Density Functional Theory simulations of water adsorption and activation on the (-201) β-Ga2O3 surface Roozbeh Anvari,[a,b] Dino Spagnoli, [b] Giacinta Parish, [a] Brett Nener, *[a]

[a] R. Anvari, Prof Dr G. Parish, Prof Dr B. D. Nener School of Electrical, Electronics and Computer Engineering

University of Western Australia35 Stirling Highway, Perth WA 6009 AustraliaE-mail: brett.nener@uwa.edu.au

[b] R. Anvari, Dr. D. SpagnoliSchool of Molecular Sciences,

University of Western Australia35 Stirling Highway, Perth WA 6009 Australia

E-mail: dino.spagnoli@uwa.edu.auSupporting information for this article is given via a link at the end of the document.

Abstract: Density functional theory (DFT) calculations are used to study the molecular and dissociative adsorption of water on the (-201) β-

Ga2O3 surface. The effect of adsorption of different water-like species on geometry, binding energies, vibrational spectra and the electronic

structure of the surface are discussed. The study shows that while the hydrogen evolution reaction requires a small amount of energy to

become energetically favourable, the over-potential for activating the oxygen evolution reaction is quite high. The results of our calculations

provide insight as to why a high voltage is required in experiments to activate the water-splitting reaction, while previous studies of gallium

oxide predicted very low activation energies for other energetically more favourable facets. Application of this work to studies of GaN-based

chemical sensors with gallium oxide surface shows it is possible to select the gate bias so that the sensors are not influenced by water

splitting reactions. It was also found that in the region where water-splitting does not occur, the surface can exist in two states: water or

hydroxyl terminated.

Introduction

The investment into research on the splitting of water by photocatalytic methods has risen in recent years to address the growing

demand for sustainable energy, and the reduction of the use of carbon dioxide emitting fuels. [1] Gallium oxide is a transparent oxide

with a wide band gap of around 4.8-5.3 eV, [2] that has a wide range of applications from semiconducting lasers and UV detectors [3] to

high temperature gas sensors.[4] Moreover, gallium oxide is a p-block material and exhibits very high photocatalytic activity. The

conduction band of p-block metal oxides with a d10 electronic configuration consists of hybridized sp orbitals with large dispersion that

enhances photoexcitation of electrons with high mobility. [5] As a result, interactions of hydrogen with various Ga2O3 phases/surfaces

has been studied extensively in applications such as water splitting,[6] catalysis,[7] and hydrogen detectors.[8]

The physicochemical characteristics of different polymorphs of gallium oxide are different when exposed to hydrogen. [9] Ga2O3 can

form five different crystalline structures, designated as α, β, γ, δ and ε phases, among which α and β and recently γ phases have

been used to realize water splitting.[9-10] β-Ga2O3 (monoclinic with a space group C2/m) is the most stable phase at room

temperature,[11] and exhibits higher photocatalytic activity toward decomposition of aromatics than α and γ phases. [10a, 12] There have

been numerous investigations into the water splitting efficiency of β-Ga2O3. The high catalytic activity of β-Ga2O3 can be attributed to

an abundance of under coordinated Ga3+ surface sites and the conjugated effect of proton and oxide.[7d] Moreover, although the effect

of tunable phase-junctions,[13] addition of co-catalysts,[11b, 14] and doping[15] on the water splitting efficiency of Ga2O3 have been

investigated, a comprehensive model of the water splitting reaction on Ga2O3 surfaces still does not exist.

Theoretical studies based on first-principles have been used extensively to investigate various physical and chemical properties of

the bulk and low-index surfaces of Ga2O3.[2c, 16] Zhou et al. studied water adsorption and activation on (001), (100), (110) and (012)

surfaces of α-Ga2O3. Their study shows that (100) and (110) facets, which have low stability, are the most favourable surfaces for

hydrogen evolution reaction (HER), and oxygen evolution reaction (OER), respectively.[10a] Ma et al. studied the effect of vacancy and

chalcogen (S, Se, Te) doping on the adsorption and partial decomposition (H2O → H+OH) of water on the (100) surface of β-phase.[17] Their study concludes that water is present at the surface of this facet in molecular form, and the presence of defects (vacancies or

doping) has no effect on the reaction parameters. In another study, Zhou et al. showed that adsorption of water on a clean (100)

surface is energetically unfavourable. However, addition of NiOx compounds makes the hydration process exothermic and reduces

the required overpotential barrier (required potential difference above the equilibrium value) for OER. [18] Qiu et al. studied the effect of

the addition of Ca, La and Ti on the water splitting efficiency of (100) β-Ga2O3.[6c] They found that the position of the states that are

formed due to doping determines the relative changes of efficiency of the water splitting process. Aharon et al. used a DFT+U

method to study the water oxidation behaviour of (001) Fe2O3 partially coated with a hydrogenated monolayer of Ga2O3.[19] Their study

concluded that the improved performance of the combined system can be explained by the role of the Ga 2O3 in enhancing the charge

separation and transport. Ju et al. studied the role of strain and lattice misfit on band alignment of α/β-Ga 2O3 phase junctions and its

effect on water splitting efficiency of the junction.[20] Furthermore, Jin et al. proposed that in order to improve the photocatalytic

activity, the mixed phase γ-β should not be defective or disordered. [6b] Despite all the experimental and theoretical work into the water

splitting properties of different phases and various low-index surfaces of Ga2O3, the properties and dynamics of the water splitting

reaction on the (-201) surface of β-Ga2O3 has not been studied.

