Eighteen functional monolayer metal oxides: wide bandgap semiconductors with superior oxidation resistance and ultrahigh carrier mobility

18 monolayer metals have superior oxidation resistance, wide bandgap, high carrier mobility and notable absorption in the ultraviolet region.


Introduction
Materials with open-air stability and superior carrier mobilities are highly desirable for applications in electronic and optoelectronic devices such as field-effect transistors (FETs), logic circuits and optical modulators. [1][2][3] The recently emerged two-dimensional (2D) materials have attracted intensive interest due to their novel physical properties, e.g., high carrier mobility in certain 2D materials. However, not all 2D materials with high carrier mobility are suitable for advanced electronics. For example, despite the exceptionally high carrier mobilities of B10 5 and B10 3 cm 2 V À1 s À1 for graphene and phosphorene, 3,4 respectively, the poor on/off ratio due to absence of a bandgap for graphene and the low open-air stability of phosphorene notably hinder their electronic and optoelectronic applications. 5,6 It is thus desirable to explore new functional 2D materials with high carrier mobility, moderate bandgap, and excellent open-air stability.
Metal oxides (MOs) are known wide bandgap (42 eV) semiconductors with electron transition energy in the range of visible and ultraviolet light, 7-10 while exhibiting excellent reliability in harsh operating conditions. 11,12 Moreover, ZrO 2 and HfO 2 are known as high-k materials to replace the silicon dioxide gate dielectric layer of a microelectronic device. 13,14 Since many metal oxides are made from the abundant elements in the earth's crust, they are cost effective and often environmentally friendly. All these merits render the MOs promising for versatile applications. [7][8][9][10] Moreover, a number of MOs, such as MoO 3 , TiO 2 and MnO 2 , possess layered crystal structures with weak van der Waals (vdW) interaction between adjacent layers. 15,16 Thus, metal oxide sheets could be mechanically exfoliated from the bulk materials. 15,16 Furthermore, high carrier mobility was also revealed in layered MOs, e.g., B1000 cm 2 V À1 s À1 for MoO 3 flakes, 16 comparable to that of bulk silicon and 2D phosphorene. 4,17 Major advances of layered metal oxide films in electronic applications have already been achieved, including multigate FETs, 8,18 gas sensors, 18 p-n junctions and complementary circuits, 19,20 printable metal oxide electronics technology [21][22][23] and flat panel displays. 7,24 These findings and technological advancements indicate that the layered MOs represent an important class of 2D materials with great potential in cutting-edge electronics and optoelectronics.
To date, atomically thin films of MOs, including HfO 2 , Al 2 O 3 , and Gd 2 O 3 , with the thickness down to 0.5 nm have been successfully fabricated in the laboratory. 10 Theoretically, the electronic properties of several monolayer metal oxides (MMOs), such as GeO, SnO, MoO 2 , WO 2 and MoO 3 , with different phases have been studied. [25][26][27][28][29][30] It was found that the bandgap of monolayer MOs decreases with increase of the thickness. Nonmagnetic layered metal oxides could be transformed to magnetic ones with both sides of the layer being functionalized. 31,32 It was also found that Li and Na atoms can easily transport on the surface of MMOs with low diffusion barrier due to their weak binding with the MMOs, 32,33 demonstrating an advantage of MMOs as potential electrode materials in batteries. Moreover, an unexpected multiferroic phase was predicted for the SnO monolayer with a certain range of doped hole density. 34 The carrier mobility of monolayer MoO 3 could reach up to 3000 cm 2 V À1 s À1 , 29 suggesting that MoO 3 is a promising candidate in high-performance 2D electronic devices.
Although the electronic properties of several monolayer metal oxides with different phases have been studied previously, little is known about their carrier transport and optical properties. Based on systematical first-principles calculations, for the first time, we explore the atomic structures, energetic and chemical stability, and carrier transport properties of 18 monolayer metal oxides. All 18 MMOs entail negative formation energies, suggesting likelihood of synthesis in the laboratory. These MMOs exhibit superior oxidation resistance in the openair environment. They also possess moderate to wide bandgaps (up to 6.48 eV), high carrier mobilities (up to B8540 cm 2 V À1 s À1 ), pronounced in-plane anisotropy ratio of the carrier mobility (up to 115), and notable absorption coefficients in the ultraviolet wavelength region (up to 10 6 cm À1 ). All these satisfactory properties render them promising candidates for carrier transport as well as for rectifier devices and ultraviolet photodetectors. Moreover, monolayer GeO, SnO, SnO-1, TiO 2 , ZrO T 2 and HfO T 2 can be suitable as photocatalysts for water splitting. Our comprehensive study of the 2D MMO materials will promote future experimental efforts in exploration of these materials in 2D electronic and/or optoelectronic devices.

