Ba₂SiSe₄: a promising candidate with visual light transparency and p-type electrical conductivity

Abstract

Commercially available transparent conducting materials (TCMs) are typically n-type, and high-performance p-type TCMs are rare, which would impede the development of optoelectronics. Previous studies have shown that Ba₂SiSe₄ possesses a wide band-gap, low hole effective mass and high transmittance in the visible light region [R. Kormath Madam Raghupathy et al., Chem. Mater., 2018, 30, 6794–6800]. These characteristics imply that Ba₂SiSe₄ is a potential p-type TCM. However, research studies on its electrical conductivity are limited. In this work, p-type defects are screened based on HSE hybrid functional calculations. We find that Cs substituting Ba(Cs_Ba) is an ideal p-type defect with a transition energy (ε(0/−)) of 0.081 eV above the valence band maximum. Under the thermodynamic equilibrium fabrication scheme, Cs₂Se is the ideal dopant source for Cs dopants, and Se-rich, Ba (Si)-poor conditions are necessary to fabricate Cs_Ba defects. When doped samples are quenched from the preparation temperature to room temperature, their hole density reaches 4.04 × 10¹⁷ cm⁻³, and their p-type electrical conductivity reaches 32.3 S m⁻¹. When a non-equilibrium fabrication scheme is considered, as the hole density reaches 10²⁰ cm⁻³, the corresponding p-type electrical conductivity exceeds 10⁴ S m⁻¹. These results indicate that Ba₂SiSe₄ is a promising p-type TCM, which is valuable in developing high-performance transparent electronic devices.

---

1. Introduction

Wide gap semiconductors (WGSs) are widely used in solar cells,¹ nonvolatile memristors,² and photodetectors³ owing to their visible light transparency and excellent electrical conductivity. Currently, most optoelectronic devices are constructed by coating a polymer substrate with indium tin oxide.⁴ It is well known that indium is a toxic and rare metal element, which limits its large-scale applications. It is urgent to explore inexpensive, environmentally friendly and high-performance WGSs. Owing to the mutually exclusive nature of visible light transparency and electrical conductivity, high-performance WGSs are found only in few systems. According to the types of carriers, WGSs are categorized into n- and p-type. Among them, the transparent n-type conductive oxides (TCOs), such as Sn-doped In₂O₃ (ITO)⁵ and Al-doped ZnO (AZO),⁶ are commercially used. However, in most TCOs, it is challenging to introduce hole carriers owing to deeper O-2p orbitals.^7,8 In high-performance p-type WGSs, high electronegativity elements (oxygen) are usually avoided. Recently, non-oxide WGSs have attracted the attention of many researchers.^9–11 Owing to their better tunability, ternary compounds exhibit excellent application prospects in photovoltaics, lasers and infrared detection.¹² Huang et al. reported the p-type electrical conductivity of Ca-doped NaYTe₂.¹³ Kang et al. demonstrated that introducing a small amount of Ag into LiAlTe₂ can significantly enhance its p-type electrical conductivity.¹⁴ Ba₂SiSe₄, as a WGS, exhibits favorable optoelectronic properties and is cost-effective.^15,16 Its unique crystal structure and higher VBM make Ba₂SiSe₄ a potential p-type WGS. To date, studies on its p-type defects and electrical conductivity have been limited.

In this work, p-type defects and electrical conductivity are investigated using the Heyd–Scuseria–Ernzerhof (HSE) hybrid functional method.^17,18 Ionization energy values and the position of valence band edges with respect to vacuum energy levels show that Ba₂SiSe₄ can be doped to form p-type WGSs. The Cs substituting Ba₁ (labeled as Cs_Ba1) is a promising p-type defect, and Cs₂Se is an ideal dopant source. Thermodynamic equilibrium simulations predict that a hole density of 4.04 × 10¹⁷ cm⁻³ can be achieved when the doped samples are quenched to room temperature. The corresponding hole mobility and p-type electrical conductivity are 5.2 cm² V⁻¹ s⁻¹ and 32.3 S m⁻¹, respectively. These findings address the challenge of achieving high p-type electrical conductivity in WGSs and establish a design framework for next-generation p-type optoelectronics via controlled band-defect engineering.

