Two-dimensional Ga₂O₂ monolayer with tunable band gap and high hole mobility

Abstract

By means of density functional theory and unbiased structure search computations, we systematically investigated the stability and electronic properties of a new Ga₂O₂ monolayer. The phonon spectra and ab initio molecular dynamics simulations show that the Ga₂O₂ monolayer is dynamically and thermally stable. Moreover, it also shows superior open-air stability. In particular, the Ga₂O₂ monolayer is an indirect semiconductor with a wide band gap of 2.752 eV and high hole mobility of 4720 cm² V⁻¹ s⁻¹. Its band gap can be tuned flexibly in a large range by applied strain and layer control. It exhibits high absorption coefficients (>10⁵ cm⁻¹) in the ultraviolet region. The combined novel electronic properties of the Ga₂O₂ monolayer imply that it is a highly promising material for future applications in electronics and optoelectronics.

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Introduction

Gallium oxide (Ga₂O₃) is an especially important III–VI semiconductor and it has unique physical and chemical properties that make it interesting for next generation power electronics and UV photodetector applications.^1,2 There are five polymorphs labeled α, β, γ, δ, and ε analogous to alumina, and β-Ga₂O₃ is the most stable phase with a monoclinic structure.³ β-Ga₂O₃ is regarded as a promising candidate for the fabrication of electronic devices due to its wide band gap of 4.7–4.9 eV, expected high breakdown field of 8 MV cm⁻¹, and good thermal stability up to its melting point (∼1800 °C).^4,5 α-Ga₂O₃ with a corundum-like R3̄c crystal structure can be heteroepitaxially grown on sapphire substrates.⁶ γ-Ga₂O₃ has a defective spinel-type structure, while δ-Ga₂O₃ has a defective cubic bixbyite-like one.¹ Hexagonal ε-Ga₂O₃ is very interesting because of internal polarization that could form a high-density two-dimensional electron gas (2DEG) at the (AlGa)₂O₃/Ga₂O₃ interface.³ Ga₂O₃ has pushed the definition of wide bandgap semiconductors to a new level.

Two-dimensional (2D) materials with atomic thickness have attracted extensive attention due to novel properties and potential applications in electronics and optoelectronics.⁷ In the past several years, research enthusiasm was mainly focused on graphene,⁸ transition metal dichalcogenides (TMDs),⁹ phosphorene,¹⁰ and so on to design novel nanoelectronic devices such as field effect transistors and solar cells. Although the 2D materials mentioned above usually possess outstanding properties, it is temporarily hard to adapt multifunctional application because of the drawbacks of them, such as the zero band gap of graphene, low carrier mobilities of TMDs, and poor stability of phosphorene in a humid environment or air. Therefore, the subject of finding and designing new 2D semiconductors with moderate band gaps, superior carrier mobilities, and excellent open-air stability for applications is one of the most active fields of current material research.

Recently, many efforts have been made to study 2D gallium oxide sheets, both experimentally and theoretically. On the experimental side, for example, Zhang et al.² prepared freestanding single layer nanosheets of non-layered material γ-Ga₂O₃ with unprecedented thickness (∼1.25 nm) by a facile hydrothermal method and found that the nanosheets can enhance the photocatalytic efficiency of water splitting and durably photocatalyze overall water splitting into hydrogen and oxygen. Feng et al.¹¹ fabricated 2D Ga₂O₃ with a thickness of less than 10 nm and found that the solar blind photodetector based on 2D β-Ga₂O₃ nanosheets shows a sensitive, fast and stable photoresponse to 254 nm light. β-Ga₂O₃ nano-belts with a [100] orientation were obtained by Kim et al.¹² from a bulk β-Ga₂O₃ crystal using a mechanical exfoliation technique and subsequently processed into a thin film transistor structure. This β-Ga₂O₃ nano-belt based transistor displayed an on/off ratio that increased from approximately 10⁴ to 10⁷ over the operating temperature range of 20 °C to 250 °C and the electrical characteristics were not degraded after month-long storage in ambient air. Using a facile grinding method, Wang et al.¹³ prepared γ-Ga₂O₃ nanosheets (a thickness of about 15 nm) with a very high specific surface area (93.9 m² g⁻¹) and they showed improved solar-blind detection performance (e.g., light–dark ratio, 1.64 × 10⁴) compared to devices based on 3D structured γ-Ga₂O₃. Using nontoxic eutectic gallium-based alloys as a reaction solvent and co-alloying desired metals into the melt, Zavabeti et al.¹⁴ produced extremely thin subnanometer layers of HfO₂, Al₂O₃, and Gd₂O₃, and, at the same time, they also obtained gallium oxides (mostly Ga₂O₃ with a small Ga₂O content) with a thickness of about 2.78 nm. On the other hand, motivated by the successful synthesis of layered gallium oxide sheets, some theoretical work has been focused on the quest of studying the intriguing characteristics of 2D Ga–O systems using ab initio methods. Peelaers et al.¹⁵ used first-principles techniques to investigate the structural and electronic properties of Ga₂O₃ nanolayers created from bulk β-Ga₂O₃ and surprisingly found that freestanding films do not exhibit any signs of quantum confinement and exhibit the same electronic structure as the bulk material.

