Unusual Electronic and Optical Properties of Two-Dimensional Ga2O3

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C: Energy Conversion and Storage; Energy and Charge Transport

Unusual Electronic and Optical Properties of TwoDimensional GaO Predicted by Density Functional Theory 2

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Jie Su, Rui Guo, Zhenhua Lin, Siyu Zhang, Jincheng Zhang, Jingjing Chang, and Hao Yue J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b08650 • Publication Date (Web): 11 Oct 2018 Downloaded from http://pubs.acs.org on October 16, 2018

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The Journal of Physical Chemistry

Unusual Electronic and Optical Properties of Two-Dimensional Ga2O3 Predicted by Density Functional Theory Jie Su,†‡ Rui Guo,† Zhenhua Lin,† Siyu Zhang,† Jincheng Zhang,† Jingjing Chang,†* Yue Hao† †Wide

Bandgap Semiconductor Technology Disciplines State Key Laboratory, School of Microelectronics,

Xidian University, Xi’an, 710071, China ‡State

Key Lab of Solidification Processing, College of Materials Science and Engineering, Northwestern

Polytechnical University, Xi’an, Shaanxi, 710072, China Abstract: β-Ga2O3 is a great potential wide band gap semiconductor for the applications in electronic and optoelectronics. Here, we predict the natural physical properties of atomic monolayer and bilayer Ga2O3 using density functional theory. Although β-Ga2O3 is not a van der Waals material, it is found that two-dimensional (2D) Ga2O3 is stable and can be fabricated by exfoliation. Different to unpassivated 2D Ga2O3, H-passivated 2D Ga2O3 possesses obvious quantum confinement effects. Remarkably, monolayer and bilayer Ga2O3 show larger indirect band gaps (6.42 and 5.54 eV, respectively) and far higher electron mobilities (up to 2684.93 and 24485.47 cm2V-1s-1, respectively) than those of bulk β-Ga2O3. Moreover, evident variation of band gaps and an indirect-to-direct transition are induced by uniaxial strain. The electron transport of 2D Ga2O3 is anisotropic due to the stronger contribution of O-pz orbitals to conduction band minimum than O-py orbitals. Such characters promote the promising application of 2D Ga2O3 in electronic nanodevices. In addition, the electron relaxation time and exciton binding energies of 2D Ga2O3, especially bilayer, are enhanced to 3.77 ps and 0.89 eV, respectively. Moreover, pronounced optical absorbance (up to 105 cm-1) of 2D Ga2O3 in the solar-blind spectrum enhances its applications in optoelectronic nanodevices. INTRODUCTION 1

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As an intriguing wide-band-gap semiconductor, β-Gallium oxide (β-Ga2O3) has received considerable attentions due to its ultra-wide band gap of ~ 4.9 eV, high breakdown voltage of ~ 8 MV/cm, high saturation electron velocity, and excellent thermal and chemical stability,

1-3

etc. Moreover, compared to other

wide-band-gap semiconductors, such as GaN and SiC, β-Ga2O3 has the higher Baliga’s figure-of-merit (FOM) of ~3214.1 and Johnson’s FOM of ~2844.4 4-5, making it a promising candidate for the next-generation power electronic devices with higher power-switching capability and efficiency. For instance, β-Ga2O3 based Schottky rectifiers, metal oxide semiconductor field-effect transistor (MOSFETs), and finFETs have been fabricated successfully

6-10.

Moreover, the β-Ga2O3 based FETs showed excellent on/off ratios (up to 1010), and the low

drain leakage currents of about 3 μA 4, 6, 10. In addition, the ultra-wide band gap with small energy difference between the direct and indirect gaps 11-12, high ultra-violet (UV) transparency and large intrinsic light emission 13

enabled β-Ga2O3 to be potentially applicable in deep-UV detection and emission. The fabricated β-Ga2O3

based solar-blind photodetectors exhibited photoresponse and blindness to 254 and 365 nm light, respectively, with a high spectral selectivity 13-15. Recently, β-Ga2O3 has been cleaved into quasi-2D Ga2O3 by the mechanical exfoliation technique and plasma etching methods

16-18,

although it is not a van der Waals material. Moreover, its performance has been

extended and enhanced upon forming the quasi-2D Ga2O3. For example, when β-Ga2O3 was cleaved into quasi-2D Ga2O3, the breakdown voltage of FETs was improved from 113 V to 344 V, and such performance could be operated up to 250 ℃

19-20.