Although the most stable surface of β-Ga2O3, i.e (100), has been most extensively studied, the photoexcited electron-hole pairs might

migrate to different facets of the surface.[10a, 21] Moreover, the calculated reaction coordinates of water-splitting process have

reasonable energy requirements, which does not agree with the experimental results. [10a] Therefore it is important to study the water-

splitting characteristics of different surface terminations. The (-201) surface of β-Ga2O3 is available commercially and has been used

in different applications.[22] For example, various experiments indicate that (-201) is the preferred growth direction for thin films grown

on c-plane sapphire.[23] This orientation can be related to the fact that the oxygen atoms of the (001) plane of sapphire substrate have

a similar atomic arrangement to the (-201) plane of β-Ga2O3.[23d, 23f] Interestingly, the XRD pattern of catalytically grown Zn doped p-

type β-Ga2O3 nanowires shows a significant peak at (-201).[14d] The (-201) orientation is a common index when thin films of gallium

oxide form as a native or thermally annealed oxide on wurtzite GaN-based semiconductors. [24] Lee et al. characterized the interface

between (-201) β-Ga2O3 oxide and (002) GaN as a function of oxygen flow when the oxide is grown epitaxially by pulsed laser

deposition.[24a] Moreover, (-201) β-Ga2O3 has become an efficient substrate to grow (001) GaN epilayers. [25] Recently Song et al. grew

single crystalline (-201) β-Ga2O3 nanowires using a flexible (001) GaN seed.[24d] The characteristics of PtOx Schottky contacts to the

thin film and bulk (-201) β-Ga2O3 were also studied.[26]

The frequent occurrence of the (-201) peak on the surface of the oxidized GaN is another reason that stimulates the study of the

interface between this facet and water.[24a, 24b, 27] GaN-based sensor technologies have been investigated extensively to detect gas,[28]

pH,[29] bio-chemicals[30] and various ions in solution. [31] Although today commercial devices already exist in the market for various

applications, noise and drift are still limiting factors for realization of robust sensors. [32] The surface of GaN-based sensors, electrodes

and devices is covered with a layer of native or thermally grown oxide, and it is suggested that water strongly contributes to corrosion

and degradation of these devices.[33] Moreover, chemical sensors are frequently used with a reference electrode and are immersed in

strong acidic and basic solutions. Therefore, it is necessary to find the conditions under which the (-201) β-Ga2O3 surface does not

react with water, conditions which can be regarded as being within the safe range of operation for GaN-based chemical sensors.

Due to the experimental evidence of the existence of the (-201) β-Ga2O3 surface on the many important materials described above,

we have used DFT to study the water activation and splitting reactions on this surface. The manuscript is organized as follows: the

theoretical framework for modeling the water splitting reaction and the corresponding energies are summarized in the Method and

Computational details, and the Results and Discussion section discusses adsorption energies, vibrational contribution, electronic

structure, HER and OER. All the findings are summarized in the Conclusion.

Method and Computational details

Vibrational energy

The most stable surface composition minimizes the surface energy, and at the temperature T and pressure p is given by:

γ (T , p )= 1A

¿] (1 )

Here, G (T , p ,{N i}) is the Gibbs free energy of the slab, A is the surface area, and N i, µi are the particle number and chemical

potential of the species of the ith type. In our system, the surface is in contact with an environment consisting of oxygen and water in

the gas phase. The surface energy is normalized to energy per unit area by dividing by the surface area. Configurational entropy, the

pV term and the vibrational free energy also contribute to the surface energy.[34]

Reuter et al. showed that the vibrational and entropic contributions of the bulk oxide to the surface energy cancel out and those of

adsorbates can be neglected.[35] However, hydroxyl groups and water-like adspecies are an exception due to their high-energy modes

and contribute a large vibrational energy to the surface. [36] The lattice vibration is accounted for by adding the zero-point vibrational

energy, ∆ γ vib ,ad, to the DFT derived total energy, Etot. The vibrational free energy contribution of adsorbates is defined as:[34, 37]

∆ γ vib ,ad (T )=Fadsorbatevib −F free

vib (2)

where Fadsorbatevib and F free

vib are the vibrational free energies of the adsorbed molecule on the surface and in the free gas state

respectively. Fvib ( T , ωi ) is the contribution of a given vibrational mode, within the harmonic approximation, at frequency ωi and

temperature T , and is defined as:[38]

F vib ( T ,ωi )=12

h ωi+K BTln (1−e−h ωi

K BT ) (3)

To calculate the total vibrational energy, for a given T, the above equation is summed with respect to the frequency spectrum of the

slab with N fundamental modes (with frequencies of ωi):

F vib (T )=∑i=1

3N

F vib (T ,ωi ) (4)

Here, F vib is obtained from detailed vibrational analysis of the various surface species, diagonalizing the complete dynamic matrix

while leaving the substrate fixed.[37b]

DFT energy vs Gibbs free energyThe chemical potentials and boundary conditions are defined as Gibbs free energies. The DFT used in this study is a zero

temperature, no applied pressure technique, and hence the calculated energies are Helmholtz free energies by thermodynamic

definition. Moreover, depending on the experimental conditions, either ultra-high vacuum (UHV) stoichiometric or high-pressure

terminations can exist.[35] Here, ab initio thermodynamics is used to determine the equilibrium composition and geometry of the

surface with the environment. Helmholtz free energy of the system is defined as: [35, 39]

