New stable ultrawide bandgap As2O3 semiconductor materials

Ultrawide band gap materials have numerous potential applications in deep ultraviolet optoelectronics, as well as next-generation high-power and radio frequency electronics. Through the first-principles calculations based on density functional theory calculations, we demonstrate that the As2O3 bulk and monolayer structures have excellent energetic, mechanical, and thermal stabilities. The bulk and monolayer of As2O3 come in two distinct structures, namely st1-As2O3, and st2-As2O3. We show that the st1-As2O3 and st2-As2O3 monolayer and bilayer could be mechanically exfoliated from their bulk material and found that the cleavage energy values are significantly lower than those reported for similarly layered materials. By performing Perdew–Burke–Ernzerhof (PBE) and Heyd–Scuseria–Ernzerhof (HSE06) band structure calculations, we found that the bulk and monolayers of As2O3 structures exhibit wide (PBE) and ultra-wide (HSE06) indirect band gaps. We further evaluate the As2O3 layered thickness-dependent band gaps and found that band gap decreases uniformly as the number of st1-As2O3 and st2-As2O3 layers increases. Our findings demonstrate the potential of the As2O3 structures for the future design of ultra-wide band gap semiconductor electronic devices.


Introduction
Interest in low-dimensional (LD) materials is increasing as they offer the opportunity to develop alternative or even substitute materials for silicon-based devices, which can meet the demands of modern device design and contribute to a sustainable semiconductor industry. To achieve this goal, it is essential to focus on LD materials, which have properties better than or similar to their bulk forms. Among numerous LD materials, two-dimensional (2D) oxide semiconductors possess useful functionalities in a variety of applications [1][2][3] such as optoelectronics [4,5], catalysis [6,7], and energy-related exploration [5,[8][9][10][11][12]. Their suitability for these applications is mainly attributed to the quantum confinement effect that keeps their band gaps in the visible region of the solar spectrum. For example, recent experimental reports have demonstrated the synthesis of 2D β-Ga 2 O 3 nanosheets by mechanical exfoliation, chemical synthesis, and molecular beam epitaxy methods [13][14][15][16]. It has been theoretically reported that a β-Ga 2 O 3 monolayer and bilayer have an electronic structure similar to the Ga 2 O 3 bulk form [17,18]. In another recent study, both monolayer and bilayer of β-Ga 2 O 3 were found to exhibit an indirect to direct band gap transition by doping their structures with Mg, Ca, and Sr atoms [19]. Following this trend, monoclinic Al 2 O 3 has been shown to have an optical band gap (5.16 eV to 5.80 eV) in the mid-ultraviolet (mid-UV) spectrum [20][21][22]. The γ-Al 2 O 3 monolayer was found to exhibit optical absorption anisotropy in the near-UV to the far-UV range and large exciton binding energy with an ultrawide band gap suitable for UV photodetection applications [23].
To date, only group III sesquioxide semiconductors [24] in monolayer form have been reported, while group VI sesquioxides particularly As 2 O 3 structures are rarely reported. To consolidate the prospect of a class of sesquioxide semiconductors for many potential applications, we have proposed a new As 2 O 3 monolayer/ few layers that can be mechanically exfoliated from its bulk form. We are aware that As 2 O 3 crystallized in the layered monoclinic P2 1 /c space group and can be synthesized using the reactive ion etching (RIE) method. The RIE method is known for its precision in producing smooth surfaces but is costly due to the equipment and technical expertise required. Therefore, we expect that the As 2 O 3 monolayer could be synthesized by the mechanical exfoliation method since As 2 O 3 is layered in bulk form.
Experimental and theoretical studies have confirmed that group VI sesquioxides are beneficial for various semiconductor-related applications. For example,Šiškins et al. showed the experimental exfoliation of an As 2 S 3 membrane, which exhibits strongly anisotropic mechanical and optical properties [25]. Patel's group revealed that As 2 S 3 has an indirect band gap of 2.31 eV for monolayers and 2.08 eV for bulk, and both exhibit good thermoelectric properties [26]. Mortazavi et al. reported that ground-state properties and photocatalytic potentials of monoclinic As 2 X 3 (X = S, Se, and Te) layers. Among them, As 2 Te 3 is found to exhibit unique super stretchability, and As 2 Se 3 shows good potential for solar water splitting due to its high carrier mobilities and optical responses [27]. Lora da Silva et al. studied the effects of hydrostatic pressures on β-As 2 Te 3 nanostructure exhibiting an insulator-to-metal transition above 6 GPa with the band gap closing. Their results also indicate ultra-low lattice thermal conductivities, which are expected to enable high-efficiency thermoelectric materials [28].
