Electronic properties and photoactivity of monolayer MoS₂/fullerene van der Waals heterostructures

Abstract

van der Waals (vdW) heterostructures have attracted immense interest recently due to their unusual properties and new phenomena. Atomically thin two-dimensional MoS₂ heterostructures are particularly exciting for novel photovoltaic applications, because monolayer MoS₂ has a band gap in the visible spectral range and exhibit extremely strong light–matter interactions. Herein, first-principles calculations based on density functional theory is used to investigate the effects of vdW interactions on changes in the electronic structure, charge transfer and photoactivity in three typical monolayer MoS₂/fullerene (C₆₀, C₂₆, and C₂₀) heterostructures. Compared to monolayer MoS₂, the band gap of the heterostructures is smaller, which can enhance the visible light absorption and photoinduced electrons transfer. The amount of charge transfer at interface induced by vdW interaction depends on the size of fullerenes. Most importantly, a type-II, staggered band alignment can be obtained in the MoS₂/C₂₀ heterostructure, leading to significantly reduced charge recombination and thus enhanced photocatalytic activity. These results reveal that fullerene modification would be an effective strategy to improve the photocatalytic performance of semiconductor photocatalysts.

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1. Introduction

Semiconductor photocatalytic technology has attracted considerable attention due to its great potential in solving current environment and energy problems with abundant solar light.^1–3 To date, various kinds of semiconductor photocatalysts including metal oxides, sulfides and nitrides have been explored.^4,5 However, the development of efficient, sustainable, visible (vis-) light-driven photocatalysts remains a significant challenge. For example, TiO₂, as a paradigm photocatalyst, is a large-band-gap semiconductor (∼3.2 eV),⁵ only showing photocatalytic activity under ultraviolet (UV-) irradiation. Therefore, the pursuit of photocatalysts with high performance under vis-light irradiation would be very desirable.^4,6

In recent years, the use of carbonaceous materials such as fullerene, carbon nanotubes (CNTs) and graphene (GR) for the enhancement of photocatalytic performances of semiconductors has been demonstrated because of their special structures and unique electronic properties.^7,8 Many novel heterojunction photocatalysts by combination of C₃N₄ with carbonaceous materials have been explored. For instance, the graphene/C₃N₄ heterostructures, prepared by the impregnation–chemical reduction strategy, show high vis-light photocatalytic activity for hydrogen production.⁹ Graphene, CNTs and fullerene have also been used to interface with TiO₂ to achieve extended photocatalytic activities well beyond that of pure TiO₂ materials.¹⁰ The enhanced photocatalytic performance of semiconductor/carbon heterostructures is generally attributed to the electron-accepting and transport properties of carbon nanomaterials since they provide a convenient way to direct the flow of photogenerated charge carriers.^11,12

Density functional theory (DFT) has been used to reveal the underlying mechanisms for superior photocatalytic performance of semiconductor/carbons nanomaterials. It has been demonstrated that coupling carbon nanomaterials can reduce the band gap of semiconductors, thus enhancing optical absorption in the visible region.¹³ It is found that graphene is the sensitizer for TiO₂ (ref. 14) and g-C₃N₄,¹⁵ whereas significant charges transfer from anatase TiO₂ to graphene at the ground electronic state is also revealed due to the different crystal structure. The simulations by long et al. rationalized the photocatalytic activity of CNT/TiO₂ heterostructures materials under vis-light is higher than UV-irradiation, and showed that the photoactivity of a semiconducting CNT decorating TiO₂ is better than that of the metallic CNT/TiO₂ heterostructures.^10,16,17 The DFT calculations also suggest that C₆₀-interfaced TiO₂ in both the mechanical mixture and covalent linking cannot form an efficient photovoltaic heterojunction.¹⁸ Whereas B- or N-doped C₆₀ and MoS₂ or WS₂ monolayers can form an efficient photovoltaic heterojunctions.¹⁹

