Electronic Structures of Germanene on MoS2: Effect of Substrate and

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Electronic Structures of Germanene on MoS: Effect of Substrate and Molecular Adsorption Si Zhou, and Jijun Zhao J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b07651 • Publication Date (Web): 01 Sep 2016 Downloaded from http://pubs.acs.org on September 2, 2016

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The Journal of Physical Chemistry

Electronic Structures of Germanene on MoS2: Effect of Substrate and Molecular Adsorption Si Zhou, Jijun Zhao* Key Laboratory of Materials Modification by Laser, Ion and Electron Beams, Dalian University of Technology, Ministry of Education, Dalian 116024, China

Abstract Germanene, a two-dimensional (2D) Dirac semimetal beyond graphene, has been recently synthesized on a nonmetallic substrate, which offers great opportunities for realization of germanene-based electronic devices. Understanding the effects of substrate and chemical modification on the electronic properties of germanene is thus crucial for tailoring this novel 2D material for future applications. Herein we investigate the structure, interlayer interaction and electronic band structure of monolayer germanene supported on various transition metal dichalcogenide (TMD) substrates. A band gap of 38~57 meV can be opened by the TMD substrates due to breaking of lattice symmetry of the germanene sheet. An electron donor molecule – tetrathiafulvalene (TTF) – is exploited to noncovalently functionalize the germanene on MoS2 substrate. The electron transfer from TTF to germanene disturbs the Dirac cone of germanene, and leads to an augment of the band gap up to 180 meV. Meanwhile, the charge carriers of the hybrid system are still mobile possessing small effective masses (≤ 0.16 m0). Applying a vertical electric field can increase the interface dipole of the hybrid system, and further enhance the band gap up to 214 meV. These theoretical results provide an effective and reversible route for engineering the band gap and work function of germanene without severely affecting the transport properties of this material.

*

Corresponding author: Email: [email protected] (J. Zhao), Phone: 86-024-84709748 1

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1. Introduction The boom of graphene has stimulated tremendous efforts in exploring other elementary two-dimensional (2D) materials.1 Among them, silicene and germanene, the silicon and germanium counterparts of graphene, respectively, are particularly attractive due to the following advantages: (1) resemblance of the electronic band structure of graphene with Dirac cone and high Fermi velocity;2 (2) stronger effect of spin–orbit coupling (SOC) than graphene, which may allow the observation of quantum spin Hall (QSH) effect at experimentally accessible temperatures;3 (3) easier band gap engineering, which is crucial for the applications in field effect transistor (FET) and other electronic devices.4 Ever since the theoretical validation in 20092 and the experimental synthesis in 2012,5-7 silicene has been intensively studied.8 The first silicene based FET was reported recently.9 However, exfoliation of silicene from the metal substrates remains challenging due to their strong interfacial interaction, which hinders the development of silicene based electronics.9-10 Growth of silicene on nonmetallic substrates with relatively weak interaction, although being theoretically proposed,11-12 has not been fully realized in experiment yet.13 Compared to silicene, germanene with stronger SOC effect is less explored from both experimental and theoretical points of view. In 2014, Gao’s group synthesized germanene on Pt(111) surface, with a superstructure of 3×3 germanene and √19×√19 Pt(111).14 Le Lay’s group fabricated monolayer and few-layer germanene on Au(111) substrate, and presented some angle-resolved photoemission (ARPES) evidences of Dirac cone in the few-layer germanene.15-16 Pirri’s group obtained a continuous germanene layer on Al(111) with a 3×3 surface periodicity of the substrate lattice.17-18 Germanene sheets were also fabricated on Ge2Pt crystals19 and on hexagonal AlN buffer layer on Ag(111) substrate,20 respectively. As an important step toward future devices, Zandvliet’s group recently reported the growth of germanene on MoS2 – a 2D band gap material.21 A superstructure of 5×5 germanene and 6×6 MoS2 lattice was proposed. The 2D Dirac signature of the hybrid material was supported by the V-shape density of states in the measured scanning tunneling spectroscopy (STS). Parallel to the experimental progresses, intensive first-principles calculations 2


