Tin and silicon incorporate on gallium sites in Ga2O3 and act as shallow donors. The monoclinic structure of Ga2O3 has two inequivalent Ga sites; density functional theory calculations for bulk show that Sn prefers the octahedral site, while Si prefers the tetrahedral site. Experiments have indicated that Si and Sn can also incorporate on the thermodynamically less preferred site. We use density functional theory to study the adsorption of Si and Sn and also the co-adsorption of these impurities with Ga and O adatoms on the Ga2O3(010) surface. We identify a number of surface reconstructions in which Si adatoms prefer octahedral sites and Sn adatoms prefer tetrahedral sites. By applying the electron counting rule, we also study the mechanisms of the preferred adsorption sites for Si and Sn. We conclude that Si and Sn can also occupy the thermodynamically unfavored site due to surface reconstructions during the growth, which potentially leads to Si and Sn occupying both octahedral and tetrahedral sites in Ga2O3.

Monoclinic β-Ga2O3, a wide-bandgap (4.8 eV) semiconductor with a high breakdown field, is a promising material for field-effect transistors1,2 and deep-ultraviolet photodetectors.3 The n-type conductivity of Ga2O3 can be tuned by doping4 with Si, Ge, or Sn.5 Silicon doping has been achieved in high-quality epitaxial growth of Ga2O3 thin films by plasma-assisted molecular beam epitaxy (PAMBE),6,7 low-pressure chemical vapor deposition (LPCVD),8,9 and metalorganic chemical vapor deposition (MOCVD).10 Tin has also been incorporated in epitaxial growth by molecular beam epitaxy (MBE)11 or metalorganic vapor phase epitaxy (MOVPE).12 Si and Sn doping can also be achieved in bulk growth techniques including edge-defined film-fed growth13 and the Czochralski method.14 

Figure 1(a) illustrates that there are two types of Ga sites [the tetrahedral site (Gatetra) and the octahedral site (Gaocta)] and three types of O sites (OI, OII, and OIII) in β-Ga2O3. OI is threefold coordinated to 2 Gaocta and 1 Gatetra atoms; OII is threefold coordinated to 2 Gatetra and 1 Gaocta atoms; and OIII is fourfold coordinated to 3 Gaocta and 1 Gatetra atoms. Density functional theory (DFT) calculations for bulk have shown that Si atoms preferentially occupy the tetrahedral positions, while Sn atoms prefer the octahedral sites:5,15,16 in the +1 charge state, Si on the tetrahedral site (Sitetra) is 0.68 eV lower in energy than Si on the octahedral site (Siocta), and Sn on the octahedral site (Snocta) is 0.96 eV lower in energy than Sn on the tetrahedral site (Sntetra).16 

FIG. 1.

Side (a) and top (b) view of the bare β-Ga2O3(010) surface. Symbols represent adsorption sites for adatoms. Atoms are presented in a polyhedral style, except for atoms in the top layer, which are presented in a ball-and-stick style. Color code: Gatetra (green), Gaocta (blue), OI (magenta), OII (red), and OIII (orange).

FIG. 1.

Side (a) and top (b) view of the bare β-Ga2O3(010) surface. Symbols represent adsorption sites for adatoms. Atoms are presented in a polyhedral style, except for atoms in the top layer, which are presented in a ball-and-stick style. Color code: Gatetra (green), Gaocta (blue), OI (magenta), OII (red), and OIII (orange).

Close modal

Experiments have observed, however, that Si can also occupy the thermodynamically less favored octahedral site.17 Substitutional Si donors have been identified with scanning tunneling microscopy (STM).17 The brightest features are observed in the first subsurface layer of the β-Ga2O3 (100) surface, showing almost equal number of two different Si donors, indicating that Siocta has almost the same concentration as Sitetra.17 For Sn, scanning transmission electron microscopy (STEM) studies18 revealed divacancy–interstitial complexes, in which some fraction of Sn atoms were on interstitial sites. Based on DFT calculations, it was found that the 2VGa1–Sni defect complex (in which VGa1 is a vacancy on a tetrahedral site) is most likely to form. The position of Sn in this complex indicates that it must have originated on a tetrahedral site.

