorption coefficient and scattering coefficient, respectively. We defined the band gap (Eg) as the energy at which the extrapolated α/S curve intersects the extrapolation of the background (arrows in the figure), as proposed in a previous study [23]. Figure 5 (b) shows the Eg value of Ba1−xCaxSi2 obtained from α/S as a function of x. The Eg value of BaSi2 is 1.24 eV, and Eg decreases with increasing x. The Eg values of Ba1−xCaxSi2 are smaller than those of Ba1−xSrxSi2 for all the substitution element content. The Eg value of Ba1−xCaxSi2 is 1.17 eV at x = 0.072, which corresponds to that of Ba1−xSrxSi2 at x = 0.58 (1.17 eV). The lattice parameters of Ba1−xCaxSi2 at x = 0.072 were approximately the same as those of Ba1−xSrxSi2 at x = 0.16, and the Eg values of Ba1−xCaxSi2 at x = 0.072 were approximately similar to those of Ba1−xSrxSi2 at x = 0.58. This suggests that Ca substitution can decrease the Eg value with a smaller lattice deformation than Sr substitution.  13   Fig. 5. (a) Optical absorbance (α/S) of Ba1−xCaxSi2 as a function of photon energy (hν). (b) Band gaps (Eg)of Ba1−xCaxSi2 and Ba1−xSrxSi2 [11] as functions of substitution element content (x). Red circles and green squares represent data of Ba1−xCaxSi2 and Ba1−xSrxSi2, respectively.    14  3.4 Calculated band structures      Band structures of the following six models were calculated: (a) BaSi2 (Ba8Si16) with lattice parameters and atomic positions reported in Ref. 20; (b) BaSi2 with lattice parameters and atomic positions of Ba1−xCaxSi2 with x = 0.062; (c) Ba7Ca1Si16 with lattice parameters and atomic positions of BaSi2 reported in Ref. 20; (d) Ba7Ca1Si16 with lattice parameters and atomic positions of Ba1−xCaxSi2 with x = 0.062; (e) Ba7Sr1Si16 with lattice parameters and atomic positions of BaSi2 reported in Ref. 20; and (f) Ba7Sr1Si16 with lattice parameters and atomic positions of Ba1−xSrxSi2 with x = 0.10 [11]. To create models (c) and (d), a Ba atom occupying the A1 site was replaced by a Ca atom in models (a) and (b). BaSi2 has four Ba atoms at the A1 sites in its unit cell. We calculated the total energy of Ba7Ca1Si16 with four different Ca atomic positions and confirmed that the total energies of the four models were the same within a convergence criterion of 1.0 × 10−9 Hartree. Thus, we demonstrate the band structure of Ba7Ca1Si16 in which the Ba atom at the A1 site (marked by an arrow in Fig. 1) is replaced by a Ca atom. We created models (e) and (f) by replacing the Ba atom at the A1 site (marked by an arrow in Fig. 1) with a Sr atom. Figure 6 shows the band structures of BaSi2 and Ba7Ca1Si16. The volume of Ba7Ca1Si46 is 0.982 V0, where V0 is the unit cell volume of BaSi2. Figure 6 (a) revealed that BaSi2 with V = V0 is an indirect band gap semiconductor that has a valence band maximum (VBM) at the k-point between Γ and Y point and a conduction band minimum (CBM) at the T point, which is consistent with the previously reported results [5,6,10,11,24]. The remaining five, including Ba7Sr1Si46, are also indirect band gap semiconductors with a VBM and CBM at the same k-points.   15   Fig. 6. Band structure of (a) BaSi2 at V/V0 = 1.00, (b) BaSi2 at V/V0 = 0.982, (c) Ba7Ca1Si16 at V/V0 = 1.00, and (d) Ba7Ca1Si16 at V/V0 = 0.982, where V and V0 are the unit cell volume and unit cell volume of BaSi2 at 0 GPa, respectively [20]. Red and green circles represent a valence band maximum and conduction band minimum, respectively.    BaSi2 (Ba8Si16)Ba7Ca1Si16S    X    Γ Y   T   R    U   Z  Γ(d) V/V0=0.982-1Energy (eV)012c) V/V0=1.0S    X    Γ Y   T   R    U   Z  Γ-1Energy (eV)012(b) V/V0=0.982-1Energy (eV)012S    X    Γ Y  T   R     U   Z  Γ(a) V/V0=1.0-1Energy (eV)012S  X    Γ Y  T   R     U   Z  Γ16  3.5 Comparison of experimental and calculated band gap results DFT calculations using GGA-PBE underestimate the band gap of semiconductors. Therefore, we calculated the difference in Eg between substituted BaSi2 and BaSi2, ΔEg = Eg(V/V0)−Eg0 for both experimental and computational results and compared them, where Eg0 is the band gap of BaSi2 at V = V0. Figure 7 shows ΔEg for Ba1-xCaxSi2 and Ba1-xSrxSi2 as a function of V/V0. The calculated ΔEg values of Ba7Ca1Si46 and Ba7Sr1Si46 are