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have been carried out to investigate the fundamental properties of germanene, including orbital hybridization,22 phonon dispersion and lattice stability,23-24 thermal and thermoelectric properties,25-26 elasticity,27 electronic band structure and optical absorption,28-29 electron-phonon coupling,30 and carrier mobility.31 The impacts of strain,32 electric field,33 structural defects,34 hydrogenation,35-36 adsorption of metal ions and gas molecules,37-39 and substrates40-41 on the structural stability, electronic and magnetic properties of germanene were also investigated. A variety of potential applications have been proposed for germanene, such as FETs,4 optical devices,28 spintronic devices,42-43 and thermoelectric devices.26, 44 Inspired by the above achievements, especially the successful growth of germanene on a nonmetallic substrate,21 in this paper we investigate the structure and electronic properties of germanene supported on MoS2 (abbreviated as Ger/MoS2 thereafter) by first-principles calculations, and tailor the band gap of Ger/MoS2 by applying external electric field and on-top-self-assembling a monolayer of organic molecules.

Electron

donor

acceptor

(TCNQ),45

tetracyanoquinodimethane tetrathiafulvalene

and

(TTF),47

and

(EDA)

molecules,

tetracyanoethylene

such

as

(TCNE),46

2,3-dichloro-5,6-dicyano-1,4-benzoquinone

(DDQ),48 have been extensively explored for noncovalent functionalization of the 2D layered materials. Among these EDA molecules, we show that TTF – a prototypical donor molecule – can reversibly adsorb and desorb on the MoS2 supported germanene surface. A band gap up to 214 meV can be opened in the TTF/Ger/MoS2 hybrid system under a moderate vertical electric field, paving a new way for utilizing germanene in logic circuits and photonic devices.

2. Computational methods Density functional theory (DFT) calculations were performed by Vienna ab initio simulation package (VASP),49 using the planewave basis set with an energy cutoff of 500 eV and the projector augmented wave (PAW) potentials.50 The optB86b-vdW density functional,51-52 which was recently demonstrated to be a suitable method to describe silicene-substrate interaction,53 was employed to account for the van der 3



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Waals (vdW) interactions between germanene, the substrate materials, and the adsorbed organic molecules. A vacuum space of 15 Å was added in the out-of-plane direction of simulation supercell to avoid interactions between periodic images. For the substrate, we consider various monolayers of transition metal dichalcogenide (TMD), including MoS2, MoSe2, WS2, and WSe2. Our test calculations show that few-layer TMD has almost identical effect on the structure and electronic properties of germanene compared to monolayer TMD (see Table 1). The optimized in-plane unit cell parameter of freestanding germanene is 4.06 Å with the buckling height of 0.69 Å, and the unit cell parameters for individual MoS2, MoSe2, WS2, and WSe2 monolayers are 3.18 Å, 3.32 Å, 3.16 Å, and 3.32 Å, respectively, in good agreement with the experimental values21, 54 and previous theoretical results.32, 55 To model a germanene sheet on the TMD substrates, we constructed a superstructure consisting of 4×4 germanene and 5×5 TMD unit cells with lattice mismatch below 3% (see Figure 1a and Table 1). It has been shown that germanene possesses the strain-induced self-doping behavior in the electronic band structure.41, 56 To avoid this complexity, here we fixed the cell parameter of germanene and slightly stretched or compressed the TMDs’ lattice to fit the 4×4 germanene superlattice. The Brillouin zone of the supercell was sampled by 4×4×1 uniform k-point meshes. With fixed supercell parameters, the model structures were optimized by the ionic and electronic degrees of freedom using thresholds for the total energy and forces of 10−4 eV and 0.02 eV/Å, respectively. Based on the equilibrium configurations, Hirshfield charge analysis57 was performed by CASTEP,58 using the planewave basis set with an energy cutoff of 900 eV and the norm-conserving pseudopotentials.

3. Results and discussions We first consider a germanene sheet supported on the TMD monolayer substrates (Ger/TMD). To characterize the interaction between germanene and TMD layers, we define the binding energy as Ebind = (Etot – EGer – ETMD)/n,

