As₂O₃ as an inorganic molecular crystal: a DFT study for nanoelectronics

Abstract

This study explores the structural, electronic and transport properties of arsenic oxide (As₂O₃) in its bulk form and two-dimensional surfaces, where the surfaces were cut at specific lattice planes, i.e. (001), (110) and (111), and represented as slab-(001), slab-(110) and slab-(111), respectively. The structural properties reveal that As₂O₃ shows potential as an inorganic molecular crystal (IMC) because of its three-dimensional anisotropy. Formation energy computations confirm the structural stability of As₂O₃ in its bulk and respective surface counterparts, and the mechanical stability of the materials is determined by calculating the elastic tensors and subsequent elastic constants. Electronic structure computations indicate that As₂O₃ is a wide-band-gap material in its bulk and surfaces along the (001) and (110) crystal planes, whereas the (111) surface indicates narrow-band-gap behavior. This wide band gap of the material can be attributed to the specific crystal structure of the IMC. Investigations on the bulk modulus, Young's modulus, shear modulus and Poisson's ratio reveal that the material exhibits favorable mechanical properties. Furthermore, the Poisson's ratio and B/G ratio show the brittle nature of the material. Besides these, using the non-equilibrium Green's function (NEGF) formalism, the transport properties of the narrow-band-gap slab-(111) and slab-(001) were investigated to determine their potential for application in nano-devices, and the current–voltage (I–V) profile revealed that slab-(111) has potential to be used as a Schottky device, whereas slab-(001) exhibited an ohmic nature.

Same material, new classification, new function; from ordinary metal oxides to IMC to low-indexed 2D surfaces to nanodevices.

1. Introduction

The elements from group 15 of the periodic table, i.e., antimony oxide (Sb₂O₃), arsenic oxide (As₂O₃) and bismuth oxide (Bi₂O₃), offer multiple polymorphs, and hence, they are nowhere near the simple metal oxides.¹ Because of this, these materials offer crystal structures with either lower atomic density or highly distorted configurations having greater open spaces. Furthermore, similar to bismuth and antimony, arsenic is a chalcophile, which means that it exists along with chalcogen atoms, i.e., S, Se and Te, rather than combining with silicate ions or oxides.² It has been experimentally validated that As₂O₃ offers two polymorphs, namely, monoclinic claudetite and cubic arsenolite.¹ Arsenolite, a cubic polymorph of arsenic(iii) oxide features discrete As₄O₆ molecules, while claudetite is the monoclinic crystal structure made up of infinite layers of As₂O₃.^1–5 Besides these, there exists one more polymorph named claudetite II of arsenic(iii) oxide that crystallizes within the monoclinic crystal system and is made up of layers like claudetite I. The fundamental structure of all of the polymorphs of the arsenic oxides is tetrahedron containing the atomic core of arsenic as surrounded by the three oxygen ligands along with the lone pair of electron. All the oxygen atoms are shared between the two ψ-tetrahedra in order to maintain the As₂O₃ stoichiometry. This configuration corresponds to the discrete cages in arsenolite and infinite layers in claudetites.⁶

It should be noted that arsenolite is one of the naturally existing minerals as well as a commercially available compound, whose crystal structure was determined and characterized thoroughly by X-ray diffraction.^1–6 Considering the specific crystal structure and low atomic density of arsenolite, this polymorph, i.e., cubic As₂O₃ (arsenolite), can be considered as the inorganic molecular crystal (IMC) structure, a conceptually new framework opening new doors. The IMCs are a unique class of materials, where the material comprises molecular packing instead of atomic packing, i.e. here molecules or molecular units are the building blocks of the materials, which are periodically repeating along three dimensions (3D).^7–10 These molecular¹¹ units are made by strong bonding of the constituent atoms, i.e. As and O atoms in this case, and the molecular units are separated from each other by weak van der Waals (vdW) forces. This strong bonding is formed by short-range forces, whereas the weak interactions are formed by long-range forces, which would result in different types of bonds within the single material/crystal structure, creating a 3D anisotropy in bonding that is a unique feature of the IMC.^10,12

Owing to the atomic thickness, two-dimensional (2D) materials attain exceptional compatibility with the recent industrial semiconductor nano-manufacturing technologies, providing an exceptional mechanical basis for the upcoming flexible electronic devices.^13,14 Since the seminal discovery of graphenes, the family of 2D materials is continuously expanding. The family expands to transition metal dichalcogenides (TMDs), 2D perovskites, MXenes, hexagonal boron nitride (h-BN), etc.¹⁵ Because of the novel properties like versatile bandgap, higher luminescence efficiency and light conversion efficiency, and higher photocatalytic and electro-catalytic activity, a number of 2D atomic crystals have been studied for a majority of recent groundbreaking applications including catalysts, photo-detectors, batteries, field-effect transistors and display devices.^14,15

Among various 2D materials, the 2D oxide semiconductors offer advantages in various applications such as energy-related fields,^16,17 optoelectronics^18,19 and catalysis.^20,21 The potential of these materials in such applications is basically ascribed to the quantum confinement, which maintains the band gaps of most of the materials in the solar spectrum's visible region. For instance, the 2D gallium oxides (Ga₂O₃) showed indirect to direct band gaps by doping with Sr, Mg and Ca atoms.^22–24 Similarly, the monolayer of monoclinic Al₂O₃ demonstrated an optical band gap of in the range of ∼5.16–5.80 eV following the mid-ultraviolet spectrum,^25–27 whereas the monolayer of γ-Al₂O₃ showed absorption in the near-UV to far-UV region along with a large exciton bonding energy owing to the ultrawide bandgap appropriate for the UV-photodetection application.²⁸ Likewise, As₂O₃ offers an ultra-wide band gap of ∼4.2–6 eV depending on the layer thickness.²⁰ This wide bandgap limits the use of As₂O₃ in various semi-conducting applications such as photo-catalytic water splitting and photo-catalysis.²⁹ The principal drawbacks of the wide-bandgap semiconductor devices are because of the corresponding effective masses of holes and electrons, carrier drift mobility as well as ionization energy with the increase in the band gap. With the transition from narrow band gap to wide band gap, the transport properties of the carriers are affected as they become significantly asymmetric and hence characterized by the poor p-type transport.