Here, based on a global structure searching method combined with first-principles calculations, we predict the structure of Ga–O compound monolayers. As expected, a Ga₂O₂ sheet sharing a similar honeycomb structure to a buckled graphene bilayer in AB stacking is both statically and dynamically stable. For 2D Ga₂O₂, we have calculated and reported scanning tunneling microscope (STM) images and the Raman spectrum. Its structural character, energetic and chemical stability, mechanical and electronic properties, carrier transport properties and optical properties are discussed in detail. The electronic structure calculations reveal that Ga₂O₂ is a semiconductor with a wide indirect bandgap and the band structure of the 2D Ga₂O₂ monolayer is tunable by strain and layer control. Superior oxidation resistance of the Ga₂O₂ sheet in the open-air environment has been verified via transition state computations and AIMD simulations. Moreover, Ga₂O₂ also exhibits high hole mobility and strong optical absorption in the ultraviolet region. Therefore, this work provides important guidance for the application of the 2D Ga₂O₂ sheet in electronics and photoelectronics.

Computational methods

Structural search simulations for Ga–O compound sheets were carried out for various stoichiometries (Ga_xO_y, x = 1–4, y = 1–4) using the CALYPSO code.^16,17 In our calculations, both the population sizes and number of generations are fixed to 30. The best 60% of the structures were selected through particle-swarm optimization (PSO) to generate the next generation, while the other structures were generated randomly to guarantee structural diversity. The required structure relaxations were performed using density functional theory with the generalized gradient approximation (GGA) in the form of the Perdew–Burke–Ernzerhof (PBE) functional¹⁸ with the projector augmented wave (PAW) method, as implemented in the Vienna ab initio simulation package (VASP).^19,20 The energy cutoff was taken to be 500 eV. The k-point mesh was set to 7 × 7 × 1 for the Brillouin Zone (BZ) integration in the structure optimization of the unit cell and was increased to 11 × 11 × 1 to obtain an accurate electronic structure. The van der Waals (vdW) interaction was considered using the DFT-D3 method²¹ during all the calculation processes. The Heyd–Scuseria– Ernzerhof (HSE06) hybrid functional²² was used to calculate a more accurate electronic structure and optical absorption coefficients. The vacuum pad in the z-direction was set to about 20 Å, which is sufficient to minimize the interaction between neighboring slabs. The convergence thresholds for the total energy and force were set as 10⁻⁵ eV and 10⁻² eV Å⁻¹, respectively.

The kinetic stability of the obtained Ga_xO_y sheets was checked by computing the phonon spectra using density functional perturbation theory (DFPT)²³ as implemented in the PHONOPY code.²⁴ AIMD simulations were performed to evaluate the thermal stability of Ga_xO_y sheets at different temperatures. The AIMD simulation in the NVT ensemble lasted for 10 ps or 5 ps with a time step of 1.0 fs. The temperature was controlled using the Nosé–Hoover thermostat.²⁵ The climbing-image nudged elastic band (CI-NEB) method^26,27 was employed to investigate the adsorption kinetics of the O₂ and H₂O molecules and determine the activation energy for chemisorption. To this end, a 3 × 3 × 1 supercell was built. One image was used to calculate the reaction path. Other computational details can be found in the ESI.†

Results and discussion

Fig. 1(a) summarizes the schematic of the calculated formation energies (defined in the ESI†) of various 2D Ga_xO_y sheets under conditions from Ga-rich to O-rich relative to the ground state structures of bulk Ga and O₂. The 2D Ga₂O₂ sheet with a formation energy of −1.722 eV per atom is located on the convex hull line between bulk Ga₂O₃ and solid Ga, which indicates that it is stable against all decomposition reactions. Thus, in the following sections, we will focus on the Ga₂O₂ sheet.

