Intriguing electronic and optical properties of M2CX2 (M = Mo, W; X = O, F) MXenes and their van der Waals heterostructures

Accepted Manuscript Research paper Intriguing Electronic and Optical Properties of M2CX2 (M=Mo, W; X=O, F) MXenes and their van der Waals heterostructures S.A. Khan, Gul Rehman, Iftikhar Ahmad, M. Maqbool, Cesare Franchini, B. Amin PII: DOI: Article Number: Reference:

S0009-2614(19)30586-X https://doi.org/10.1016/j.cplett.2019.136614 136614 CPLETT 136614

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Chemical Physics Letters

Received Date: Revised Date: Accepted Date:

14 April 2019 25 June 2019 16 July 2019

Please cite this article as: S.A. Khan, G. Rehman, I. Ahmad, M. Maqbool, C. Franchini, B. Amin, Intriguing Electronic and Optical Properties of M2CX2 (M=Mo, W; X=O, F) MXenes and their van der Waals heterostructures, Chemical Physics Letters (2019), doi: https://doi.org/10.1016/j.cplett.2019.136614

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Intriguing Electronic and Optical Properties of M2 CX2 (M=Mo, W; X=O, F) MXenes and their van der Waals heterostructures S. A. Khan1,5 , Gul Rehman2 , Iftikhar Ahmad2,3 , M. Maqbool4 , Cesare Franchini5 , B. Amin1,3∗ 1 2

Department of Physics, Hazara University, Mansehra 21300, Pakistan

Department of Physics, University of Malakand, Chakdara 18800, Pakistan 3

Department of Physics, Abbottabad University of

Science and Technology, Abbottabad 22010 Pakistan 4

Department of Clinical & Diagnostic Sciences,

The University of Alabama at Birmingham, Birmingham, AL 35294, USA. 5

University of Vienna, Faculty of Physics and Center for

Computational Materials Science, Vienna A-1090, Austria

Abstract M2 CX2 (M=Mo,W; X=O,F) MXenes and their van der Waals heterostructures are investigated by first-principle calculations.

Phonon spectrum has shown that Mo2 CO2 /W2 CO2

and Mo2 CF2 /W2 CO2 heterostructures and corresponding monolayers are dynamically stable. W2 CO2 exhibits the properties of topological insulator and Mo2 CO2 is narrow band gap semiconductor, while Mo(W)2 CF2 are metals. Mo2 CO2 /W2 CO2 heterostructure indicates a possible topological feature similar to corresponding monolayers and reveals type-II band alignment. Mo2 CF2 /W2 CO2 heterostructure generating n-type Schottky contact with 0.139eV barrier height. Large absorption in the visible region is observed for Mo2 CO2 and blue shift is noticed for W2 CO2 and W2 CO2 /Mo2 CO2 heterostructure, especially the part contributed by Mo2 CO2 .

1

I.

