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## Creator

[Motoharu Imai](https://orcid.org/0000-0002-5848-113X), [Masao Arai](https://orcid.org/0000-0003-0088-5649)

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This is the Accepted Manuscript version of an article accepted for publication in Japanese Journal of Applied Physics.  IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it.  The Version of Record is available online at https://doi.org/10.35848/1347-4065/ade487.[Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/)

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[Electronic structure and chemical bonding in semiconducting 3d transition-metal silicides CrSi<sub>2</sub>, Mn<sub>4</sub>Si<sub>7</sub>, and <i>β</i>-FeSi<sub>2</sub>](https://mdr.nims.go.jp/datasets/90b1615a-82ac-4435-b3b1-0134a7b78a97)

## Fulltext

Title of Paper Goes Here:1  Electronic structure and chemical bonding in semiconducting 3d transition-metal silicides CrSi2, Mn4Si7, and β-FeSi2 Motoharu Imai1* and Masao Arai2  1Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Ibaraki, 305-0047, Japan 2National Center for Basic Research on Materials, National Institute for Materials Science, Tsukuba, Ibaraki, 305-0044, Japan *E-mail: IMAI.Motoharu@nims.go.jp  The electronic properties and chemical bonding of semiconducting 3d transition-metal (TM) silicides—CrSi2, Mn4Si7, and β-FeSi2—were investigated using first-principles calculations. The density of states (DOS), orbital-projected DOS, and crystal orbital bond indices (COBIs) revealed that the electronic states of these silicides consisted of Si 3s states, bonding states of Si 3p and TM 3d orbitals, nonbonding states of TM 3d orbitals, antibonding states of Si 3p and TM 3d orbitals, and a bandgap (Eg) formed between the TM 3d nonbonding states and Si 3p-TM 3d antibonding states. The Löwdin charges and integrated COBI values indicate minimal charge transfer between the TM and Si atoms and suggest that the TM–Si interaction has a delocalized nature, similar to metallic bonding. Additionally, the Eg calculated using the generalized gradient approximation is comparable to the Eg determined experimentally for these silicides.  2  1. Introduction Transition-metal (TM) silicides were extensively investigated as electrode materials for Si devices in the 1980s,1,2) and an interaction diagram of silicides, as shown in Fig. 1, was proposed to clarify their electronic states.3) According to this diagram, the electronic structure of TM silicides consists of Si 3s states, bonding and antibonding states between the Si 3p and TM d orbitals, and nonbonding states of the TM d orbitals. Semiconducting 3d-TM silicides such as CrSi2, Mn4Si7, and β-FeSi2 have been studied extensively as thermoelectric and optoelectric materials.4-8) In the case of semiconducting silicides, the the information where the bandgap (Eg) locates in the interaction diagram is useful for band engineering of semiconducting 3d-TM silicides. However, there are no reports on this topic.  Fig. 1. Interaction diagram of TM silicides.3)  3  The electronic states and chemical-bonding characteristics of solids have been analyzed by calculating the density of states (DOS), orbital-projected density of states (pDOS), crystal orbital Hamilton population (COHP),9–13) crystal orbital bonding indices (COBIs)14,15) and Löwdin charges.16) It is efficient to clarify Eg in the interaction diagram of TM silicides using the chemical-bonding information obtained from the calculations of the DOS, pDOS, and COBIs because pDOS reveals the contribution of each orbital to the electronic states, and the bonding, antibonding, and non-bonding states can be distinguished using their COBI values. Positive and negative COBI values correspond to bonding and antibonding electronic states, respectively. Furthermore, small COBI values correspond to nonbonding states. In this study, the band structure, DOS, pDOS, COBI, and Löwdin charges were calculated for CrSi2, Mn4Si7, and β-FeSi2. On the basis of these results, we examined their chemical-bonding nature, along with the location of Eg in the interaction diagram in CrSi2, Mn4Si7, and β-FeSi2.  