Electronic properties and formation energy of chalcogen-doped (S/Se/Te) corundum Al₂O₃

Aluminum oxide (Al₂O₃), commonly recognized for its application in high-κ gate oxides,¹ planar optical waveguides,² and nonlinear optical devices,³ is an exemplary material in advanced technology. Specifically, its widespread applications in III-nitride and gallium oxide-based materials and devices highlight its critical importance at the forefront of materials science and engineering.^4–7 It is noted for exceptional physical properties, including a substantial bandgap energy (E_g) of approximately 9 eV,⁸ a high dielectric constant (ε) of around 9,⁹ and remarkable thermal stability. These characteristics make it a pivotal material in various domains such as power electronic devices,^10–12 aerospace, and defense industries.¹³ Al₂O₃ derives its exceptional properties from its stable ionic crystal structure and the electronic nature of its constituent atomic species. Specifically, its corundum structure $R 3 ¯c$ space group ensures stability and availability in high-quality, large-scale wafers, thanks to the cost-effective melt-based growth techniques.^14,15

While high-quality Al₂O₃ can be grown efficiently in large-scale wafers, fabricating nanoscale devices demands meticulous control over defects and impurities, as pristine surface quality is critical. In Al₂O₃, any defects, including native defects and impurities, contribute to defect levels in the band structure, a phenomenon well-documented across numerous studies.^16–18 Such energy levels are responsible for various effects, including optical absorption, generation, and compensation of carriers, and facilitate carrier transport through mechanisms such as hopping and tunneling.¹⁸ The presence of carrier traps and fixed charges is primarily ascribed to inherent point defects within the oxide dielectric layer, frequently situated at or adjacent to the interfaces.^17,19,20 The defect structure of Al₂O₃ profoundly influences its electrical and optical properties. Intrinsic defects, especially oxygen vacancies and aluminum interstitials, notably affect the material's dielectric properties and its performance in devices.²¹ Understanding the interaction between these intrinsic defects and the electronic states of Al₂O₃ is essential, particularly for applications in fields of electronics and optoelectronics. For instance, in Al₂O₃, the introduction of substitutional silicon, which possesses four valence electrons, may serve as a donor upon substituting an aluminum atom.²² However, the literature regarding the properties of chalcogen elements doped α-Al₂O₃ remains limited. The adoption of extrinsic doping methods using chalcogen elements presents a viable approach to customizing the electronic and optical properties of Al₂O₃, thus expanding its potential applications and enhancing its performance in various technological contexts.

Investigations of α-Al₂O₃ native defects have been widely studied.^16,23–25 However, some studies have employed local density approximation or generalized gradient approximation, resulting in inaccurate estimations of the Al₂O₃ bandgap.^24,25 This has made precise prediction of defect-level relation to the band edges challenging. To address these discrepancies, our study employs hybrid functionals. This methodology provides a more precise estimation of band structures and defect-level positions within wide-bandgap semiconductors. Despite the advantages, hybrid functionals have limitations in studying complex defect systems due to strong correlations in defect states. This study investigated native point defects in α-Al₂O₃, examining defect formation energies and transition level positions. Exploration of chalcogen elements such as sulfur, selenium, and tellurium as dopants in Al₂O₃ is motivated by their potential to modify the electronic and optical properties of materials.^26,27 Unlike traditional dopants, chalcogens offer an opportunity to enhance the functionalities of Al₂O₃ in electronic and optoelectronic devices due to their ability to introduce new defect states and alter band structures. The literature on the integration of chalcogens with sapphire, a form of Al₂O₃, is sparse,⁷ indicating that this research could open new avenues in the development of advanced III-oxide-based devices.