INTRODUCTION

Two-dimensional (2D) materials have become a major research interest in materials science, because of their unique properties [1] compared to the bulk counterparts and for their important applications in energy storage [2], sensing [3], catalysis [4], and electronic devices [5]. A novel large family of 2D materials consisting of transition metal nitrides, carbides, and carbonitrides are also known as MXenes prepared from the MAX phase by etching the A layers [6, 7], where M represents an early transition metal, A corresponds to an element of group IIIA or IVA and X=N or C. During etching process the A atom is replaced by O or F, turning MAX (Mn+1 AXn ) into MXenes (Mn+1 Xn ), with a surface that can be easily functionalized, which has been confirmed by XPS experiment [8]. Appropriate functionalization produce a drastic change in electronic structure of MXenes [9]. Considerable attention towards MXenes are due to their outstanding properties, for example conductivity of the multilayered MXenes can competed with multilayered graphene [10]. In addition these materials also have potential in electrodes for supercapacitors [11], Li-S batteries [12], Li-, Na- and K-ion batteries, [13, 14], catalysis [15, 16], sensors [17], ultra-low work function materials [18], and Schottky barrier junctions [19]. MXene alloys systems of semiconducting Ti2 CO2 , Zr2 CO2 , and Hf2 CO2 can be used to effectively tune photocatalytic performance. Some of the MXenes have also been predicated to be topological insulators (TIs) [20]. Based on first-principles calculations, M2 CO2 (M=W, Mo, and Cr) have been proposed as 2D TIs, where W2 CO2 has robust band inversion with a band gap of 0.194 (0.472) eV within GGA (HSE06) functional [21]. Doping or creating defects [22], making alloys [23], strain engineering [24–26], stacking layers [27, 28], and the formation of superlattices [29] can tuned the electronic structure of these materials. In these approaches, layers stacking to make van der Waals (vdW) heterostructures has recently appear as a new route, and give rise to intriguing phenomena. Especially, Type-II band alignment in stacked semiconducting vdW heterostructures reduces overlaping of electron-hole wave functions and demonstrated to be an effective root for light detection and harvesting [30]. Moreover, Schottky contacts in metal semiconducting heterostructures also play a key role in the performance of various electronic and photonic devices [31]. However, despite of proposed 2D topological insulating behaviour in M2 CO2 (M=W, Mo, 2

and Cr) in Ref. [21] using first principles calculations, the expected properties from these systems are still under debate. Therefore, in the present work, a comprehensive insight is gained into the phonon spectrum, electronic structure and optical properties of the semiconductorsemiconductor (Mo2 CO2 /W2 CO2 ) and metal-semiconductor (Mo2 CF2 /W2 CO2 ) vdW heterostructures and their corresponding monolayers (M2 CO2 (M=W, Mo)) are investigated. This is pave in providing fundamental insights for technologies in band gap engineering and for the preparation of potential Schottky contacts.

II.

COMPUTATIONAL DETAILS

Density functional theory (DFT) in the Vienna Ab-initio Simulation Package (VASP) [32] and Perdew-Burke-Ernzerhof (PBE) functional [33] is used. The effect of the spin-orbit coupling (SOC) and vdW interaction by empirical dispersion correction DFT-D2 of Grimme [34] are taken into account in all calculations. The vdW heterostructures and monolayers A) by using PBE are relaxed until the energy(forces) have converged to 10−4 eV(10−3 eV/˚ functional. This procedure has already shown to yields agreement with experiments [27]. A 500 eV plane wave cutoff and 6 × 6 × 1 k-meshes (Γ-centered) are used for the structural relaxation, which are further refined to 12 × 12 × 1 for the electronic structure calculations of monolayers and heterostructures. Artefacts of the boundary conditions are interrupted by a vacuum layer of 20 ˚ A in the out-of-plane direction. It has already been shown that the underestimated PBE band gap values may be corrected by the Heyd-Scuseria-Ernzerhof (HSE06) [35] functional. Therefore, HSE06 funtional is further used for electronic structure calculations. Harmonic interatomic force constants are used in the phonopy code interfaced with the VASP for phonon spectrum calculations. These calculations are performed for 3 × 3 × 1 a supercell of monolayers and heterostructures [36]. The optical spectrum are investigated by solving the Bethe-Salpeter Equation (BSE) in GW0 approach, where the quasiparticle energies are computed by using the eigenvalues and wave functions of the HSE06 functional [37, 38]. Excitonic eigenstates are calculated by taking 6×6×1 k-mesh, with NBAND set as 300, which takes into account the 10 highest(lowest) valence(conduction) bands. 3

III.