The solar blind photodetectors based on quasi-2D Ga2O3 exhibited the

extraordinarily high responsivity (~ 1.8×105 A/W), three orders of magnitude higher than those of bulk β-Ga2O3 (851 A/W), due to the large surface-to-volume ratios and quantum confinement effects 21-24. Note that, thicknesses of these previously fabricated quasi-2D Ga2O3 were in an order of 102 nm. Previous studies have 2


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demonstrated that the performances, such as the threshold voltages, mobilities, etc., of 2D materials based nanodevices were dependent on their thicknesses 25-26. Thus, when the thickness of quasi-2D Ga2O3 reduced to be atomically thin, its performance might be continuously further improved because of the enhanced surface-to-volume ratios and quantum confinement effects. Unfortunately, lack of quantum confinement in monolayer Ga2O3 without any passivations has been observed in previous reports

27-28.

Such unpassivated

monolayer Ga2O3 might be unstable due to the dangling bonds. It is interesting that, nevertheless, similar quasi-2D materials with passivations, such as H-passivated GaN and AlN, were stable and fabricated successfully in experiment, and showed strong quantum confinement 29-30. However, the fabrication and natural physics properties of 2D H-passiviated Ga2O3 with atomically thin thickness have not been focused yet. Here, by means of the first-principles calculations, the stability, mechanical, electronic, and optoelectronic properties of H-passivated monolayer and bilayer Ga2O3 with and without uniaxial strain were investigated in detail. It was found that the H-passivated 2D Ga2O3 was stable, and exhibited evident quantum confinement, in contrast to previous reports 27. The enhanced indirect band gaps of monolayer and bilayer Ga2O3 (6.42 and 5.54 eV, respectively) were transformed into direct band gaps by tension. The electron mobilities (up to 28140.38 cm2V-1s-1 for bilayer Ga2O3) with anisotropy were comparable to those of phosphorene. Moreover, the exciton binding energies were reduced, and adsorptions in the solar-blind spectrum ranged up to 105 cm-1. COMPUTATIONAL METHODOLOGY First-principles density functional theory (DFT) calculations were performed by the projector augmented as implemented in the Vienna Ab Initio Simulation Package (VASP)

32.

The

Generalized Gradient Approximaton (GGA) parameterized by Perdew-Burke-Ernzerhof (PBE)

33

was

wave (PAW) method

31,

employed to adopt for the exchange-correction functional. The cut-off energy was set to be 450 eV. The 3



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convergence criterions were 1×10-6 eV for the self-consistent field energy and 0.01 eV/Å for the residual forces on each atom, respectively. Γ-centered k-meshes of 5×19×11, 3×19×11, and 1×19×11 were used for bulk, monolayer, and bilayer Ga2O3, respectively. To minimize the interlayer interactions under the periodic boundary condition, vacuums of 15 Å were added perpendicular to the layer planes of monolayer and bilayer Ga2O3. For comparison, band structures were obtained by the GGA-PBE and Heyd-Scuseria-Ernzerhof (HSE06) screened hybrid functional

34.

Such methods have been widely used to predict the natural physical

properties of 2D wide band gap semiconductors and other 2D materials

35-38.

In addition, the phonon

dispersions were calculated by 3×3×1 supercells and linear response approach based on density functional perturbation theory (DFPT). And the convergence criterions for structures relaxation are 10-6 eV for energy and 10-3 eV/Å for force, respectively. RESULTS AND DISCUSSION For the bulk β-Ga2O3, its optimized lattice parameters are a=12.40 Å, b=3.09 Å, c=5.70 Å, and β=103.7˚, which are in good agreement with previously experimental and theoretical values

39.