In this paper, we perform density functional theory (DFT) studies to explore adsorption and diffusion of Si and Sn on the Ga2O3 surface. We study the Ga2O3(010) surface since it corresponds to the most widely used growth direction for both epitaxial growth19 and bulk growth methods.14 We investigate the structures and energetics of Si/Sn, Ga, and O adsorption on the Ga2O3 (010) surface. We find that in the majority of reconstructions, Si adatoms tend to adsorb on the octahedral site, while Sn adatoms prefer tetrahedral sites or a hollow site in between two tetrahedral sites. By analyzing the electronic properties of the adsorbed surfaces, we will explain the driving force for the preferred adsorption sites on the Ga2O3(010) surface. These findings indicate that there is a distinct possibility to achieve Sntetra and Siocta due to surface reconstructions.

DFT calculations were performed using the projector augmented-wave method implemented in the Vienna Ab initio Simulation Package (VASP).20,21 We used the Perdew–Burke–Ernzerhof (PBE) functional22 within the generalized gradient approximation. We previously established that the PBE functional yields reliable results for the trends in adsorption energies.23 The Ga 3d and Sn 4d electrons were explicitly treated as valence electrons. The energy cutoff was 520 eV. The computed lattice constants are a=12.47Å, b=3.09Å, c=5.88Å, β=103.68°, in satisfactory agreement with the experimental values24 (a=12.21Å, b=3.04Å, c=5.82Å, β=103.82°).

Each conventional cell of β-Ga2O3 contains two atomic layers along the b direction [Fig. 1(a)], which we refer to as a “double layer.” The Ga2O3(010) slab is built using a 1×5×1 multiple of the β-Ga2O3 conventional cell. Slabs are separated by a vacuum thickness of 19 Å. The Brillouin zone was sampled with a 2×1×4k-point grid. Reconstructions on both sides of the slab are identical due to the inversion symmetry of the slab, allowing us to extract the properties of a single surface. Atomic relaxations were performed by keeping the central double layer fixed, while the adatoms and all atoms in the two double layers near the surfaces of the slab were allowed to relax; final forces were smaller than 0.01 eV/Å.

To compare the stability of structures with various coverages of Si/Sn, Ga, and O adatoms, we calculate the formation energy (Ef) of a single surface, which is defined as

Ef=12(Ebare+adsEbare2μini).
(1)

Ebare+ads and Ebare are the total energies of the adsorbed and bare surfaces. ni is the number of adsorbed adatoms on the top surface, and μi is the chemical potential of species i (Si, Sn, Ga, or O). The chemical potentials are defined relative to a reference state; i.e., μi=μi,ref+Δμi. For Ga, Si, and Sn, μi,ref is the chemical potential of bulk Ga, Si, or Sn; for oxygen, the reference is that of an O2 molecule. In thermodynamic equilibrium, Δμi's is related to

2ΔμGa+3ΔμO=ΔHGa2O3f,
(2)
ΔμSn+2ΔμO=ΔHSnO2f,
(3)
ΔμSi+2ΔμO=ΔHSiO2f,
(4)

where ΔHGa2O3f=9.22 eV, ΔHSnO2f=4.95 eV, and ΔHSiO2f=8.46 eV are the calculated enthalpies of formation. Given the constraints of Δμi<0, the range of chemical potentials is 4.61eV<ΔμGa<0 eV, 4.95eV<ΔμSn<0 eV, and 8.46eV<ΔμSi<0 eV.

Simulating the growth conditions, we explore the co-adsorption of Si, Ga, and O (Sec. III A) and Sn, Ga, and O (Sec. III B) on the Ga2O3(010) surface. As each Ga2O3 layer contains four Ga atoms and six O atoms, we examined various possible adsorption configurations with one Si/Sn adatom, up to three Ga adatoms, and up to six O adatoms. For each specific Sn/Si, Ga, and O coverage, we also explored various adsorption sites to determine the most stable configuration.

Possible adsorption sites are shown in Fig. 1(b). When an adatom is adsorbed on the atop site (hollow circle), it is bonded to an OI and OIII atom and is on top of a Gaocta atom in the second layer. This adatom will be in the octahedral site in the growing layer. Adatoms can also be adsorbed on the four hollow sites indicated in Fig. 1(b). The hollow1 and hollow2 sites sit in between two tetrahedral sites. Adatoms adsorbed on hollow1, hollow2, and tetrahedral sites are likely to incorporate on a tetrahedral site in the growing layer.

The electron counting rule (ECR) can guide the search for preferred adsorption sites of Si/Sn, Ga, and O.25 According to ECR, O dangling bonds (DBs) prefer to be occupied and Ga DBs prefer to be empty, as O states appear in the lower part of the gap or in the valence band, while Ga states are in the upper part of the bandgap or in the conduction band. Therefore, the reconstructed surface tends to maximize the number of bonds formed on the surface and minimize the number of electrons localized on cation DBs.