Nevertheless, the growth of atomic crystals is considerably hindered by several shortcomings like poor mechanical properties, intrinsic defects and regulatory issues of the band gap. Hence, the idea of 2D molecular crystals (2D-MCs) was put forward. These 2D-MCs are a class of emerging ultra-thin crystals, which are the organic complements of the 2D atomic crystals that lead to the 2D solid membrane materials made by the periodic arrangement of molecules within a single molecular layer or a number of molecular layers. The 2D-MCs are formed through the periodic arrangement of the molecular units/clusters owing to the primacy of quantum tunneling effects and uniform molecular thickness by the molecular design along with band gap tunability. These advantages of the 2D-MCs have great effects on the optoelectronic and electronic devices.^14,15,30,31 Compared with the 2D atomic crystals, the 2D-MCs could be self-assembled within the greater areas having controlled molecular structural design characteristics, various molecular types, stronger flexibility and exceptional optical characteristics.³² Despite the significant development of these 2D-MCs with excellent chemical and physical properties, they suffer from several shortcomings. The investigations on 2D-MCs are limited to organic molecules and most of the organic molecules offer very poor chemical stability of materials that is a very salient property when it comes to the practical implementations and the performance of the device. In contrast, inorganic materials offer a more cost-effective alternative with superior stability compared to promising organic semiconductor materials.

The 2D inorganic molecular crystals (2D-IMCs) and the inorganic molecules are bound with each other by weak vdW forces that are dissimilar to the typical stronger chemical bonds. In general, 2D-IMCs offer greater mobility as well as greater stability as attained through improvement within the inter-molecular coupling.^33–35 However, the stronger inter-molecular forces due to the π–π interactions within the 2D organic materials have been broadly investigated, yet the studies on the interactions of 2D-IMCs are very limited.^36–39 Hence, the deficiency in understanding of the intra-molecular and inter-molecular forces within the IMCs hampers the development of new members of the class, and only very limited studies on their novel properties and applications are available.

Besides, As₂O₃ is well-utilized in various bio-medical applications^40,41 and well-studied with respect to environmental toxicity.^42,43 Furthermore, using the DFT computations, owing to the ultra-wide band gap, band-gap engineering has been done by various methods such as tuning the nano-structure, doping, and surface modification/adsorption^44–46 for appropriate applications.^20,47,48 Nevertheless, some recent studies include the DFT investigations of As₂O₃ considering their vibrational properties,⁴⁹ interaction studies⁵⁰ as well as their utilization for gas sensing applications, but all these studies have been performed using the isolated clusters or molecular structure models rather than periodic systems.

Despite the fact that the structural properties along with various physicochemical properties of As₂O₃ have been broadly investigated in the context of the behavior of metal oxides and environmental toxicity, the cubic crystal structure, made up of distinct molecular cages of As₄O₆ combined together through the vdW interactions, has not been studied within the IMC's framework. This is not just a matter of classification, as treating the material as a typical metal oxide demonstrates that its structural properties center on its actual bonding characteristics; however, its mechanical response, thermal behavior as well as cohesion have not been studied directly. In the present work, we made a reclassification of the cubic As₂O₃ as an IMC and utilized the DFT functionals along with Grimme's dispersion corrections (DFT-D3) to fully consider the vdW interactions, which is the uniqueness of these materials. Instead of demonstrating a novel physical mechanism, this study presents the incorporation of the IMC structural framework considering a material that has already been investigated only from the perspective of metal oxides. These results indicate solid evidence for cubic As₂O₃ to be an IMC, particularly showing a 3D anisotropy within the bonding (i.e., weak intermolecular and strong intramolecular bonding). This validated the structural as well as the mechanical stability and electronic responses based on the specified orientation, where the bulk as well as slab-(110) configurations retain the intrinsic wide band gap, whereas the slab-(001) and slab-(111) configurations present a transition towards a narrow band gap combined with the transport behavior in low indexes. These results offer electronic and structural bases to determine the nanodevice prospects of As₂O₃, which was not clearly available with the previous classification of materials.

2. Computational details

The detailed study of the electronic and structural properties along with the transport properties of As₂O₃ in bulk (3D) and surface (2D) configurations was performed by utilizing the density functional theory (DFT)-based Amsterdam Density Functional (ADF) (2025.106). The ADF-BAND module, designed for the periodic computations and study, utilizes the linear combination of atomic orbitals (LCAO) as basis sets.^10,51 The graphical user interface (GUI) of the respective code was utilized in order to set the input parameters.⁵² Initially, the cubic unit cell of As₂O₃ with the unit-cell formula of As₃₂O₄₈ was taken into account, for which the lattice parameters are as follows: a = 10.986, b = 10.986, c = 10.986, α = 90°, β = 90°, and γ = 90°. The space group and space group number were P1 and 1, respectively. The unit-cell volume under study was 1326.224 ų.

The computations were performed in bulk and surfaces to study the properties in the respective cases, where the surfaces were made by cutting the bulk in specified orientations, i.e. (001), (110) and (111), and denoted as slab-(001), slab-(110) and slab-(111), respectively. To consider different slabs, a vacuum spacing of 20 Å was inserted along the direction that is non-periodic to ignore the specious interactions between the periodic depictions. The slab thickness of the layers was fixed at 3 layers for slab-(111) and slab-(110), whereas the thickness was fixed at 2 layers for slab-(001) that was chosen after validating by the respective convergence test.

All the structures were fully relaxed to their respective lowest energy states at the chosen level of theory. Various exchange correlation functionals in generalized gradient approximation (GGA), i.e. Perdew–Burke–Ernzerhof^53,54 and Becke–Perdew (BP86) along with Grimme's corrections (D3) and Becke Johnson (BJ) corrections, were utilized in order to include both strong covalent bonds and weaker vdW forces.^52,55 Besides, the above-described level of theory⁵⁶ was considered, as it provides better results in terms of accuracy and computation of energy.^55,57,58 The dispersion correction parameters in the ADF are based on the damping function, and either zero-damping, i.e. D3 functional, or BJ-damping, i.e. D3-BJ functional, is used. The values of the damping functional are S₆ = 1.00, S₈ = 0.722 and R_S6 = 1.217 for the PBE-D₃ functional and S₆ = 1.0, S₈ = 0.7875, a₁ = 0.4289 and a₂ = 4.4407 for the PBE-D₃ and PBE-D3-BJ functionals, respectively, whereas the values for BP86-D3 and BP-86-D3-BJ are S₆ = 1.0000, S₈ = 1.6830 and R_S6 = 1.1390 Å, and S₆ = 1.0000, S₈ = 2.6844, and a₁ = 0.4289 and a₂ = 6.1062 (damping parameters), respectively.