As to 2D Ga2O3,

monolayer and bilayer Ga2O3 are cleaved from the (100) surface of bulk β-Ga2O3, and their surfaces are passivated by hydrogen, like that of 2D AlN and GaN 29-30, 40-41, as displayed in Figure 1(a-c). The optimized lattice parameters of monolayer Ga2O3 are b=3.185 Å and c=5.979 Å, which are slightly higher than those of bilayer Ga2O3 (b= 3.141 Å, c= 5.875 Å) because the bond lengths of Ga-O bonds for monolayer Ga2O3 are slightly larger than those of bilayer Ga2O3, as listed in Table S1. Meanwhile, these lattice parameters and bond lengths are also larger than the corresponding values of bulk β-Ga2O3. In addition, both the bond lengths of Ga-O for monolayer and bilayer Ga2O3 along the b direction are longer than those along the c direction, suggesting stronger covalent characters for Ga-O bonds along the c direction than those along the b direction. 4


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Such covalent bonds characters in the monolayer and bilyaer Ga2O3 are further evidenced by the electron localization function (ELF) in Figure 1(d, e), where the Ga-O bonds along the c direction shows larger ELF values. Kim et al.

20, 42

have obtained quasi-2D Ga2O3 flake from bulk β-Ga2O3 through mechanical exfoliation.

To explore the possibility of fabricating the monolayer Ga2O3 from its bulk crystal, we investigate the exfoliation process along different surfaces and predicted exfoliation energies with respect to separation, as demonstrated in Figure 2. Clearly, the exfoliation energy of monolayer Ga2O3 along (100) surface is lower than those along (010) and (001) surfaces since the lattice parameters and lengths of Ga-O bonds (see Table S1) in the [100] direction are larger than those in the other directions. It suggests that monolayer Ga2O3 is easier to obtained from the (100) surfaces of its bulk, consisting with the experimental results

20.

In addition, the

monolayer Ga2O3 prefers to cleave from the region I (as marked in Figure 2), because the exfoliation energy at the region I is lower than that at other regions, as displayed in Figure S2. The lowest exfoliation energy of monolayer Ga2O3 is about 2.01 J/m2 which is higher than that of graphene (0.32±0.03 J/m2), InP3 (1.32 J/m2), and GeP3 (1.14 J/m2),

38

but on the same order of magnitude, indicating that monolayer Ga2O3 might be

obtained experimentally from bulk β-Ga2O3 using exfoliation. The stabilities of monolayer and bilayer Ga2O3 are crucial for the practical application. To comprehensively evaluate the stability, the thermodynamic and lattice dynamic stability are assessed by the formation energies and phonon dispersion curves, respectively. Our calculated enthalpy of hydrogenation per H2 molecule is -4.04 eV for monolayer Ga2O3 and -4.13 eV for bilayer Ga2O3 relative to the unpassivated structures. It prefers to form H-passivated rather than unpassivated 2D Ga2O3. Similar phenomenon has been observed in 2D GaN

29-30.