2. Computational methods and details

All calculations are performed using density-functional theory (DFT)¹⁹ as implemented in VASP.²⁰ The projector augmented wave method is employed in conjunction with the Perdew–Burke–Ernzerhof generalized gradient approximation (PBE-GGA) to account for interactions between the core and valence electrons. The cutoff energy for the plane wave is set to 400.0 eV, and the optimal structure of the compound is captured with the 4 × 4 × 3 k-point grid. The energy and force convergence criteria are set as 10⁻⁵ eV and 0.02 eV Å⁻¹, respectively. Both the band structure and formation energy of Ba₂SiSe₄ are calculated with the HSE.^17,18

For defect calculations, the supercell (containing 252 atoms) is used to minimize the interactions between periodic defects. The formation energy of defect D in charge state q can be expressed as follows:^21,22

E[D^q] (E_p) represents the total energies of the supercell with (without) defect D in charge state q. n_i represents the number of atoms removed from (n_i < 0) or introduced into (n_i > 0) the host. ε_VBM is the energy level of the VBM, and Δε_F is the Fermi energy level with respect to the VBM. μ_i is the chemical potential, which represents the energy of the reservoirs, where the atoms are exchanged. The chemical potential satisfies certain boundary conditions and depends on the experimental conditions. The correction energy E_corr[D^q], used to minimize the errors induced by the finite-size supercell, is estimated by the extended Freysoldt–Neugebauer–Van de Walle scheme.^23,24 Meanwhile, the transition energy ε_D(q/q′) of defect D can be expressed as:^21,25,26

ε_D(q/q′) = [ΔH_f(D, q) − ΔH_f(D, q′)]/(q′ − q) (2)

Considering the thermodynamic equilibrium fabrication scheme, the density of defect D (charge state q) with the preparation temperature T_p and formation energy ΔH_f[D^q] is expressed as:^27,28

n(D, q) = N_siteg_qe^{−ΔH_f[Dq]/k_BT_P} (3)

N_site is the number of lattice sites D can occupy in a unit volume, and g_q is the multiple degeneracy factor of the corresponding charge state. ΔE_f[D^q] characterizes the formation energy of a specific charge state defect D. k_B is the Boltzmann constant.

The electron density (n) (hole density (p)) and Fermi energy as a function of preparation temperature T_P for Ba₂SiSe₄ are described as:

N_c and N_v are the effective state densities of the conduction and valence bands, respectively. E_g is the band-gap, and represents the effective mass of the electron (hole). h is the Planck's constant. The charge-neutral condition is necessary when introducing charged defects into the semiconductors:^27,28

N⁻_A + n = N⁺_D + p (6)

N⁻_A (N⁺_D) is the density of the negative (positive) charge. The Fermi energy level of the system can be obtained by solving eqn (3)–(6) self-consistently. In addition, when the doped samples are quenched from the preparation temperature (T_P) to room temperature, the total number of defects formed at high temperature remains constant, while the number of defects in different charge states would redistribute.^27,28

The doped samples are quenched from T_P to room temperature, and the densities of defect D with two charge states (0 and q) are as follows:

where is the total defect density. When the doped samples are quenched from T_P to room temperature, the carrier densities and Fermi energy can be obtained by solving eqn (3)–(8) self-consistently.

We constructed chemical potential diagrams by considering the total energies of all competing phases, and set the mixing parameter α with the same value for every impurity phase. The input files are generated by using the vise code²¹ and executed with the Pydefect package.²¹ All competing phases are screened from the Materials Project Database (MPD).²⁹ The chemical potentials are determined from the MPD when calculating the formation energy of each defect.^21,30

The transport properties of the carriers are evaluated using the AMSET package,³¹ in which the carrier scattering rate and mobility can be obtained via the momentum relaxation time approximation by solving the Boltzmann transport equation.³²

3. Results and discussion

3.1. Crystal and electronic structures

The crystal structure of Ba₂SiSe₄ is monoclinic, and it belongs to the P2₁/m space group. The optimized results are shown in Table S1 of the ESI.† Compared to the experimental values,³³ the difference is less than 2.5%, suggesting our geometrical optimizations are credible. Based on the doubly screened hybrid functional and a fixed μ = 0.71 Bohr⁻¹,^34–36 the calculated band gap of Ba₂SiSe₄ is 3.51 eV, which is smaller than the reported value (3.96 eV).^15,16 To reproduce the 3.96 eV band gap as reported earlier,^15,16 we chose to increase the mixing parameter α in the HSE hybrid functional.^37,38 When α is increased to 0.45, the calculated band gap for Ba₂SiSe₄ is 3.97 eV. The corresponding band structures and density of states (DOS) are shown in Fig. 1(a) and (b), respectively. The highly curved conduction band (valence band) indicates that the material has a low effective mass of electrons (holes). The effective mass of the hole for Ba₂SiSe₄ is only 0.21m₀ along the Γ–Z direction. A smaller hole effective mass means a better hole mobility and p-type electrical conductivity.³⁹ The DOS of Ba₂SiSe₄ show that the VBM is mainly from the Se-3p orbitals (Fig. 1(b)).