RESULT AND DISCUSSION

Bare MXenes, M2 C (M=Mo, W) having trigonal lattice are functionalized by O/F in four different positions, see Fig. 1; i) on top of the sub-surface transition metal atom, ii) directly on top of transition metal atom, iii) on top of the C atom, and iv) is hybrid of i) and iii). For all position of the O/F atom, the crystal structure of M2 C (M=Mo, W) MXenes were fully relaxed and the ground state energy presented in TABLE I, show that type (iii) is the most favourable phase in agreement with Ref. [21]. The stability of a specific model is controlled by several factors, like the oxidation state, number of electrons required for the formations of the functional group or the strength of the hybridization [39]. In type (iii) configuration the transition metal atom sits inside of a trigonal prism formed by the C and O/F similarly to Mo/W atoms in 1H-structured MoS2 and WS2 . The dynamical stability of these structure are further confirmed by the calculation of the phonon spectrum, see Fig. 2 (a-c). There are no imaginary frequencies, hence all these systems exhibit no structural instability. Lattice mismatch plays an important role in constructing heterostructure [40]. Similar lattice parameters allow the creation of coherent interfaces, but induced strain across the interface due to the lattice mismatch can alter the electronic properties of the heterostructures. We used in-plane lattice constants obtained by optimization of the M2 CX2 (M=Mo, W; X=O, F) (see TABLE I) to generate Mo2 CO2 /W2 CO2 (lattice mismatch < 1%) and Mo2 CF2 /W2 CO2 (lattice mismatch ≈ 5%) heterostructures. Both heterostructures show experimentally achievable lattice mismatch [41]. Since the electronic structure is mainly effected by layer stacking [42] therefore, we study various choices, differences in the position of transition metal (Mo and W) and carbon atoms: see Fig. 3. In all patterns, layer of carbon atoms lies between oxygen atoms of individual monolayer of heterostructures. In pattern A-C, all C and O layers are exactly on the top of each other, while for patterns D-F they are slightly shifted outward from each other. Further, the patterns are classified in terms on/wrt the position of Mo and W atoms, as there are two inequivalent transition metal atoms in each MXene monolayer, the bottom and top ones are labelled as 1 and 2, respectively. For pattern A: Mo1 is above W1 and Mo2 is above W2 , in B: Mo1 is directly above W2 and Mo2 is above W1 , while C: is analogous to pattern B but their positions in the top and bottom layer xy-plane are switched. Pattern D-F are similar to A-C and F 4

is analogous to D with switched xy-plane. Thermodynamic stability of heterostructure for different configurations are confirmed with binding energies (Eb ) calculations given by: Eb = EH − EMo2 CX2 − EW2 CO2

(1)

where EH , EMo2 CX2 and EW2 CO2 represent the total energy of Mo2 CX2 /W2 CO2 (X=O, F) heterostructure, Mo2 CX2 and W2 CO2 monolayers, respectively. The calculated negative binding energy and interlayer distance for all patterns, presented in Table II, recommend the fabrication of these heterostructures. It is found that stacking E is the most favourable for both Mo2 CO2 /W2 CO2 and Mo2 CF2 /W2 CO2 heterostructures due to greater binding energy and small interlayer distances. We have also investigated the phonon dispersion to further confirm the stability of stacking E, see Fig. 2(d). It is also clear from figure that obviously, there is no imaginary frequency hence, stacking E exhibit no structural instability. Therefore, stacking E was selected for further study of electronic and optical properties of heterostructures. In order to know wither the vdW forces is strengthened or weakened in the Mo2 CO2 /W2 CO2 heterostructure, we have calculated the binding energy of the Mo2 CO2 -Mo2 CO2 and W2 CO2 -W2 CO2 bilayers. The order of energy and interlayer separation found to be W2 CO2 W2 CO2 < Mo2 CO2 -W2 CO2 < Mo2 CO2 -Mo2 CO2 . These results show that the vdW forces in the Mo2 CO2 /W2 CO2 heterostructure is strengthened (weakened) than Mo2 CO2 -Mo2 CO2 (W2 CO2 -W2 CO2 ) bilayer. We now turn on the analysis of electronic properties. The electronic band structures of M2 CX2 (M=Mo, W; X=O, F) are presented in Fig. 4 (a, b, d, e) and the band gap values are given in TABLE I. Using PBE functional without including the effect of SOC, in W2 CO2 band structure a degenerate band touch point is found on the Fermi level, indicate semimetallic nature. Similar to W2 CO2 , Mo2 CO2 also found to be semimetal having certain compensated electron-hole Fermi pockets at Γ and M-points, while a well defined band gap settle at other points of the Brillouin zone. Further, including the effect of SOC in PBE functional shifts these degenerate states and establish a well define indirect band gap of 0.23 eV in W2 CO2 , see inset of Fig. 4(b). According to the analysis proposed in Ref. [21] the opening of the gap due to SOC led to the onset of a topological insulating state, where the band-inversion occur between the bonding-antibonding states of Mo(W)-d orbitals. A Dirac-cone like dispersion was found in 5