F (T ,V , NGa ,NO , N H )=E tot (T ,V , NGa , NO , N H )+F vib (T ,V , NGa, NO , N H )

(5)

where

F vib ( T , V , NGa , N O , N H )=Evib (T , V , NGa , NO , N H )−TS (T , V , NGa , NO , N H )

(6)

The Helmholtz free energy is associated with the Gibbs free energy via

G (T , p , NGa , NO ,N H )=F (T , p , N Ga , NO , NH )+ pV (T , p , N Ga, NO ,N H )

(7)

where the temperature dependence of μO(T , pO2) includes the contributions from vibrations and rotations of the molecule, as well

as the ideal gas entropy at p0=1atmosphere.[39] Since the range of atmospheric pressure of interest is below 100 atm, and the pV

term is to be normalized to surface area, the pV term can be neglected.[35] Consequently, this leaves the only additional contribution

to the Gibbs free energy, apart from the DFT total energy, to be the vibrational contribution term.

Water splitting reactionThe intermediate water-like groups that are derived from the water decomposition process determine the characteristics of the overall

reaction.[10a, 40] The water splitting reaction can be divided into two separate half-redox reactions, i.e. HER and OER. The cathodic and

anodic activation of water can lead to various intermediate surface phases.[41] HER involves one electron transfer:[10a]

¿+H liq+¿+e−¿ →∗H ads¿ ¿ (8)

OER involves a four step electron transfer, and hence is more complicated:[10a]

¿+H2 Oliq →∗OH ads+H liq+¿+ e−¿ ¿¿ (9)

¿OH ads →¿Oads+ H liq+¿+ e−¿¿¿ (10)

¿Oads+ H 2Oliq →∗OOH ads+H liq+¿+e−¿¿ ¿ (11)

¿OOH ads→∗+O2+ H liq+¿+ e−¿¿¿ (12)

where * represents a surface site. Here we only consider the thermochemistry of the surface; the mechanism and the reaction

activation barrier[42] are not studied. At standard environmental conditions (298 K, pH 0, 1 bar H 2), and no bias (U=0 V) vs normal

hydrogen electrode (NHE), the above proton/electron-transfer reactions differ by n¿, which allows a natural relationship to the

normal hydrogen electrode, defined by the equilibrium

H liq+¿+e

−¿↔ 12

H 2gas ¿

¿ (13)

where the reaction energy is zero at pH liq=0 and pgas=1 atm. Therefore, by setting the reference potential to that of the

standard hydrogen electrode, i.e. 0 V, the free energy of the equations 8−12 is equal to the free energy of the following equations:

¿+ 12

H2gas→∗H ads (14)

¿+H2 Oliq →∗OH ads+12

H 2gas

(15)

¿OH ads→¿Oads+12

H 2gas

(16)

¿Oads+ H2Oliq →∗OOH ads+12

H2gas

(17)

¿OOH ads→∗+O2+12

H2gas

(18)

where the reaction free energy of the equations 14−18 can be written as:

ΔGwater+surfacecorrected =ΔEwater+surface

DFT +Δ F vib−TΔS (19)

Moreover, the finite potential of the electron will be linearly dependent on the bias U (V):[42]

ΔGU=−eU (20)

and the effect of the pH of the electrolyte can be described as:

ΔG pH=−KTln¿ (21)

To model the effect of the water environment of the electrochemical cell, we can write the reaction free energy:

ΔG ¿ (22)

where the change of the vibrational contribution Δ F vib also includes the difference in point energy between the adsorbed and gas

phase (ΔZPE). The entropy of adsorption of 1/2H2 is approximately equal to the negative value of the H2 in the gas phase at

standard conditions.[10a] The entropies of adsorption of O and H2O were calculated in a similar way. Moreover, gas phase water at

0.035 bars is used as the reference state for water because at this pressure the gas phase water is in equilibrium with liquid water at

300 K.[43] Here, the values of entropy and enthalpy are obtained from standard thermodynamic tables.[43-44]

Computational details

All simulations were performed using the Vienna ab initio simulation program (VASP), which is a plane-wave basis set code. [45] The

electron wave functions were described using the Blochl projector augmented wave (PAW) method in the implementation of Kresse

and Joubert. [45a, 46] The simulations are performed within the generalized-gradient approximation (GGA), using the exchange-

correlation potential developed by Perdew, Burke and Ernzerhof (PBE). [47] A cut-off energy of 700 eV is applied to limit the error of the

bulk energy to within 5%. For integration within the Brillouin zone, specific k points around gamma were selected using a 4×8×6

Monckhorst-Pack grid for bulk studies and a 1×8×6 grid for surface studies. All surfaces were modelled by periodically repeated

slabs. Slabs consisting of 6 Ga- layers were used to minimize the residual internal electric field. Perfect (1×2) surface unit cell with

different combinations of surface adsorbate i.e. (H, H2, O, O2, OH, H2O, H.OH, OOH) were subsequently fully relaxed by minimizing

the atomic forces to within 1x10-6 eV Å-1. Symmetric adsorption of adsorbates on both sides of the slab was used to avoid a spurious

dipole moment normal to the surface. The slab is separated from its periodic image by 17 Å vacuum gap. The simulations included

spin polarization and van der Waals forces, using the Grimme D3 method, [48] to describe the surface adsorption and H-bonds more

accurately. Bader analysis was performed on the converged charge density profile to obtain the integral charge of isolated atoms. [49]

For all the surfaces and adsorption structures, the vibrational analysis was simplified by keeping all the bulk and surface atoms fixed

in their relaxed equilibrium positions, and analysing the vibrational spectra of the adsorbates by only permitting all the atoms of the

adsorbate groups to move along the perpendicular or the parallel directions to the surface. Dynamical matrix calculations are

performed using the code VASP.