Results and discussion
Atomic structures and stability of monolayer metal oxides  Fig. S1 and Table S1 in the ESI, † respectively. The representative atomic structures with the lower energies are shown in Fig. 1 with the lattice parameters listed in Table 1. First, to assess the energetic stability of these MMOs, we calculate their formation energy DH defined as where E tot is the energy of the MMOs; E M and E O are the energy of a metal in its solid phase and an oxygen atom in a gaseous O 2 molecule, respectively; n 1 and n 2 are the numbers of atoms for each element in the unit cell of MMO, and n is the total number of atoms in the unit cell. MMOs show negative DH of À0.47 to À4.27 eV per atom (see Table 1), indicating that the formation of MMOs is exothermic. For a material to be viewed as thermodynamically stable, it is necessary but not sufficient that DH o 0. We calculate the energy of the MMOs with respect to the convex hull of competing bulk phases, 35 as shown in Fig. S2 (ESI †). The convex hull is currently constructed from the most stable binary bulk compounds of the MMOs. Clearly, most MMOs lie above the convex hull and are thus predicted to be thermodynamically metastable in their freestanding form under standard conditions. However, monolayer W 2 O 5 and TiO 2 lie on the convex hull, indicating the thermodynamic stability of these two monolayers. The kinetic stability of these MMOs is confirmed by their phonon dispersions, as shown in Fig. S3 and S4 (ESI †). Although there are tiny imaginary branches (around À1.0 cm À1 ) near the gamma point in their phonon dispersions, these imaginary frequencies could be removed by having higher numerical accuracy in total energy calculation and structural optimization, or by using larger supercells. Therefore, these MMOs are kinetically stable. We also performed Born-Oppenheimer molecular dynamics (BOMD) simulations to assess the thermal stability of MMOs (see Fig. S5, ESI †). The 10 ps BOMD simulations suggest that these MMOs can maintain their structure at least up to 500 K (except TiO 2 monolayer), indicating their good stability even above the room temperature.
To examine the chemical stability of MMOs in the open-air environment, we consider adsorption of an O 2 molecule on these 2D sheets. The interaction between O 2 and the MMO layer is described by the adsorption energy (E ad ) defined as: where E ox , E mono and E O 2 are the energies of an MMO sheet with an adsorbed O 2 molecule, the pristine MMO sheet, and an individual O 2 molecule in the triplet spin state, respectively. By definition, a positive E ad means endothermic adsorption of an O 2 molecule. In particular, E ad of O 2 adsorbed on these MMOs ranges from À0.091 eV to 0.271 eV (see Table 1 (taking InO or SnO H 2 monolayer as a representative), clearly showing the oxidation resistance of MMOs. The superior open-air stability of MMOs is a distinct advantage compared to many other 2D materials with poor chemical stability in an open-air environment. A well-known example is phosphorene, which can be easily oxidized in an air and moisture environment, with a low activation energy of 0.70 eV. 6 In turn, oxidation of phosphorene leads to higher contact resistance, lower carrier mobility, and possible mechanical degradation and breakdown. 36 Therefore, MMOs with superior oxidation resistance could sustain the device performance for long-term durability.