larger than those of BaSi2 at all V/V0 values, suggesting that the substitution of Ba atoms by Sr and Ca increases ΔEg value when the unit cell volume remains the same after the substitution. The calculated ΔEg values of BaSi2, Ba7Ca1Si46, and Ba7Sr1Si46 decrease with decreasing V/V0. The calculated ΔEg value of Ba7Sr1Si46 at V/V0 = 0.988 agrees well with the experimental ΔEg value of Ba1−xSrxSi2 with x = 0.10. Thus, the volume reduction due to Sr substitution is a main reason for decrease of band gap in Ba1-xSrxSi2. These results suggest that both substitution at V = V0 and volume reduction are required to explain the experimental Eg value of Ba1−xSrxSi2. The decrease in Eg in Ba1−xCaxSi2 can also be explained by a combination of substitution and volume reduction effects qualitatively. However, the magnitude of experimental ΔEg value of Ba1−xCaxSi2 with x = 0.062 (0.065 eV) is larger than that of calculated ΔEg value of Ba7Ca1Si46 at V/V0 = 0.982 (0.008 eV). This indicates that considering the additional effect along with the substitution and volume reduction effects, such as the effect of defects introduction, is essential to more precisely explain the Eg value of Ba1−xCaxSi2.  Fig. 7. Difference in Eg between substituted BaSi2 and BaSi2: ΔEg = Eg(V/V0)−Eg0 as a function of V/V0, where Eg0 is the band gap of BaSi2 at V/V0 = 1.00. Solid and empty symbols represent the experimental and computational data, respectively.   17  4. Conclusion The effects of substituting Ba with Ca atoms on the crystal structure and band gap (Eg)of BaSi2 were investigated both experimentally and computationally. The solid-solution limit of the Ca atoms in BaSi2 was approximately 2.3 at.%. Single-crystal XRD measurements of Ba1−xCaxSi2 (0.025 ≤ x ≤ 0.072) revealed that the unit cell volume decreases with x, and the Ba atoms at the A1 crystallographic site are preferentially substituted by Ca atoms. Diffuse reflectance spectroscopy results revealed that Eg decreases with x (1.24 eV at x = 0 and 1.17 eV at x = 0.072). The decreases in the lattice parameters, unit cell volume, and Eg in Ba1−xCaxSi2 were larger than those in Ba1−xSrxSi2 for a given substitution element content. The band gap calculations demonstrate that Ba1−xCaxSi2 is an indirect band gap semiconductor with VBM at a k-point between Γ and Y points and CBM at the T point; the same features were observed for BaSi2 as well. The decrease in Eg by substitution observed experimentally can be explained qualitatively by a combination of substitution at V=V0 and volume reduction. Volume reduction due to Ca substitution is mainly responsible for decrease of Eg in Ba1-xCaxSi2. To discuss the decrease in Eg by Ca substitution, considering additional effects such as defect introduction is essential. Practically, Ca substitution would be more effective for band gap tuning of BaSi2 because it can decrease the Eg value with a smaller lattice deformation than Sr substitution. These results will be significant as a basic knowledge for band gap tuning in fabricating BaSi2-based solar cell.   Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.   CRediT Authorship contribution Statements M. Imai: Conceptualization, Supervision, Project administration, Funding acquisitions, Resources, Investigation, Formal analysis, Validation, Data Curation, Visualization, Writing - Original draft, Writing – Review & editing. Y. Matsushita: Investigation, Formal analysis, Writing – Review & editing.  Funding This study was partially supported by Grants-in-Aid for Scientific Research (KAKENHI) 18  [grant numbers JP19H05819, JP22H00268] from the Japan Society for the Promotion of Science (JSPS).  Acknowledgments The authors thank Mitsuaki Nishio of the National Institute for Materials Science (NIMS) for the EPMA and Masahiko Kawasaki of NIMS for sealing the samples in quartz tubes.    19  References [1] Nakamura, T. Suemasu, K. Takakura, F. Hasegawa, A. Wakahara, M. Imai, Investigation of the energy band structure of orthorhombic BaSi2 by optical and electrical measurements and theoretical calculations, Appl. Phys. Lett. 81 (2002) 1032–1034. https://doi.org/10.1063/1.1498865. [2] T. 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