(1)

where Etot is the energy of the Ger/TMD superstructure; EGer and ETMD are the 4


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energies of isolated germanene and TMD sheets, respectively; n is the number of Ge atoms in the superstructure. As presented in Table 1, germanene sheet adsorbs on the TMD substrate via weak vdW interactions, with binding energy of about −0.17 eV per Ge atom. The interlayer spacing d (as labeled in Figure 1a) between germanene and the TMD surface ranges from 3.02 Å to 3.14 Å. In comparison, low-buckled silicene on MoS2 (Sil/MoS2) exhibits a binding energy of −0.158 eV per Si atom and an interlayer spacing of 3.15 Å, according to a previous DFT calculation using the optB86b-vdW functional.53 Thus the interlayer binding strength of Ger/MoS2 is slightly stronger than that of Sil/MoS2. We also vary the stacking of germanene and TMD sheets. The resulted changes in Ebind and d are negligible, suggesting that the interlayer binding of Ger/TMD is not sensitive to the stacking geometry. Generally speaking, the interaction with the TMD substrate breaks the sublattice symmetry of germanene. The Ge atoms of the bottom sublattice are pulled downwards, yielding a larger buckling height ∆ = 0.73 Å (as labeled in Figure 1a), compared to 0.69 Å for the freestanding germanene. Hirshfield charge analysis indicates a charge transfer of 0.05 e per supercell from germanene to the TMD substrate, resulting in an intrinsic interface dipole pointing from germanene to TMD. According to a tight-binding model,59 the on-site energies of the two sublattices in germanene are no longer identical, leading to the opening of a band gap Eg. Figure 1b displays the electronic band structure of the Ger/MoS2 superstructure with Eg = 57 meV, which is larger than the gap of Sil/MoS2 (40 meV) predicted by using the optB86b-vdW functional.53 The interaction with substrate disturbs the Dirac cone of germanene, and the dispersion near the K point becomes parabolic with a carrier effective mass of 0.04 m0 (m0 is the electron rest mass). By taking SOC into account for the Ger/MoS2 superstructure, energy is split between the majority spin and minority spin bands for both electrons and holes. As a consequence, energy gaps of 83 meV and 22 meV are induced between the majority and minority bands, respectively, compared to 24 meV (spin degeneracy) for the freestanding germanene according to our calculations. These enhanced SOC gaps may create opportunities for spintronic applications.3 5



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Similar results are obtained for germanene on MoSe2, WS2 and WSe2 substrates, as illustrated in Table 1. The four Ger/TMD systems present almost the same buckling height of germanene, as well as the interlayer spacing and binding strength between germanene and the TMD substrate. The band gap decreases from 57 meV, 53 meV, 40 meV to 38 meV as the substrate goes from MoS2, MoSe2, WS2 to WSe2, attributed to their decreasing bond polarity (Pauling electronegativities are 2.58 and 2.55 for S and Se, 2.16 and 2.36 for Mo and W, respectively60). In consistency, more charge transfer occurs in Ger/MoS2 and Ger/MoSe2 (0.05 e per supercell) than that in Ger/WS2 and Ger/WSe2 (0.03 e per supercell), resulting in larger band gap for the former systems than the latter ones. After including the SOC effect, the gaps between majority spin bands show similar behavior as those without SOC for various Ger/TMD systems; Ger/MoSe2 has larger SOC gap between minority spin bands than those of the other three systems due to its smaller energy splitting. To further tune the band gap of Ger/TMDs, we apply a vertical electric field (F) perpendicular to the 2D materials. The variation of Eg versus F is plotted in Figure 2. Under this external field, the structural modification of Ger/TMDs is very small and causes negligible variation in Eg (≤ 5 meV). A positive F (pointing from TMDs to germanene) pushes electrons transferring from germanene to TMD substrates, enhancing the interface dipole. As a consequence, Eg linearly increases with F up to 112 meV under a moderate field strength of 0.6 V/Å. In comparison, Sil/MoS2 shows Eg = 92 meV under a vertical electric field of 0.5 V/Å from the previous calculations.61 When a negative F is applied, the external field first compensates the interface dipole, and then reverses the dipole. Accordingly, Eg first decreases as the field strength increases, almost varnishes under F ≈ −0.5 V/Å, and then increases with the field strength. EDA

molecules

have

been

extensively

exploited

for

noncovalent

functionalization of 2D materials via surface charge transfer.45-48 To manipulate the electronic band structure of Ger/TMDs, we choose several organic EDA molecules including TCNQ, TCNE, DDQ and TTF. Due to the similarity of various TMD substrates (as demonstrated by Table 1), we consider only the Ger/MoS2 6