2. Methods Electronic structures such as DOS and band structures were calculated using the projector augmented wave (PAW) method, as implemented in the Vienna Ab initio Simulation Package (VASP) code within the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE).17,18) Spin–orbit coupling (SOC) was included self-consistently. The energy cutoff of 400 eV was used. The Γ-centered 15 × 15 × 8, 9 × 9 × 3, and 8 × 8 × 6 k-meshes were used for CrSi2, Mn4Si7, and β-FeSi2, respectively. The electronic convergence criterion was set as 10-8 eV. The crystal structure was fully 4  optimized without the SOC using a criterion of 0.02 eVÅ-1. The VASPKIT code was used to create the input files and analyze the output.19) The COBI and Löwdin charges were calculated from the VASP output using the Local Orbital Basis Suite Towards Electronic Structure Reconstruction (LOBSTER) code.12–16) The PAW functions were projected onto local orbitals using the basis-function set pbeVaspFit2015 with the autorotate option.12) The orbitals included were 3p, 3d, and 4s for the TM atoms and 3s and 3p for the Si atoms.   3. Results and discussion 3.1 Crystal structure Table I presents details regarding the calculated crystal structures of (a) CrSi2, (b) Mn4Si7, and (c) β-FeSi2. The calculations reproduced the experimental lattice parameters reported in refs. 20-23 within an error of 1.5%, as shown in Table II, and the experimental internal parameters within an error of 2.1%. Table I. Calculated crystal structure (a) CrSi2 Space group: P6222 (No. 180)  Number of formula units in unit cell Z: 3 Lattice parameters (Å): a = 4.38040, c = 6.32897 Site Elements Wycoff position x y z Cr1 Cr 3d 1/2 0 1/2 Si1 Si 6j 0.166157       0.332314 1/2  (b) Mn4Si7 Space group: P-4c2 (No. 116) Number of formula units in unit cell Z: 4 5  Lattice parameters (Å): a = 5.46915, c = 17.27104 Site Elements Wycoff position x y z Mn1 Mn 2c 0 0 0 Mn2 Mn 4i 1/2 0 0.065034 Mn3 Mn 4h 1/2 1/2 0.130021 Mn4 Mn 4i 0 1/2 0.191643 Mn5 Mn 2a 0 0 1/4 Si1 Si 8j 0.155344 0.199730 0.112640 Si2 Si 8j 0.320660 0.841127 0.182430 Si3 Si 4e 0.333636 0.333636 1/4 Si4 Si 8j 0.346457 0.230434 0.961206  (c) β-FeSi2 Space group: Cmce (No. 64)  Number of formula units in unit cell Z: 16 Lattice parameters (Å): a = 9.86469, b = 7.7562, c = 7.7974 Site Elements Wycoff position x y z Fe1 Fe 8d 0.21644 0 0 Fe2 Fe 8f 1/2 0.30777 0.1873 Si1 Si 16g 0.12825 0.27375 0.05013 Si2 Si 16g 0.37351 0.04500 0.226735   Table II. Latice parameters of CrSi2, Mn4Si7, and β-FeSi2 (Cal: calculation, Exp: experiment). 20-23)    Lattice parameters (Å)   Silicide Structure type Crystal system a b c Remark Ref. CrSi2 CrSi2 Hexagonal 4.38039 - 6.32897 Cal Present    4.42758(7) - 6.36805(11) Exp 20 Mn4Si7 Mn4Si7 Tetragonal 5.46914 - 17.27104 Cal Present    5.510 - 17.418 Cal 21    5.5259(5) - 17.5156(8) Exp 22 β-FeSi2 FeSi2 Orthorhombic 9.84694 7.75623 7.797395 Cal Present    9.863(7) 7.791(6) 7.833(6) Exp 23   6 3.2 Band structure 3.2.1 CrSi2 Fig. 2(a) shows the band structure of CrSi2, in which the valence-band maximum (VBM) is set as 0 eV, indicating that CrSi2 is an indirect-bandgap semiconductor with VBM and conduction-band minimum (CBM) located at the L and M points, respectively. Its Eg value is 0.368 eV (0.369 eV without SOC), which is consistent with a previously reported calculation result (0.35 eV).24) This calculated Eg value is comparable to the experimental one determined via optical absorption coefficient (α) measurement (0.35 eV).25)    7  Fig. 2. Band structures of (a) CrSi2, (b) Mn4Si7, and (c) β-FeSi2.  