conducting edges of bandstructure for W2 CO2 near the Γ-point. It is well known, in DFT, PBE funtional underestimate the band gap while HSE06 functional lead to better agreement with experiments [43]. Therefore, we have used HSE06 functional including the effect of SOC to investigate the band structure. Mo2 CO2 (W2 CO2 ) is found to be an indirect (direct) band gap semiconductor with 0.59 eV (0.64 eV) band gap value. In contrast, Mo2 CF2 and W2 CF2 show metallic behaviour for both PBE and HSE06 functionals with and without including the effect of SOC, see Fig. 4 (d, e), due to effective electron doping associated with the substitution of O with F. The PBE band structure without including the effect of SOC shows that Mo2 CO2 /W2 CO2 heterostructure is a semimetal, with a band topology similar to the one of the corresponding monolayers. Also in the case SOC lifts the band degeneracy at Γ, suggesting that Mo2 CO2 /W2 CO2 heterostructure should exhibit topological features similar to those observed in the isolated monolayers. Mo2 CO2 /W2 CO2 is found to be a semiconductor of 0.3 eV band gap by using HSE+SOC calculations see Fig. 4 (c). In case of Mo2 CF2 /W2 CO2 heterostructures, an n-type Schottky contact is formed, see Fig. 4(f), which will be discussed later on. Projected partial density of states clearly show that Mo(W)-4d(5d) orbitals are dominant around the Fermi level and hybridize with p orbitals of C and O, see Fig. 5(a and b). An interesting feature arises from the PDOS of the Mo2 CO2 /W2 CO2 heterostructure in Fig. 5(c), is that W-d states of the W2 CO2 monolayer mainly contribute to the VBM, while CBM is mostly populated by Mo-d state of the Mo2 CO2 layer, establish type-II band alignment in Mo2 CO2 /W2 CO2 heterostructure. To further understand type-II band alignment, weighted band structures are calculated and presented in Fig. 5 (d-f) show that the VBM at Γ-point is due to the W-dxy orbital with a small contribution of W-dxz and -dyz states, whereas Mo-dxy , -dxz , and -dyz are mainly contributing to the CBM. The confinement of CBM(in Mo2 CO2 layer) and VBM(in W2 CO2 layer) in different layer of Mo2 CO2 /W2 CO2 heterostructure (type-II band alignment) favours the separation of electron-hole pairs obtained without any external effects. As band bending between the two different layers induces intrinsic electric field may generate type-II band alignment [44–46], which enhances(reduces) electron-hole separation(recombination) time, applicable for light detection and harvesting [47]. Furthermore, the analysis of work function of isolated Mo2 CO2 and W2 CO2 monolayer (see Table 1) and their charge density difference, see Fig. 6 (b), where the holes are 6

gathered in the W2 CO2 layer while electrons are congregated near the Mo2 CO2 region of the heterostructure. We confirm that the type-II band alignment in Mo2 CO2 /W2 CO2 heterostructure. Formation of the vdW heterostructures not only modulate the band structure, but also tailor the effective masses. Therefore, effective mass of carriers for vdW heterostructur and corresponding monolayers are calculated by using the ¯ −2 (∂ 2 E(k)/∂k 2 ) and band fitting to parabola deformation potential theory m∗ = h [48], see TABLE III. Effective masses of the heterostructure are different than corresponding monolayers due to the variation of the band gap.