In this work, our study ventures into a detailed examination of α-Al₂O₃, a material distinguished by its extensive bandgap and versatile applications across electronic and optoelectronic domains. The utilization of density-functional theory-based methods facilitates a comprehensive exploration of the properties of α-Al₂O₃ when doped with chalcogens (S, Se, Te). Leveraging standard modeling tools, we constructed supercells of α-Al₂O₃ to enable meticulous calculations of both chalcogen-related and native point defects. Our analytical focus zeroes in on the formation energies and transition levels associated with chalcogen (S, Se, Te) doping in oxygen (or aluminum) sites in Al-rich (or O-rich) limits. The trend we discerned, where an increase in atomic number from S to Te correlates with a heightened challenge in forming anion-doped Al₂O₃ yet a reduced barrier to cationic doping, opens new avenues in understanding dopant behavior in such materials. Furthermore, the study reveals a proclivity for chalcogen atoms to substitute for Al in O-rich limits, a finding that could have significant implications for the fabrication and optimization of electronic and optoelectronic devices. This investigation, therefore, not only extends the corpus of knowledge in the field of semiconductor physics but also paves the way for novel applications and technological advancements in the use of α-Al₂O₃.

In this research, we employ the Vienna Ab initio Simulation Package (VASP) for our computational analysis, leveraging the principles of DFT. VASP utilizes the projector augmented-wave (PAW) pseudopotential approach. Plane wave cutoff energy is established at 520 eV for all computational tasks. For structural optimization, the generalized gradient approximation Perdew–Burke–Ernzerhof (GGA-PBE) functional is applied, targeting a convergence threshold of 1 × 10⁻⁵ eV/atom. Band structure calculations are conducted using the HSE06 hybrid functional, setting the mixing parameter at 0.32. This parameterization results in a calculated bandgap of 8.87 eV (total energy −293.28 eV) for α-Al₂O₃, closely aligning with the experimental values reported as 8.8–9.4 eV.^28,29 Our computed lattice parameters, a = 4.73429 Å and c = 12.89 Å, are in near-perfect agreement with the experimental findings of a = 4.76 Å and c = 12.99 Å.³⁰ Furthermore, the calculated Al–O bond lengths, 1.84 Å for the shorter bonds and 1.96 Å for the longer ones, correspond well with the experimental measurements of 1.86 and 1.97 Å, respectively.³⁰ 

For ensuring the validity and accuracy of our computational modeling, including the use of a single gamma point approximation, we perform a detailed analysis of the intrinsic defects in alumina. This step is crucial for benchmarking our methodology against the established theoretical and experimental data. In our comprehensive analysis of native point defects within α-Al₂O₃, we meticulously examine several defect types: (i) vacancies, including aluminum vacancy (V_Al) and oxygen vacancy (V_O); (ii) interstitials, specifically aluminum interstitial (Al_i) and oxygen interstitial (O_i); and (iii) antistites, encompassing aluminum on oxygen site (Al_O) and oxygen on aluminum site (O_Al). For Al_i and O_i, the interstitial sites are located at the largest void regions within the crystal structure while simultaneously accounting for Coulombic repulsions, thus determining the feasible interstitial positions for both cationic and anionic species.³¹ This analysis delves into the energetics of these point defects in α-Al₂O₃, particularly under charge neutrality conditions to determine the most stable defect configurations.

Figures 2(a) and 2(b) illustrate the formation energies of these native defects, plotted against the Fermi level in Al-rich and O-rich limits, respectively. Our findings show substantial concordance with the prior studies conducted by Choi et al., employing similar HSE mixing parameters 0.32,¹⁶ with minor discrepancies potentially stemming from differing calculations in Futazuka et al.'s study.²⁹ The permissible range of the Fermi level in α-Al₂O₃ is constrained by the necessity for charge compensation in the presence of charged defects.⁴¹ In Fig. 2(a), in the Al-rich limit, our analysis indicates that Al_i (Al_i1, Al_i2, Al_i3) near the valence band manifests the lowest formation energies. This trend is complemented by relatively low formation energies for V_O, aligning with the prevalent notion in the existing literature that V_O is ubiquitous in common oxides.^42–44 As the Fermi level ascends toward the conduction band, the formation energy for V_Al becomes minimal, dominating the defect landscape, which is in agreement with previous studies.¹⁶ However, for O_Al defects, our findings suggest that their formation is energetically unfavorable across the entire Fermi level range. The same observation closely mirrors the behavior of O_i (O_i1, O_i2, O_i3), predominantly due to the prevailing Al-rich limit, corroborating earlier research findings.²⁹ In O-rich limits, as depicted on the right side of Fig. 2(b), V_Al emerges as the predominant defect species with lower formation energy. Here, Al_i is more energetically favored near the valence band. The formation energy of Al_O defects ranks the highest, followed by that of Al_i, indicating a marked difficulty in the formation of aluminum-related point defects in the O-rich limit. This is in line with the established understanding of defect formation energetics in α-Al₂O₃.