Fig. 1 (a) Formation energy per atom as a function of the molar fraction of O atoms for different Ga–O phases. (b) Top and side views of the optimized 2D Ga₂O₂ sheet. The black dashed line shows the unit cell. (c) Charge density difference of Ga₂O₂ with an isovalue of ±0.1 e Å⁻³ (top and side views). (d) ELF map for the Ga₂O₂ sheet with an isosurface of 0.75 (top and side views).

As shown in Fig. 1(b), one unit cell of this Ga₂O₂ sheet consists of two Ga and two O atoms inside, which is isostructural to the structure of the T-B₂S₂ monolayer²⁸ but with slightly different structure parameters. The crystal structure of the Ga₂O₂ sheet possesses two stacked Ga–O layers with a bulking height d (the distance between the two external O atomic planes) of 4.065 Å. Its in-plane lattice constants are a = b = 3.062 Å. Each O atom is tri-coordinated with three adjacent Ga atoms, and each Ga atom bonds with three intra-layer O atoms and one Ga atom in the other layer. The average Ga–O bond distance is 1.926 Å, while that of the interlayer Ga–Ga bond is 2.501 Å.

The atomic charges estimated from Hirshfeld charge analysis show that the more electronegative O atoms get 0.32 e from the less electronegative Ga atoms on average. The deformation electron density (DED) images confirm the Hirshfeld analysis results. The DED is defined as the total electronic density of the Ga₂O₂ sheet with the contribution of isolated Ga and O atoms at their respective positions being subtracted. The result is visualized in Fig. 1(c), which indicates that the transferred electrons are shifted toward O atoms, showing ionic bond character. Yellow and blue refer to electron loss and accumulation regions, respectively. The calculated electron localization function (ELF)^29,30 with an isosurface of 0.75 shown in Fig. 1(d) provides deeper insight into the chemical bonds of the predicted Ga₂O₂ sheet. A substantial concentration of electrons is tightly localized around O atoms and absent in the middle region between Ga and O atoms, which indicates distinct features of ionic bonding. Ga–Ga atoms interact in relatively weak covalent bonds in the Ga₂O₂ sheet. We also found that the length of the Ga–Ga bond in the H₂Ga–GaH₂ molecule³¹ is 2.464 Å, which is shorter than those in the Ga₂O₂ monolayer (2.501 Å). It means that the Ga–Ga bond in the H₂Ga–GaH₂ molecule is stronger than those in the Ga₂O₂ sheet. The electron transfer demonstrated by the DED and the bonding character indicated by the ELF partially contribute to the high structural stability of the Ga₂O₂ sheet.