The slater-type orbitals (STO's) with triple zeta polarization (TZP) basis sets were used for the entire study, as this is known for the accurate estimation of the electronic interactions in a region close to the nucleus. Moreover, to evaluate the impact of basis set superposition error (BSSE), i.e. inherent to the localized STOs, a counterpoise (ghost-atom) correction was executed. The computed BSSE value was 55 meV that is analogous to the benchmarks available in the literature for the TZP basis sets.^59,60

Considering the electronic configuration of As: [Ar] 3d¹⁰, 4 s², 4p³ and O: 1s², 2s², 2p³, the frozen core approximation was utilized to freeze the core electrons. Besides, the relativistic effects using the zero-order relativistic approximation (ZORA) Hamiltonian were considered due to the high atomic number of As (Z = 33).^61–63 The convergence criteria for force, energy and gradient were 1 × 10⁻⁴ Hartree Å⁻¹, 1 × 10⁻⁶ eV and 1 × 10⁻⁴ Å, respectively. K-Point convergence tests were performed systematically by utilizing various Monkhorst–Pack grids. A 5 × 5 × 5 K-point mesh was found to provide a total energy convergence of 1 × 10⁻⁵ eV per atom and was used for all bulk computations. However, the 5 × 5 × 1 sample was used for the slab models, with the single K-point along the non-periodic direction compatible with the generalized slab-model practice. Nevertheless, for the NEGF transport computation, the Γ-point sampling was utilized since it is the routine for implementation in the quantum transportation model through this method.

To compute the NEGF transport properties, gold leads (Au-leads) were utilized as the left and right electrodes with 3 principle layers incorporated in each electrode region. Besides, the central scattering region of As₂O₃ was taken, which was compatible with the coupling distance given below. The electronic and elastic properties were computed by utilizing the single-point strategy that computes the nuclear gradients as well as the Hessian derivatives of the relaxed structures at a single point, i.e. a single geometry. Besides, the computation of the electronic transport characteristics was studied by utilizing DFT along with the non-equilibrium Green's function (NEGF) strategy.^64,65 The NEGF assists in developing a quantitative quantum transport model. The self-consistency based on the Poisson equation through the real space was used for investigating the electrostatics. The equations of current (I) in the integral form for the energy as well as voltage-dependent magnitudes are as follows:^66,67where G^r and G^a represent the retarded Green's functions, whereas Γ and f are the spatial density of the electrons and the Fermi–Dirac distribution of the electrodes from left to right, respectively. The transmission function was computed as follows:T̄(E, V_b) = trance[Γ_LV_bG^R(E, V_b)Γ_RV_bG^A(E, V_b)]

The conductance of the two terminal devices was computed by using the transmission coefficient as follows:

The density functional tight binding (DFTB) module^68–70 as executed within the ADF/DFTB was utilized to model the Hamiltonian and the overlap matrices of the electrode and channel region. Additionally, the computation of the equilibrium Fermi energies was considered. The Slater–Koster parameter, i.e. default setting in the ADF/DFTB, was implemented without any changes, as provided in the ADF code manual. For this work, no parameter fitting was employed. The other parameters (e.g. basis sets) utilized were analogous to the DFT computations, validating the methodological consistency between the structural and the transport studies. In this strategy, the PBC in the Γ-point approximations was used in order to exhibit the crystals for the computation of the transport properties.^71–73 The changes within the coupling surface distances for Au–As and As–O were established in the range of 1.5–3.5 Å due to the following reasons: first, the selected range of coupling distances surrounds the spectra of interactions from short distances to long distances, and second, the model verifies the numerical convergence by capturing the coupling impacts with accuracy. Very short distances would lead to fast convergence problems because of the higher strength of interactions, whereas the considerably larger distance could lead to problems regarding negligible coupling. Therefore, appropriate ranges should be chosen in order to overcome these challenges. Further, to demonstrate the physically realistic interface between the Au electrodes and the scattering region, i.e. As₂O₃, the potential energy surface (PES) was drawn as a function of the coupling distance in the range of 1.70–5 Å, and is provided in Fig. 1 in the SI. A distinct minimum was recognized at 1.85 Å, with an energy of −8162 eV that was adopted as the equilibrium geometry for the rest of the transport computations for the said material. Furthermore, d = 3.86 Å shows an uncoupled asymptotic state. To validate the effectiveness of the predicted coupling distance, transmission energy spectra (TES) were recorded at 0.5 V for each coupling distance and for some representative coupling distances, i.e. 1.85 Å, 2.2 Å. 2.43 Å and 3.86 Å; the TES was drawn, and is provided in Fig. 2 in the SI. With the increase in the coupling distance over equilibrium, the amplitude of the transmission decays exponentially, from a peak value of ∼0.20 at 1.85 Å to ∼1.4 × 10⁻⁵ at 3.86 Å, corresponding to the generalized quantum tunneling theory. Further, the subsequent transport characteristics showed minimal fluctuations, validating the fact that the device attributes are resilient and well-founded at the specified realistic equilibrium distance for the transport channel.

Fig. 1. Crystal structure of As₂O₃ at bulk and surfaces/slabs, where slab-(001), slab-(110) and slab-(111) indicate the cutting of surfaces/slabs in the (001), (110) and (111) orientations, respectively. The As and O atoms are represented by gray and red spheres, respectively.

Fig. 2. Hirshfeld charge analysis of the bulk and surfaces, where the O and As atoms are represented by red and purple spheres, respectively.