In this study, we have theoretically investigated the stability and electronic properties of the As 2 O 3 monolayer, including its bulk phase. We have also demonstrated the possible etching route for As 2 O 3 few layers from its bulk form. Finally, thickness-dependent band gaps are also investigated.

Computational method
First-principles DFT [29] approach had been used to obtain all the ground state properties as implemented in Vienna ab initio simulation package [30]. The exchange-correlation had been treated with generalized gradient approximation of Perdew-Burke-Ernzerhof (PBE) [31] parametrization. The projected augmented wave pseudo-potentials method [32] had been adopted to treat the core and valence electrons for all atoms in the As 2 O 3 structure. For the dispersion correction, DFT-D2 correction of Grimme [33] had been used. The irreducible Brillouin zone (BZ) in reciprocal space had been described by Monkhorst-Pack set of k-points grid meshes [34]. We used (9 × 9 × 1) and (18 × 18 × 1) grid meshes for the As 2 O 3 structural optimization and total density of state calculations, respectively. In all calculations, the plane wave basis set was expanded using an energy cut-off of 500 eV. A vacuum space of 16 Å along the z-direction was set to avoid interaction between the adjacent layers of As 2 O 3 . The criteria for convergence of the total energy and remaining force on each atom for two iterative steps were set smaller than 10 −5 eV and 0.001 eV Å −1 respectively. The dynamic stability of the As 2 O 3 monolayer had been evaluated with aid of phonon dispersions calculations using the finite difference method (FDM). In the FDM calculations, we used (3 × 3) supercell of As 2 O 3 monolayer with 3 × 3 × 1 k-points grid meshes. The phonon band structure and atom projected DOS had been plotted using PHONOPY code [35]. To access the thermal stability of the As 2 O 3 monolayer, we carried out ab-initio molecular dynamics (AIMD) simulations with a time step of 1.0 fs. The temperature was monitored using the Nose-Hoover thermostat [36].

Results and discussions
Our predicted As 2 O 3 structures extend the family of sesquioxide non-magnetic semiconductors. There are two types of As 2 O 3 structures according to their primitive unit cell which crystallizes in the monoclinic P2 1 /c space group. Both As 2 O 3 structures are layered van der Waals (vdW) materials consisting of two separated As 2 O 3 layers. However, one of them has in the (0, 1, 0) direction oriented, As 2 O 3 layers (labeled as st1) while the other has in the (0, 0, 1) direction oriented As 2 O 3 layers (labeled as st2). The optimized bulk of As 2 O 3 structures from top and side views are displayed in figure 1(a). The optimized lattice constants for the bulk st1-As 2 O 3 and st2-As 2 O 3 structures are given in table 1. The bottom panel of figure 1(a) shows the electron localization functions which are calculated to examine the chemical bonding nature of the As 2 O 3 sheet. Based on the charge density accumulation and depletion, we have concluded that polar covalent bonds exist in As 2 O 3 structures. These bonding properties are correlated to the difference in electronegativity between the As (2.18) atom and the O (3.44) atom. The Bader charge analysis [37] is used to estimate the charge shifts in the As 2 O 3 structure. We found that each As atom loses 0.68 e − while each O atom gains 1.12 e − . The net charge transfer of electrons from As to O indicates ionic bonding, while polar covalent bonding is caused by the difference in electronegativity between the two bound As and O atoms, which ranges from 0.4 to 1.8. These ionic-covalent mixed bondings are illustrated in supporting information (S.I.) figure S1 with the aid of charge contour plots.  Having established the bonding nature of As 2 O 3 structures, we estimate the energies of a monolayer of st1-As 2 O 3 and st2-As 2 O 3 separate from their corresponding bulk structures. The layered structure of bulk As 2 O 3 offers the opportunity to exploit the relatively weak, non-covalent interlayer interactions, thereby enabling the reduction of the bulk phase to a single monolayer configuration. As shown in the inset of figure 1(b), a slab is constructed from few layers of As 2 O 3 to obtain a cleavage energy (E cl ). Firstly, we have performed a series of calculations by increasing the interlayer distance gradually between the topmost As 2 O 3 layer and bilayer and those below them (total six layers of As 2 O 3 structures are considered) until the exfoliated layer/bilayer are isolated. Figure 1(b) illustrates the calculated E cl vs d for st1-As 2 O 3 and st2-As 2 O 3 monolayers and bilayers using PBE-D2 method. The calculated E cl values are 0.602 and 0.610 J m −2 for monolayer and bilayer exfoliation from st1-As 2 O 3 structure, respectively while these values are 0.585 and 0.594 J m −2 for st2-As 2 O 3 structure. The obtained values are significantly lower than those reported for GeP 3 (1.14 J m −2 ) [38], Ca 2 N (1.09 J m −2 ) sheets [39] and NaSnP (0.81 J m −2 ) [40] as well as α-PbO (0.67 J m −2 ) [11]. In addition, the E cl is slightly higher than the E cl for graphene exfoliated from bulk graphite [41]. Our estimated E cl low values suggest that the st1-As 2 O 3 and st2-As 2 O 3 monolayers could be easily exfoliated from their bulk phases.