Moreover, the enthalpy of H-passivated 2D Ga2O3 with respect to bulk Ga2O3 and 5



the H2 molecule is -161 meV for monolayer Ga2O3 and -489 meV for bilayer Ga2O3. H-passivated monolayer and bilayer Ga2O3 are therefore thermodynamically stable structures. It suggests that monolayer and especially bilayer Ga2O3 are thermodynamically stable. Figure 3 demonstrates the phonon dispersion curves of monolayer and bilayer Ga2O3. No imaginary phonon mode is observed, indicating that monolayer and bilayer Ga2O3 are dynamically stable. Figure 4 demonstrates the electronic structures of monolayer and bilayer Ga2O3 obtained by the GGA method, which is known to give correct electronic structures except for underestimating the band gap. It can be seen that monolayer Ga2O3 is an indirect band gap semiconductor, as the conduction band minimum (CBM) is at the Γ point, while the valence band maximum (VBM) is at the S point, which is slightly higher in energy than the Γ point. Similar characteristics are also obtained in bilayer Ga2O3, as displayed in Figure 4b. The calculated indirect band gaps of monolayer and bilayer Ga2O3 from the GGA method are 3.27 eV and 2.22 eV, respectively, which are larger than that of the bulk β-Ga2O3 of about 1.963 eV (See Figure S3). In other words, quasi-2D Ga2O3 is suitable for the application of high power nanodevices. To obtain more accurate band gap of 2D Ga2O3, the band gaps of monolayer and bilayer Ga2O3 are further calculated by HSE06 method and displayed in Figure 4. The accurate indirect band gaps of monolayer and bilayer Ga2O3 are about 6.42 eV and 5.54 eV, respectively, larger than the experimental and theoretical values (about 4.78 eV) obtained by HSE06 method (See Figure S3) of bulk β-Ga2O3

43-44.

These larger band gaps mean that 2D Ga2O3, especially

monolayer Ga2O3, based nanodevices could show larger ON/OFF ratio and threshold voltage than those of bulk β-Ga2O3 based nanodevices 45. To further investigate the electronic structures of 2D Ga2O3, density of states (DOS) and projected charge density of band edges for monolayer and bilayer Ga2O3 are exhibited in Figure 5. The CBM of monolayer 6


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Ga2O3 is mainly contributed by the O s+py+pz orbitals and the Ga s orbitals, while the VBM is dominated by the O px+py+pz orbitals coupling with some Ga s+pz orbitals and s orbitals of H passivation atoms. In other words, the VBM of monolayer Ga2O3 is evidently affected by the passivation atoms. It suggests that by substituting H passivation atoms by other elements, such as fluorine, the VBM of monolayer Ga2O3 might be changed and resulting in a direct band gap for monolayer Ga2O3 (Figure S4). Such method has been used in 2D GaN 36, 46. In addition, from Figure 5d, it is obvious that the charge density of the lowest conduction band near the Γ point coincides with that of the py+pz orbitals of O element and the s orbital of Ga element, and the highest valence band near the S point exhibits strong py and pz characters. These projected charge densities provide consistent and complementary information with the analysis of the orbitals shown in Figure 5(a-c). Compared to monolayer Ga2O3, similar characters of DOS and projected charge densities are observed for the bilayer Ga2O3, as demonstrated in Figure S5. Note that these orbitals distributions are different to those of unpassivated 2D Ga2O3

27-28

and bulk Ga2O3, whose CBM is dominated by O s and Ga s orbitals with

negligible contribution from the O p orbitals, as exhibited in Figure S3. These difference electronic characters indicate strong quantum confinement effects in H-passivated 2D Ga2O3, in contrast to that of unpassivated 2D Ga2O3. As we know, strain engineering is an effective approach to tune the electronic structures. The calculated electronic band gaps of monolayer and bilayer Ga2O3 under various uniaxial strains are depicted in Figure 4(c-d). Interestingly, the band gaps of both monolayer and bilayer Ga2O3 increase at first and then gradually reduce from the uniaxial compression to uniaxial tension. Moreover, the VBMs of monolayer and bilayer Ga2O3 move from the S-point to the Γ-point when the uniaxial tension is larger than 4% (See Figure S6), resulting in an indirect-to-direct band gap transition. When the uniaxial compressive strain is up to 10%, the 7



lowest band gaps of about 2.80 eV for monolayer Ga2O3 and about 1.89 eV for bilayer Ga2O3 are still enough for the application of nanoelectronics. The electron effective masses of monolayer Ga2O3 dependent of the uniaxial compressive and tensile strains were also studied (Figure S7). The results indicate that the transport properties of monolayer Ga2O3 might not be deteriorated by the uniaxial strain along both b and c direction, and the excellent transport properties can be kept. These results indicate that the electronic properties of 2D Ga2O3 can be effectively tuned by applying external strain, which could lead to wide applications in flexible electronics. To better understand the electronic properties of 2D Ga2O3 and its potential for electronic applications, the transport properties of monolayer and bilayer Ga2O3 are calculated by the deformation potential theory which has been used to effectively predict the transport properties of many semiconductors, including MoS2, phosphorene, GaN, etc.