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superstructure as a representative. We find that germanene is vulnerable to oxygen and nitrogen atoms in the organic molecules – it forms covalent bonds with TCNQ, TCNE and DDQ. Such covalent interaction is detrimental to reversible adsorption/desorption of EDA molecules and would also destruct the electronic band structure of the isolated germanene layer to some extent. In contrast, TTF, an electron donor molecule, physisorbs on the germanene surface, and thus is a candidate for noncovalent modification of Ger/MoS2. Figure 3a depicts the atomic structure of a TTF molecule physisorbed on the surface of the Ger/MoS2 superstructure (1TTF/Ger/MoS2), corresponding to a coverage of 0.44 molecule per nm2. The average distance between the molecule and the germanene surface dm (as labeled in Figure 3a) is 3.11 Å. The buckling height of germanene increases slightly to 0.74 Å due to the interactions with both TTF molecule and MoS2 substrate. To characterize the energetics of the adsorbed TTF molecules, we define the sequential adsorption energy as follows Eads = EnTTF/Ger/MoS2 – E(n−1)TTF/Ger/MoS2 – ETTF,

(2)

where n is the number of TTF molecules in the system; EnTTF/Ger/MoS2 and E(n−1)TTF/Ger/MoS2 are the energies of Ger/MoS2 sheets adsorbed by n and (n – 1) TTF molecules, respectively; ETTF is the energy of an individual TTF molecule. Apparently, Eads gives the energy gain by adsorbing an additional TTF molecule to the original system. We have explored different positions and orientations of the adsorbed TTF molecules, and the configuration given in Figure 3a corresponds to the most stable one with Eads = −1.26 eV per TTF molecule (i.e. 0.09 eV per atom). The TTF molecule lies on the hollow site of germanene lattice, with the central C=C bond parallel to the Ge−Ge bond. The TTF is nearly flat with the molecular plane parallel with the germanene basal plane. The other considered adsorption configurations of TTF give higher energies by 0.05~0.1 eV per molecule, and the resulted variations in the band gap and band dispersion are minor (see Figure S1 and Table S1 of Supporting Information). Therefore, we consider only the lowest energy configuration in Figure 3a. Figure 3b displays the electronic band structure of 1TTF/Ger/MoS2. The 7



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parabolic dispersion of Ger/MoS2 around the K point is further disturbed by the coupling with the TTF molecule. However, the location of Fermi level remains in the middle of band gap, irrelevant to molecular adsorption. Most importantly, the band gap is significantly enhanced from 57 meV to 102 meV, and is shifted to the region between Γ and K points in the reciprocal space. The band dispersion is slightly reduced, giving effective masses of 0.08(0.07) m0 for electrons (holes), respectively. Figure 4a shows the partial charge density of 1TTF/Ger/MoS2 from the top valence band (VB) and the bottom conduction band (CB). The charge of the top VB distributes on both the TTF molecule and germanene sheet, indicating electron coupling between them. For the bottom CB, the charge is delocalized mainly on germanene and marginally on MoS2. Therefore, the carrier transport of the hybrid system is still dominated by the charge on germanene, and may be only minorly affected by molecular adsorption. The modification of the electronic band structure of 1TTF/Ger/MoS2 can be explained by the surface charge transfer. Hirshfield charge analysis reveals that there are 0.32 electrons transferring from TTF to Ger/MoS2. Accordingly, the differential charge density in Figure 5b, c shows electron accumulation on the germanene sheet and depletion on the TTF molecule. The charge transfer process is predominantly controlled by the energy difference between the highest occupied molecular orbital (HOMO) of TTF molecule and the conduction band edges of Ger/MoS2 superstructure,62 both of which are calculated by referring to the vacuum level. Figure 5a schematically shows the alignment of band edges for each component 2D sheet, and the frontier orbital energies for a TTF molecule. The electrostatic potential profile of 1TTF/Ger/MoS2 along the out-of-plane direction is plotted in Figure 5c. The potential attains minima on the sublayers of MoS2 and germanene, as well as on the TTF molecular plane; it reaches a plateau away from the hybrid material, which is used as the vacuum level. From our calculation, the work function Φ of bare MoS2 and germanene monolayer are 5.18 eV and 4.60 eV, respectively, in good agreement with the other theoretical values (5.20 eV and 4.57 eV)63-64 (Φ is defined as the energy required to extract an electron from the Fermi level to the vacuum level62). The 8