A smaller

effective mass leads to higher carrier mobility, which is strongly desired for high performance device applications. Type-II band alignment coveted in the designing of optoelectronic devices. Therefore we have further explored the absorption spectra in term of the ε2 (ω) of Mo2 CO2 /W2 CO2 (semiconductor/semiconductor) heterostructures and corresponding monolayers, see Fig.6 (a). It is clear from the figure that the range of the optical absorption for Mo2 CO2 and W2 CO2 monolayers about 1 to 4.5 eV, while for W2 CO2 /Mo2 CO2 heterostructure from 1.2 to 5 eV. Large absorption in visible region is observed in the Mo2 CO2 due to smaller band gap than W2 CO2 , where blue shift is observed in the later. A further blue shift is observed in the Mo2 CO2 /W2 CO2 vdW heterostructure, especially the part contributed by Mo2 CO2 . The absorption peaks of the heterostructure almost similar to Mo2 CO2 monolayer at 2 to 5 eV with little blue shift and promotion of the oscillator strength of peak at 1.2 to 1.6 eV. Increasing carrier density of heterostructure than parent monolayers are basically broaden the optical absorption [49]. Obviously, stacking of materials in terms of vdW heterostructure is an effective way to understand the manageable modulation of absorption performance of the 2D materials. Electronic structure and absorption spectra of heterostructures are modified with respect to parent monolayers due to the efficient interlayer charge transfer. Therefore, to understand the charge rearrangement in heterostructures, Bader population analysis and charge density difference are investigated. The charge density difference are calculated as; Δρ = ρH − ρM o2 CO2 − ρW2 CO2 , where ρH , ρM o2 CO2 and ρW2 CO2 are charge density of heterostructures (Mo2 C(O/F)2 /W2 CO2 ), charge density of Mo2 CO2 and W2 CO2 monolayers, respectively. These investigations indicate the interlayer charge transfer and also redistribution within 7

the layers, see Fig 6 (b). All transition metal atoms in Mo2 CO2 /W2 CO2 gain charges, while the C and O atoms losses except O3 which gain charge of -0.0041|e|. In heterostructure, W2 CO2 layer loss charge of 0.0113|e|. This charge is gain by Mo2 CO2 layer with a very small leakage of charge to vacuum, confirmed by Fig. 6(b). In case of metal-semiconductor heterostructure (Mo2 CF2 /W2 CO2 ), the charge are mainly transfer from Mo2 CF2 to W2 CO2 making W2 CO2 n-type doped. A very small amount of charge is also distributed within the layer. In metal/semiconductor contact, the Schottky barrier height controls the transport performance of devices, which is relative alignment of metals Fermi level and semiconductors CBM (n-type barrier, ΦB,n ) or VBM (p-type barrier, ΦB,p ). According to Schottky-Mott model [50, 51], the n- and p-type of barrier heights are defined as, ΦB,n = EC − EF and ΦB,p = EV − EF , where EC , EV , and EF are CBM, VBM and Fermi level, respectively. The calculated n-type of Schottky barrier height for Mo2 CF2 /W2 CO2 is 0.139 eV from its bandstructure. As discussed before, the charge transfer at Mo2 CO2 /W2 CO2 interface is small, being semiconductor/semiconductor contact.

However, in case of metal/semiconductor

(Mo2 CF2 /W2 CO2 ), the situation is more difficult. It can be seen clearly from Fig. 6(d), a cutoff of 0.3902 eV between the vacuum levels on Mo2 CF2 and W2 CO2 sides of plane-average electrostatic potential. For comparison plane-average electrostatic potential of monolayer are also shown, in Fig. 6(c). The charge rearrangement during interface formation induces this interface dipole (μIS = 0.3902 eV), which modifies the n-type barrier from the SchottkyMoot condition to ΦB,n = ΦM + μIS − χS [52], where ΦM (6.453 eV) and χS (6.7039 eV) are work function of metal and electron affinity of semiconductor. The barrier height according to Schottky-Mott condition is 0.14 eV, which is consistent to the band structure results. The small difference in value may result from other factor than interface dipole such as hybridization between different orbitals [52].