3. Results and discussion

In this section, the structural, electronic and elastic properties of the bulk and surfaces of As₂O₃ were considered, where the surfaces were sliced in specific orientations, i.e. specific miller indices. The specific orientations that were taken into accounts are (001), (110) and (111), and denoted as slab-(001), slab-(110) and slab-(111), respectively. These low-indexed miller indices were chosen because of the high atomic packing, resulting in a smaller surface energy due to the fewer dangling bonds on surfaces. These surfaces offer more stability than high-indexed surfaces.^74–76 Furthermore, the feasibility and fabrication of these low-indexed surfaces of conventional IMCs, i.e. Sb₂O₃ (ref. 8 and 77) and P₄Se₃ (ref. 78) are reported.

3.1. Structural properties at the GGA-PBE-D3 level of theory

The structural properties computed using the theoretical codes are usually described by various parameters as per requirement. Here, since the said material was considered as an IMC, in which the structural anisotropy is a prime feature, some important features of the materials, i.e. bond length/bond distance, describe the inter-molecular and intra-molecular bonding discussing the structural anisotropy. The top view, side view and tilted view of the optimized structure of the bulk and surfaces are shown in Fig. 1 in order to represent the complete structure. As can be seen, the material is composed of molecular units instead of atoms, which repeat in three dimensions in bulk and surfaces. This depicts one of the most important aspects of the IMC, indicating that the material is an IMC. Furthermore, the molecular units are like the closed-cage structure and each molecular unit is made up of 10 atoms, i.e. 4 atoms of As and 6 atoms of O. All molecular units are similar, but two adjacent molecular units face differently to each other. The material is similar to the well-known material from a similar family, i.e. Sb₂O₃.¹⁰ To further verify this, the inter-molecular and intra-molecular distances were taken into account.

For the specified bond type, the short bond length is normally associated with the strong bond, representing the greater overlap of the orbital and the respective electronic density between the bonded atoms. The correlation implemented here is of great importance to the intramolecular As–O bonds that present the covalent bonding in the molecular units of As₄O₆ in contrast to the intermolecular As–As and As–O bond distances that rather relate the spacing between the adjacent molecular cages. As presented in Table 1, the intramolecular As–O bond distance is 1.85 Å within the bulk configuration that is highly analogous with the respective slabs, i.e. 1.84–1.85 Å for slab-(110), 1.86 Å for slab-(001) and 1.80–1.90 Å for slab-(111). The extensive range of bond-distances for the (111) surfaces shows the localized heterogeneous environment along the As–O bonds that are emerging from the suppressed coordination as well as the structural relaxation of the atoms in the specified orientation. However, the (110) and (001) slabs maintain intramolecular bond distances near the respective bulk values, indicating the relatively minor disturbance towards As–O bond strengths at such terminations.

Table 1. Structural parameters, i.e. inter-molecular and intra-molecular distances, of the bulk and surfaces of As₂O₃ with different periodicities at the GGA-PBE-D3 level of theory.

	Intermolecular distance (Å)		Intramolecular distance (Å)
	As–O	As–AS	As–O
Bulk	2.93	3.93	1.85
Slab-(111)	2.52–3.37	3.83	1.80–1.86–1.90
Slab-(110)	3	3.9–4	1.84–1.85
Slab-(001)	2.97	3.95	1.86

Furthermore, the computed results show the intramolecular bond length in the range of 1.8–1.9 Å, whereas the bond length is mostly 1.84 Å, showing that the bond length is in the range of primary/strong type of bonding as the bond distance is less than 2.4 Å. Besides these, the inter-molecular bond length is between 2.52 and 2.97 Å, indicating that the weak type of bonding occurs since the bond distance is greater than 2.4 Å.^52,63 Therefore, it can be said that there exist strong intramolecular bonding and weak intermolecular bonding, and this trends occurs throughout the structure, i.e. repeated periodically. It can be said that the three-dimensional anisotropy in bonding exists for As₂O₃ in bulk and its 2D counterparts.

The As–O bond between the As₄O₆ molecular units presents a polar covalent character, as shown by the Pauling scale's electronegativity difference, i.e. 1.26.^10,63 Furthermore, the Pauling formula indicates ∼37% ionic character between the As–O bonds, validating a primarily covalent character (i.e. >50% covalent character). However, it should be noted that the provided intramolecular bond polarity is quite different, and intermolecular cohesion of the corresponding crystal is not associated with it. The weak forces between the adjacent molecular units of As₄O₆ are of vdW (dispersion) origin emerging from the London-type forces between the closed-cage-like chemically saturated molecular units. Conclusively, the discrete molecular units sustain the stronger internal networks, whereas the structural arrangement within the crystal is maintained through a balanced long-range dispersion interaction as well as the localized electrostatic polarization. The well-defined vdW gap suppresses the orbital overlap between the adjacent molecular units, highlighting the conventional transport and electronic structure profiles of such molecular solids. These results are validated as follows: (i) the intermolecular bond distances in As–O and As–As are 2.52–2.97 Å, considerably greater than the primary bond lengths, (ii) the nonexistence of the electronic density in the vicinity of the intermolecular bonds, as supported by the charge density plots (Fig. 3) and (iii) the need for Grimme's correction i.e. DFT-D3 exchange correlation functional to precisely reproduce the lattice parameters by different experiments.

Fig. 3. Total electron density iso-surfaces around the atoms representing the density cloud around the molecular units of As₄O₆ for the bulk, slab-(001), slab-(110) and slab-(111) configurations plotted at an iso-value of 0.03 a.u. (e bohr⁻³).

Besides, the lattice parameters are a = 10.986 Å, b = 10.986 Å, and c = 10.986 Å, whereas α = 90°, β = 90°, γ = 90°, validating the perfect cubic crystal structure and well in agreement with the literature.^2,79

3.1.1. Hirshfeld charge analysis

To further explore the structural properties, the charge distribution within the structure is an important aspect to be discussed. Here, the Hirshfeld charge analysis was taken into account in order to discuss the charge distribution within the structure. Fig. 2 presents the Hirshfeld charge analysis for the bulk and respective surfaces, where the color legend is the representation of the charges in which the red and blue colors represent negative and positive charge distribution respectively. In general, As behaves as the +ve charge entity, i.e. cation, whereas O behaves as the −ve charge entity, i.e. anion. In bulk and slab-(110) configurations, almost all the As and O atoms have the same amount of charges, whereas the slab-(001) and slab-(111) configurations exhibit the non-uniform distribution of the charges. In general, the overall charge on all the systems is neutral as O is the charge-donating specie, whereas As is the charge-accepting specie.