3.2.2 Mn4Si7 The band structure of Mn4Si7 indicates that Mn4Si7 is an indirect-bandgap semiconductor with the VBM at the Γ point and CBM at the Z point, respectively, as shown in Fig. 2(b). The Eg value is 0.817 eV (0.818 without SOC), which slightly exceeds a previously reported  8 calculation result (0.769 eV).21) As suggested by Migas, the Eg values for direct transitions at the Γ (0.840 eV) and Z (0.845 eV) points are close to the indirect-Eg value. The reported experimental Eg values range from 0.42 to 0.98 eV, as shown in Table III. In previous studies, α measurements using single-crystal and thin-film samples indicated that the Mn4Si7 phase had a direct bandgap of 0.78 eV.26,27) Spectral ellipsometry of polycrystalline thin films with a preferred orientation relationship with the Si substrate revealed an indirect Eg of 0.4 eV.28) Recent α measurements using Mn4Si7 thin film samples containing a nearly strain-free Mn4Si7 phase had an Eg of 0.78 eV, and samples containing embedded strained Mn4Si7 precipitates exhibited an Eg of 0.93 eV.29) When the experimental Eg value is assumed to be 0.78 eV, the present calculated Eg value is consistent with the experimental value. The α for a direct transition is expected to be observed when the indirect-Eg value is close to the direct Eg value, because the magnitude of α for a direct transition is far larger than that for an indirect transition. This situation may occur in Mn4Si7, because the indirect-Eg value is close to the direct Eg values at the Γ and Z points in the present calculation. This is plausibly why the experimentally observed α has photon-energy dependence for a direct transition although the calculations indicate that Mn4Si7 is an indirect-Eg semiconductor.  Table III. Bandgap Eg of Mn4Si7. Experimental Eg values were obtained through optical absorption coefficient measurements (Cal: calculation, Exp: experiment). Eg (eV) Transition type Remarks Ref. 0.816 Indirect Cal Present 0.836 Direct at Γ point Cal Present 0.841 Direct at Z point Cal Present 0.769 Indirect Cal 21 0.78 Direct Exp 26,27 0.4 Indirect Exp 28 0.78 Direct Exp 29 0.92 Direct Exp, strained 29  3.2.3 β-FeSi2 β-FeSi2 is an indirect-Eg semiconductor with the VBM at the Y point and CBM at a k point between the Γ and Z points (conventionally denoted as Λ*), as shown in Fig. 2(c). The Eg value was 0.724 eV (0.723 wo SOC), which slightly exceeds the previously reported calculation result (0.68 eV).30) This calculated Eg value is comparable to the experimental one based on α measurements (0.814 eV).31)  9 Notably, the calculated Eg values for these three semiconducting silicides were comparable to the experimental Eg values, although the Eg values calculated using PBE-GGA underestimated the experimental values in many cases.32)   3.3 DOS, COBI, and Löwdin charge The left panels of Figs. 3 (a), (b), and (c) show the total DOS and pDOS of CrSi2, Mn4Si7, and β-FeSi2, respectively. The pDOS was calculated using LOBSTER code. The total DOS and pDOS of these three materials have the following common features: (1) the DOS located from –15 to –5 eV consists of Si 3s and Si 3p states, (2) the total DOS has two large peaks—P1 and P2—in the valence band (VB), (3) the peak at a higher energy P1 consists of TM 3d states and the peak at lower energy P2 consists of TM 3d and Si 3p states, and (4) the conduction band (CB) near bandgap mainly consists of TM 3d states. The energies of peaks P1 and P2 are presented in Table IV. Thus, the TM 3d states significantly contribute to the DOS of the VB and CB near Eg.  Table IV. Energies of two large peaks P1 and P2 in the DOS of the VB. Silicide Energy of P1 (eV) Energy of P2 (eV) CrSi2 –0.65 –2.30 Mn4Si4 –0.20 –2.05 β-FeSi2 –0.55 –1.60 eV  Figs. 4 (a), (b), and (c) illustrate the crystal structures of CrSi2, Mn4Si7, and β-FeSi2, respectively. Figs. 4 (d), (e), and (f) show the local structures around the transition-metal atoms highlighted by the orange circles in Figs. 4 (a)–(c). In these silicides, the nearest neighbors of the TM atoms are the Si atoms, and those of the Si atoms are the TM atoms. Therefore, we calculated the COBI of the TM–Si pairs with the shortest interatomic distances, as indicated by the red solid lines in the figure, and averaged them. The right panels of Figs. 3 (a), (b), and (c) present the COBI for the Cr-Si bond of CrSi2, the Mn-Si bond of Mn4Si7, and the Fe-Si bond of