Over the last few years, aroused by the discovery of graphene, two-dimensional (2D) nanomaterials have been largely researched in the field of industrial and scientific for their unique properties and wide potential applications.¹¹ Recently, there has been a continual growth in research and a broad interest in monolayer MoS₂, which has a similar structure to graphene.^20,21 The monolayer MoS₂ consists of molybdenum atoms sandwiched between two layers of hexagonally close packed sulfur atoms, that the adjacent atomic sandwiches are held together by weakly vdW forces,^22,23 which have become particularly interesting due to their enhanced structural complexity and the potential to exploit the functionalities of these nanomaterials, making it a up-and-coming candidate for many useful applications, such as outstanding photoluminescence,²⁴ lithium battery cathodes, sensors, phototransistor and photocatalytic hydrogen production applications.²⁵ However, photocatalytic and field emission abilities of MoS₂ are not productive enough for large scale applications in industry because of the relatively sizable band gaps (1.9 eV), a rapid recombination rate of photogenerated electrons and holes and lacking of effective emission sites.²⁶ Nevertheless, lots of previous studies revealed the fact that forming hetero-nanostructure can give the nanomaterials a better performance in electronics, optoelectronics and other aspects because of the generation of hetero-junction, enlarged specific surface area and so on, such as MoS₂/CdS,²⁷ MoS₂/TiO₂,²⁸ MoS₂/SnO₂ (ref. 29) and MoS₂/Ag₃PO₄.³⁰

More recently, MoS₂/carbon-nanomaterials heterostructures have been attracting increasing attention due to their highly efficient vis-light photocatalytic performances. For instance, the MoS₂/graphene heterostructures prepared by different methods show superior vis-light-driven photocatalytic activity.²⁰ Similarly, Yuan and coworkers reported that TiO₂ grown on layered MoS₂/graphene heterostructures showed an enhanced photocatalytic H₂ evolution activity.³¹ It is also found that MoS₂/CNT heterostructures exhibits high catalytic activity for electrocatalytic hydrogen evolution.³² Compared with graphene and CNTs, fullerene have been attracted particular interest owing to their functional characteristics and potential applications in the fields of nanomaterials and biomedical science.³³ Therefore, it is expected to improve the photocatalytic performance of MoS₂ by fullerene modification, just as the case of C₆₀/TiO₂.³⁴

In this work, the structural and electronic properties of monolayer MoS₂/fullerene vdW heterostructures have been investigated using large-scale DFT computations to explore the effects of non-covalent interactions on enhancing the photoactivity of monolayer MoS₂ by fullerene modification. Here, C₆₀, C₂₆ and C₂₀ are taken as the typical fullerenes, motivated by their special structure and properties.^35,36 The fullerene C₆₀ is a closed-shell configuration consisting of 30 bonding molecular orbitals with 60 π-electrons, which is favorable for efficient electron transfer reduction;³⁷ C₂₀ consisting solely of pentagons, is the smallest unconventional fullerene which breaks the “isolated pentagon rule”,³⁸ while fullerene C₂₆ is pure and intermediate open-shell compound.³⁹ Moreover, these fullerenes are well established as single oxygen sensitizers for electron donor–acceptor assemblies and applies in the field of photocatalysis.^7,11,40 Most importantly, Remskar M. et al. have successfully prepared hybrid MoS₂/C₆₀ crystals, and found that the inherent close proximity of photovoltaic-active MoS₂ monolayers to C₆₀ molecules with strong electron affinities suggests a new kind of material for solar-cell applications with high quantum yields of photoinduced charge generation.⁴¹ The role of fullerene in these photocatalytic systems can be speculated to be as follows: (1) it can form the space potential difference promoting the photogenerated electron–hole separation effectively; (2) it can tune the band gap by changing the band structure of the photocatalysts. The calculated results showed that the band gap can be largely reduced due to interfacing with fullerene, resulting into a strong absorption in the entire visible region and thus superior photocatalytic activity. The electrostatic potential distribution in the interface, where the potential at MoS₂ is higher than that in fullerene, can effectively inhibit the electron–hole pair's recombination and therefore improving its photocatalytic. This work would provide some new insight into optimizing the photocatalytic properties of MoS₂-based or carbon-based nanomaterial heterostructures.

2. Computational method

All of our calculations, including geometry relaxation and electronic structure calculation are performed by using DFT method implemented in the plane wave basis CASTEP code.^42,43 The local density approximation (LDA) with inclusion of the vdW interaction is chosen because long-range vdW interactions are expected to be significant in such these complexes. The cutoff energy for plane waves is chosen to be 400 eV. A Monkhorst–Pack mesh of k points, 2 × 2 × 1 and 4 × 4 × 1 points, is used, respectively, to sample the two-dimensional Brillouin zone for geometry optimization and for calculating the density of states, and the convergence tolerance of force on each atom during structure relaxation is set at 0.01 eV Å⁻¹.⁴⁴