3.1.2. Electron density plots

To further explore the structure of the material, i.e. As₂O₃, the electronic density of the materials was plotted and analyzed. The electronic density plots represent the density of the electrons around the atoms and show the strength of the bond present between the bonded atoms. The density is maximum where the bonding is stronger and minimum where the bonding is weaker. The electronic density plots were plotted for the bulk and surfaces of As₂O₃, and are given in Fig. 3. The results showed that the electronic density is localized around the atoms present within the single molecular unit, i.e. in the vicinity of each individual molecular unit, whereas the electronic density is not present between two molecular units, i.e. in the inter-molecular region. This shows that the strong bonding is present in the region of intramolecular units, whereas the absence of the electronic density cloud in the region of intermolecular units showed the presence of weak forces, i.e. vdW forces. This also validated the fact that the materials show 3D anisotropy in bonding, i.e. intramolecular strong bonding and intermolecular weak bonding.

3.2. Stability analysis

3.2.1. Formation energy analysis

The formation energy (E_f) of As₂O₃ was calculated for bulk and slab structures using the following equation:where E_AsaOb, E_As and E_O2 represent the total energy of the respective optimized structures of As₂O₃, As (in crystal form) and O (in molecular form) (as obtained by full geometry optimization). a and b represent the total number of atoms of As and O, respectively, whereas n represents the total number of atoms present in the respective bulk or slab configuration. Besides, the paramagnetic behavior was considered through the spin-polarized computation. A similar formula was implemented in order to compare the bulk and respective slabs.

The formation energy per atom (eV per atom) for the bulk and surfaces of As₂O₃ is given in Table 2. The formation energy was computed using 4 different functionals, i.e. GGA-PBE-D3, GGA-PBE-D3-BJ, GGA-BP86-D3 and GGA-BP86-D3-BJ, as all the respective structures were relaxed using these functionals. First and foremost, the formation energy is negative for all the cases representing the exothermic reaction and having a greater probability of materials to occur independently. Second, the least formation energy was computed by the GGA-BP86-D3-BJ functional, showing the most optimized structure obtained by the functional. Third, the minimum energy out of all the cases considered was attained for the bulk periodicity, showing the most feasible periodicity. Furthermore, on the basis of the formation energy, the stability of the materials can be showcased as bulk > slab-(110) > slab-(001) > slab-(111). This means that there are more possibilities for the formation of slab-(110) than the slab-(001) and slab-(111) configurations. Similarly, there would be the least probability of formation of slab-(111) of As₂O₃ compared to the other cases, as the formation energy is maximum compared with all the cases taken into consideration.

Table 2. Formation energy analysis of the bulk and surfaces of As₂O₃.

Sr. no	Periodicity	Formation energy per atom (eV per atom)
		GGA-PBE-D3	GGA-PBE-D3-BJ	GGA-BP86-D3	GGA-BP86-D3-BJ
1	Bulk	−5.93	−5.99	−5.95	−6.08
2	Slab-(001)	−5.75	−5.81	−5.76	−5.88
3	Slab-(110)	−5.89	−5.94	−5.89	−6.01
4	Slab-(111)	−5.66	−5.70	−5.65	−5.82

Furthermore, by implementing the BSSE correction, i.e. 55 meV (subtract from the formation energy values) in Table 2, the corresponding stability trend for the slabs remained unchanged, validating the resilience of the reported results.

3.2.2. Mechanical stability

The elasticity of crystalline materials was identified through the 4th-rank tensor and expressed through the 6 × 6 matrix.⁸⁰ The number of independent elastic constants is based on the symmetry of the crystals. The general trend is that the lower the symmetry, the greater would be the elastic constants. For instance, the cubic crystal shows high symmetry and has a less number of elastic constants, whereas the triclinic crystals have lower symmetry and offer a higher number of independent elastic constants. The cubic crystal structure has 3 independent elastic constants, i.e. C11, C12 and C44.

The Born criterion is considered as the ideal mechanical stability criterion under the application of mechanical loading, provided the quadratic form ∑C_rsδq_rδq_s > 0, where q_r represents the generalized strain variable, whereas C_rs denotes the strain-dependent elastic modulus, and C_rs = ∂²E/∂q_r∂q_s, where E is considered as the internal energy of the system.⁸¹

The general criterion as per the Born criterion for the mechanical stability of the cubic crystal structure is as follows: C11–C12 > 0; C11 + 2C12 > 0; C44 > 0.^81,82 The computed values for the respective elastic constants in GPA are as follows: C11 = 21.92, C12 = 7.428, and C44 = 11.095, which are in good agreement with the available literature data.^83,84 All the three criteria are being fulfilled by the crystal structure under consideration, and now it can be said that cubic As₂O₃ is a mechanically stable material.

3.3. Electronic properties

The electronic properties, providing insights into the electronic structure, of the materials are characterized by the band diagram and density of states (DOS). The electronic properties of As₂O₃ in the bulk, slab-(001), slab-(110) and slab-(111) configurations are discussed in detail.

The electronic properties of the materials are generally evaluated by the band gap. Here, the band gaps of the bulk and various surfaces under considerations were computed at different levels of theory, and are given in Table 3. The results showed that As₂O₃ is a wide-band-gap material in its bulk and respective slab-(110) configurations, which is consistent with the available literature data.^1,20 Besides, most of the IMCs such as conventional Sb₂O₃ offer wide band gaps.¹⁰ This may be attributed to the specific crystal structure, in which the molecular units act as individual entities, as each molecular unit becomes chemically inert. Hence, the electrons are highly localized within the molecular units, which makes the excitation difficult. This is evident from the other long-range-based materials such as water.⁸⁵

Table 3. Band gap analysis for the bulk and surfaces under consideration using various functionals.