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Ger/MoS2 superstructure possesses Φ = 4.28 eV, larger than the HOMO of TTF (3.85 eV). Moreover, the HOMO of TTF is higher than the conduction band minimum (CBM) of Ger/MoS2 by 0.4 eV, driving the electrons flowing from TTF to Ger/MoS2. Owing to their close energy levels, the HOMO of TTF strongly interacts with the bottom CB of Ger/MoS2, as corroborated by the partial charge density in Figure 4a. Such electron coupling significantly lowers the valence band maximum (VBM) of 1TTF/Ger/MoS2, and thus enlarges the band gap of the hybrid system. Further increasing the concentration of TTF molecules to a maximum of four TTF molecules per superstructure (coverage of 1.76 molecules per nm2) leads to a self-assembled monolayer of TTF on germanene surface, as presented in Figure 6a. Due to the lateral intermolecular interaction, the TTF molecules are slightly distorted and inclined. The average distance between TTF and germanene surface increases from 3.11 Å to 3.43 Å for n = 1 to 4 (see Table 2). The adsorption of the 2nd and 3rd TTF molecules are energetically more favored than the 1st one with Eads of −1.27 eV and −1.29 eV, respectively, ascribed to the attractions between TTF molecules. Including the 4th TTF molecule becomes less favored giving Eads of −1.18 eV, due to the larger separation between TTF and the germanene sheet and hence the loss of interaction from germanene. On the other hand, higher molecular coverage leads to stronger interaction between germanene and the MoS2 substrate, indicated by the decreasing interlayer distance down to 2.98 Å and larger buckling height of germanene up to 0.75 Å, which is beneficial for band gap opening. Noticeably, the electronic band structure of nTTF/Ger/MoS2 can be engineered by the concentration of adsorbed TTF molecules. The band gap of the system increases with n from 102 meV up to 180 meV (see Table 2, Figure 6b, Figure S2 and Figure S3 of Supporting Information). The system with higher TTF concentration exhibits stronger electron coupling between the molecules and germanene, as revealed by the partial charge density of the top VB and bottom CB in Figure 4b. Consequently, the charge carriers become less mobile with larger effective masses up to 0.16 m0. Nevertheless, the top VB and bottom CB show predominant charge densities on the germanene sheet, and hence the electronic properties of the hybrid system may be 9



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only moderately deteriorated by the molecular adsorption. On the other aspect, the total amount of charge transfer from the TTF molecules to Ger/MoS2 increases with the concentration of the adsorbed molecules, from 0.34 e to 0.52 e per supercell for n = 1 to 4. As more electrons flow into the bottom CB of the underneath Ger/MoS2 sheet, the Fermi energy of nTTF/Ger/MoS2 is raised, and the work function of the hybrid system decreases from 4.26 eV down to 3.84 eV. Therefore, self-assembling a monolayer of TTF molecules on the surface of Ger/MoS2 is an effectively way to tune both band gap and work function of the material, which would be useful for the applications of germanene in electronic devices, solar cells, and photovoltaic devices.47, 65 We have also explored the effect of supercell size on the band gap of nTTF/Ger/MoS2. A supercell consisting of 6×6 germanene on 8×8 MoS2 unit cells is considered. A monolayer of TTF molecules adsorbed on the germanene sheet, corresponding to a coverage of 1.56 molecules per nm2, leads to the opening of a band gap of 140 meV (see Figure S4 of Supporting Information), consistent with the results obtained by using the smaller supercell. Last, we apply a vertical electric field to further modulate the band gap of the nTTF/Ger/MoS2. As discussed above, the Ger/MoS2 system exhibits charge transfer from germanene to MoS2, and the adsorbed TTF molecules donates electrons to germanene, increasing the interface dipole. Then a positive electric field (pointing from Ger/MoS2 to TTF) pushes electrons from TTF to the underlying Ger/MoS2 sheets, leading to a further augment of the interface dipole. As displayed in Figure 7, the band gap of nTTF/Ger/MoS2 increases with F up to 214 meV for F = 0.4 V/Å, which is actually a superposition effect of the MoS2 substrate, adsorbed TTF molecules and electric field. On the contrary, a negative electric field induces charge transfer in the opposite direction and cancels out the interface dipole of nTTF/Ger/MoS2; thus the band gap decreases as the field strength increases. The critical field strength to close the band gap is expected to be greater than 0.6 V/Å, and would increase with the TTF concentration due to the larger charge transfer from TTF to germanene. Our strategy by synergizing the effects of TMD substrate, molecular adsorption, 10


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and external electric field is efficient for band gap opening compared to the other proposed approaches. For instance, silicene opens a band gap of 42 meV simultaneously under a biaxial compress strain of 0.05 and a vertical electric field of 0.5 V/Å;33 germanene achieves a maximum band gap of 260 meV by adsorption of high concentrations of alkali metal ions on the surface.39 Most importantly, we offer a possible route for engineering the band gap and work function of germanene in a nonconstructive manner, which would be useful for practical applications in the future.