To further clarify the energetic stability of the predicted new structure, we calculate the cohesive energy, E_c, of the Ga₂O₂ sheet and bulk Ga₂O₃. The calculated cohesive energies of them are 5.349 and 5.497 eV per atom, respectively. A rather favorable E_c indicates a stably connected network and its synthetic feasibility. E_c of the Ga₂O₂ sheet is slightly smaller than that of bulk Ga₂O₃, but it is higher than those of some experimentally synthesized 2D compounds, such as silicene (4.659 eV per atom)³² and germanene (4.051 eV per atom),³³ and is just lower than that of borophene (5.582 eV per atom),^34,35 computed at the same level of theory. The dynamical stability of the Ga₂O₂ sheet is confirmed by the phonon spectrum calculation. As shown in Fig. 2(a), the absence of appreciable imaginary vibrational modes in the entire Brillouin zone confirms the robustness of the interaction between Ga and O at 0 K and the Ga₂O₂ sheet can exist as a free-standing 2D structure. It is noteworthy that the maximum frequency of the Ga₂O₂ sheet is 603 cm⁻¹ (18.1 THz), which is greater than those of AuGaS₂ monolayers (∼450 cm⁻¹),³⁶ the Cu₂S monolayer (∼390 cm⁻¹),³⁷ the GeP₂ monolayer (∼500 cm⁻¹),³⁸ the InO monolayer (∼400 cm⁻¹),³⁹ and gold sulfide monolayers (∼400 cm⁻¹),⁴⁰ attesting robust chemical bonds in the sheet. On the other hand, to examine the thermal stability of the Ga₂O₂ sheet, AIMD simulations were carried out. The fluctuation of the total potential energy as a function of simulation time is plotted in Fig. 2(b). After heating at 300 and 1000 K for 10 ps, we can find that the original configuration of the Ga₂O₂ monolayer does not experience serious disruption and the total energy is fluctuant between −535 eV and −527 eV during the entire simulation. At a temperature of 1500 K, the Ga₂O₂ sheet is highly distorted within 10 ps of AIMD simulation (Fig. S1(a) in the ESI†). A temperature of 1000 K is high enough for many practical applications. These results reveal that the Ga₂O₂ sheet possesses good thermal and dynamical stability and is expected to be synthesized under certain experimental conditions.

Fig. 2 (a) Phonon dispersion of the Ga₂O₂ sheet. (b) Total energy fluctuation as a function of molecular dynamics simulation time and corresponding snapshots after equilibration for the Ga₂O₂ sheet at 300 K (top) and 1000 K (down). The reaction pathway and energy barrier for O₂ (c) and H₂O (d) molecules from physisorption to chemisorption on the surface of a Ga₂O₂ sheet.

Note that phosphorene will experience rapid degradation after exfoliation because it can be easily oxidized by the O₂ and H₂O in the open-air environment, which restricts its applications.^41,42 Therefore, examining the oxidation capability of the Ga₂O₂ sheet under ambient conditions becomes critical. Various O₂/H₂O adsorption geometries are compared by calculating their adsorption energies. It is found that the O₂/H₂O molecule tends to be adsorbed on the hollow site above the center of the Ga–O hexagon with three nearest-neighbor O atoms of Ga₂O₂. The small absolute adsorption energy of −0.178/−0.275 eV indicates a feature of physical adsorption, suggesting the oxidation resistance of the Ga₂O₂ sheet. To further support this conclusion, we calculated the energy barrier from physisorption to chemisorption of an O₂/H₂O molecule on the surface of the Ga₂O₂ sheet with the CI-NEB method. The activation energy barriers are 3.150/1.610 eV, much higher than that of phosphorene (∼0.7 eV),⁴³ indicating that the Ga₂O₂ monolayer might be chemically stable in the air at low temperatures. As presented in Fig. 2(c) and (d), the product of the reaction has an energy 0.523/0.243 eV higher than that of the reactant, indicating that this reaction process is endothermic. Furthermore, we simulated dynamical oxidation processes at 300 K, by using AIMD simulations, with twelve O₂/H₂O molecules preadsorbed above and below a 5 × 5 × 1 Ga₂O₂ supercell. As shown in Fig. S1 (ESI†), after 5 ps of MD simulation with a time step of 1 fs, the Ga₂O₂ monolayer retains its initial configuration and O₂/H₂O molecules move away from the monolayer without dissociation. As a result, the Ga₂O₂ monolayer is expected to exhibit reasonable chemical inertness in ambient air and this unique stability might be attributed to the repulsion between O atoms of the Ga₂O₂ monolayer and O atoms in O₂/H₂O.

The mechanical stability is also indispensable for its applications in the real world. The linear elastic constants, Young's modulus, and Poisson's ratio of the Ga₂O₂ sheet are computed and listed in Table 1. The calculated elastic constants satisfy the stability criteria for 2D materials: C₁₁ > |C₁₂| and C₆₆ > 0,^44,45 implying that the proposed structure is mechanically stable. The in-plane Young's modulus Y and Poisson's ratio ν can be deduced from the elastic constants by Y = (C₁₁² − C₁₂²)/C₁₁ and ν = C₁₂/C₁₁, respectively. To evaluate the accuracy, the results of graphene are also presented at the same level of DFT. The calculated Y and ν values for graphene are in good agreement with previous theoretical studies.^46,47 We found that the Y value of graphene (353.1 N m⁻¹) is almost triple that of the Ga₂O₂ sheet (121.3 N m⁻¹), while the ν value of the Ga₂O₂ sheet is about double that of graphene.