Knowledge of adsorption and dissociation of water on the surface of 2D materials is of crucial importance for evaluating the use of these metal oxides in humid air environment. To this end, we investigate H 2 O adsorption and dissociation on MMOs Fig. 1]. Here, we define the adsorption energy (E ad *) to describe the interaction between H 2 O and the MMO, as follows:   Since the 2D monolayer or few-layer materials are usually fabricated by mechanical exfoliation from their bulk solids, we calculate the interlayer binding energy to assess the ability for exfoliation from bulk counterparts. We define the interlayer binding energy E B as follows: where E bulk and E ML are the total energies of bulk and monolayer metal oxides in the unit cell, respectively; n 1 is the number of layers in the bulk structures; n 2 is the total number of atoms in the unit cell of bulk metal oxides. Since the bulk phases of NiO T 2 , PtO T 2 , SnO T 2 , TiO 2 , MoO 3 , Mo 2 O 5 , W 2 O 5 , SnO and SnO-1 exhibit layered structures, 37,38 the monolayers of these systems could be obtained directly by mechanical exfoliation. 39 As displayed in Table 1, the calculated binding energies of two monolayers are in the range of À0.001 and À0.075 eV per atom, comparable to or even less than those of two phosphorene (À0.055 eV per atom), 40 graphene and h-BN sheets (both around À0.065 eV per atom). 41 These results demonstrate high possibility of exfoliating MMOs from the layered bulk solids.
Electronic structures and carrier transport properties of monolayer metal oxides Previously, the geometric and electronic structures of monolayer GeO, SnO, SnO 2 , MoO 2 , WO 2 , MoO 3 and NiO 2 were studied, [25][26][27][28][29][30] but the carrier mobilities of only MoO 3 and SnO monolayers were reported. 27,29 Here, the carrier transport properties of the MMOs are systematically investigated. The electronic band structures of the MMOs are presented in Fig. 2, and their bandgaps are given in Table 1 3 , GeO, SnO and SnO-1 monolayers, are wide bandgap semiconductors with 5.17 eV 4 E g 4 2 eV. Thus, these MMOs are suitable for potential applications as electronic and optoelectronic devices to operate at much higher voltages, frequencies and temperatures than the conventional semiconductor materials like silicon and gallium arsenide. [43][44][45][46] On the other hand, ZrO 2 and HfO 2 monolayers possess exceptionally large bandgaps of 6.0 and 6.48 eV, and should be considered as 2D insulators. Their carrier transport properties will not be discussed below. Nevertheless, the large bandgaps for monolayer ZrO 2 and HfO 2 render their possible application in ultraviolet photodetectors. [47][48][49] Based on the band structures shown in Fig. 2, the effective masses of carriers for 16 MMOs are calculated and summarized in Table 2. The effective masses are in the range of 0.73-6.73 m 0 (0.73-4.52 m 0 ) for holes, and 0.31-6.12 m 0 (0.10-6.74 m 0 ) for electrons along the x direction ( y direction), respectively.  1 for holes). The carrier effective mass in this work is distinct from that in ref. 35 since the unit cell or supercell adopted is different, hence the x-direction of the effective mass. The monolayer metal oxides as a photocatalyst for water splitting are demonstrated in ESI, † S7. By comparing the band edges with the redox potentials of water, we identified that monolayer TiO 2 , GeO, SnO, SnO-1, ZrO T 2 and HfO T 2 can be potential functional photocatalysts for water splitting at acidic or neutral environments. However, considering the overpotentials for oxygen and hydrogen evolution processes, 50 only the GeO monolayer satisfies the basic requirement for water splitting. Table 1 The calculated structural parameters (a/a 0 ) defined in Fig. 1, formation energy (DH), interlayer binding energy (E B ), bandgap (E g ), valence band maximum (VBM) and conduction band minimum (CBM) with vacuum level set at zero energy as the reference, adsorption energy (E ad ) of an oxygen molecule on metal oxide monolayer. ' To further estimate the carrier transport properties of MMOs, we calculate their acoustic phonon-limited carrier mobility m based on the Takagi model within the deformation potential approximation: 51,52

'd'' (''i'') in the parentheses indicates a direct (indirect) bandgap