After these analyses, we have created a monolayer form of st1-and st2-As 2 O 3 structures. The unit cells of both st1-As 2 O 3 and st2-As 2 O 3 monolayers contain equal numbers of As(4) and O(6) atoms. It can be clearly seen that each As (O) atom is doubly-coordinate, with each O atom chemically linked by two As atoms and vice versa for O atom (see figure 1(c)). Table 2 summarizes the calculated lattice constants for monolayer As 2 O 3 structures. The lattice constant of st1-As 2 O 3 is lower than that of the st2-As 2 O 3 structures. In keeping with the lattice constants, the st1-As 2 O 3 structures have shorter average optimized bond lengths than st2-As 2 O 3 structures in the x-y plane which may means that the attractive forces are favorable more for st1-As 2 O 3 formation. This variation in lattice parameters is expected to affect the electronic properties of these structures. The obtained lattice constants of As 2 O 3 monolayers in this study are larger than or comparable to the reported values for similar As 2 X 3 (S, Se, Te) monolayers [27]. The cohesive energy (E coh ) and formation energy (E f ) per atom, as well as the mechanical, dynamic, and thermal stabilities of these st1-As 2 O 3 and st2-As 2 O 3 monolayers, are then investigated. The E coh can be obtained with the expression given as: Here, E As , E O and n, m represent the total energy of an isolated As, O atoms and the number of particular atoms in the bulk or monolayer As 2 O 3 form, respectively. E total denotes the total energy of st1-As 2 O 3 (st2-As 2 O 3 ) in monolayer or bulk phases. According to equation (1), a positive value of E coh is indicative of the thermodynamic stability of a bulk or monolayer phase of st1-As 2 O 3 or st2- It has been observed that the lowest value of E coh pertains to the st2-As 2 O 3 for bulk and monolayer. This indicates low atomic bonding in the st2-As 2 O 3 structures, which is reflected in their expanded lattice constants in both the bulk and monolayer phases. In addition, layer dependent E coh is calculated and all E coh values are within the range obtained for bulk and monolayer As 2 O 3 structures. All calculated E coh values indicate that all considered As 2 O 3 structures are energetically feasible. We then evaluate the thermodynamic stability of the As 2 O 3 sheets via the E f , which is expressed as; where µ As and µ O represent the chemical potentials of As and O atoms, respectively. The µ As is obtained from the trigonal arsenic structure which hasR3m space group and the µ O is obtained from the O 2 molecule. The estimated values of E f of st1-As 2 O 3 (st2-As 2 O 3 ) for bulk phases presented in Here E N−layers represents the energy of the layered As 2 O 3 structure, E monolayer stands for the energy of the monolayer As 2 O 3 , N is for the number of layers and n + m is for the total number atoms (As atoms plus O atoms) in the considered cell. The calculated E int values are listed in table 1 (for bulk) and table 2 (for few-layer). The obtained E int values for bulk As 2 O 3 structures indicate that layers of st2-As 2 O 3 are strongly bonded to each other than the st1-As 2 O 3 . However, these are comparable with graphite which has been reported as 48 meV/atom by Lebégue et al [41] and as 56 meV/atom by Spanu et al [42]. In addition, the E int values are increased and approached to the bulk E int values with the increasing number of layers.