Results and Discussion

Bulk and (-201) surface properties The bulk unit cell of β-Ga2O3 contains four formula units each of which contains two non-equivalent Ga (Ga(I), Ga(II)) and three non-

equivalent O sites (O(I), O(II), O(III)). The computed bond length and lattice constants are summarized in Table 1.

Table 1.

The (-201) surface is created by cleaving the optimized bulk cell and was modelled as slabs, periodically repeated. There are two

non-polar stoichiometric terminations in this direction (cut A and B). The relaxed atomic coordinates are depicted in Figure 1. For

each surface, the difference in surface energy between slabs with 6 (32 formula units) and 8 (40 formula units) layers of Ga was

below 1%. Cut A and B correspond to a surface energy of 1.01 J/m2 (0.063 eV/ Å2) and 0.86 J/m2 (0.054 eV/ Å2), respectively. We

calculated the following surface energies (eV/ Å2) for other low index surfaces of β-Ga2O3: 0.035 for (100), 0.081 for (010), 0.086 for

(10-1), 0.088 for (110) and 0.93 for (001) terminations. Comparison of these values indicates the relative stability of the (-201)

termination (after (100) as the most stable termination). Cut A is O terminated and is higher in energy, and therefore, cut B is used in

the rest of the paper. The (-201) β-Ga2O3 surface consists of three types of Ga (Ga1, Ga2, Ga3) and 4 types of oxygen (O1, O2, O3, O4),

which are labelled in Figure 1d). The O1 and Ga1 surface sites of the cut B were considered for adsorption. The surface had an area

of 92.56 Å2.

Figure 1.

Adsorption energies A previous study by Zhou et al. shows that the adsorption energies of H on low coordinated OS sites, where the superscript S

indicates surface atoms, on the (100), (001), (012), and (110) α-Ga2O3 surfaces are energetically more favourable by 1.8-2.4 eV than

those adsorbed on GaS.[10a] Their study also showed that the most favourable adsorption occurs when the oxygen of the water

molecule (OW) is adsorbed to the surface Ga, such that the plane of water is parallel to the surface. Moreover, their study concluded

that the stable geometry does not vary significantly as a function of surface coverage. [10a] The study of Ma et al. also shows no

significant variation in adsorption energies as a function of coverage. [17] They attributed this phenomena to the weak bonding of the

water molecules to the surface. As a result, the study presented in this paper is limited to the adsorption of water like species on O 1

and Ga1 surface adsorption sites. All the adsorbed species are relaxed and unlike other studies, we do not fix the position of the

surface and bulk atoms. Therefore, all surface and bulk atoms are in their lowest energy configuration.

The relaxed coordinates of the water species are depicted in Figure 2, the relaxed structural features are tabulated in Table 2, and

the adsorption energies are summarized in Table 3. The molecular adsorption of H2O onto the Ga1 site is exothermic by 0.148 eV per

molecule, while the dissociative adsorption of water requires just 0.1 eV. As a result, the water molecule can easily dissociate on the

surface. However, the adsorption of a single OH group onto the Ga1 site is highly exothermic by 2.03 eV per OH group. The dipole of

the adsorbed water molecule is almost parallel to the surface (∡ Hw-Ow-Ga1 =96∘and ∡ Ow-Ga1-Ga1 =95∘), while the dipole

moment of the OH group of the dissociated water (H.OH) is pointing outwards, (∡ Hw-Ow-Ga1 =112∘, ∡ Ow-Ga1-Os =98∘). These

results are consistent with the previous study of the hydration of Ga2O3 by Ma et al.[17] Their study shows that the most stable

geometry for the adsorption of water is when the plane of water is parallel to the surface, OW lies above the surface Ga atom, and two

HW atoms point toward surface OS atoms.[17]

The molecular adsorption of H2, with a relaxed bond length of 0.76 Å after adsorption, requires a trivial energy of 0.15 eV per

molecule and has no effect on the surface coordinates. However, through the process of the dissociative adsorption of hydrogen the

surface O1 moves out of the surface by 0.5 Å. The dipole of the formed surface OH group, with a bond length= 0.99 Å, is parallel to

the corrugated surface. The adsorption energy of H onto the O1 site is endothermic by 0.514 eV. This result agrees with the

experimental studies on the other surfaces of the gallium oxide.[7d, 8a, 52] The adsorption energy of dissociative adsorption of O is 2.5

eV, comparable to that of OH. However, the adsorption energy of the molecular adsorption of O2 (with a bond length of 1.23 Å after

relaxation) is 0.33 eV, comparable to that of molecular adsorption of H2. The calculated high adsorption energy of oxygen, and

negative adsorption energy of water can be a contributing factor to the low and high photoresponse of Ga2O3 nanowires when

exposed to the oxygen and humid air, respectively. [53] Coordinates of all the relaxed structures are listed in the supporting

information.

Figure 2.