Fig. 1 Band structures for Ba₂SiSe₄, calculated using the HSE, α = 0.45, are plotted in (a). The corresponding DOS are shown in (b). The Fermi energy is set to 0 eV.

3.2. The tendency of p-type electrical conductivity of Ba₂SiSe₄

To understand the doping tendency, the band arrangement, along with the ionization energies of the donor and acceptor, is investigated. The empirical guidelines show that it is easier to achieve n (p)-type doping in WGSs if the conduction band maximum (valence band maximum) is deeper (shallower) than −4.00 (−6.00) eV.^40,41 The band arrangement of Ba₂SiSe₄ with other existing WGSs are shown in Fig. 2(a). Based on the vacuum energy levels, we calculated the positions of the VBM and CBM of Ba₂SiSe₄, and the corresponding results are −4.80 eV and −0.80 eV, respectively. The VBM of Ba₂SiSe₄ is significantly higher than those of common WGSs, which can be attributed to the dominance of the high Se-p orbitals (Fig. 1(b)). A higher VBM suggests p-type defects and electrical conductivity in Ba₂SiSe₄.

Fig. 2 Electronic band alignment of Ba₂SiSe₄ with existing typical WGSs plotted in panel (a). The value for Ba₂SiSe₄ is calculated using the HSE, while the others are experimental values.^40,47–52 The ionization energy difference of Ba₂SiSe₄ with existing WGSs is shown in panel (b).

Ionization energy has a significant impact on the defect properties of wide-gap semiconductors. A lower (higher) acceptor (donor) ionization energy is beneficial for increasing the number of hole carriers, thereby enhancing p-type conductivity.⁴² The ionization energy criterion, proposed by Gao et al., is expressed as:⁴³

ΔE = |E^A_I − E^D_I| (9)

where E^A_I (E^D_I) represents the acceptor (donor) ionization energy. The ionization energies can be estimated using the hydrogen-like model:^44,45Here, m* (m₀) represents the effective mass of carriers (mass of the electron), and ε_r is the relative dielectric constant. According to the ionization energy criterion, compounds with an ionization energy difference (ΔE) of less than 0.15 eV can be identified as intrinsic p-type WGSs.⁴⁶ The ionization energy is calculated and tabulated in Table S2 of the ESI.† Also, comparisons with other WGSs are shown in Fig. 2(b). A smaller ΔE (only 0.008 eV) suggests that Ba₂SiSe₄ can be doped to form p-type WGS.⁴³ Which defect is the shallow p-type defect, and how to realize the shallow p-type defect is an interesting issue.

3.3. Screening of p-type defects

To study the behavior of defects, the point defects with all unequal sites are considered (including vacancies, anti-sites, and interstitial sites). The screening of the defects is performed using the GGA method, and the corresponding results are shown in Fig. S1 of the ESI.† The defects, with lower formation energies (less than 3.0 eV), are recalculated with the HSE hybrid functional scheme (α = 0.45).

Considering all possible competing compounds, the chemical potential diagrams for Ba₂SiSe₄, with Ba, Se, and Se as variables, are plotted in Fig. 3(a). The stable region for single-phase Ba₂SiSe₄ is depicted by the saffron polygon, indicating that the Se-rich, Ba (Si)-poor condition is beneficial for forming Ba₂SiSe₄. Under the Se-rich, Ba (Si)-poor condition, the formation energies for all considered defects are calculated, and the corresponding results are plotted in Fig. 3(b).

Fig. 3 Under thermodynamic conditions, the stable phase regions for Ba₂SiSe₄ in the Ba–Si–Se chemical-potential diagram are shown using the orange polygon (a). The defect formation energies, under Se-rich and Ba (Si)-poor conditions, are shown in panel (b). The chemical potential of Cs is determined from Cs₂Se. The formation energy of externally doped Cs is also shown in panel (b).