The slopes in Figs. 2(a) and 2(b) signify the charge states of α-Al₂O₃ native defects, highlighting the most energetically favorable states. Figure 3 further details these transitions and associated charge states, clarifying the defect thermodynamics. Our comprehensive analysis reveals that V_Al and O_i predominantly act as deep acceptors, while Al_i is characterized as a deep donor. V_O, on the other hand, demonstrates a dual role, functioning as either a donor or an acceptor contingent on the Fermi level, as illustrated in Fig. 3. Regarding the acceptor levels of V_Al, the transitions (2+/1+), (1+/0), (0/1−), (1−/2−), and (2−/3−) are located at 0.53, 1.03, 1.67, 2.23, and 2.28 eV above the VBM, respectively. This categorizes V_Al as a deep acceptor, characterized by high formation energies when close to the VBM. However, the relatively lower formation energies at higher positions within the bandgap, in both O-rich and Al-rich limits, indicate that V_Al is a predominant acceptor-type defect. In the case of O_i, we observe close formation energy values for the three configurations (O_i1, O_i2, O_i3). Specifically, for O_i, the (0/1−) and (1+/0) transition levels are positioned at 3.48 and 1.76 eV above the VBM, respectively, while for O_i2, the (1+/0) transition level is situated at 1.10 eV, closer to the VBM. In the bandgap of α-Al₂O₃, V_O exhibits both donor and acceptor characteristics. Specifically, V_O presents a donor–acceptor transition level (2+/1+) at 3.71 eV and (1+/0) at 4.34 eV above the VBM. On the other hand, Al_i predominantly acts as a donor within α-Al₂O₃. The donor transition levels of Al_i are situated near the conduction band minimum (CBM), with the (3+/1+) level at 1.87 eV and a notable (1+/1−) level at 1.03 eV below the CBM. Notably, the formation energies of these donor defects, Al_i, and V_O, are lower when the Fermi level is positioned toward the lower part of the gap. This indicates that Al_i and V_O are the primary compensating donors in α-Al₂O₃. Their roles in charge compensation are critical to the electronic properties of the material, especially in contexts where Fermi level manipulation is essential.

Both neutral and various charged states (4−, 3−, 2−, 1−, 0, 1+, 2+, 3+, 4+) of substitutional doping are simulated in this study. The formation energy of chalcogen element related defects is shown in Fig. 4. In Fig. 4(a), in the Al-rich limit, anionic doping (chalcogen substituting for oxygen) exhibits significantly lower formation energies compared to cationic doping (chalcogen substituting for aluminum). This indicates a preferential substitution of chalcogens for oxygen atoms. The sequence of formation energies, S < Se < Te, indicates increasing difficulty for anionic doping with Se and Te in α-Al₂O₃. Notably, Se_O has the lowest formation energy near the VBM, highlighting its relative ease of formation under these conditions. This behavior aligns with the elemental trends of chalcogens, where a higher atomic number corresponds to an increase in ionic radius and a decrease in electronegativity, favoring anionic over cationic substitution. Consequently, the higher formation energies of S_Al, Se_Al, and Te_Al make them less stable and less likely to form. In contrast, Te_O exhibits the highest formation energies due to its large atomic radius, whereas S_O forms more readily due to the generally lower formation energies of oxygen substitutional defects in the Al-rich limit. The formation energies stay negative until ɛ_F values reach 0.33 (S_O), 0.35 (Se_O), and 0.12 (Te_O) eV for Al-rich conditions, and 2.25 (S_Al), 1.89 (Se_Al), and 2.54 (Te_Al) eV for O-rich conditions, respectively, further illustrating the distinct stability profiles of these dopants under varying chemical environments.