Table 2.

Vibrational contribution

The calculated vibrational frequencies of the adsorbed species onto the (-201) surface are summarized in Table 3. The calculated

vibrational frequency for the adsorbed O is 293 cm -1 for a single chemisorbed O atom, and 563 cm-1 in the adsorbed hydroxyl group

when no Ga-H bond is present. While the O of water still resonates at a frequency close to that of OH i.e. 208 cm -1, the H of water,

OH and H.OH vibrate at 3033, 2584 and 3187 cm-1, respectively. The vibrational contributions of these surface species to the surface

energy as a function of temperature are depicted in Figure 3. However, when the water molecule is dissociated, the O W-HW and HW-

OS vibrate with a maximum frequency of 3187 and 2841 cm -1, respectively. These results are consistent with the previous FTIR

experiments on the vibrational frequencies of the dissociative adsorption of H 2 onto the (100) β-Ga2O3 surface that assigned a

frequency range of 3000-3800 to the OS-H bond, and a frequency range of 1980-2003 to the GaS-H bond.[8a, 52, 54] Moreover, the

theoretical work of Zhou et al. on the (001, 100, 110 and 012) surfaces of α-Ga2O3 obtained a vibrational frequency of about 3750 cm-

1 for the OW-HW bond, and 2417 to 3627 cm-1 for the OS-HW bond. A comparison between the calculated and experimental

frequencies, and taking into account the negligible energy that is required for the water molecule to dissociate on the surface of the (-

201) β-Ga2O3, indicates that the surface of the oxide is always water terminated in air, and the majority of the water molecules are

dissociated.

Electronic structure A well-known deficiency of DFT using a GGA functional is the underestimation of the band gap for solids. Ju et al. showed that

although PBE significantly underestimates the band gap of the Ga2O3, it predicts identical density of states and line shapes to that

calculated by HSE06 hybrid functional, which can predict the exact band gap. [18b, 20] Angle resolved photoemission spectroscopy and

DFT studies agree that β-Ga2O3 is an indirect material with the CBM at Gamma and VBM at M(½ ½ ½). [16a] The calculated indirect

band gap for the bulk structure is 2.15 eV, while the band gap is narrowed down by 9% to 1.955 eV for a clean (-201) surface, and

further decreases to 1.75 eV when the surface is hydrogenated (monolayer (ML)=0.25 coverage). Band gaps of the (-201) surface

with the adsorption of surface species are tabulated in Table 3.

Partial density of states (PDOS) at the vicinity of the valence band maximum (VBM) and the conduction band minimum (CBM) for the

bulk structure, and the perfect (-201) surface with and without water-like species adsorbed on the surface (ML=0.25 coverage) are

summarized in the supporting material. The VBM of the bulk material consists of hybridization of the p orbital of O (Obulkp ) and the d

orbital of Ga (Gabulkd

), while its CBM consists of the s orbital of Ga (Gabulks

) and the s and p orbitals of O (Obulksp

). VBM of the (-201)

surface is made up of the hybridization of the d orbital of the Ga2 and Ga3 at the surface, with the p orbital of the O2 and O3 type

surface O, while the CBM at the surface consists mostly of the s, p and d orbitals of all the surface gallium hybridized with the s and p

orbital of the surface oxygen. Analysis of the O4 atom shows that it behaves more like a surface O than a bulk O. For the electronic

structure of the bare surface with and without water-like species, in all cases, bulk atoms contribute to the electronic structure of the

surface such that Gabulk /surfd and Obulk / surf

p contribute to the VBM, and Gabulk /surfs and Obulk / surf

sp contribute to the CBM. The

addition of adsorbates changes the band-gap at the surface by introducing localised states at the CBM or VBM.

Table 3.

Figure 3.

Adsorption of H introduces no surface traps, while the corresponding band gap is narrowed down to 1.75 eV because of the

introduction of localized states to the VBM. The Fermi level after the adsorption of a hydrogen atom is located in the conduction band.

However, the Fermi level is located slightly below the VBM after the adsorption of all the other water-like species. Although the

hydrogen orbital mostly contributes to the CBM in the form of hybridization with Osurfsp and Gasurf

d , the introduction of localized states

to the VBM has narrowed the band gap. For the molecular adsorption of hydrogen, H2, the s orbital of H strongly mixes with the CBM,

but makes less contribution to the VBM compared to the atomic adsorption of H.

Adsorption of O on a Ga1 site introduces significant asymmetry to the surface. The Osurfsp and Gasurf

spd orbitals of the surface are

hybridized with the p-orbital and to a lesser degree to the s-orbital of the adsorbed oxygen (Oadssp ) to form surface traps. The

introduced surface states are located close to VBM and above the Fermi level (the band gap is reduced to 1.28 eV). Molecular

adsorption of O2 introduces a band of localized states formed next to the CBM. The CBM is highly asymmetric. On the other side, the

formation of the transient OOH group introduces a more significant disturbance to the electronic band structure. A wide band of

localized states is formed just 0.13 eV above the VBM that reduces the band gap from that of adsorbed O (1.28 eV) to 1.05 eV. The

hybridization of Gasurfspd , Osurf

sp and OWp forms the electronic structure of the localized states. Moreover, while Gabulk

spd and Obulkp

contribute to the electronic structure of the localized states for the adsorption of O, bulk states have a minor contribution to the

localized states that are introduced as a function of the formation of O2 and OOH groups.