Fig. 3(b) shows that two anti-site defects (Se_Ba1, Se_Ba2) possess low formation energies. This result is mainly due to the similar ionic radii of Se²⁻ and Ba²⁺, which allows Se to occupy the octahedral sites through lattice relaxation. Conversely, the smaller radius of Si⁴⁺ induces significant localized lattice distortions, resulting in the higher formation energies for Si_Ba2 and Si_i. Moreover, the transition energies ε(0/−) of Se_Ba1 and Se_Ba2 are higher than 2.50 eV above the VBM. These results indicate that Se_Ba1 and Se_Ba2 cannot be ionized and a high density of hole carriers is therefore impossible, which would seriously hinder p-type electrical conductivity. Hence, introducing an external impurity is necessary. We find that Cs substituting Ba₁ (Cs_Ba1) is a promising p-type defect. The formation energy for Cs_Ba with the E_F (dashed line) is shown in Fig. 3(b). Under the Se-rich, Ba (Si)-poor condition, the formation energy of neutral Cs_Ba1 is 0.90 eV, indicating that the Cs_Ba1 defects could be fabricated using the thermodynamic equilibrium fabrication scheme. The transition energy ε(0/−) for Cs_Ba1 is only 0.081 eV above the VBM, suggesting that the defects Cs_Ba1 could be ionized with a high density of holes in the samples.

3.4. The density of holes

Thermodynamic simulations of Cs doping in Ba₂SiSe₄ are conducted, taking into account the calculated defect formation and ionization energies, as well as the chemical potential stabilization region that was previously determined. Utilizing the electrically neutral condition, the defect density and hole density are calculated by self-consistently solving eqn (3)–(8). We employed a method of heating and quenching to room temperature (RT), which is a mature carrier density engineering method, to increase the hole density.^27,28,53 Under thermodynamic equilibrium preparation conditions, Ba₂SiSe₄ is grown at high preparation temperatures (T_P) to increase the hole density. At the same time, when Ba₂SiSe₄ is quenched to RT, the total number of defects does not change, and the hole density increases sharply due to redistributions in different charge states.¹⁰

Under the Se-rich, Ba (Si)-poor condition, the calculated Fermi energies, hole density, and major charge defect densities are plotted in Fig. 4, and the gray dashed line indicates the experimental preparation temperature (974.0 K) of Ba₂SiSe₄.³³ The E_f decreases from 0.40 eV to 0.27 eV (point A, Fig. 4(a)) when the T_P increases from 300.0 to 974.0 K. This finding suggests an increase in the hole density of Ba₂SiSe₄. As illustrated in Fig. 4(b), the hole density exhibits an increase from 8.31 × 10¹¹ cm⁻³ to 4.04 × 10¹⁷ cm⁻³ due to quenching from 974.0 K to 300.0 K (orange line). This phenomenon is primarily attributed to the high solubility of Cs_Ba1 at high T_P. At the same time, the higher formation energy of the hole killers Si_Ba2 and Si_i makes thesehole quencher defects play a minor role compared to that of Cs_Ba1 under the same growth conditions. As illustrated in Fig. 4(c), the density of Cs_Ba1 can reach 1.06 × 10¹⁸ cm⁻³ (974.0 K). This result is attributed to the lower defect formation energy and transition energy ε(0/−) of Cs_Ba1. Compared to the traditional p-type WGSs, such as ZnGa₂O₄ (1.60 × 10¹⁵ cm⁻³)⁵⁴ and CuAlO₂ (1.3 × 10¹⁷ cm⁻³),⁵⁵ Ba₂SiSe₄ possesses competitive p-type electrical conductivity. The detailed discussion of carrier densities is tabulated in Table S4 of the ESI.† To achieve a higher density of holes in Cs-doped Ba₂SiSe₄, it is necessary to consider non-equilibrium preparation methods,⁵⁶ such as the molecular beam epitaxy scheme.⁹

Fig. 4 The calculated Fermi energy, hole density, and defect density in Cs-doped Ba₂SiSe₄ are shown in panels (a)–(c). PT (RT) represents the results calculated at preparation temperatures (after quenching to room temperature).