36, 47-48.

The details of the transport properties of monolayer and bilayer Ga2O3 are

provided in the supporting information (Figure S8 and S9). Table 1 lists the deformation potential constant, elastic constant, effective mass, carrier mobility, and relaxation time of monolayer and bilayer Ga2O3. It can be found that most electronic quantities of monolayer and bilayer Ga2O3 are anisotropic along the b and c directions. Moreover, the deformation potential constants EDP of CBM along the b direction are lower than those along the c direction. Because the CBMs of monolayer and bilayer Ga2O3 originate from the O-pz, Ga-pz and O-py orbitals, they are sensitive to the in-plane strain. Moreover, the weight contribution of pz orbitals (along the c direction) on CBM is obviously higher than that of py orbitals (along the b direction), as shown in Figure 5 and Figure S5. In addition, the elastic constants C2D along the b direction are lower than those along the c direction, and the elastic constants C2D of monolayer Ga2O3 are lower than those of bilayer Ga2O3. That is because the lattice parameters along b direction are shorter than that along c direction. The largest elastic 8


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constants of monolayer and bilayer Ga2O3 are about 140.47 and 168.71 N/m, respectively, which are higher than that of 2D GaN and bulk β-Ga2O3 36, 49. For the effective mass, the calculated effective masses of electrons are one order of magnitude smaller than those of holes, due to the flat valence band and more dispersive conduction band of monolayer and bilayer Ga2O3, as displayed in Figure 4 and S4. Moreover, the electron effective masses along b and c directions are 0.58 m0 and 0.77 m0 for monolayer Ga2O3, and 0.27 m0 and 0.26 m0 for bilayer Ga2O3, respectively, which are larger than those of bulk β-Ga2O3, but smaller than those of monolayer GaN 12, 36, 50. It predicts that 2D Ga2O3, especially bilayer Ga2O3, may shows higher electron mobility than monolayer GaN, but lower than bulk Ga2O3. The detailed room temperature electron and hole mobilities of monolayer and bilayer Ga2O3 are listed in Table 1. Indeed, the electron mobility is severalfold larger than the hole mobility due to the lower electron effective mass. However, it is surprising that the room-temperature electron mobilites of monolayer and bilayer Ga2O3 are far higher than those of bulk bulk β-Ga2O3 and monolayer GaN 36. Moreover, the largest room-temperature electron mobilities of monolayer and bilayer Ga2O3 are up to 2684.93 and 24485.47 cm2V-1s-1, respectively, which are significantly higher than that of monolayer MoS2 (~400 cm2V-1s-1) phosphorene (~104 cm2V-1s-1)

47.

48,

and comparable to that of

Such high room-temperature electron mobility suggests that monolayer and

bilayer Ga2O3 are great potentials for nanoelectronics. In addition, bilayer Ga2O3 possesses higher electron mobilities compared to its monolayer counterpart, which is expected already form the band structure and phonon dispersion relation. Meanwhile, these electron mobilities along the c direction are one order of magnitude higher than those along the b direction. Compared to the carrier mobilities, similar characters are also observed for the relaxation time of monolayer and bilayer Ga2O3. Moreover, the electron relation times of monolayer and bilayer Ga2O3 are larger than those of bulk β-Ga2O3, and monolayer GaN, as listed in Table 1. 9



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Note that, the electron relaxation time of bilayer Ga2O3 reaches up to one order of ps, and it is close to that of black phosphorus (1.29 ps)

51,

and far larger than that of MoS2 (16.58 fs)

48.