Adsorption of the OH group does not introduce any trap level to the band gap, and the corresponding electronic structure is quite

symmetric. The calculated band gap is 1.8 eV, and the VBM is located slightly above the Fermi level. OWsp and H s orbitals contribute

to CBM, while OWp and H s orbitals hybridize with VBM. In the dissociative adsorption of water, H.OH, the band gap is further

reduced to 1.77 eV, the electronic structure is symmetric and no trap levels are introduced into the band gap. However, the VBM and

CBM have a shape very similar to that of OH. A comparison between the dissociated H (HW2) and the H of OH (HW1) shows that the

dissociated H contributes more significantly to both CBM and VBM. The band gap of dissociated water is narrow compared to that of

OH. Moreover, the Fermi level is lifted slightly upwards.

While the band gap of the perfect surface is just 7% narrower than that of the bulk, the band gap corresponding to the adsorption of

water-like species ranges from 16% for OH to 54% for O narrower than that of the bulk. However, the narrowing band gap indicates

better performance of the photocatalyst.[17] The electronic structure corresponding to the molecular adsorption of water is quite

symmetrical and introduces no localized states with a band gap that is reduced to 1.77 eV. The contribution of surface species to

CBM and VBM is similar to that of H.OH with the difference that the band gap of the molecular adsorption is slightly wider.

Table 4.

Badar charge analysis of the adsorption of different water-like species on the (-201) β-Ga 2O3 surface (Table 4) shows that when the

Hads-O1 bond is formed (dissociated H, or dissociated H2O), the total surface charge is a large negative number, which indicates a

flow of charge from HW to O1 of the surface. In contrast, where Oads-GaS bond is formed, the total surface charge becomes much less

negative, which indicates a flow of charge from GaS to OW. For example, in the case of the molecular adsorption of water, the total

surface charge is a smaller negative number than that for H.OH and H. The large magnitude of the transferred charge from H to the

surface is also consistent with the location of the Fermi level, as was discussed in the above paragraph. Comparison of the charges

of H in the molecular adsorption of water shows that one H has lost more charge compared to the other, and this charge is

transferred to the surface. The total transferred charge of the OW, HW1 and HW2 is -0.172|e| (where |e| is the magnitude of the charge

of the electron), 0.362|e| and 0.126|e|, respectively. This phenomenon indicates that the charge flow occurs from H W atoms to surface

O atoms, and from surface Ga atoms to OW atoms simultaneously. In contrast, for a single OH group, the charge of the OW is -0.137|

e|, which is between that of OW in an adsorbed water molecule and that of OW in a dissociated water molecule, respectively. This

phenomenon can be explained by the fact that, while the adsorbed O are gaining electrons, the adsorbed H are always donating

electrons to the surface. As a result, an OW atom bonded to H atoms would gain more charge. Therefore, the magnitude of the

transferred charge of the H bonding to the OS is higher (more basic H), than that of H bonding to OW. When the surface is exposed to

reagents, it is expected that the OS (which is in contact with several Ga atoms) induces a larger polarization of the OS-HW bond, such

that the electron density is increased on the H (compared to OW-HW bond that is in contact with one surface Ga). [10a, 55] Therefore, HW

bonding to OS is a stronger Lewis acid. This is consistent with the results of this calculation that in the ground state, the HW bonding to

OS has lost more charge (more positive in the convention used in this study) than the HW bonding to OW. The observed trend is

consistent with the results from previous work.[10a]

Hydrogen and oxygen evolution reactions An optimal catalyst would have Gibbs free energy close to zero. [10a] The calculated value of the Gibbs free energy of HER, ΔGHER, for

the (-201) β-Ga2O3 surface on O1 site is 0.82 eV (pH=0 and U=0). Table 5 summarizes the ΔGHER and the required over potential of

OER based on results from this study and also, as a comparison other low index surfaces of the α and (-201) β-Ga 2O3 from the

literature. Zhou et al. predicted the ΔGHER for α-Ga2O3 to be 0.15 eV for the (001) surface, -0.08 eV for the (100) surface, -0.58 eV for

the 110 surface, and 0.21 eV for the 012 surface. [10a] Moreover, they calculated the ΔGHER for (100) β-Ga2O3 to be 0.47 eV for a clean

(perfect) surface, while they obtained a value of -0.31 eV for the same surface doped with Ni. [18a] Figure 4 shows the behaviour of the

(-201) β-Ga2O3 surface when exposed to different pH and bias based on results from this study. HER would only become

energetically favourable at pH=0, 7 and 12 when an over potential of -1.53, -1.29 and -0.82 V is applied between the surface and bulk

electrolyte (bulk electrolyte in is in equilibrium with NHE), respectively. The first step of the OER reaction becomes energetically

favourable when an over potential of 2.04, 2.51 and 2.75 V is applied for pH=0, 7 and 12 respectively. However, the second step of

OER is highly endothermic and for pH=0, 7 and 12, the OER would become energetically favourable only when an over potential of

3.0, 3.4, and 3.71 V is applied between the surface and NHE, respectively. Within the range over which the surface is water-

terminated, the third and fourth steps of OER are energetically more favourable. However, a much larger overpotential is required to

make the first and second steps of OER energetically favourable, and therefore the former mentioned terminations cannot occur.