When a single Si adatom is adsorbed on the Ga2O3(010) surface, it prefers the atop site (Siatop). Its formation energy of 1.19 eV (under Si-rich conditions) is much lower than the formation energy of a Ga adatom (0.03 eV under Ga-rich conditions) due to the fact that the Si–O bond is much stronger than the Ga–O bond.26 

Formation energies as a function of Si and Ga chemical potentials are shown in Fig. 2. The figure shows results for the subset of reconstructions that have relatively low formation energies in some part of the phase space spanned by the Si and Ga chemical potentials. The corresponding structures are shown in Fig. 3.

FIG. 2.

Formation energies Ef (in eV/1×1 unit cell) for surfaces with different adatom coverage, as a function of the Si chemical potential when (a) ΔμGa=0 eV and (b) ΔμGa=0.6 eV. (c) Phase diagram of the Ga2O3(010) surface as a function of ΔμSi and ΔμGa. ΔμGa=0 and ΔμSi=0 correspond to bulk Ga and Si.

FIG. 2.

Formation energies Ef (in eV/1×1 unit cell) for surfaces with different adatom coverage, as a function of the Si chemical potential when (a) ΔμGa=0 eV and (b) ΔμGa=0.6 eV. (c) Phase diagram of the Ga2O3(010) surface as a function of ΔμSi and ΔμGa. ΔμGa=0 and ΔμSi=0 correspond to bulk Ga and Si.

Close modal
FIG. 3.

Structures of surfaces with (a) Siatop+2Ga, (b) Sih1+2Ga, (c) Sih1+3Ga+2O, (d) Siatop+3Ga+2O, (e) Siatop+3Ga+4O, (f) Siatop+3Ga+5O, (g) Sitetra+3Ga+5O, (h) Siatop+3Ga+6O, and (i) Sitetra+3Ga+6O. The color code is as in Fig. 1, and in addition, O adatoms are highlighted in red, Si adatoms in purple, and Ga adatoms in green. The formation energies (Ef) are given for ΔμSi=ΔμGa=0.

FIG. 3.

Structures of surfaces with (a) Siatop+2Ga, (b) Sih1+2Ga, (c) Sih1+3Ga+2O, (d) Siatop+3Ga+2O, (e) Siatop+3Ga+4O, (f) Siatop+3Ga+5O, (g) Sitetra+3Ga+5O, (h) Siatop+3Ga+6O, and (i) Sitetra+3Ga+6O. The color code is as in Fig. 1, and in addition, O adatoms are highlighted in red, Si adatoms in purple, and Ga adatoms in green. The formation energies (Ef) are given for ΔμSi=ΔμGa=0.

Close modal

Figure 2(a) shows formation energies under Ga-rich conditions (ΔμGa=0 eV) and the surfaces with the lowest formation energies at different Si chemical potentials. Under Si-rich conditions (ΔμSi>0.42 eV), the Siatop+2Ga structure [Fig. 3(a)] is the most stable one. At lower Si chemical potentials (2.45 eV <ΔμSi<0.42 eV), Sih1+3Ga+2O [Fig. 3(c)] is the most stable one. The surface with Siatop+3Ga+4O [Fig. 3(e)] has the lowest formation energy at 3.23 eV <ΔμSi<2.45 eV. Under more Si-poor conditions (4.72 eV <ΔμSi<3.23 eV and ΔμSi<4.72 eV), the most stable surfaces become Siatop+3Ga+5O [Fig. 3(f)] and Si+3Ga+6O; for the latter, the surfaces with Si occupying the atop site [Siatop+3Ga+6O, Fig. 3(h)] and with Si occupying the tetrahedral site [Sitetra+3Ga+6O, Fig. 3(i)] have the same formation energy.

The formation energies of the surface reconstructions also depend on the Ga chemical potential. Figure 2(b) shows formation energies for less Ga-rich conditions, ΔμGa=0.6 eV. This value was chosen to illustrate that the surface reconstructions with lowest formation energies differ from those at ΔμGa=0 eV [Fig. 2(a)]. Since both Si and Ga chemical potentials play a role in determining which structures are stable, it is informative to display the results in the form of a surface phase diagram [Fig. 2(c)]. The surface reconstructions with the lowest formation energies in Fig. 2(a) can be seen by looking along a horizontal line at the top of the phase diagram. The surface reconstructions seen along a horizontal line at ΔμGa=0.6 eV in Fig. 2(c) correspond to the surfaces with the lowest formation energies in Fig. 2(b). The surface phase diagram indicates that several surfaces are stable over a wide range of Si and Ga chemical potentials.