This large relaxation time

suppresses the carrier recombination and enables bilayer Ga2O3 suitable for the optoelectronic nanodevices. Since the effective electron masses are significant different to the effective hole masses (as listed in table 1), the exciton binding energies of monolayer and bilayer Ga2O3 are small according to the Bethe-Saleter equation52. These small exciton binding energies indicate the fast photo-induced carrier dissociation, which is important for the application of optoelectronic. The detailed exciton binding energies (Eb) of 2D Ga2O3 are obtained by the simplified Bethe-Salpeter equation Eb=μ*Ry/m0Ɛr2, where μ* is the reduced exciton mass (μ*=me*×mh*/(me*+mh*)), Ry is the atomic Rydberg energy, and Ɛr is the relative dielectric constant53. The calculated exciton binding energies of monolayer and bilayer Ga2O3 are high to 1.82 eV and 0.93 eV, respectively, which are larger than those of β-Ga2O3 and 2D GaN

30, 50.

To further investigate the optical

properties, the optical absorptions of monolayer and bilayer Ga2O3 are calculated through α(ω) = 2𝜔

[

𝜀21(𝜔) + 𝜀22(𝜔) ― 𝜀1(𝜔)]

1/2

, where the imaginary part of the dielectric function ε2(ω) is calculated by

summation over empty states, the real part ε1(ω) is obtained according to the usual Kramers-Kronig transformation54. It can be clearly seen from Figure 6 that the absorption coefficients of monolayer and bilayer Ga2O3 reach to the order of 105 cm-1, which is comparable to those of lead-free inorganic perovskites 52-53, and higher than that of bulk β-Ga2O3. Moreover, bilayer Ga2O3 exhibits a higher absorption coefficient in the solar-blind spectrum than that of monolayer Ga2O3. In addition, out-plane absorption is always larger, suggesting that flakes are better to be aligned parallel to the surface of optoelectronic nanodevices for most efficient application. CONCLUSION 10


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In summary, we have theoretically predicted that the 2D Ga2O3 is possibly fabricated from bulk β-Ga2O3 by exfoliation. In contrast to previously reported unpassivated 2D Ga2O3, the H-passivated 2D Ga2O3 shows thermodynamic and dynamic stability and has obviously quantum confinement effects. Monolayer and bilayer H-passivated Ga2O3 show indirect band gaps (6.42 and 5.54 eV, respectively) which are larger than that of bulk β-Ga2O3. Moreover, evident variation of band gaps and an indirect-to-direct transition are induced by strain engineering. In addition, we found that 2D Ga2O3, especially bilayer Ga2O3, exhibits significant electron transport properties with anisotropy. This value is several orders of magnitudes higher than those of β-Ga2O3. The effective electron mass, electron mobility, and relaxation time of bilayer Ga2O3 are reached to 0.26 m0, 24485.47 cm2/Vs, 3.77 ps, respectively. In addition, the optical absorbance in the solar-blind spectrum reaches up to 105 cm-1, and the exciton binding energies are enhanced to 1.82 eV and 0.93 eV for monolayer and bilayer Ga2O3, respectively. These favorable features extend the applications of Ga2O3 in the electronic and optoelectronic devices with higher performances. ASSOCIATED CONTENT Supporting Information Additional Tables and Figures: Geometric structures of bulk, monolayer and bilayer Ga2O3, Exfoliation energies along different directions and positions, Electronic structures of bulk and bilayer Ga2O3 with different strain, details of carrier transport. AUTHOR INFORMATION Corresponding Author *E-mail:

[email protected]