where e is the electron charge; h is the reduced Planck constant; k B is the Boltzmann constant; T is the temperature; m is the effective mass along the transport direction; m d ¼ ffiffiffiffiffiffiffiffiffiffi ffi mm ? p is the average effective mass (m > is the effective mass perpendicular to the transport direction); C 2D is the elastic modulus of the 2D sheet, determined by varying the lattice parameter l along the transport direction via DE/S 0 = C 2D (Dl/l) 2 /2 (DE is the energy change of the system under lattice deformation Dl, S 0 is the area of the 2D sheet); the term E 1,i represents the deformation potential constant of the valence band maximum (VBM) for a hole or the conduction band minimum (CBM) for an electron along the transport direction, defined by DV/(Dl/l) (DV is the band edge shift under lattice deformation). All data are calculated using a strain step of 0.5%. The temperature considered  Table 2 Effective mass m h of hole carriers, deformation potential constant E 1 , elastic modulus C and hole mobility m h for monolayer metal oxides. m 0 is the electron rest mass. The subscripts x and y represent the directions defined in Fig. 1 Materials in the mobility calculations is 300 K. The present carrier mobility calculation has been evidenced to be not only computationally efficient but also physically reasonable. 53,54 The mobilities of electrons and holes calculated by the HSE06 functional are given in Table 3 and schematically shown in Fig. 3. At first glance, the mobilities of electrons ranging from 4.46 to 8541 cm 2 V À1 s À1 are substantially larger than those of holes (3.37-990.93 cm 2 V À1 s À1 ). Also note that the carrier mobility shows rather pronounced anisotropy with large longitudinal/horizontal ratio up to 115 (see Table S3, ESI †). This feature could be utilized to enhance the device performance by controlling the direction of carrier transport. Generally speaking, the carrier mobilities of most MMOs are in the order of magnitude of hundreds of cm 2 V À1 s À1 , which is comparable with those of common 2D materials like phosphorene and MoS 2 . 53,55 More importantly, five monolayers of InO, SnO T 2 , TiO 2 , MoO 3 , SnO and GeO exhibit outstanding electron mobilities above 1000 cm 2 V À1 s À1 and even reach up to 8540 cm 2 V À1 s À1 for InO, implying that MMOs should be promising candidates for high-speed electronic devices. Our present results, taking MoO 3 monolayer as a representative (1466 and 61.86 cm 2 V À1 s À1 for electrons, and 698.56 and 50.78 cm 2 V À1 s À1 for holes along x and y directions, respectively), are in good agreement with previous theoretical values (1608.80 and 37.52 cm 2 V À1 s À1 for electrons, and 800.57 and 25.56 cm 2 V À1 s À1 for holes along x and y directions, respectively). 29 The 2D elastic contant (C 2D ) is attained by a quadratic fitting of the total energy versus strain (Fig. S11, ESI †) and the deformation potential constant (E 1,i ) is calculated by the linear fitting of the CBM (VBM)-strain relation (Fig. S12, ESI †). Furthermore, electronic properties of MMOs containing heavy elements (Hf, Pt, W) are calculated by considering spin-orbit coupling, as displayed in Fig. S13 and Table S4 (ESI †). The results show that electonic properties, including the bandgap, carrier effective mass, deformation potential and carrier mobility, are little influenced by the spin-orbit coupling. For example, after inclusion of the spinorbit coupling effect, the bandgaps and carrier mobilities change only slightly by 0.03-0.05 eV and 2-40 cm 2 V À1 s À1 , respectively. Similarly, the electronic properties of MMOs are calculated by using the DFT+U method with Hubbard U parameters of 2.0 eV for Hf, 4.8 eV for Mo, 6.2 eV for W, 5.1 eV for Ni, 3.0 eV for Pt, and 4.2 eV for Ti. 38,[55][56][57][58] The results indicate that the Coulomb interaction results in changes of 0.06-0.25 eV Table 3 Effective mass m e of electron carriers, deformation potential constant E 1 , elastic modulus C and hole mobility m e for monolayer metal oxides. The subscripts x and y represent the directions defined in Fig. 1   for the band gaps, compared with the values of HSE06 calculation. Meanwhile, carrier mobilities calculated by using the DFT+U method range from 6.89 to 1784.39 cm 2 V À1 s À1 , a similar trend as calculated by using the HSE06 functional (see Fig. S14 and Table S5, ESI †).