It is notable that Si prefers to be adsorbed in the atop position (i.e., on the octahedral site) in most of the structures in Fig. 2(c). A surface with Si adsorbed on the hollow1 or tetrahedral site will raise the formation energy by 0.42 eV [Sih1+2Ga in Fig. 3(b)], 0.51 eV [Sih1+3Ga+4O in Fig. 4(b)], and 0.84 eV [Sitetra+3Ga+5O in Fig. 3(g)]. There are two cases where the atop site is not the preferred position for Si adsorption. One case is Si+3Ga+6O (which is stable only under rather Si-poor conditions): Si occupying the tetrahedral site [Fig. 3(i)] is as favorable as Si occupying the atop site [Fig. 3(h)] on this surface. The other case is Sih1+3Ga+2O [Fig. 3(c)], where a surface reconstruction with Si adsorbed on the octahedral site [Siatop+3Ga+2O in Fig. 3(d)] raises the formation energy by 0.66 eV. We note that the surface with Sih1+3Ga+2O is stable only over a narrow range of ΔμGa. We also note that surfaces with Siatop+2Ga+2O and Siatop+Ga+2O, where Si prefers the atop site, are stable over a wide range of ΔμGa and ΔμSi.

FIG. 4.

Band structures of surfaces with (a) Siatop+3Ga+4O and (b) Sih1+3Ga+4O. The green and pink bands are surface states. The blue band is the valence-band maximum (VBM), and the red dotted line is the Fermi level (EF).

FIG. 4.

Band structures of surfaces with (a) Siatop+3Ga+4O and (b) Sih1+3Ga+4O. The green and pink bands are surface states. The blue band is the valence-band maximum (VBM), and the red dotted line is the Fermi level (EF).

Close modal

Taking the surface with Siatop+3Ga+4O as an example, we apply the ECR to elucidate how adatoms form bonds on the surface and why Si prefers the atop site. Since each Ga, Si, or O adatom contributes three, four, or six valence electrons, the total number of electrons localized on cations (ncation) can be calculated as

ncation=4nSi+3nGa+6nO2nbonds2nODB.
(5)

nODB is the number of occupied dangling bonds of O adatoms. nbonds is the number of cation-O bonds, which includes cation-O bonds formed among adatoms and bonds formed between O adatoms and Ga atoms from the top layer of the slab. Bonds between Si or Ga adatoms and O atoms in the top layer of the substrate are not included in nbonds. This is because, on the bare Ga2O3(010) surface, all Ga DBs are empty and all O DBs are filled with two electrons;23 the bonds formed between cation adatoms and O atoms from the substrate thus cannot accommodate electrons from adatoms.

The Siatop+3Ga+4O [Fig. 4(a)] surface comprises seven O DBs (nODB=7) and nine cation-O bonds (nbonds=9): two Si–O bonds and seven Ga–O bonds. This yields ncation=(4×1)+(3×3)+(6×4)(2×9)(2×7)=5. There is also a bond formed between two Ga adatoms on the surface, which accommodates two electrons; the corresponding state is in the valence band. The remaining three electrons occupy the two surface states in the gap [green bands in the band structure shown in Fig. 4(a)]; the higher-energy band is half occupied.

To understand the preference for the atop site, we compare with the Sih1+3Ga+4O structure [Fig. 4(b)] in which Si is adsorbed on the hollow1 site. Here, we have nODB=4 and nbonds=12 (two Si–O bonds and ten Ga–O bonds), which yields ncation=(4×1)+(3×3)+(6×4)(2×12)(2×4)=5. There is no bond formed between Ga adatoms on the surface. These five electrons occupy the three surface states in the gap [green bands in Fig. 4(b)]. Compared with the Siatop+3Ga+4O surface [Fig. 4(a)], there is an additional surface state in the gap, and this raises the formation energy by 0.51 eV. On both surfaces, there is also a surface state close to the valence-band maximum (VBM) [pink band in Fig. 4]; electrons occupying this state are located on the O adatoms and have negligible effect on the formation energies. We conclude that Si is preferentially adsorbed on the atop site because this allows more bonds to be formed among adatoms and lowers the number of electrons localized on cation DBs. Adsorption of Si on the atop site will, in turn, lead to incorporation on an octahedral site in the growing layer.