For the monolayer MoS₂, the calculated lattice constant is in good agreement with the previous theoretical results.⁴⁵ The monolayer MoS₂/fullerene vdW heterostructures are composited by using a supercell as illustrated in Fig. 1. The supercell (18.69 × 18.69 × 25.00 ų) contains C₆₀, C₂₆, C₂₀ (containing 60, 26, and 20 atoms, respectively) and one 6 × 6 monolayer MoS₂ (containing 36 Mo and 72 S atoms). A vacuum layer of 15 Å is used in the direction normal to the interface, representing the isolated slab boundary condition. Note that there is no tensile or compressed deformation of MoS₂ surface in the x–y plane, different from other models (CeO₂/GR,⁴⁶ MoS₂/GR,²⁰ g-C₃N₄/GR,⁹ TiO₂/CNT,¹⁰ SrTiO₃/GR⁴⁷).

Fig. 1 The (a) top and (b) side view of the simulating interface between C₆₀ and MoS₂ heterostructures, (c) and (d) side view of the simulating interface between C₂₆, C₂₀ and MoS₂ heterostructures. Gray, green and yellow spheres represent C, Mo and S atoms, respectively.

The strong light absorption is one of fundamental premises for a high-efficiency photocatalyst. The dielectric function of the semiconductor materials is mainly connected with the electronic response. The frequency-dependent dielectric matrix is calculated for pure MoS₂, and MoS₂/fullerene (C₆₀, C₂₆, and C₂₀) heterostructures by the Fermi golden rule within the dipole approximation. The imaginary part ε₂ of the dielectric function ε is calculated from the momentum matrix elements between the occupied and unoccupied wave functions, as given by:

where ħω is the energy of the incident photon, p is the momentum operator r(ħ/i)(∂/∂x), (|kn〉) is a crystal wave function and f(kn) is Fermi function. The real part ε₁ of the dielectric function ε is evaluated from the imaginary part ε₂ by Kramer–Kronig transformation. The absorption coefficient I(ω) can be derived from ε₁ and ε₂, as given by:which depends on ε₁ and ε₂ and thus on the energy. Taking into account the tensor nature of the dielectric function, ε₁(ω) and ε₂(ω) are averaged over three polarization vectors (along x, y, and z directions). All other optical constants can also be obtained. The relations above are the theoretical basis of band structure and optical properties analyzing which reflected the mechanism of absorption spectral caused by electronic transition between different energy levels.

3. Results and discussion

3.1. Geometric structure and adhesion energy

Fig. 1(a–d) show the fully optimized geometric structures of the monolayer MoS₂/fullerene vdW heterostructures. Parts a and b respectively present the top and side views between monolayer MoS₂ and C₆₀ heterostructures, part c and d displays side view of the MoS₂/C₂₆ and MoS₂/C₂₀ heterostructures used in our calculations. Geometry optimizations have first been performed for all of the systems using the conjugate gradient method. The equilibrium distances between fullerene and the top-most atoms of the monolayer MoS₂ are calculated to be 3.04, 2.97 and 3.02 Å for MoS₂/C₆₀, MoS₂/C₂₆ and MoS₂/C₂₀ (as listed in Table 1), which is about equal to those between the GR sheet and other materials (2.65 Å and 2.62 Å for TiO₂(110)/GR,⁴⁸ 2.85 Å for TiO₂(001)/GR,^49,50 2.42–2.87 Å for ZnO(0001)/GR,⁵¹ 3.32 Å MoS₂/GR⁵²). The smaller distance shows that the interaction between monolayer MoS₂ and C₂₆ is stronger than that between monolayer MoS₂ and C₆₀ (C₂₀). After optimization, the MoS₂ and fullerene are nearly unchanged, indicating that the monolayer MoS₂/fullerene interaction is indeed vdW rather than covalent, in accordance with the others' results.⁵⁰ Closer inspection of the atomic position at the interface reveals that, due to the interface interaction between MoS₂ and fullerene, the top-most S atoms are pushed upward about 0.005 and 0.006 Å by C₆₀ and C₂₀, respectively; whereas the Mo atoms move upward about 0.001 and 0.004 Å. In the MoS₂/C₂₆ heterostructures, however, the corresponding S and Mo atoms move about 0.018 Å. It is indicates that the interaction of MoS₂/C₂₆ heterostructures is stronger. The displacement discrepancy of the atoms in the top layer of MoS₂ demonstrates that the interface interaction depends on the carbon number of fullerene. The rearrangements of atoms in the monolayer MoS₂ indicate that the electron transfer occurs at the interface, which will be discussed later.