Figure 5 depicts various reaction paths as a function of applied potential and the pH of the aqueous solution. At pH=0 and U=0, the

first two steps of the OER (formation of *OH and *O) are exothermic by 2.03 and 2.99 eV, respectively, while the third and fourth step

(formation of *OOH and O2 from *OOH), is exothermic by 1.12 and 0.7 eV. However, commencing from U=3.0 V (pH=0), the reaction

path becomes downhill and the OER is energetically favourable.

The previously calculated low energy barriers are not consistent with the experiments which showed that the water splitting reaction

on Ga2O3 is unlikely to happen without a co-catalyst or phase-junction.[10a, 13] Therefore, the higher calculated energy barriers in this

study are closer to what would be expected from the experimental values. Moreover, in OER reactions (equations: 14-18), it was

assumed that no other surface group was present when the OER reaction is taking place on O 1 surface site. However, considering

the very low energy required for dissociation of water on (-201) β-Ga2O3 i.e. 0.1 eV, H.OH formation can be another intermediate step

in the reaction path. It was discussed in the previous sections that the calculated vibrational spectrum of the dissociated water

molecule is more consistent with the experimental values. The required extra positive energy for the water molecule to dissociate

sums to the required energy barrier for water splitting and makes the calculation more consistent with the experiment.

Figure 4.

Table 5.

Figure 6 depicts the phase diagram in which the pH-U space is dissected into four regions where OER, HER, OH-termination and

water-termination are energetically favourable. This study can also provide insight into the surface dynamics of GaN-based chemical

sensors. Firstly, because the terminating oxide layer of the sensor determines the behaviour of the sensor, the bias of the reference

electrode should be adjusted according to the pH of the solution such that OER and HER reactions are not energetically favourable.

Secondly, according to the pH and the bias of the reference electrode, the surface of the sensor can be H-terminated, water-

terminated or hydroxylated. Therefore, different equilibrium reaction rates can be effective in between the oxide and the solution,

which can in turn initiate non-Nernstian response of the sensor.

Figure 5.

Figure 6.

ConclusionAdsorption of various water like species on (-201) β-Ga2O3 were studied, and the corresponding energies, atomic coordinates,

vibrational spectra and the electronic structure were analysed in detail. The calculated vibrational spectra were close to that of the

hydrated surface (H2O, H.OH) of the gallium oxide measured by experimental methods. As expected, the study of the electronic

structure showed a strong sp hybridization in the bulk and surface of the (-201) β-Ga2O3. The relative changes of the band structure

showed that hydration has a significant effect on the electronic structure. The studies indicated that dissociated H is more basic and

vibrates at lower frequencies than the more acidic H, which keeps intact to the adsorbed oxygen of the water molecule. Moreover, the

conditions under which HER and OER would become energetically favourable were investigated and compared with that of other low

index surfaces of gallium oxide. It was shown that the higher calculated overpotential required to initiate the reaction is more

consistent with the experimental observations. Finally, the concept of the conditions under which the OER and HER reactions

become energetically favourable were extended to determine the safe range of operation for GaN-based chemical sensors with

gallium oxide surface.

ACKNOWLEGMENTS

This research was undertaken with the assistance of resources from the Pawsey Supercomputing Centre with funding from the

Australian Government and the Government of Western Australia. This research was partially supported under Australian Research

Council's Discovery Projects funding scheme (project number DP140100827).

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Figure legends

Figure 1. (a) Relaxed bulk β-Ga2O3. Two non-polar stoichiometric terminations: (b) cut A and (c) the more stable cut B, in the (-201) direction. Red and grey represent O and Ga. (d) The convention used for labelling the surface atoms.

Figure 2. Top (left) and side (right) views of the adsorption of the different water species. Red, Green and white represent O, Ga and H, respectively. H.OH represents the dissociative adsorption of water.

Figure 3. Vibrational contribution of the surface hydrogen groups to the surface free energy of various adsorbates to the stoichiometric (-201) surface of β-Ga2O3.

Figure 4. The phase diagram showing the free energy for different surface structures for water at (pH=0,7,12) in contact with (-201) β-Ga2O3. The hydrogen termination becomes energetically more favourable at potentials ≤-1.53 V, -1.29 V, and -.82 V for pH=12, 7, and 0, respectively. Likewise, the OH termination becomes energetically more favourable at potentials ≥ 2.04 V, 2.51 V and 2.75 V, respectively. The potential (U) is relative to the standard hydrogen electrode at pH=0.

Figure 5. Calculated reaction free energy diagram for OER of (-201) β-Ga2O3 surface. The potential (U) is relative to the standard hydrogen electrode at pH=0.

Figure 6. Calculated phase diagram of (-201) β-Ga2O3 surface. The potential (U) is relative to the standard hydrogen electrode at pH=0. The area to the left of the red line corresponds to the condition where HER is energetically favourable and the surface is H-terminated. The area to the right of the dashed line indicates the region where OER occurs. However, before OER is energetically favourable, the surface transitions from being water-terminated (the trapezoid region in between the red and blue lines) to being hydroxylated.