IV.

CONCLUSION

Using first principle calculations, the electronic structure and optical properties of out-of-plane semiconductor-semiconductor (Mo2 CO2 /W2 CO2 ) and metal-semiconductor (Mo2 CF2 /W2 CO2 ) heterostructures and their corresponding monolayers are investigated. Stability of the systems under study are confirmed by the phonon dispersion spectra. 8

W2 CO2 monolayers exhibiting the properties of two dimensional topological insulator. Mo2 CO2 monolayer show semiconducting behaviour, while Mo2 CF2 and W2 CF2 are metals. Mo2 CO2 /W2 CO2 van der Waals heterostructure has type-II band alignment and with band topology similar to corresponding monolayers. Schottky contact (n-type) with barrier height of 0.139 eV is generated in Mo2 CF2 /W2 CO2 heterostructure. The discontinuity of 0.39 eV between the vacuum levels on the either sides of Mo2 CF2 /W2 CO2 heterostructure suggesting the barrier is due to interface dipole as a result of charge rearrangement. In the visible range, large absorption is observed in the Mo2 CO2 than W2 CO2 , where blue shift is noticed in the absorption spectra of W2 CO2 . A further blue shift is observed in the W2 CO2 /Mo2 CO2 , especially the part contributed by Mo2 CO2 .

ACKNOWLEDGEMENT

The authors acknowledge financial support from Higher Education Commission of Pakistan (HEC), Project No. 5727/KPK/NRPU/R&D/HEC2016 and 20-3959/NRPU/R&D/HEC2014/234 and IRSIP program.

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[28] B. Amin, T.P. Kaloni, G. Schreckenbach and M.S. Freund, Materials properties of out-of-plane heterostructures of MoS2 -WSe2 and WS2 -MoSe2 , Appl. Phys. Lett. 108 (2016) 063105-5. [29] N. Lu, H. Guo, L. Wang, X. Wu and X.C. Zeng, Van der Waals trilayers and superlattices: modification of electronic structures of MoS2 by intercalation, Nanoscale 6 (2014) 4566-4571. [30] X.L. Wei, H. Zhang, G.C. Guo, X.B. Li, W.M. Lau and L.M. Liu, Modulating the atomic and electronic structures through alloying and heterostructure of single-layer MoS2 , J. Mater. Chem. A 2 (2014) 2101-2109. [31] I. Popov, G. Seifert, and D. Tomnek, Designing electrical contacts to MoS2 monolayers: A computational study, Phys. Rev. Lett. 108 (2012) 156802-5. [32] G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47 (1993) 558-4. [33] J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 80 (1998) 891. [34] S. Grimme, Semiempirical GGAtype density functional constructed with a longrange dispersion correction, J. Comput. Chem. 27 (2006) 1787-1799. [35] J. Heyd, G.E. Scuseria and M. Ernzerhof, Hybrid functionals based on a screened Coulomb potential, J. Chem. Phys. 118 (2006) 8207-8215. [36] A. Togo, F. Oba, and I. Tanaka, First-principles calculations of the ferroelastic transition between rutile-type and CaCl2 -type SiO2 at high pressures, Phys. Rev. B 78 (2008) 134106. [37] M. Shishkin and G. Kresse, Implementation and performance of the frequency-dependent GW method within the PAW framework, Phys. Rev. B 74(3) (2006) 035101. [38] M. Rohlfing and S.G. Louie, Electron-Hole Excitations in Semiconductors and Insulators, Phys. Rev. Lett. 81(11) (1998) 2312. [39] M. Khazaei, M. Arai, T. Sasaki, C.-Y. Chung, N.S. Venkataramanan, M. Estili, Y. Sakka and Y. Kawazoe, Novel electronic and magnetic properties of twodimensional transition metal carbides and nitrides, Adv. Funct. Mater. 23 (2013) 2185-2192. [40] L. Huang, B. Li, M. Zhong, Z. Wei and J. Li, Tunable Schottky Barrier at MoSe2/Metal Interfaces with a Buffer Layer, J. Phys. Chem. C 121(17) (2017) 9305-11. [41] J. Li, Z. Shan and E. Ma, Elastic strain engineering for unprecedented materials properties, MRS Bull. 39 (2014) 108-114. [42] Q. Zhang, X. Chen, W.C. Liu and Y. Wang Comp. Mater. Sci. 158 (2019) 272-81.