Table 1 The elastic constants (N m⁻¹), Young's modulus (N m⁻¹), and Poisson's ratio of the Ga₂O₂ sheet and graphene

	C 11	C 12	C 66	Y	ν
Ga2O2	142.4	54.8	17.6	121.3	0.385
Graphene	366.0	68.6	136.3	353.1	0.187

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The band structure of the Ga₂O₂ sheet at the PBE level is presented in Fig. 3(a). The Ga₂O₂ monolayer has an indirect gap (E_g) of 1.550 eV with the valence band maximum (VBM) located in the interval of K–Γ and the conduction band minimum (CBM) situated at the Γ point in the irreducible BZ. To get a more accurate band gap, we have also calculated the band structure and density of states (DOS) of the Ga₂O₂ monolayer by the hybrid HSE06 scheme. The results using HSE06 yield similar band shapes, but the E_g value increases to 2.752 eV (Fig. 3(a)). It is much smaller than that of bulk Ga₂O₃ (∼4.8 eV).^1–6 The projected DOS (PDOS) suggests that the VBM of the Ga₂O₂ sheet is mainly dominated by the hybridization of Ga_4s orbitals and O_2p orbitals, while the contributions of Ga_4p states are negligible.

Fig. 3 (a) Computed PBE (red dashed lines) and HSE06 (blue solid lines) band structure of the Ga₂O₂ sheet and its HSE06 PDOS. The Fermi level is set to zero. The band gap of the Ga₂O₂ sheet at the PBE level as a function of strain ε_a, ε_b and ε_ab (b) and number of layers (c).

As a 2D monolayer material, the electronic properties of the Ga₂O₂ sheet can be engineered by applying strain. We have investigated uniaxial and biaxial (tensile and compressive) strains and the simulated strains ε_a, ε_b and ε_ab vary from −10% to 10%. We found that the Ga₂O₂ sheet shows no obstructive structural change under strain in the range of −10 to 10%. The evolution of the band structure with strain is demonstrated in Fig. S2 (ESI†). As seen in Fig. 3(b) and Fig. S2 (ESI†), the band gap increases with compressive strain and decreases with tensile strain for ε_a and ε_ab in the Ga₂O₂ sheet. E_g increases for smaller compressive strain and starts to decrease at a strain of −6% for ε_b, which differs from the trend of monotonic decreasing from compression to tension as found for ε_a and ε_ab. The decreasing tendencies are quasi-linear from −3% to 10% for the three strains. The bandgaps are more sensitive to biaxial strains than to uniaxial ones. The indirect-gap semiconducting nature of the Ga₂O₂ sheet is sustained independently of the directions of the applied strains except E_g declines to 0 at the PBE level under 10% biaxial tensile stress. These properties suggest that the band gap of the Ga₂O₂ sheet can be easily tuned by uniaxial and biaxial strains.