Sr. no	Periodicity	Band gap analysis (eV) at different level of theory/functional
		GGA-PBE-D3	GGA-PBE-D3-BJ	GGA-BP86-D3	GGA-BP86-D3-BJ
1	Bulk	4.01	4.02	4.00	4.01
2	Slab-(001)	3.10	3.08	3.09	3.01
		0.34	0.32	0.33	0.25
3	Slab-(110)	4.03	4.03	4.03	4.02
4	Slab-(111)	0.88	1.14	0.90	2.16

Furthermore, the band gap of the materials increases as we slice the materials in the direction along the (110) plane as per the quantum confinement effect. The band gap decreases drastically along slab-(111) due to p–p hybridization from the constituent elements. Similarly, the band gap decreases as the bulk is sliced along the (001) plane, and the impurity state appears while cutting along this specific direction. It should be taken into account that although the band gap varies, the results⁸⁶ are similar while computing with different functionals. Furthermore, the narrow band gap of slab-(001 and slab-(111) may be attributed to the generation of the dangling As–O bonds, as these high-energy surfaces are cleaved. These bonds result in the introduction of the localized surface states, which shift towards the band-edges, a general observation, while considering the superficial instability of the molecular crystals.^87,88

Though the electronic properties were computed at different levels of theory, as given in Table 3, for detailed analysis, the density of states (DOS) and band structure were studied, which were computed at the GGA-BP86-D3 level of theory.

3.3.1. Bulk

The band diagram of bulk As₂O₃ is shown in Fig. 4, where the Fermi level is set at 0 eV, as shown by the blue dotted line. The Brillouin zone was cubic, and the results revealed that the material was a wide-band-gap material with a band gap of 4 eV. The analysis of the band edge positions reveals that the material is a direct-band-gap material, as the conduction band minima (CBM) and valence band maxima (VBM) lie at the Γ point. Further detailed analysis of the electronic structure can be done by using the total and partial density of states. The DOS analysis results are given in Fig. 3 in the SI, revealing that in both the CB and the VB, there is overlapping of states from As and O atoms. However, in the CB, the major contribution arises from the As atoms along with the considerable contribution of the O atoms. In more detail, there exists the p–p hybridization, more specifically 4pz from As and 2px and 2pz from the O atoms. Hence, there is more probability of the π–π bond. Similarly, the major contribution is from O atoms in VB with considerable contribution from the As atoms. There exists the p–p hybridization with the overlapping of 2px and 4pz from the O and As atoms, respectively.

Fig. 4. Electronic band structure for bulk As₂O₃, where the Fermi level is set at 0 eV.

3.3.2. Slab-(001)

To consider the electronic structure of As₂O₃ slab-(001), the band diagram along the high-symmetry Γ–M–Γ Brillouin zone was computed. As shown in Fig. 5, the surface termination breakage introduces a bulk translation symmetry, referring to the appearance of distinct isolated electronic states present within the fundamental band gap. The mid-gap state shows the dispersion spanning from ∼0.3 to 1.6 eV above the Fermi level (as presented by the blue horizontal dashed line). The energetic channel's isolation from the conduction and valence manifolds shows the subsequent localized energy state arising from the distinct atomic termination along the (001) plane, instead of the usual bulk continuum attribute. Furthermore, the total and partial DOSs reveal that the subsequent mid-gap state is the overlapping of the As and O states with major contribution from the As atoms, as given in Fig. 4 in the SI. Furthermore, this state belongs to the CB, as in the CB, major contributions arise from the states of As atoms with considerable contribution from the O atoms. Moreover, there would be the p–p hybridization in the CB. Likewise, in the VB, there would be the p–p hybridization with the major contribution of O atoms and 2px–2pz hybridized along with the 4pz–4px hybridization. Besides all these, the impurity state is conducive to the easy movement of charge carriers from the VB to the CB, and this material can be used for similar applications.

Fig. 5. Electronic band structure for the slab-(001) of As₂O₃, where the Fermi level is set at 0 eV.

3.3.3. Slab-(110)

The band diagram for slab-(110) of As₂O₃ reveals that the material is a wide-band-gap material, as provided in Fig. 6. The material is also a direct-band-gap material with a band gap of 4.02 eV. Similar to the previous cases, there exists the p–p hybridization in both the VB and the CB, where the major contribution is from the O and As atoms, respectively, as given in Fig. 5 in the SI. Furthermore, at the CBM, all the three p sub-orbitals of As overlap along with a very minor contribution of 2py from the O atoms. Similarly, at the VBM, 2py hybridizes with 2pz, giving rise to the π–π hybridization.

Fig. 6. Electronic band structure for the slab-(110) of As₂O₃, where the Fermi level is set at 0 eV.

3.3.4. Slab-(111)

The electronic band structure of slab-(111) As₂O₃ reveals that the material is a narrow-band-gap material with a band gap of ∼0.90 eV, as shown in Fig. 7. Similar to previous cases, As makes major contributions in the CB and O makes major contributions in the VB. The p–p hybridization is visible at the edge positions, as shown in Fig. 6 in the SI.

Fig. 7. Electronic band structure for the slab-(111) of As₂O₃, where the Fermi level is set at 0 eV.

Conclusively, it can be said that cutting the three-dimensional/bulk material in a specific direction can have a strong influence on the structure, and hence, all the other properties such as electronic characteristics can be seen in this case.

3.4. Mechanical properties

The elastic modulus of As₂O₃ could be calculated through the elastic constants of the single crystal, as given above. In general, there exist three well-defined computation methods for the calculation of the elastic modulus, namely the Hill approximation, Voigt approximation and Reuss approximation.⁸⁹ In this case, the Voigt approximation was used in order to compute the elastic constants. The mechanical properties of the materials were computed on the basis of bulk modulus (B), shear modulus (G), Young's modulus (E) and Poisson's ratio. The bulk modulus shows the ratio of stress to the applied strain, which represents the capability of the material to resist under the applied strain and is closely related to the binding energy of the atoms within the crystals, which could be utilized to compute the average valence bond strength (structural relaxation).⁹⁰ The greater the value of bulk modulus, the stronger the average valence bond strength, which in turn shortens the bond length. The bulk modulus computed for As₂O₃ is 12.556 GPA, which is in the range of typical molecular crystals and well in agreement with the available literature data.⁹¹ Furthermore, the lower value of bulk modulus is attributed to the weak vdW interactions.