Tables

Table 1. Experimental and theoretical properties of bulk Ga2O3. This study

HSE06 B3LYP Experiment[c]

a (Å ) 12.21 12.25[a] 12.34[a] 12.23

b (Å ) 3.04 3.05[a] 3.035[a] 3.04

c ( Å) 5.63 5.84[a] 5.79[a] 5.8

β (deg) 103.55 103.9[a] 103.9[a] 103.7

volume( Å3)209.23 209.24

Δ H (eV / f .u . )-9.99 -11.29

ε r10.2

Eg(eV ) 2.15[d] 4.83[a] 4.66[a] 4.9

Ga(I)-O(I) 1.836 1.864[b] 1.8 Ga(I)-O(II) 1.842 1.867[b] 1.83Ga(I)-O(III) 1.865 1.894[b] 1.85Ga(II)-O(I) 1.948 1.969[b] 1.95Ga(II)-O(II) 1.936 1.951[b] 1.95Ga(II)-O(III) 2.01 2.073[b] 2.02

[a] Reference,[50]

[b] Reference,[18b] [c] Reference,[51]

[d] The behaviour of the underestimated band-gap and its relative changes with the adsorption are discussed in section 3.4.

Table 2. Structural parameters.Surface group

ΔzGa-O

[Å ]GaS-Oads

[ Å ]GaS-OS

[ Å ]OS-H1

[ Å ]OW-H1

[Å ]OW-H2

[ Å ]H-OW-GaS

∡H 0.514

1.83 0.99

H2 1.82 2.72O 0.24 2.07 1.85O2 1.82OH 1.097 1.8 1.86 .977 112.3o

H2O 0.24 2.29 1.83 0.98 0.98 96.53o

H.OH 1.165 1.79 1.84 .984 .976 2.94 113.08o

OOH Δz indicates the displacement of the surface Ga and O site of adsorption in the direction normal to the surface. Superscripts S and ads stand for surface and adsorbed species. Bond lengths are in [ Å ] and the angles are in degrees.

Table 3. Adsorption energies (Eads), band gap (Eg) and vibrational frequencies (ω).

Surface group Eads

(eV )Eg

(eV )

ωOs-H

(1/cm) ωOw-Hw

(1/cm) ωGa-Ow

(1/cm)

Expt.[a]

(100) βExpt. [b]

(100) βExpt. [c]

(100) βExpt. [d]

(100) β

H 0.709 1.75 3265 20252010 1980 1970

20031980

19902070

H2 0.15 1912961

O 2.63 1.28 293O2 .332 82

1254OH 2.03 1.8 2584 563 3500 3000

to3800

3730370036303600

2680275036343720

H2O -0.148 1.771 3033 208H.OH 0.1 1.768 2841 3187 591

OOH 3139 108

814Only the highest calculated frequency is mentioned. In the case of O 2, H2 and OOH, the top number corresponds to the vibration of the atom that is closer to the surface. Experimental values for H and OH correspond to OS-H and GaS-H bonds, respectively. Note that the attribution of the experimental values to particular atoms/molecules can only be inferred. [a] Reference,[52b]

[b] Reference,[52a], contributed the vibrational frequencies to dissociative adsorption. [c] Reference,[8a] contributed the vibrational frequencies to dissociative adsorption of H2. [d] Reference, [54]

Table 4. Bader charge analysis.

H H2 O O2 OH H2O H.OH OOH

Surf

ace

atom

s

O1 -0.348 -0.018 0.140 -0.010 -0.024 -0.045 -0.344 -0.010O2 0.070 0.005 0.048 0.011 0.117 0.0245 0.091 0.011O3 -0.005 -0.016 -0.006 -0.057 0.056 -0.047 0.022 -0.057

O4 0.026 -0.008 0.011 0.006 0.153 0.009 0.009 0.006

Ga1 -0.213 0.018 -0.010 0.017 -0.058 -0.001 -0.100 0.017

Ga2 -0.139 -0.002 0.001 0.001 -0.044 0.001 -0.015 0.001

Ga3 -0.186 0.016 0.002 0.005 0.042 0.016 -0.029 0.006

Total -0.796 -0.005 0.1944 -0.239 0.242 -0.056 -0.366 -0.024

A

dsor

bate

s OW1 -0.230 -0.582 -0.137 -0.173 -0.128 -0.582OW2 -0.1832 -0.1832H1 0.559 -0.652 0.188 0.362 0.078H2 -0.609 0.126 0.267 0.148

The +¿ and −¿ signs indicate charge loss and charge gain, respectively. The charge difference for O 2 and OOH is calculated relative to the charge of O in O2,

and for the rest of surface O groups relative to the charge of O in H2O, and for all H relative to that of H in water.

Table 5. Calculated values for ΔGHER and UOER

Surface ΔGHER (eV) UOER (V) Reference P (-201) β-Ga2O3 -0.82 2.93 This study P (100) β-Ga2O3 0.47 2.57 [18a]

C (100) β-Ga2O3 -0.31* 1.71 [18a]

P (001) α-Ga2O3 0.15 [10a]

P (100) α-Ga2O3 -0.08 [10a]

P (110) α-Ga2O3 -0.58 1.83 V [10a]

P (012) α-Ga2O3 0.21 [10a]

P and C correspond to a perfect and a surface with co-catalyst, respectively. ΔG HER and UOER correspond to the Gibbs free energy of HER, and the over potential at which the OER reaction coordinates becomes downhill (at pH=0).* lowest value for different surface sites.

Text for the table of contents

The results of our DFT calculations of the adsorption of water on the (-201) β-Ga 2O3 surface provide insight as to why a high voltage is required in experiments to activate the water-splitting reaction on the surface of a real world multi facet β-Ga2O3 based electrode.

Keywords: Ga2O3, Water-splitting, Density Functional Calculations, Catalysis,