Figure 4(b) demonstrates that under O-rich conditions, cationic doping with S and Se (substituting for Al) results in significantly lower formation energies compared to anionic doping, highlighting a clear preference for the substitution of aluminum with S and Se elements. The formation energy increases with the atomic number among the chalcogens, indicating that anionic doping with S is more facile than with Se. Consistently, both S_Al and Se_Al exhibit relatively low formation energies, aligning with the behavior observed for Te_Al. The notably negative formation energies for cationic doping with S and Se imply the feasibility of introducing S- or Se-doped α-Al₂O₃ under O-rich conditions. In both Al-rich and O-rich environments, Te_O is distinguished by its consistently high formation energy, attributed to the substantial ionic radius of tellurium, which elevates the energy required for its integration into the lattice. Under n-type conditions, where ɛ_F is closer to the CBM, Te_Al is identified as the most stable dopant. Conversely, under p-type conditions, with ɛ_F near the VBM, the formation energies for substitutional chalcogens (S_Al, Se_Al, and Te_Al) become negative in O-rich conditions, indicating their stability.

As depicted in Fig. 5, the transition levels for S_Al, Se_Al, and Te_Al dopants are observed near the conduction band. However, it remains ambiguous whether S_Al and Se_Al act unequivocally as donors or acceptors, as this behavior is highly dependent on the position of the Fermi level. Te_Al exhibits a versatile electronic character in α-Al₂O₃, functioning as both a deep donor and a deep acceptor. This dual behavior is evidenced by its charge states, with the (1+/0) transition occurring at 5.60 eV, indicative of its donor capability, and the (0/1−) transition at 5.78 eV, characteristic of an acceptor role. For O related defects such as S_O, Se_O, and Te_O, the transition levels from their neutral to the nearest positively charged states are found to be 2.07, 2.68, and 4.11 eV, respectively. The absence of transition levels from a neutral to a negatively charged state in S_O, Se_O, and Te_O suggests that these defects are unlikely to function as acceptors within the material.

Figure 6 presents the charge density distribution in the 〈010〉/〈100〉 plane of the α-Al₂O₃ structure, with the c-axis oriented perpendicular to the plane of the paper. Figures 6(a)–6(c) depict the planar charge density for various defect types: pristine aluminum oxide at the oxygen site, O_Al, and Al_O antistites defects, focusing specifically on the charge density of the oxygen layer. In Figs. 6(d)–6(f), the focus shifts to cationic doping where chalcogen elements substitute for aluminum. Here, the charge density distribution is centered around the chalcogen dopant, serving as a reference for visualizing alterations in the local charge environment. Figures 6(g)–6(i) illustrate the charge density for anionic doping, where chalcogens replace oxygen atoms, with particular attention to charge distribution in the plane where the substituted oxygen atom is located. This method of illustration is adopted to depict the planar charge density distribution more clearly. Notably, Fig. 6(b) demonstrates a charge concentration phenomenon at O_Al antistites, highlighting an area that was previously charge-devoid. This is primarily due to the increased propensity for charge localization at the oxygen atomic sites. Conversely, Fig. 6(c) shows a notable charge depletion, indicative of the changes brought about by Al_O antistites. From the observations in Figs. 6(d)–6(f), it become apparent that the substitution of Te for Al leads to a distinctly higher concentration of charge at the neighboring oxygen sites, compared to similar substitutions by S and Se. In the case of anionic doping, shown in Figs. 6(g)–6(i), an increase in atomic number correlates with a more pronounced charge deficiency. However, this does not significantly alter the charge density distribution in the adjacent oxygen atomic layers.

Figure 7 delineates the densities of states (DOS) for pristine alumina, intrinsic antistites defects (Al_O, O_Al,), and chalcogen substitution defects in α-Al₂O₃ (S_O, Se_O, Te_O, S_Al, Se_Al, and Te_Al). The DOS profiles, whether intrinsic or defect-induced, are primarily defined by O 2p and Al 3s orbitals. As Figs. 7(a)–7(c) demonstrate, the conduction band edges of intrinsic alumina, along with Al_O and O_Al defects, are predominantly composed of Al 3s orbitals. In contrast, O 2p orbitals majorly contribute to the valence band edges. The impact of chalcogen element doping on α-Al₂O₃'s DOS is examined in Figs. 7(d)–7(i). In general, after chalcogen doping, distinct and non-continuous peaks within the bandgap are introduced even though the DOS profiles of Al and O orbitals exhibit minimal alterations. O 2p orbitals maintain their dominance at the valence band edge, whereas the conduction band edge continues to be largely influenced by Al 3s orbitals. Interestingly, the peaks introduced in the bandgap exhibit different profiles for cationic site and anionic site substitution.