The shear modulus (G) is the ratio of the shear stress and the respective shear strain, and represents the resistance offered by the objects towards the applied shear strain. The shear modulus is greatly associated with the bending of the chemical bond present between the atoms. The value of the shear modulus declines by increment in the ionic character of the chemical bonds. The value of the shear modulus for three-dimensional As₂O₃ is 9.537 GPA, and it is greatly in agreement with the value reported in the literature for various molecular crystals and IMCs.⁹² In general, the values of the shear modulus diamond is sky high, i.e. ∼520 GPA, whereas the neighboring metals offer a shear modulus of ∼10–80 GPA, and contrary to this, polymers show a shear modulus of 1 GPA.⁸⁸ Furthermore, the comparatively less shear value computed for As₂O₃ is due to the presence of weaker vdW forces in addition to the presence of the ionic character, i.e. 37% ionic character, as described in the previous section.

Young's modulus describes the ratio between the normal (perpendicular) stress and the respective normal (perpendicular) strain, exhibiting the capability of materials to resist under the normal strain. The stiffness of the material is dependent on Young's modulus as well as the geometry of the materials. Young's modulus, as computed for As₂O₃, was 22.830 GPA, showing stiffness in the materials, and this material offers high Young's modulus as compared to the famous IMC. Young's modulus was calculated for the famous IMC, i.e. Sb₂O₃, which was 14.9 ± 0.8 GPA.⁹³ Furthermore, Poisson's ratio exhibits the absolute value of the ratio of the transverse strain to the respective axial strain under the uniformly distributed axial stress and shows the rate of expansion or shrinkage of the material, as they are stretched or squeezed. Poisson's ratio is a measure of shear stability, with the fact that a greater value of Poisson's ratio leads to a more plastic attribute of the substance. The Poisson ratio calculated for As₂O₃ was 0.197, which showed the very less probability of the material to exhibit plastic attributes of the materials. This is also supported by the B/G ratio as both the Poisson ratio and B/G decide whether the materials are ductile or brittle. The threshold value for B/G is 1.75 to decide the mechanical nature of the material.⁹⁴ The material would be ductile, if B/G is greater than 1.75 and the Poisson ratio is greater than 0.26.^89,90 Similarly, the material would be brittle as B/G is less than 1.75. The B/G value, as computed for As₂O₃, was 1.31, revealing that the material exhibits a brittle nature, and because of this, there would be less plastic character.

The elastic properties of As₂O₃ show that the said material is feasible to be used in various flexible and optoelectronic devices.

3.5. Estimation of materials to be used as nano-devices

In this section, the narrow-band-gap surfaces, i.e. slab-(111) and slab-(001), are studied to be used in nano-devices, as the narrow-band-gap materials offer several advantages such as better electrical conductivity, greater charge transport, effective charge transfer and tunable properties. This is because low energy is needed for charge excitation, resulting in enhanced transmission and better responses, which in turn lead to improved bipolar transport. This is evident from several narrow-band-gap materials,⁹⁵ besides various organic molecular materials and polymers.⁹⁶ Considering this, the NEGF studies were performed, and the results are given in the upcoming sections. These studies were not performed on the other materials, i.e., bulk and slab, as these materials are wide-band-gap materials, and for nano-devices, narrow-band-gap materials are required, as they provide better transmission and current flow.

3.5.1. Slab-(111)

The computed electronic transport characteristics of the materials will be discussed in the following section. The transport characteristics of slab-(111) were determined by NEGF calculations. The tunneling current movement can be computed theoretically on the open states and the non-equilibrium states between the two contacts. The NEGF was successfully applied in order to study the transport characteristics of slab-(111) of As₂O₃ under already developed strategies/theories.⁹⁷ Owing to the utilization of this material as the transistor, the external electric field was applied along the z-axis that is perpendicular to the surface of the materials, and hence, the I–V curves were obtained and the transport of the electrons was studied.⁹⁸

The system that was accounted is the two-probe device consisting of the right electrode, left electrode and the central region.^73,99 The central region is made up of slab-(111) and slab-(001) owing to the various lengths accompanying the electrode extensions in order to form smooth conduction between the central regions and the electrodes. The left and right electrodes are made up of gold leads (Au leads), and the overall device is Au-Slab-(111)-Au, as shown in Fig. 8.

Fig. 8. Schematic of the arrangement of the NEGF setup. The right and left yellow portions are right and left electrode regions, whereas the central region is slab-(111) of As₂O₃, in which the gray and red spheres represent the As and O atoms, respectively.

The distance between the central region and the left and right electrodes was kept constant. The right and left electrodes are directly combined with the As and O atoms, respectively.

The transmission eigen states (TES) close to the Fermi level were also computed, as shown in Fig. 9. The TES represents the class of the eigen states within the NEGF methodology that describes the transport properties of the system under consideration.¹⁰⁰ The rational electronic transport modes through the scattering region are connected with either two or more leads, as shown by eigen states described here.¹⁰¹ The TES shows a higher amplitude at the central part, as represented in Fig. 9. The TES at the left-hand side exhibits the incident as well as the reflective states, and therefore, such states could interfere either destructively or constructively. There exists the constructive interference in a very small portion of the central part, as there is the considerable amplitude of eigen states, as shown in Fig. 9 (HOMO part), whereas for the remaining structure, the destructive interference were observed, as the amplitude of the eigen state is majorly zero.

Fig. 9. Frontier orbitals, i.e., highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO), for the slab-(111) of As₂O_3, where the As and O atoms are represented by gray and red balls, respectively.

First of all, the transport characteristics of the n-slab-(111) of As₂O₃ at equilibrium were taken into consideration. The transmission spectra are shown in Fig. 10, and the results revealed the presence of the multiple peaks within the energy range and such peaks are related to the presence of the multiple transmission channels within that region. At close to the Fermi level (that was set at 0 eV and represented by the blue line), the transmission spectra exhibited different behaviors as the transmission peak is relatively very low, i.e. about to zero but non-zero. This is because of the presence of the narrow band gap (Fig. 7) in the material, leading to the direct tunneling of the electrons from one electrode to another, which is responsible for the lower transmission close to the Fermi level. Besides these, the occurrence of the wide resonance around the Fermi level is a salient attribute of the transmission spectra, as given in Fig. 10. The strong transmission spectra have two salient attributes:¹⁰² (i) a wide resonance that minimizes current-induced impacts over the interfacial geometry and (ii) a greater transmission probability around the Fermi level of the electrode, which enhances conduction across the nano-wire junction.