β-FeSi2, respectively. The states with positive and negative COBI values are bonding and antibonding states, respectively. The states with small COBI values are nonbonding states. As mentioned previously, the pDOS of the TM 3d states exhibited two peaks in the VB. The ratio of COBI to DOS corresponding to the P1 peak in the DOS has a much smaller value than that to the P2 peak, indicating that this TM-3d state is a nonbonding state. The COBI corresponding to the P2 peak in the DOS has a large positive value, indicating that these TM pDOS states are the bonding states of the TM  10 3d–Si 3p states. The COBI that corresponds to the DOS in the CB has a large negative value, indicating that these states are antibonding states of the TM 3d–Si 3p states. Therefore, a bandgap exists between the TM-3d nonbonding states and TM 3d-Si 3p antibonding states, as shown in Fig. 5. These results provide a strategy for band engineering of semiconducting 3d-TM silicides: substituting Si atoms with other atoms affects the CB, whereas substituting TM atoms with other atoms affects both the VB and CB. This is helpful for tuning the electronic properties of semiconducting 3d-TM silicides.  Fig. 3. Total DOS, p-DOS, and COBI of (a) CrSi2, (b) Mn4Si7, and (c) β-FeSi2.  11   Fig. 4. Crystal structures of (a) CrSi2, (b) Mn4Si7, and (c) β-FeSi2. The blue lines depict the unit cell. The numbers in the figures are the Löwdin charges (in units of elementary charge e). (d)–(f) Local structures around the transition-metal atoms, highlighted by the orange circles in Figs. 4 (a)–(c). The red solid lines indicate TM–Si pairs whose COBI values were calculated. The numbers in the figures are interatomic distances (in units of Å).    12  Fig. 5. Interaction diagram of semiconducting 3d-TM silicides CrSi2, Mn4Si7, and β-FeSi2.  The Löwdin charges and the integrated COBI (ICOBI) values for CrSi2, Mn4Si7, and β-FeSi2 are presented in Table V. The Löwdin charge of an atom is defined as the difference between the number of valence electrons and the gross orbital population, including all orbitals associated with the atom. The Löwdin charges suggest that no charge transfer occurs in CrSi2 and that slight charge transfer occurs in Mn4Si7 and β-FeSi2. The ICOBI value is the integrated value of COBI per bond up to the Fermi energy. Regarding two-center interactions, the ICOBI values tend to be >0.6 for purely covalent bonding, 0.2–0.6 for delocalized interactions such as metallic bonding, and <0.2 for ionic bonding.15) The calculated ICOBI values suggest that the three semiconducting silicides have delocalized metallic bonds, as in the case of MoSi2.15)  Table V. Löwdin charges and ICOBI for CrSi2, Mn4Si7, and β-FeSi2.   Löwdin charge  Silicide TM atom Si atom ICOBI CrSi2 0e 0e 0.33 Mn4Si7 0.32e or 0.33e –0.17e or –0.19e 0.43 β-FeSi2 0.12e –0.06e 0.36  4. Conclusion  13 The electronic properties and chemical bonding of the semiconducting 3d-TM disilicides CrSi2, Mn4Si7, and β-FeSi2 were investigated using first-principles calculations. We confirmed that the Eg calculated using the generalized gradient approximation was comparable to the Eg determined experimentally for these silicides. The calculated DOS, pDOS, and COBI revealed that the electronic states of these silicides consist of Si 3s states, bonding states of Si 3p and TM 3d, nonbonding states of TM 3d, and antibonding states of Si 3p and TM 3d and that Eg is formed between nonbonding states of TM 3d and antibonding states of Si 3p and TM 3d. The Löwdin charges and ICOBI suggest that the TM–Si interaction has a delocalized nature, such as metallic bonding with minimal charge transfer.  The proposed interaction diagram provides the information necessary for band engineering of semiconducting 3d-TM silicides via substitution: substituting Si atoms with other atoms affects the CB, whereas substituting TM atoms with other atoms affects both the VB and CB. This information is helpful for the development of materials with enhanced properties.  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