Materials
Since the experimentally synthesized metal oxide sheets could be multilayer rather than monolayer, we calculate the carrier mobilities of InO bilayer and trilayer. As given in Table S6 (ESI †), multilayer InO sheets still retain ultrahigh carrier mobility up to 7490 cm 2 V À1 s À1 , rather close to 8540 cm 2 V À1 s À1 for InO monolayer. Our results indicate that layered metal oxides hold great promise for the next-generation 2D electronic devices. The high carrier mobility of the 2D metal oxides can be attributed to their relatively small effective mass, large elastic modulus, and small deformation potential constant. These systems show large C 2D values up to 290 J m À2 , approaching the value of graphene (330 J m À2 ). In these stiff sheets, the acoustic phonons possess a large group velocity, leading to the small amplitude of lattice waves and weak scattering with charge carriers. The deformation potential constant E 1,i is another important factor for carrier mobility. It approximates the strength of electron-phonon coupling and is determined by the band edge shift under lattice variation due to acoustic phonons. E 1,i for MMOs could be as low as 0.36 eV, comparable with 0.15 eV of phosphorene, 53 which is able to significantly promote the carrier mobility.

Optical absorption properties of monolayer metal oxides
Semiconductors with wide bandgaps can serve as potential visible-blind ultraviolet photodetectors. To this end, we computed optical absorption coefficients of several MMOs with wide bandgap in the ultraviolet region (i.e., wavelength from 10 nm to 400 nm), as shown in Fig. 4 and Fig. S15 (ESI †). Mostly, the optical absorption coefficients can reach as high as 10 5 cm À1 , comparable to that of zincblende, rock salt and wurtzite AlN. 43,59 The majority of MMOs exhibit outstanding optical adsorption properties at far ultraviolet (wavelength range of 122-200 nm). In particular, the optical absorption coefficient of ZrO T 2 monolayer exhibits a value of nearly 10 6 cm À1 at a wavelength of B69 nm. Prototype devices of ultraviolet detectors made up of h-BN and group-IV chalcogenide sheets have been demonstrated in previous experiments. [60][61][62] The h-BN based deep ultraviolet optical sensor showed very good response to ultraviolet light with wavelengths below 254 nm. 63 The detector by group-IV chalcogenide films (such as SnS 2 ) exhibited a remarkable photoresponse above 300 nm, dependence of photocurrent on optical power and wavelength, fast-response, and excellent photo-switch and longterm stability. 64,65 By analogy, the present monolayer MMOs with wide bandgap could be promising functional materials for ultraviolet detectors.

Conclusion
We have theoretically explored the atomic structures, energetic stability, electronic and optical properties of 18 monolayer metal oxides. Among them, the most stable structures of 9 monolayer metal oxides are predicted from the unbiased particle-swarm optimization while structures of the other 9 monolayer metal oxides can be simply exfoliated from the bulk counterparts. All 18 monolayer metal oxides are energetically favorable with negative formation energies of À4.27 to À0.47 eV per atom, suggesting high experimental feasibility for the synthesis or mechanical exfoliation of the monolayers. Many of these monolayer metal oxides are wide bandgap semiconductors with chemical inertness, and some entail high carrier mobility up to 8540 cm 2 V À1 s À1 as well as pronounced in-plane anisotropy of the carrier mobility with large longitudinal/horizontal ratio up to 115. Moreover, the computed band gaps and band edge positions of monolayer TiO 2 , GeO, SnO, SnO-1, ZrO T 2 and HfO T 2 suggest their potential applications as functional photocatalysts for water splitting at acidic or neutral environments. Several monolayer metal oxides also exhibit notable absorption spectra in the ultraviolet wavelength region, with adsorption coefficients above 10 5 cm À1 . Hence, these monolayer metal oxides with band gaps in the range of 1.22-6.48 eV may serve as functional 2D materials in visible light or ultraviolet photodetectors, as well as high-temperature and high-power electronic devices for electron and hole transport.

Computational methods
Density functional theory (DFT) calculations 66 were performed by using the Vienna ab initio simulation package 5.4. 67 More specifically, we used the planewave basis set with an energy cutoff of 500 eV, 68 the projector augmented wave (PAW) potentials, 69 and the generalized gradient approximation parameterized by Perdew, Burke and Ernzerhof (PBE) for the exchange-correlation functional. 70 Since the conventional GGA functional like PBE tends to underestimate the band gaps, a hybrid functional (HSE06) was used to compute the electronic structures and optical properties of the 18 metal oxide sheets. The convergence criterion of total energy was set to 10 À7 eV. The geometry optimization was considered to be successful when the residual force on each Fig. 4 Optical absorption coefficients in the ultraviolet wavelength region for monolayer WO H 2 , TiO 2 , ZrO T 2 and HfO T 2 . l is the wavelength.