3.5. Hole mobility and p-type electrical conductivity

In order to further characterize the p-type electrical conductivity of Ba₂SiSe₄, the charge transport behaviors are analyzed using the AMSET package.³¹ Hole mobility with the hole density at room temperature is presented in Fig. 5(a), which shows that at lower carrier densities (not exceeding 10¹⁸ cm⁻³), the maximum mobility of holes is approximately 5.20 cm² V⁻¹ s⁻¹. When the hole density reaches 2.5 × 10¹⁷ cm⁻³, the hole mobility for conventional p-type WGSs SnO is only 2.4 cm² V⁻¹ s⁻¹,⁵⁷ while the hole mobility of Ba₂SiSe₄ could reach 5.1 cm² V⁻¹ s⁻¹. The effects of scattering mechanisms on the hole mobility for Ba₂SiSe₄ at a carrier density of 4.04 × 10¹⁷ cm⁻³ are shown in Fig. 5(b). The polar optical phonon scattering (POP) emerges as the predominant limiting factor at higher temperatures. At the same time, the mobility of Ba₂SiSe₄ declines with increasing temperature, which is similar to most semiconductors.⁵⁸

Fig. 5 The calculated hole mobility of Ba₂SiSe₄ as a function of carrier density at room temperature is shown in panel (a). The effect of the scattering mechanism on the mobility at specific hole densities is plotted in panel (b). ADP is acoustic deformation potential scattering, IMP is ionized impurity scattering, and POP is polar optical phonon scattering. The p-type electrical conductivity of Ba₂SiSe₄ with temperature at different hole densities is shown in panel (c).

The p-type electrical conductivity as a function of temperature at different hole carrier densities is shown in Fig. 5(c). In general, the electrical conductivity of a material decreases with increasing temperature. The main reason is that the vibration of the lattice structure increases with temperature, which leads to an increase in the probability of carrier scattering.⁵⁹ This inhibits the movement of free carriers, thereby reducing the conductivity of Ba₂SiSe₄. After quenching from 974.0 K to RT, hole density (4.04 × 10¹⁷ cm⁻³) and p-type electrical conductivity (32.3 S m⁻¹) (based on the thermodynamic impurity simulations) can be obtained in Ba₂SiSe₄. Under similar hole density conditions, the p-type electrical conductivity of Ba₂SiSe₄ is significantly higher than that of CuGaO₂ (2.0 S m⁻¹)⁶⁰ and Cu₂O (19.0 S m⁻¹).⁶¹

4. Conclusion

In this work, the p-type electrical conductivity for Ba₂SiSe₄ is studied. Our analysis reveals that Ba₂SiSe₄ exhibits superior potential for p-type conductivity, as evidenced by its band alignment, ionization energy, and electronic band structure characteristics. Under the Se-rich, Ba (Si)-poor condition, the formation energy of Cs_Ba1 is 0.90 eV with high defect solubility. Based on the thermodynamic equilibrium simulation, Ba₂SiSe₄ was quenched to room temperature from the preparation temperature, and the hole density reached 4.04 × 10¹⁷ cm⁻³. The hole mobility of Ba₂SiSe₄ at this carrier density is 5.2 cm² V⁻¹ s⁻¹, and the p-type electrical conductivity is 32.3 S m⁻¹, which exceeds the traditional p-type WGSs. The simulation results indicated that Cs-doped Ba₂SiSe₄ may be a new p-type WGS with higher hole mobility and p-type electrical conductivity. The p-type electrical conductivity could exceed 10⁴ S m⁻¹ using the non-equilibrium preparation method. This work stimulates the development of p-type WGSs and provides a fundamental guideline for fabricating high-efficiency optoelectronic devices.

Author contributions

Yuhang Deng: investigation, visualization, validation, conceptualization, methodology formal analysis, and writing – original draft. Qiao Wei: visualization, validation, investigation, and data curation. Liu Yang: writing – review and editing, visualization, methodology, and funding acquisition. Shuaiwei Fan: supervision, software, resources, project administration, investigation, conceptualization, data curation, funding acquisition, and writing – review and editing.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the ESI.†

Acknowledgements

This work is supported by the Natural Science Foundation of Hubei Province (No. 2025AFB092) and Natural Science and Technology Foundation of Yichang (No. A22-3-006).