Notes 11



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The authors declare no competing financial interest. ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundation of China (61604119, 61704131, and 61804111), Natural Science Foundation of Shaanxi Province (2017JQ6002, and 2017JQ6031), Initiative Postdocs Supporting Program (Grant BX20180234); Fund of the State Key Laboratory of Solidification Processing in NWPU (Grant SKLSP201857). The numerical calculations in this paper have been done on the HPC system of Xidian University. References (1) Higashiwaki, M.; Sasaki, K.; Murakami, H.; Kumagai, Y.; Koukitu, A.; Kuramata, A.; Masui, T.; Yamakoshi, S., Recent progress in Ga2O3 power devices. Semicond. Sci. Tech. 2016, 31, 034001. (2) Mastro, M. A.; Kuramata, A.; Calkins, J.; Kim, J.; Fen, F.; Pearton, S. J., Opportunities and future directions for Ga2O3. ECS J. Solid. State Sc. 2017, 6, 356-359. (3) Orita, M.; Ohta, H.; Hirano, M.; Hosono, H., Deep-ultraviolet transparent conductive β-Ga2O3 thin films. Appl. Phys. Lett. 2000, 77, 4166-4168. (4) Higashiwaki, M.; Sasaki, K.; Kuramata, A.; Masui, T.; Yamakoshi, S., Gallium oxide (Ga2O3) metal-semiconductor field-effect transistors on single-crystal β-Ga2O3 (010) substrates. Appl. Phys. Lett. 2012, 100, 013504. (5) Sasaki, K.; Higashiwaki, M.; Kuramata, A.; Masui, T.; Yamakoshi, S., MBE grown Ga2O3 and its power device applications. J. Cryst. Growth 2013, 378, 591-595. (6) Zhou,

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(54) Liu, H.; Liu, Z.-T.; Ren, J.; Liu, Q.-J., Structural, electronic, mechanical, dielectric and optical properties of TiSiO4: first-principles study. Solid State Commun. 2017, 251, 43-49.

Figures and Tables

(a)

(d)

(b)

b

(e)

c a

(c)

b c

b

b a

0 18


0.5

1.0

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Figure 1. Crystal structures of (a-b) monolayer and (c) bilayer Ga2O3. (d-e) Electron localization functions of corresponding monolayer and bilayer Ga2O3, respectively.

Figure 2. Calculated exfoliation energy as functions of separation distance d-d0. The light black dash lines represent three possible stripping positions along (100) surface.

(a)

(b)

Figure 3. Phonon dispersion of (a) monolayer and (b) bilayer Ga2O3, respectively.

19



(a)

Page 20 of 24

(b)

(d)

(c)

Figure 4. Band structures of (a) monolayer and (b) bilayer 2D Ga2O3. Band gaps of (c) monolayer and (d) bilayer Ga2O3 as functions of the uniaxial strain along the b and c directions, respectively.

20


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(a)

(b)

(d)

(c)

CBM

VBM

Figure 5. (a-c) Density of states of monolayer Ga2O3. (d) Projected charge densities of CBM and VBM of monolayer Ga2O3.

21



(a)

(b)

Figure 6. Calculated absorption spectra for monolayer and bilayer Ga2O3 along the (a) a and (b) c directions, respectively.

22


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Table 1. calculated deformation-potential constant EDP (in units of eV), elastic modulus C2D (in units of N/m), effective mass m* (in units of m0), carrier mobility μ (in units of cm2V-1s-1), relaxation time τ (in units of ps) along the b and c directions for monolayer and bilayer Ga2O3 at 300 K. For comparison, the corresponding values of bulk β-Ga2O3 and monolayer GaN are added in table 1.

Electron

Hole

Direction EDP

C2D

me*

μ

τ

EDP

C2D

mh*

μ

τ

Monolayer

b

1.48

140.47

0.58

2684.93

0.89

4.91

140.47

3.11

8.58

0.02

Ga2O3

c

4.25

117.69

0.77

156.25

0.07

18.78

117.69

25.11

0.01

0.001

Bilayer

b

1.16

168.71

0.27

24485.47

3.77

3.19

168.71

4.63

11.02

0.03

Ga2O3

c

3.24

125.94

0.26

2526.61

0.37

17.37

125.94

5.30

0.34

0.01

0.23~

110~

0.01~

-

-

-

3.01~

0.004~

9.09

0.007

Bulk β-Ga2O3

-

6.9

~45

110~ ~45

0.28

150

0.03

0.44~

198.27~

0.05~

150

13, 39, 49-50

Monolayer GaN 36

-

68.57~75.41

0.45

225.92

0.06

23


68.57~75.41

1.38~2.33


TOC Graphic:

24


Page 24 of 24

Unusual Electronic and Optical Properties of Two-Dimensional Ga2O3

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