When a Sn adatom is adsorbed on the Ga2O3(010) surface, it prefers the atop site [Fig. 5(a)] with a formation energy of 0.76 eV under Sn-rich conditions, which is lower than the formation energy of a Ga adatom (0.03 eV under Ga-rich conditions), as the Sn–O bond is stronger than the Ga–O bond,26 though not as strong as the Si–O bond.

FIG. 5.

Structures of surfaces with (a) Snatop, (b) Snh1+2Ga+4O, (c) Snatop+2Ga+4O, (d) Sntetra+3Ga+6O, (e) Snatop+3Ga+6O, (f) Snh1+3Ga+4O, and (g) Snatop+3Ga+4O. The color code is as in Fig. 1, and in addition, O adatoms are highlighted in red, Sn adatoms in gray, and Ga adatoms in green. The formation energies (Ef) are given for ΔμSn=ΔμGa=0.

FIG. 5.

Structures of surfaces with (a) Snatop, (b) Snh1+2Ga+4O, (c) Snatop+2Ga+4O, (d) Sntetra+3Ga+6O, (e) Snatop+3Ga+6O, (f) Snh1+3Ga+4O, and (g) Snatop+3Ga+4O. The color code is as in Fig. 1, and in addition, O adatoms are highlighted in red, Sn adatoms in gray, and Ga adatoms in green. The formation energies (Ef) are given for ΔμSn=ΔμGa=0.

Close modal

As can be seen in Fig. 6, this structure with a single Sn adatom is stable only under Ga-poor and very Sn-rich conditions. Structures with co-adsorption of Sn, Ga, and O are more stable, as shown in Figs. 6(a) and 6(b) for two different Ga chemical potentials, ΔμGa=0 eV and ΔμGa=2.5 eV. We chose ΔμGa=2.5 eV to illustrate that the surface with a single Sn adatom becomes favored only under Ga-poor (and Sn-rich) conditions. The corresponding structures are shown in Fig. 5. In particular, we find two structures to be particularly stable over a wide range of host chemical potentials [Fig. 6(c)]: Snh1+2Ga+4O [Fig. 5(b)] under Sn-rich conditions and Sntetra+3Ga+6O [Fig. 5(d)] under less Sn-rich conditions. The surface with Snh1+3Ga+4O [Fig. 5(e)] also has a relatively low formation energy: Ef is only 0.23 eV higher than the Snh1+2Ga+4O surface at ΔμGa=0 eV. On all these surfaces, Sn prefers to be adsorbed on either the tetrahedral site or the hollow1 site (which is between two tetrahedral sites).

FIG. 6.

Formation energies Ef (in eV/1×1 unit cell) for surfaces with different adatom coverage, as a function of the Sn chemical potential when (a) ΔμGa=0 eV and (b) ΔμGa=2.5 eV. (c) Phase diagram of the Ga2O3(010) surface as a function of ΔμSn and ΔμGa. ΔμGa=0 and ΔμSn=0 correspond to bulk Ga and bulk Sn.

FIG. 6.

Formation energies Ef (in eV/1×1 unit cell) for surfaces with different adatom coverage, as a function of the Sn chemical potential when (a) ΔμGa=0 eV and (b) ΔμGa=2.5 eV. (c) Phase diagram of the Ga2O3(010) surface as a function of ΔμSn and ΔμGa. ΔμGa=0 and ΔμSn=0 correspond to bulk Ga and bulk Sn.

Close modal

To investigate the energetic cost for Sntetra or Snh1 to adsorb on an atop site (which corresponds to the octahedral site in the bulk), we also examine surfaces where Sn adsorbs on the atop sites [Figs. 5(c) and 5(f)]. Taking the surface with Sntetra+3Ga+6O as an example, we will explain how adatoms form bonds on the surface and the origin of Sn prefers the hollow1/tetrahedral site.

Each Sn, Ga, or O adatom carries four, three, or six valence electrons. The total number of electrons localized on the cations (ncation) can be calculated as

ncation=4nSn+3nGa+6nO2nbonds2nODB.
(6)

nODB is the number of occupied dangling bonds of O adatoms. nbonds is the number of cation-O bonds, which includes cation-O bonds formed among adatoms and bonds formed between O adatoms and Ga atoms from the top layer of the slab.