References

1. S. C. Liu, Y. S. Yang, Z. B. Li, D. J. Xue and J. S. Hu, Mater. Chem. Front., 2020, 4, 775–787.
2. V. Q. Le, T. H. Do, J. R. D. Retamal, P. Shao, Y. H. Lai, W. Wu, J. H. He, Y. L. Chueh and Y. H. Chu, Nano Energy, 2019, 56, 322–329.
3. Z. Wang, Y. J. Gu, X. M. Li, Y. Liu, F. H. Liu and W. P. Wu, Adv. Opt. Mater., 2023, 11, 2300970.
4. Z. R. Wang and G. Z. Shen, Mater. Chem. Front., 2023, 7, 1496–1519.
5. I. Hamberg and C. G. Granqvist, J. Appl. Phys., 1986, 60, R123–R160.
6. D. Y. Zhang, W. H. Yu, L. Zhang and X. Y. Hao, Materials, 2023, 16, 5537.
7. A. N. Fioretti and M. Morales-Masis, J. Photonics Energy, 2020, 10, 042002.
8. V. Ha, F. Ricci, G. Rignanese and G. Hautier, J. Mater. Chem. C, 2017, 5, 5772–5779.
9. S. W. Fan, Y. Chen and L. Yang, J. Phys. Chem. C, 2022, 126, 19446–19454.
10. Y. Chen, S. W. Fan and G. Y. Gao, Mater. Sci. Semicond. Process., 2022, 151, 107024.
11. Y. Chen, L. Yang, Z. L. Wang and S. W. Fan, Solid State Commun., 2022, 359, 115013.
12. S. Hadke, M. L. Huang, C. Chen, Y. F. Tay, S. Y. Chen, J. Tang and L. Wong, Chem. Rev., 2022, 122, 10170–10265.
13. X. T. Zhang, C. Q. Lin, X. Y. Guo, Y. Xue, X. Q. Liang, W. Z. Zhou, C. Persson and D. Huang, J. Phys. Chem. Solids, 2024, 190, 112002.
14. S. X. Kang, J. Y. Wang, L. Yang and S. W. Fan, Phys. Scr., 2024, 99, 035923.
15. J. Y. Wang and S. W. Fan, ACS Appl. Opt. Mater., 2024, 2, 1999–2010.
16. R. Kormath Madam Raghupathy, H. Wiebeler, T. D. Kühne, C. Felser and H. Mirhosseini, Chem. Mater., 2018, 30, 6794–6800.
17. J. Heyd, G. E. Scuseria and M. Ernzerhof, J. Chem. Phys., 2003, 118, 8207–8215.
18. A. V. Krukau, O. A. Vydrov, A. F. Izmaylov and G. E. Scuseria, J. Chem. Phys., 2006, 125, 224106.
19. W. Kohn and P. Hohenberg, Phys. Rev., 1964, 136, B864–B871.
20. G. Kresse and J. Furthmüller, Comput. Mater. Sci., 1996, 6, 15–50.
21. Y. Kumagai, N. Tsunoda, A. Takahashi and F. Oba, Phys. Rev. Mater., 2021, 5, 123803.
22. Y. Kumagai, Phys. Rev. Appl., 2023, 19, 034063.
23. J. Neugebauer, C. G. Van de Walle and C. Freysoldt, Phys. Rev. Lett., 2009, 102, 016402.
24. F. Oba and Y. Kumagai, Phys. Rev. B: Condens. Matter Mater. Phys., 2014, 89, 195205.
25. Y. Kumagai, F. Oba and T. Gake, Phys. Rev. Mater., 2019, 3, 044603.
26. S. W. Fan, J. Y. Chang, L. Yang and G. W. Hu, J. Mater. Chem. C, 2025, 13, 7150–7158.
27. S. H. Wei, T. A. Gessert, K. K. Chin and J. Ma, Phys. Rev. B: Condens. Matter Mater. Phys., 2011, 83, 245207.
28. J. Park, J. Kang, W. Metzger, T. Barnes, S. H. Wei and J. H. Yang, Phys. Rev. B: Condens. Matter Mater. Phys., 2014, 90, 245202.
29. A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder and K. A. Persson, APL Mater., 2013, 1, 011002.
30. A. Wang, R. Kingsbury, M. Mcdermott, M. Horton, A. Jain, S. P. Ong, S. Dwaraknath and K. A. Persson, Sci. Rep., 2021, 11, 15496.
31. A. M. Ganose, J. Park, A. Faghaninia, R. Woods-Robinson, K. A. Persson and A. Jain, Nat. Commun., 2021, 12, 2222.