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13

monolayer Mo2 CO2 W2 CO2 Mo2 CF2 W2 CF2 Ei (eV)

-46.10

-51.11

-40.45

-44.61

Eii (eV)

-43.90

-48.93

-40.29

-44.42

Eiii (eV)

-47.56

-52.89

-40.86

-45.07

Eiv (eV)

-44.98

-50.01

-40.33

-44.51

a (˚ A)

2.87

2.85

3.00

2.94

M-C (˚ A)

2.16

2.17

2.10

2.10

M-O(F) (˚ A)

2.05

2.06

2.28

2.31

Eg (eV)

0.59

0.64

—

—

Φ (eV)

7.99

7.60

6.24

6.08

TABLE I. Total ground state energies (Ei , Eii , Eiii , Eiv ) for the four possible configurations of M2 CX2 (M=Mo, W; X=O, F), optimized lattice constant (a), bond length (M-C, M-O(F)), band gap (Eg(HSE06+SOC) ) values and work function (Φ). Configuration

A

B

C

D

E

F

Mo2 CO2 /W2 CO2 E (eV) -0.223 -0.222 -0.222 -0.310 -0.314 -0.312 d (˚ A)

2.79

2.79

2.78

2.25

2.21

2.24

Mo2 CF2 /W2 CO2 E (eV) -0.295 -0.294 -0.294 -0.388 -0.395 -0.294 d (˚ A)

2.74

2.74

2.75

2.23

2.20

2.22

TABLE II. Binding energy (Eb ) and interlayer distance (d) for the out-of-plane heterostructures.

System

m∗hΓ→K m∗hΓ→M m∗eΓ→K m∗eΓ→M

Mo2 CO2

0.054

0.092

0.146

0.152

W2 CO2

0.018

0.020

0.405

0.116

Mo2 CO2 /W2 CO2 0.020

0.026

-

0.157

TABLE III. Effective masses of holes (m∗h ) and electrons (m∗e ) of Mo2 CO2 and W2 CO2 monolayers, and Mo2 CO2 /W2 CO2 heterostructure, obtained by parabolic fitting to the VBM and CBM along different directions in the reciprocal space.

14

ii

iv

iii

Side view

Top view

i

Mo(W)

C

O(F)

FIG. 1. Top and side views of MXene (M2 C (M=Mo, W)) functionalized by O(F) at different positions.

(a)

(b)

(c)

(d)

-1

Frequency (cm )

800 600 400 200 0

-1

Frequency (cm )

800 600 400 200 0 Γ

Κ

Γ Γ

Μ

Κ

Μ

Γ

FIG. 2. Phonon spectrum of monolayers (a) Mo2 CO2 , (b) Mo2 CF2 , (c) W2 CO2 and heterostructure (d) Mo2 CO2 /W2 CO2 .

15

(A-C)

Bottom view

Side views

Top view

Top view

(D-F)

Bottom view

O4(F2) Mo2

Mo

C2 Mo1 O3(F1)

W

O2 W1 C2 W2 O1

A

B

C

O(F)

C

D

E

F

FIG. 3. Top and side views of Mo2 CO2 /W2 CO2 (Mo2 CF2 /W2 CO2 ) heterostructure for different stackings.