To determine the mechanical robustness, such as hardness, stiffness, and brittleness/ductility, of the As 2 O 3 structures, we first estimate the bulk phase elastic moduli as listed in table 1. These moduli, bulk modulus (B), Young's modulus (Y), and shear modulus (G), could be evaluated using Hill's approximation [43] from Voigt [44] and Reuss [45] models and expressed as follows: Here, B V and B R denote the upper limit of B (Voigt bulk modulus) and the lower limit of B (Reuss bulk modulus), respectively. Then, the average values of Voigt (G V ) and Reuss (G R ) are estimated for G based on the following equations: By following these expressions for B and G, Young's modulus (Y) and Poisson's ratio (v) can be derived using the equations given below: and Table 1 summarizes the calculated B, G and Y moduli values for both st1-As 2 O 3 and st2-As 2 O 3 bulk structures. The bulk modulus values which are obtained by three different methods for st2-As 2 O 3 are lower than the st1-As 2 O 3 phase. However, Young's and shear moduli of the bulk st1-As 2 O 3 phase have higher values than the st2-As 2 O 3 phase. It can be inferred that the required uniform pressure to change the volume of the st2-As 2 O 3 is comparatively lower from the st1-As 2 O 3 phase. In addition, the calculated G and Y values for the st2-As 2 O 3 may imply that the plastic strain region is larger than the st1-As 2 O 3 phase.
We evaluate the anisotropic behavior of mechanical properties in both st1-As 2 O 3 and st2-As 2 O 3 structures by employing the open-source software package ELATE [46]. In comparison with the 2D visualization of Young's modulus, shear modulus, and Poisson's ratio of As 2 O 3 structures are shown in figures S2 to S4. For elastically isotropic materials, the 2D projection plots have formed a perfect circle and sphere shape. The deviation from a circular or spherical shape illustrates the degree of anisotropy of the corresponding elastic property. The degree of anisotropy is calculated by the variable values of the mechanical properties in all directions. Figure S2 illustrates the anisotropic nature of the elastic properties, showing that the st1-As 2 O 3 phase is more anisotropic compared to the st2-As 2 O 3 phase.
We then use the energy-strain method [47][48][49] to obtain the elastic constants. The dependence of strain-energy on strained lattice constants in low dimensional materials can be fitted into a quadratic polynomial equation. Thus, we can estimate the in-plane stiffness (C x and C y ) and Poisson's ratio (ν xy and ν yx ) of st1-As 2 O 3 and st2-As 2 O 3 monolayers. Figure 2 illustrates the obtained energy as a function of strained lattice constants. The calculated C x (ν xy ) and C y (ν yx ) values for the st1- Here, x and y represent the stretching directions for the lattice constant. The obtained C and ν values clearly show anisotropic tensile strength since there exists a difference between the in-plane lattice constant in the unit cells of both As 2 O 3 structures. We expect a stiffer bonding network in the st1-As 2 O 3 monolayer than in the st2-As 2 O 3 monolayer, which is consistent with the previous assertion. The minimum Born criterion for the elastic stability of 2D materials [50] was met based on the positive values of C x and C y for all structures. The results clearly confirm the mechanical stability of the As 2 O 3 monolayers.
As a further verification of the energetic and mechanical stabilities of the As 2 O 3 , we performed both the phonon dispersion and AIMD simulations. Figure S5 shows the phonon dispersions and corresponding atom-projected phonon density of states (PDOS) throughout the first BZ. These phonon calculations are performed by using (3 × 3 × 1) supercells for both As 2 O 3 monolayers. The plots for both st1-As 2 O 3 and st2-As 2 O 3 demonstrate small imaginary modes for the acoustic branches. The slope of the acoustic dispersion, ∂ω ∂k , is known as the speed of sound in the lattice (which is the speed of propagation of an acoustic phonon). At long wavelengths (low values of k), the speed of sound is almost independent of the phonon frequency and the dispersion relation is approximately linear. However, this phenomenon fails at short wavelengths (large values of k). Therefore, these imaginary modes in the Brillouin zone could result from the utilized supercell size. It is important to mention that each unit cell of As 2 O 3 monolayer contains ten atoms, and constructing a larger supercell for the phonon calculations would necessitate substantial computational resources, which is expensive for our current exploration.
Concerning the thermal stability of the As 2 O 3 monolayers, we have performed AIMD at 800 K for 10 ps using a (3 × 3 × 1) supercell of st1-As 2 O 3 and (3 × 5 × 1) supercell of st2-As 2 O 3 monolayers. Figure 3 displays no structural deformation in all As 2 O 3 monolayers and only negligible atomic height variation can be seen in structures. Moreover, the oscillation range for the total energy against the time step is provided. The obtained energies are of the order of ∼7 meV for each atom in the considered supercell of As 2 O 3 without obvious variations. The AIMD results indicate that these monolayers are thermally stable above room temperature. Overall, all the findings on stability indicate that the As 2 O 3 monolayers hold promise for reasonable experimental synthesis.