Figures 7(d)–7(f) illustrate that cationic doping with S 3p, Se 4p, and Te 5p induces the emergence of new discontinuous bands within the bandgap. This occurrence is associated with spin polarization effects following the substitution of Al, resulting in an asymmetry in the partial density of states. This asymmetry, influenced by the substitution of Al, modifies the electronic structure and charge distribution within the lattice. Chalcogen cationic doping is seen to induce sharp, localized gap states, as observed in Figs. 7(d)–7(f), emanating from the s states of chalcogen dopants and the 2p states of adjacent oxygen atoms.

On the other hand, Figs. 7(g)–7(i), focusing on anionic doping with chalcogen elements, show that such doping does not lead to spin polarization. Specifically, Al 3s orbitals remain largely unchanged, residing near the conduction band edge. The DOS in this scenario is characterized by three distinct peaks near the valence band edge, originating from the S 3p, Se 4p, and Te 5p orbitals. These orbitals split into three localized gap states, distributed almost evenly across the gap, closely aligning with the results of Zheng et al.⁴⁵ 

DOS profiles shown in Fig. 7 revealed that chalcogen doping results in localized states within the bandgap of Al₂O₃ with a certain degree of hybridizations of O 2p orbitals and chalcogen p orbitals across the energy range. With the localized states emerging within the energy bandgap and near the band edges, it is possible that chalcogen-doped Al₂O₃ can be used to engineer the band profile for deep ultraviolet and beyond photodetector applications. As the work on chalcogen-doped Al₂O₃ remains extremely limited at present, we hope that such a work could offer an intriguing perspective and paves the way for future exploration into the optoelectronic properties of chalcogen-doped α-Al₂O₃.

Our investigation into the native point defects and chalcogen doping of alumina (α-Al₂O₃) has provided comprehensive insights into the material's defect chemistry. Results of α-Al₂O₃ reveal that formation energies of native defects, consistent with prior studies, vary with the Fermi level and chemical environment, highlighting Al_i and V_O low formation energies in Al-rich conditions and V_Al dominance in O-rich limits. Subsequent analysis under Al-rich conditions demonstrates a pronounced preference for anionic doping, with Se_O displaying notably low formation energies near the VBM, indicative of its favorable formation. Contrastingly, in O-rich environments, the results favor cationic doping with S and Se, suggesting that these dopants are more viable under such conditions. However, the consistently high formation energy of Te_O, attributed to tellurium's extensive ionic radius, poses challenges for its lattice integration. Charge density analysis further illuminates the spatial distribution of electrons, highlighting regions of electron concentration and depletion associated with various defects. DOS results underscore the significant impact of chalcogen p orbitals' role in the electronic structure, with discrete peaks observed. These findings not only deepen our understanding of the intrinsic and extrinsic defect landscapes in α-Al₂O₃ but also underscore the potential for engineering its electronic and optoelectronic properties through selective doping. The distinct behavior of dopants under varying chemical conditions invites further exploration to fully harness the capabilities of alumina-based materials for advanced applications.

The work is supported by C. K. Tan start-up fund from Hong Kong University of Science and Technology (Guangzhou). NSF-IUCRC Project (Grant No. 5AN398) and Guangzhou Municipal Science and Technology Project (Nos. 2023A03J0003 and 2023A03J0013). The authors used ChatGPT to revise their original text. We gratefully acknowledge HZWTECH for providing computation facility.

The authors have no conflicts to disclose.

Yimin Liao: Conceptualization (equal); Data curation (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Visualization (equal); Writing – original draft (lead). Hanzhao Song: Conceptualization (supporting); Formal analysis (supporting); Investigation (equal); Methodology (equal). Zhigao Xie: Software (equal). Chuang Zhang: Formal analysis (equal); Funding acquisition (equal). Zhuolun Han: Resources (supporting); Validation (supporting). Yan Wang: Data curation (supporting); Formal analysis (supporting). Chee-Keong Tan: Conceptualization (lead); Data curation (equal); Supervision (lead); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.