4. Conclusion We investigate the electronic band structure of a germanene sheet supported by various TMD substrates and noncovalently functionalized by an electron donor molecule – TTF – by first-principles calculations. Our results show that the TMD substrates induce small displacement of the Ge atoms on the bottom sublayer and opens a band gap of 38~57 meV for germanene. The TTF molecules, which can reversibly adsorb and desorb on the Ger/MoS2 sheet, cause electron coupling between TTF and germanene, and enlarge the band gap up to 180 meV without severely degrading the transport properties of the system. Applying a vertical electric field can further drive the electrons to transfer from TTF to the underlying Ger/MoS2 sheets, and enhance the band gap up to 214 meV. These theoretical results provide an efficient route to tailor the electronic properties of germanene, facilitating the utilization of this 2D material for future electronic and photonic devices.

Associated content The Supporting Information is available free of charge on the ACS Publications website. The electronic band structures of 1TTF/Ger/MoS2 with various configurations, 2TTF/Ger/MoS2, 3TTF/Ger/MoS2, and 8TTF/Ger/MoS2 using a large simulation supercell (Figure S1, S2, S3 and S4), and the band gap and effective mass of 1TTF/Ger/MoS2 with various configurations (Table S1). 11



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Acknowledgement This work was supported by the National Natural Science Foundation of China (11504041, 11574040), the China Postdoctoral Science Foundation (2015M570243, 2016T90216), the Fundamental Research Funds for the Central Universities of China (DUT15RC(3)014, DUT16-LAB01), the Scientific Research Fund of Department of Education of Liaoning Province (L2015124), and the Supercomputing Center of Dalian University of Technology.

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Table 1. Geometrical parameters, energies, and band gaps of Ger/TMDs, including the lattice mismatch (δ, +/− represents expansion/compression of TMDs’ lattice), buckling height of germanene (∆), interlayer spacing between germanene and TMDs (d), binding energy per Ge atom (Ebind), band gap (Eg), SOC gap between the majority (Egu) and minority (Egd) spin bands. The supercell consists of 4×4 germanene and 5×5 TMD unit cells. The corresponding values of freestanding germanene, and germanene on bilayer MoS2 are also listed for comparison. substrate

δ

∆ (Å)

Ebind

Eg

Egu

Egd

(eV)

(meV)

(meV)

(meV)

d (Å)

freestanding

--

0.69

--

--

0

24

24

MoS2

−2.07%

0.73

3.02

−0.17

57

83

22

MoSe2

+2.12%

0.73

3.02

−0.17

53

76

29

WS2

−1.95%

0.73

3.09

−0.16

40

69

14

WSe2

+2.10%

0.73

3.14

−0.16

38

58

15

MoS2 (bilayer)

−2.07%

0.73

3.00

−0.17

56

82

21

16


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Table

2.

Geometrical

parameters,

energies,

and

electronic

properties

of

nTTF/Ger/MoS2 (n = 1, 2, 3, 4), including the average distance between TTF and germanene (dm), buckling height of germanene (∆), interlayer spacing between germanene and MoS2 (d), sequential adsorption energy of TTF (Eads), band gap (Eg), SOC gap between the majority (Egu) and minority (Egd) spin bands, effective mass of electron (me) and hole (mh) carriers, work function (Φ), and total charge transfer (CT) from TTF to germanene by Hirshfield analysis. The supercell consists of 4×4 germanene and 5×5 MoS2 unit cells. dm

∆

d

Eads

Eg

Egu

Egd

me

mh

Φ

CT

(Å)

(Å)

(Å)

(eV)

(meV)

(meV)

(meV)

(m0)

(m0)

(eV)

(e)