On the surface with Sntetra+3Ga+6O [Fig. 7(a)], there are 12 ODBs (nODB=12) and 12 cation-O bonds (nbonds=12): two Sn–O bonds and ten Ga–O bonds. This yields ncation=(4×1)+(3×3)+(6×6)(2×12)(2×12)=1. This electron is localized on the Sntetra adatom DB, which gives rise to the top surface state in the gap [green band in Fig. 7(a)]. By swapping the Sntetra with one Gaatop atom on Sntetra+3Ga+6O, we built the surface with Snatop+3Ga+6O [Fig. 7(b)]. The electron counting remains the same as the surface with Sntetra+3Ga+6O (ncation=1). This electron is localized on the Snatop DB, and the energy level of the surface state is higher than the surface where Sn is adsorbed on the tetrahedral site [green band in Fig. 7(b)], which raises the formation energy by 0.17 eV. On both surfaces, there is also a surface state close to the valence-band maximum (VBM) (pink band in Fig. 7). Electrons occupying this state are located on the O adatoms and have negligible effect on the formation energies.

FIG. 7.

Band structures of surfaces with (a) Sntetra+3Ga+6O and (b) Snatop+3Ga+6O. The green and pink bands are surface states. The blue band is the valence-band maximum (VBM), and the red dotted line is the Fermi level (EF).

FIG. 7.

Band structures of surfaces with (a) Sntetra+3Ga+6O and (b) Snatop+3Ga+6O. The green and pink bands are surface states. The blue band is the valence-band maximum (VBM), and the red dotted line is the Fermi level (EF).

Close modal

The calculations show that on the surface, Sn prefers to occupy the tetrahedral site or the hollow1 site that sits in between two tetrahedral sites. This is different from the bulk, where Sn strongly prefers the octahedral site: Snocta (in a positive charge state) is 0.96 eV lower in energy than Sntetra.16 This preference for the octahedral site in the bulk can be attributed to the large atomic radius of Sn. The volume associated with the octahedral site is larger than for the tetrahedral site: in bulk Ga2O3, the Ga–O bond length is 2.02 Å for Gaocta and 1.87 Å for Gatetra. The Sn–O bond length in bulk SnO2, where Sn is octahedrally coordinated, is 2.2 Å; the fact that the size of Sn is larger than the size of Ga drives Sn to occupy the octahedral site in bulk Ga2O3. On the surface, there are fewer constraints. The average Sn–O bond lengths are 2.40 Å, 2.13 Å, and 2.28 Å on the Snh1+2Ga+4O [Fig. 5(b)], Sntetra+3Ga+6O [Fig. 5(d)], and Snh1+3Ga+4O [Fig. 5(f)] surfaces, respectively. The volume-induced preference for Sn to occupy the octahedral site thus greatly decreases, and the preferred occupation site for Sn is determined by ncation and by the energy levels of occupied surface states, which (as we saw above) favors Sn preferentially occupying tetrahedral sites. The surface reconstructions during growth can thus lead to Sn occupying the tetrahedral site, in addition to the octahedral site, in bulk Ga2O3.

We have used DFT to investigate the adsorption of Si and Sn and also the co-adsorption of these impurities with Ga and O adatoms on the Ga2O3 (010) surface and found several surface reconstructions that are stable over a wide range of Sn/Si and Ga chemical potentials. Even though Sitetra atoms have a lower formation energy in bulk Ga2O3, we found that Si prefers the octahedral site in most surface reconstructions. Similarly, even though Snocta is lower in energy in the bulk, Sn prefers the tetrahedral or hollow1 site on the surface. By analyzing the surface electronic structure, we show that Sntetra and Siocta allow surface states to have lower energy levels, which results in lower formation energies of the corresponding surface reconstructions. Our results explain why it is to be expected that Siocta and Sntetra will be observed in the grown material.

The authors acknowledge valuable discussions with J. Hwang and J. Johnson. This work was supported by the GAME MURI of the Air Force Office of Scientific Research (AFOSR) (No. FA9550-18-1-0479). Use was made of computational facilities purchased with funds from the National Science Foundation (NSF) (No. CNS-1725797) and administered by the Center for Scientific Computing (CSC). The CSC is supported by the California NanoSystems Institute and the Materials Research Science and Engineering Center (MRSEC; No. NSF DMR 1720256) at UC Santa Barbara. Computing resources were also provided by the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by NSF (Grant No. ACI-1548562).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

The authors have no conflicts to disclose.

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