Furthermore, we evaluate the electronic band structures of the few-layers (from monolayer to four-layer) and bulk phases of As 2 O 3 , which are obtained with the PBE and Heyd-Scuseria-Ernzerhof (HSE06) methods. The computed band gaps of these As 2 O 3 structures are listed in tables 1 and 2. The obtained HSE06 band structures are illustrated in figure 4. Alongside PBE band structures, we provide the projected density of states (PDOS) plots (see figure S7). It should be emphasized that the PBE underestimates band gaps for all structures. However, the HSE06 method is well known to predict reliable band gap values. When compared to PBE results, HSE06 enhances band gap values for As 2 O 3 structures exhibiting wide and insulating band gaps properties.
The As 2 O 3 structures exhibit both direct and indirect wide gap semiconducting/insulating properties depending on the location of conduction band minimum (CBM) and valence band maximum (VBM) along the high symmetric points in the BZ (see figure S5) as well as the PBE or HSE06 method used. For example, both the PBE and HSE06 methods predict bulk st1-As 2 O 3 as an indirect band gap material, while its monolayer shows both direct (PBE) and indirect (HSE06) wide and insulating band gap. For the st2-As 2 O 3 bulk and monolayer cases, both the PBE and HSE06 methods predict indirect wide and insulating band gaps, respectively.
As clearly shown in the PBE and HSE06 band structure plots, the band gaps for the st1-As 2 O 3 and st2-As 2 O 3 monolayers increase compared to their st1-As 2 O 3 and st2-As 2 O 3 bulk counterparts. The enhancement in band gap for monolayer As 2 O 3 structures confirms the quantum confinement effects mentioned above that are common to 2D materials. In the majority of the band structure plots, both CBM and VBM have relatively narrow curvature energy bands. The narrow energy band means a small radius of curvature, which could lead to low effective masses of holes and electrons. From the PDOS plots of all As 2 O 3 structures, the contributions from the p orbital of As atom dominate the CBM, while the VBM has a dominant feature of the p orbital of the O atom.
Following this trend, the layered thickness-dependent band gaps for As 2 O 3 structures have been investigated. As evidently displayed in figure 5, the band gap decreases uniformly as the number of st1-As 2 O 3 and st2-As 2 O 3 layers increases while maintaining the indirect insulating band gap properties. This indicates unique layered band gap alignments. The energy of the usual particle in a box model for quantum confinement decays as ∼1/N 2 , to compare our results with this model we have fitted the obtained band gap values to a general power law of the form as follows: where E gap (bulk) is the band gap energy value which is obtained by fitting the band gap values of the few-layer As 2 O 3 structures. N is the number of layer, A and κ are the fitting parameters which are found as A = 0.455(0.604) and κ = 1.305(1.210) for st1-As 2 O 3 (st2-As 2 O 3 ) with HSE06 functional results. As can be seen the band gap values of both As 2 O 3 structures from monolayer to bulk, abruptly decrease until the four-layered structure. However, the effect of increasing the thickness of the structure on band gap value is relatively small beyond four layered As 2 O 3 structures. In addition, this is also related to the magnitude of the electrostatic potential energy of valence electrons in the field of the periodic ion cores in the crystal. The standing waves created at the edges of the BZ has been experienced a similar electrostatic potential energy with the increase in the number of layers in As 2 O 3 structures, thus resulting in minimal alterations to the band gap.

Summary
In summary, this study reveals the ground state properties of the As 2 O 3 bulk and monolayer structures, a newly found member of the group III sesquioxide, based on the combined PBE and HSE06 methods. There are two types of As 2 O 3 , namely st1-As 2 O 3 and st2-As 2 O 3 in bulk and monolayer form, and both have nonmagnetic insulating properties with good stability. We have found that both PBE and HSE06 methods predict bulk st1-As 2 O 3 as an indirect band gap material, while its monolayer has both direct (PBE) and indirect (HSE06) wide and insulating band gaps. For the st2-As 2 O 3 bulk and monolayer cases, both the PBE and HSE06 methods have been predicted as indirect wide and insulating band gaps, respectively. Additionally, st1-As 2 O 3 and st2-As 2 O 3 layered thickness-dependent band gaps have also been determined.
The band gap decreases sharply as the number of st1-As 2 O 3 and st2-As 2 O 3 layers increases. We also have represented the mechanical exfoliation of the As 2 O 3 monolayer and bilayer from their bulk material and have found that the E cl values are significantly lower than those reported for similar 2D layered materials. Our theoretical predictions serve as a guide for the experimental feasibility of st1-As 2 O 3 and st2-As 2 O 3 structures for optoelectronic applications.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).