32. S. Hachmioune, A. M. Ganose, M. B. Sullivan and D. O. Scanlon, Chem. Mater., 2024, 36, 6062–6073.
33. C. Brinkmann, B. Eisenmann and H. Schäfer, Z. Anorg. Allg. Chem., 1985, 524, 83–89.
34. Z. H. Cui, Y. C. Wang, M. Y. Zhang, X. Xu and H. Jiang, J. Phys. Chem. Lett., 2018, 9, 2338–2345.
35. J. Yang, S. Falletta and A. Pasquarello, Npj Comp. Mater., 2023, 9, 108.
36. I. B. Garba, L. Trombini, C. Katan, J. Even, M. Zacharias, M. Kepenekian and G. Volonakis, Acs Mater. Lett., 2025, 7, 1922–1929.
37. M. Lorke, B. Aradi, T. Frauenheim and P. Deák, Phys. Rev. B, 2019, 99, 085206.
38. S. X. Kang, S. W. Fan, L. Yang and G. W. Hu, Appl. Mater. Today, 2025, 42, 102572.
39. M. Zhong, W. Zeng, F. S. Liu, D. H. Fan, B. Tang and Q. J. Liu, Mater. Today Phys., 2022, 22, 100583.
40. Z. W. Xiao, C. Qiu, S. H. Wei and H. Hosono, Chin. Phys. Lett., 2025, 42, 016103.
41. M. T. Greiner and Z. Lu, NPG Asia Mater., 2013, 5, e55.
42. S. J. Clark and J. Robertson, Phys. Rev. B: Condens. Matter Mater. Phys., 2011, 83, 075205.
43. J. Gao, W. Zeng, R. B. Luo, Z. T. Liu and Q. J. Liu, Cryst. Growth Des., 2024, 24, 3777–3785.
44. D. M. Eagles, J. Phys. Chem. Solids, 1960, 16, 76–83.
45. C. Tablero, Comput. Mater. Sci., 2010, 49, 368–371.
46. R. Y. Cao, H. X. Deng and J. W. Luo, ACS Appl. Mater. Interfaces, 2019, 11, 24837–24849.
47. M. Liao, S. Takemoto, Z. W. Xiao, Y. Toda, T. Tada, S. Ueda, T. Kamiya and H. Hosono, J. Appl. Phys., 2016, 119, 165701.
48. J. Pellicer-Porres, A. Segura, A. S. Gilliland, A. Muñoz, P. Rodríguez-Hernández, D. Kim, M. S. Lee and T. Y. Kim, Appl. Phys. Lett., 2006, 88, 181904.
49. R. Brahimi, B. Bellal, Y. Bessekhouad, A. Bouguelia and M. Trari, J. Cryst. Growth, 2008, 310, 4325–4329.
50. M. N. Islam and M. O. Hakim, J. Mater. Sci. Lett., 1986, 5, 63–65.
51. H. Köstlin, R. Jost and W. Lems, Phys. Status Solidi A, 1975, 29, 87–93.
52. R. Summitt, J. A. Marley and N. F. Borrelli, J. Phys. Chem. Solids, 1964, 25, 1465–1469.
53. Y. Chen, S. W. Fan and P. Xu, Appl. Phys. Lett., 2022, 121, 252102.
54. M. Minohara, Y. Dobashi, N. Kikuchi, A. Samizo, K. Tsukuda, K. Nishio, K. Mibu, H. Kumigashira, I. Hase, Y. Yoshida and Y. Aiura, Inorg. Chem., 2021, 60, 8035–8041.
55. H. Kawazoe, M. Yasukawa, H. Hyodo, M. Kurita, H. Yanagi and H. Hosono, Nature, 1997, 389, 939–942.
56. J. B. Xia, J. Semicond., 2021, 42, 060402.
57. Y. Ogo, H. Hiramatsu, K. Nomura, H. Yanagi, T. Kamiya, M. Hirano and H. Hosono, Appl. Phys. Lett., 2008, 93, 032113.
58. J. Willis, R. Claes, Q. Zhou, M. Giantomassi, G. Rignanese, G. Hautier and D. O. Scanlon, Chem. Mater., 2023, 35, 8995–9006.
59. K. Li, J. Willis, S. R. Kavanagh and D. O. Scanlon, Chem. Mater., 2024, 36, 2907–2916.
60. K. H. L. Zhang, K. Xi, M. G. Blamire and R. G. Egdell, J. Phys.: Condens. Matter, 2016, 28, 383002.
61. R. B. Xue, G. Gao, L. Yang, L. G. Xu, Y. M. Zhang and J. Q. Zhu, J. Mater. Chem. C, 2023, 11, 13681–13690.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5tc01703c

---