Fig. 10. Transmission spectra as calculated by the NEGF for slab-(111) of As₂O₃ in the range of 0–1.5 V, where the Fermi level is set at 0 eV.

Fig. 10 and 7 in the SI show the transmission spectra, as computed by utilizing the NEGF methodology for slab-(111) of As₂O₃ under varying bias voltages (0–5 V) with a step size of 0.5 V. The Fermi level was set at 0 V, as shown by blue dotted lines. The spectra explain the electronic transmission probability, as the material changes by the function of energy and applied voltage. The results revealed the presence of sharp peaks that showed the energy level at which transmission is high, showing the allowed routes for the movement of the electrons within the materials. The changes within the spectra by the increase in bias voltage indicate the voltage dependence of the transport properties and the electronic structures of slab-(111) of As₂O₃. The regions having a lower magnitude of the transmission spectra, i.e. weaker transmission, represent the band gap presence or the energy region in which the transmission of the electrons is subdue, which may be associated with the vdW gaps present within the materials. Furthermore, the width and the positions of such gaps are also influenced by the applied bias voltage. With the increase in the applied bias voltage, the band gap decreases, which may in turn lead to a decrease in the vdW gap present between the molecular units, which means that the molecular units are much closer and the material's transmission is much improved. Furthermore, the appearance of the sharp transmission peaks may be an indication of the resonant tunneling, from where the electrons tunnel within the material at the specified energy level, which aligns with the quantum states within the structure.

Apart from the above-mentioned transmission spectra, the current–voltage (I–V) profiles for n-Au-As₂O₃ were computed to present the complete picture. The I–V curves were computed in the range of 0–5 V, and the graph was plotted, where the x-axis and y-axis represent the voltage (V) and current in milli-ampere (mA), respectively, as shown in Fig. 11. The I–V curves showed non-linear behavior representing the changes in the resistance by the applied bias voltages. Furthermore, the step-like increment in current at some specified voltage values indicates the presence of the discrete energy levels, as validated by the transmission spectra of the said materials. Furthermore, the curves seem to be roughly symmetric close to the origin/Fermi level, suggesting the similar response of the material under both negative and positive voltages. Besides, in general, by the increase in the applied bias voltages, the current increases, yet the specified features and shape of the curves vary, showing the complex relationship between the current and the voltage. The results revealed that the near-linear I–V curves observed across the full-bias range for the slab As₂O₃ verify the ohmic-dominated transport at low-to-moderate bias, whereas the moderate asymmetric behavior starting at the higher gate voltages (≥3 V) shows the emergence of a Schottky-like barrier, consistent with the band alignment investigations.^73,103

Fig. 11. Current–voltage (I–V) profile for the slab-(111) of As₂O₃ at different applied bias voltages.

3.5.2. Slab-(001)

Similar to the above case, the transmission spectra at varying applied bias voltages, i.e. 0–5 V, demonstrating the probability of the transmission of electrons in slab-(001) was calculated, as shown in Fig. 12. The results showed the stronger transmission without the presence of any specified band gaps. However, the presence of the smaller transmission at the Fermi level is attributed to the wide band gap, as given in Fig. 5, and it authenticates the fact that the material has a wide band gap, as given in Fig. 5.

Fig. 12. Transmission spectra as calculated by the NEGF for slab-(001) of As₂O₃ in the range of 0–5 V, where the Fermi level is set at 0 eV.

Furthermore, similar to the previous case, by the increment in the applied bias voltage, the amplitude of the transmission peaks was suppressed. Moreover, the presence of the spectra that is broad to some extent represents the presence of impurities, or specifically the impurity states, as validated by the electronic properties (Fig. 12). However, the sharp peaks are associated with the discrete energy states, and explain the tunneling of electrons within the materials.

The current–voltage (I–V) profiles at varying bias voltages (0–5 V) for slab-(001) of As₂O₃ were computed, and are given in Fig. 13. The x-axis and y-axis represent the voltage (V) and current (µA), respectively, and each line depicts the specified I–V profile at specified voltages. The graph represents the change in current by the applied voltage, giving information regarding the electrical behavior of the material under consideration. The curves generally showed roughly linear behavior between the voltage and the current, proposing the ohmic behavior, though some variations were observed at distinct voltages. These variations might reveal the presence of non-linear impacts or transition within the conductivity of the materials by the application of distinct voltages.

Fig. 13. Current–voltage (I–V) plots for slab-(001) of As₂O₃ at different applied bias voltages in the range of 0–5 V.

4. Conclusions

The exploration of the properties of novel materials and the evaluation of the respective potential applications are always required to meet the ever-increasing demand of efficient materials. Because of their unique crystal structure, i.e. the presence of weak vdW forces between the molecular units that are building blocks of these materials, the IMCs are currently a significant area of research. In this paper, the As₂O₃ material in its cubic polymorph was taken into account and considered as the novel IMC. The properties and prospects of potential applications in bulk and surfaces with specific orientations, i.e. (001), (110) and (111), were presented. The results revealed that As₂O₃ is a novel IMC as the material is characterized by the three-dimensional anisotropy in bonding, i.e. strong forces within the molecular units and weak forces between the molecular units. The specific crystal structure raises concerns regarding the stability of the materials; hence, the mechanical and structural stability of the material is considered. The material is mechanically and structurally stable. The electronic properties revealed that the bulk and slab-(110) configurations of As₂O₃ are wide-band-gap materials, whereas the slab-(001) and slab-(111) configurations are narrow-band-gap materials. Furthermore, the transport properties of slab-(001) and slab-(111) were determined, and the transmission spectra, transmission eigen states and current–voltage (I–V) curves were plotted. The slab-(001) configuration showed a linear response in the I–V profile, showing ohmic behavior, whereas the slab-(111) configuration exhibited a non-linear response, indicating its potential for application in the Schottky device, and the overall results revealed that the material is suitable for use in nano-devices.

Conflicts of 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.

Data availability

The Amsterdam density functional (ADF) code can be found at https://www.scm.com/.

Supplementary information (SI) is available. See DOI: https://doi.org/10.1039/d6ra01280a.