0

--

0.73

3.02

--

57

83

22

0.04

0.04

4.28

--

1

3.11

0.74

3.00

−1.26

102

120

80

0.07

0.08

4.16

0.32

2

3.20

0.74

2.99

−1.27

110

127

88

0.08

0.09

4.05

0.39

3

3.23

0.75

2.99

−1.29

127

148

107

0.09

0.10

3.97

0.45

4

3.43

0.75

2.98

−1.18

180

195

156

0.16

0.17

3.84

0.52

n

17



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Figure 1. (a) The top (left) and side (right) views of Ger/MoS2. The dashed box in the top view shows the in-plane dimension of the simulation supercell, consisting of 4×4 germanene and 5×5 MoS2 unit cells. The Ge, Mo and S atoms are shown in green, blue and yellow, respectively. In the side view, ∆ indicates the buckling height of germanene, defined as the vertical distance between the Ge atoms from the top and bottom sublayers; d is the interlayer spacing between germanene and MoS2, defined as the vertical distance between the Ge atoms from the bottom sublayer of germanene and the S atoms from the top sublayers of MoS2. (b) The electronic band structure of the Ger/MoS2 superstructure (as shown in a), without (left) and with (right) SOC. The zero energy level is shifted to the Fermi energy. The arrows upwards and downwards in the right panel indicate the majority and minority spin bands, respectively.

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Figure 2. The band gap of the Ger/TMDs superstructures (as shown in Figure 1a) as a function of the vertical external electric field (F). The inset shows the direction of the electric field (up for positive).

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Figure 3. (a) The top (left) and side (right) views of 1TTF/Ger/MoS2. In the top view, the dashed box indicates the in-plane dimension of the simulation supercell; the atomic structure of the MoS2 substrate is eliminated for clear visualization. The Ge, Mo, S, C and H atoms are shown in green, blue, yellow, grey and white, respectively. In the side view, dm indicates the average distance between TTF and germanene, defined as the vertical distance between the TTF molecular plane and the top sublayer of germanene. (b) The electronic band structure of the 1TTF/Ger/MoS2 superstructure (as shown in a), without (left) and with (right) SOC. The zero energy level is shifted to the Fermi energy. The arrows upwards and downwards in the right panel indicate the majority and minority spin bands, respectively.

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Figure 4. (a) Partial charge densities of 1TTF/Ger/MoS2 (as shown in Figure 3a) from the top valence band (left panels) and bottom conduction band (right panels), with top views (top panels) and side views (bottom panels). (b) Same as (a) for 4TTF/Ger/MoS2 (as shown in Figure 6a). The Ge, Mo, S, C and H atoms are shown in green, blue, yellow, grey and white, respectively. The orange color indicates the charge density isosurface of 0.005 e/Å3. In the top views, the dashed boxes indicate the in-plane dimension of the simulation supercell; the atomic structure of the MoS2 substrate is eliminated for clear visualization.

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Figure 5. (a) Schematic diagram of the alignment of band edges and Fermi energy (EF) for MoS2, germanene, Ger/MoS2 (as shown in Figure 1a) and 1TTF/Ger/MoS2 (as shown in Figure 3a), and the frontier orbital energies for a TTF molecule. The vacuum energy level (Evacuum) is used as the reference for energy alignment. The vertical line segments with arrows indicate the work function (Φ) for each crystal system. (b) Top and (c) side views of differential charge densities of 1TTF/Ger/MoS2. The Ge, Mo, S, C and H atoms are shown in green, blue, yellow, grey and white, respectively. The purple and orange colors represent the regions of electron accumulation and depletion, respectively, with an isosurface of 0.003 e/Å3. For clear visualization, the atomic structure of the MoS2 substrate is eliminated in (b). The electrostatic potential (U) along the out-of-plane direction is plotted in (c).

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Figure 6. (a) The top (left) and side (right) views of 4TTF/Ger/MoS2. In the top view, the dashed box indicates the in-plane dimension of the simulation supercell; the atomic structure of the MoS2 substrate is eliminated for clear visualization. The Ge, Mo, S, C and H atoms are shown in green, blue, yellow, grey and white, respectively. (b) The electronic band structure of the 4TTF/Ger/MoS2 superstructure (as shown in a), without (left) and with (right) SOC. The zero energy level is shifted to the Fermi energy. The arrows upwards and downwards in the right panel indicate the majority and minority spin bands, respectively.

23



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Figure 7. The band gap of nTTF/Ger/TMDs (n = 1, 2, 3, 4) as a function of the vertical external electric field (F). The inset shows the direction of the electric field (up for positive).

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Table of contents image

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Electronic Structures of Germanene on MoS2: Effect of Substrate and

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