The electronic properties of 2D materials change with the layer numbers and the stacking patterns. Two possible high-symmetry stacking patterns of the Ga₂O₂ bilayer, namely AA and AB configurations, were considered (Fig. S3, ESI†). The optimized interlayer distance of AA stacking of the Ga₂O₂ bilayer (2.655 Å) is less than that of the AB bilayer (2.751 Å). The binding energy of the Ga₂O₂ AA bilayer (74 meV) is comparable to that of the AB bilayer (73 meV). As expected, the band gap of the Ga₂O₂ bilayer in the AA stacking configuration is reduced to 1.325 eV (Fig. 3(c) and Fig. S3, ESI†) compared to that of the monolayer (1.550 eV) from the PBE calculation. Increasing the stacking to tri- and four-layer (AA stacking), the corresponding band gaps are 1.255 and 1.199 eV (PBE level), respectively. The indirect-gap semiconducting feature in the AA stacking Ga₂O₂ bulk is kept but with a further reduced band gap of 1.028 eV. Therefore, the bandgap of Ga₂O₂ can also be tuned by increasing the number of layers, and shows a monotonic decreasing trend with increasing layers. The exfoliation energy of the Ga₂O₂ monolayer is 0.382 J m⁻², which is smaller than that of the P₃C monolayer (0.404 J m⁻²),¹² δ-InP₃ monolayer (0.827 J m⁻²),⁴⁸ and Cd₂C monolayer (∼0.48 J m⁻²).⁴⁹ It holds great promise to fabricate this novel Ga₂O₂ monolayer in the laboratory by exfoliating Ga₂O₂ multilayer materials. For the convenience of experimental comparison in the future, we calculated scanning tunneling microscopy (STM) images of the Ga₂O₂ sheet (using the constant height model⁵⁰ with a height of 1.0 Å and a negative bias of 0.2 V, Fig. S4(a), ESI†). The Raman spectrum was also simulated based on the phonon vibrational modes at the first BZ center, as shown in Fig. S4(b) (ESI†). The Raman active mode at 197 cm⁻¹ for the Ga₂O₂ monolayer is slightly lower than the characteristic band centered at approximately 200 cm⁻¹ of β-Ga₂O₃ thin films.⁵¹ The Raman feature would be useful for future experimental characterization of the Ga₂O₂ monolayer.

The performance of electronic and photoelectronic devices is strongly affected by the carrier transport properties of semiconducting materials. Here, the model of the Ga₂O₂ monolayer was rebuilt in an orthogonal supercell to estimate the carrier mobility along the x and y directions. The atomic structure of the supercell and the corresponding electronic band structure with the HSE06 hybrid functional are presented in Fig. S5 (ESI†). The obtained effective mass m*, elastic modulus C_2D, deformation potential constant E_DP, carrier mobility μ, and relaxation time τ for the Ga₂O₂ monolayer are summarized in Table 2. As listed in Table 2, the effective mass shows an obviously anisotropic feature, due to the different atomic arrangements along the x and y directions. The effective mass of a hole is approximately six times larger than that of an electron along the x direction, which can be understood by the quite flat valence band and more dispersive conduction band (Fig. S5, ESI†). The shifts of the band edges as a function of uniaxial strain show significant distinction for electrons and holes (Fig. 4(a)). To our surprise, the absolute values of the deformation potential constants in Ga₂O₂ are 0.38 eV (x direction) and 0.41 eV (y direction) for holes, which are an order of magnitude smaller than those of electrons (5.93 and 5.54 eV along the x and y directions, respectively). The calculated acoustic-phonon-limited hole mobilities in Ga₂O₂ at room temperature (T = 300 K) are 3027.94 and 4720.40 cm² V⁻¹ s⁻¹ along the x and y directions, respectively. The electron mobilities are remarkably smaller than those of holes in both transport directions with values of 397.60 (x direction) and 407.09 cm² V⁻¹ s⁻¹ (y direction). Electrons display less pronounced anisotropy than holes in mobility along the two directions. The large difference between the electron and hole mobilities is more ascribed to their different deformation potential constants rather than effective masses. The disparity in the electron and hole mobilities (e.g., 10 times larger for holes along the y direction) may be utilized for separating electrons and holes. These results can be explained by the real-space charge density distributions of the VBM and CBM in Fig. 4(b) and (c), respectively. Fig. 4(b) shows that VBM electron states are distributed more along the y direction than along the x direction, indicating that the lattice deformation in the x direction has less effect on the VBM positions. So, the carrier transport along the y direction is relatively easier than along the x direction. Meanwhile, for the CBM, the charges are almost symmetrically distributed (Fig. 4(c)), leading to the similar electron mobility along different directions. Interestingly, the hole mobilities of the Ga₂O₂ monolayer far surpass those of the recently reported SN₂ monolayer (1160 cm² V⁻¹ s⁻¹)⁴⁶ and hydrogenated PtP₂ monolayer (2260 cm² V⁻¹ s⁻¹),⁵² and are comparable with those in the kagome-Sb monolayer (4570 cm² V⁻¹ s⁻¹)⁵³ at room temperature. Our predicted Ga₂O₂ monolayer has both a large band gap and high hole mobilities, novel features highly desirable for practical applications.