(a)

(d)

-2 (b) 2

(e)

Energy (eV)

Energy (eV)

2 1 0 -1

1 0 -1

Energy (eV)

-2 (c) 2

(f)

1 ΦB, n

0 -1 -2

Γ

Κ

Μ

ΓΓ

Κ

Μ

Γ

FIG. 4. Bandstructures; (a) Mo2 CO2 (b) W2 CO2 (c) Mo2 CO2 /W2 CO2 ; where red, blue, and dashed-black lines represent PBE, PBE+SOC, and HSE06+SOC calculations. (d) Mo2 CF2 (e) W2 CF2 (f) Mo2 CF2 /W2 CO2 ; with HSE06+SOC calculations. see the text for details.

16

DOS (1/eV)

0.8

Mo-d C-p W-d C-p O-p

W-d C-p O-p

Mo-d C-p O-p

0.6 0.4 0.2 0

-2

-1

(d)

2 -2

0 1 E-EF(eV)

-1

(e)

0 1 E-EF(eV)

-1

2

0 E-EF(eV)

(f)

1

3 dxz

dxy

2

dyz

Energy (eV)

1 0

Mo W

-1 -2 -3

FIG. 5.

K

Γ

M

K

Γ Γ

M

K

ΓΓ

M

Γ

Density of states of monolayer Mo2 CO2 (a), W2 CO2 (b), and heterostructure

Mo2 CO2 /W2 CO2 (c). Weighted band structure of Mo2 CO2 /W2 CO2 heterostructure ((d) dxy , (e) dxz , and (f) dyz )). visible spectrum

(b)

{

(a)

40

Mo2CO2

30

W2CO2/Mo2CO2

20 W2CO2

ε 2 (ω )

Mo2CO2

W2CO2

10 0

1

2

Electrostatic potential (eV)

(c)

3 Energy (eV)

10

5

Δρ W2CO2/Mo2CO2

V∞ for Mo2CO(F)2

V∞ for W2CO2

ΔV∞ (0.39 eV)

0 -10

Mo2CO2

Mo2CO2/W2CO2

W2CO2

Mo2CF2/W2CO2

Mo2CF2 W2CF2

-20 -30

0

10

20

30 0

10

20

30

40

z (Å)

z (Å)

FIG. 6.

4 (d)

Imaginary part of the dielectric function ε2 (ω) Mo2 CO2 (red), W2 CO2 (blue) and

Mo2 CO2 /W2 CO2 (black) obtained by BSE-GW0 scheme (a); Charge density difference of Mo2 CO2 /W2 CO2 (b), The isovalue for the isosurface is 0.0004 eV ˚ A−3 ; Plane-average electrostatic potential solid black (blue) line Mo2 CF2 (Mo2 CO2 ) and dashed-green (red) line for W2 CF2 (W2 CO2 ) (c), Plane-average electrostatic potential along the interface normal of Mo2 CO2 /W2 CO2 (Mo2 CF2 /W2 CO2 ) represent by red (blue) dashed lines (d). The vertical dashed line represent the interface positions in (d).

17

I.

RESEARCH HIGHLIGHTS The fundamental electronic structure and opical properties of the semiconductor-semiconductor

(Mo2 CO2 /W2 CO2 ) and metal-semiconductor (Mo2 CF2 /W2 CO2 ) heterostructures and their corresponding monolayers M2 CX2 (M=Mo, W; X=O, F) are investigated by first principle calculations so that technologies for band gap engineering and preparing good Schottky contacts can be developed for a wide variety of device applications. The bandstructure topology of Mo2 CO2 /W2 CO2 (semiconductor-semiconductor) heterostructure indicates a possible topological nature similar to corresponding monolayers and having type-II band alignment. The novel work presented in this paper is based on the exploration of the properties of 2D materials known as MXenes (prepared from the MAX (Mn+1 AXn ) phase of the bulk materials by etching the layers of A element) and their van der Waals heterostructure for device applications.

1