Table 2 Calculated effective mass m* (m_e), elastic modulus C_2D (N m⁻¹), absolute value of the deformation potential constant E_DP (eV), carrier mobility μ (cm² V⁻¹ s⁻¹), and relaxation time τ (ps) along the x and y directions for a Ga₂O₂ monolayer at 300 K. m_e is the electron rest mass

Carrier type	Direction	m*	C 2D	E DP	μ	τ
e	x	0.42	121.31	5.93	397.60	0.09
	y	0.47	121.31	5.54	407.09	0.11
h	x	2.49	121.31	0.38	3027.94	4.28
	y	1.62	121.31	0.41	4720.40	4.34

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Fig. 4 (a) Band edge position shifts of the VBM and CBM of the Ga₂O₂ monolayer with respect to the lattice distortion along the x and y directions. Charge densities for the VBM (b) and CBM (c) of the Ga₂O₂ monolayer (top and side views). The isosurface value is taken as 0.05 e Å⁻³.

The Ga₂O₂ monolayer is an indirect and wide gap semiconductor and it is beneficial to restrain the recombination of photo-activated electron–hole pairs.⁴⁶ Thus, the light-harvesting performance of the Ga₂O₂ monolayer and bilayer is explored by computing the absorption coefficients based on the HSE06 functional and the absorption spectra for electric field polarizations along the x, y and z directions are displayed in Fig. 5. Both of them show high absorption coefficients (>10⁵ cm⁻¹), which are comparable to those of perovskites used in solar cells.^54,55 Moreover, their absorption coefficients along the x and y directions are nearly equal, as observed in hydrogenated PtP₂⁵² and PC₆ monolayers,⁵⁶ but different from those of 2D B₄O,⁵⁷ while the intrinsic anisotropy between the in-plane x/y direction and out-of-plane z direction absorption coefficients is also observed due to the 2D nature. The bilayer exhibits stronger absorption than the monolayer. The position of the first absorption peak is located at about 4.0 eV (310 nm) for the Ga₂O₂ monolayer, which is higher than those (240 and 255 nm) of the response peaks of β-Ga₂O₃ thin films.⁵¹ Hence, with sizable absorption coefficients in the ultraviolet range, the Ga₂O₂ monolayer and bilayer may be very promising materials for future optoelectronic devices.

Fig. 5 Calculated optical absorption spectra of the Ga₂O₂ monolayer and bilayer at the HSE06 level.

Conclusions

In summary, we have identified a hitherto unknown 2D Ga₂O₂ monolayer material with desired electronic properties based on comprehensive first-principles swarm-intelligence structural search calculations. The Ga₂O₂ monolayer has excellent thermal and dynamical stabilities, providing a high possibility for its experimental viability or mechanical exfoliation from a multilayer. We have also verified that the Ga₂O₂ monolayer can withstand oxidation in air. The Ga₂O₂ monolayer has an indirect band gap of 2.752 eV on the basis of the HSE06 hybrid functional, and the band gap has a response to uniaxial and biaxial strains as well as the layer number. It possesses high room-temperature hole mobility up to 4720 cm² V⁻¹ s⁻¹ and the large difference between the hole and electron mobility can be valuable for the efficient separation of holes and electrons. It exhibits notable optical properties in the ultraviolet wavelength region, with adsorption coefficients above 10⁵ cm⁻¹. All these data make the Ga₂O₂ monolayer a very promising material for 2D electronic and photoelectronic applications.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We gratefully acknowledge the financial support from the National Natural Science Foundation of China (No. 11704344 and 11404253), the Aeronautical Science Foundation of China (No. 2017ZC55006 and 2019ZF055002), key scientific and technological project of Henan Province (No. 202102210052), and the Key Research Project of Colleges and Universities in Henan Province (No. 18A140033 and 19A140020). We thank Pengyue Gao and Bo Gao for helpful suggestions.

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Footnote

† Electronic supplementary information (ESI) available: Computational details, AIMD simulations, band structures, STM image, Raman spectrum, and atomic structure. See DOI: 10.1039/d0cp05171c

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