Table 1 The adhesion energy (E_ad), band gap E_g (eV), mean distance (d) of optimized MoS₂/C₆₀, MoS₂/C₂₆, and MoS₂/C₂₀ heterostructures

Structure	Ead (eV)	Eg (eV)	d (Å)	Bader charge (e)
				MoS2	C
MoS2/C60	−1.77	1.75	3.04	−0.007	0.007
MoS2/C26	−0.99	0.41	2.97	0.01	−0.01
MoS2/C20	−0.76	0.85	3.02	−0.04	0.04

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The stability of the monolayer MoS₂/fullerene heterostructures can be assessed by the interface adhesion energy, which is defined as

E_ad = E_comb − E_fullerene − E_MoS2 (3)

where E_comb, E_fullerene, and E_MoS2 represent the total energy of the relaxed monolayer MoS₂/fullerene, pure fullerene, and pure MoS₂, respectively. By this definition, negative E_ad suggests that the adsorption is stable. The interface adhesion energy is calculated to be −1.77, −0.99 and −0.76 eV for the MoS₂/C₆₀, MoS₂/C₂₆ and MoS₂/C₂₀ heterostructures, respectively, which indicates a rather strong interaction between monolayer MoS₂ and fullerene heterostructures, and the high thermodynamically stability of these heterostructures. Compared with the MoS₂/C₂₀ (C₂₆) heterostructures, the MoS₂/C₆₀ heterostructures with lower adhesion energy can form more easily.

3.2. Density of states

To explore the effect of vdW interaction on the electronic properties of MoS₂, we have calculated the density of states (DOSs) of individual MoS₂, fullerene, and their heterostructures, as shown in Fig. 2. Pure monolayer MoS₂ is a direct semiconductor with a band gap (E_g) of 1.89 eV, which agrees well with the MoS₂ photoluminescence experiment and previous theoretical studies (∼1.9 eV).⁵³ The CB bottom of pure MoS₂ (Fig. 2(a1)) is mainly constituted of Mo 4d and S 3d states, while the upper VB is composed of Mo 4d states. This is one of the most important factors for the lower photocatalytic properties of pure MoS₂. The calculated DOSs show that energy gaps for individual C₆₀ and C₂₆ are 1.61 and 1.64 eV, respectively (Fig. 2(a2–a4)), which are consistent with other theoretical values of 1.6–1.9 (ref. 54) and 1.6 eV,³⁹ respectively. Interestingly, the energy gap for individual C₂₀ is 1.90 eV, in agreement with the value of 1.94 eV with using hybrid B3LYP functional calculations,³⁸ and 1.95 eV with B3LYP/6-31G density functional level of theory calculations.⁵⁵ Therefore, the LDA method is also effective method to correctly characterize the electronic structures of the specific MoS₂ monolayer and C₂₀ fullerene.

Fig. 2 DOS for (a1–a4) pure MoS₂, C₆₀, C₂₆, and C₂₀; (b1–b3) MoS₂/C₆₀, MoS₂/C₂₆, and MoS₂/C₂₀, respectively. The Fermi level is set to zero energy.

The calculated DOSs of the above four heterostructures characterize the interface electronic properties and energy levels alignment in detail, as shown in Fig. 2(b1)–(b3) and Table 1. One can see that the each component of the combined DOS changes slightly compared to the individual DOSs (Fig. 2(a1)–(a4)), indicating that the interface interaction between monolayer MoS₂ and fullerene is indeed weak. The calculated band gaps of four heterostructures are 1.75, 0.41, and 0.85 eV, respectively, as listed in Table 1. The reduced band gaps can make the heterostructures absorb the most sunlight, and the photogenerated electron transfer from the valence band (VB) to the conduction band (CB) of the monolayer MoS₂/fullerene heterostructures becomes easier. Interestingly, the CB bottom is only consisted of states from C₆₀ (C₂₆, C₂₀) which greatly broadens the CB bottom of the monolayer MoS₂/fullerene heterostructures. It should be specially mentioned that when the band gap of C₆₀ is 5.08 eV (using GW approximations⁵⁶), the CB bottom of MoS₂/C₆₀ heterostructure is only consisted of states from MoS₂, thus forming a type-II staggered band alignment, which is in favor of the separation of photogenerated electron–hole pairs. However, the upper part of VB of the monolayer MoS₂/fullerene heterostructures shows complex types. For the MoS₂/C₂₀ heterostructures, the upper part of VB is formed from Mo 4d orbits, which can be more clearly seen from the electron density distributions of the highest occupied and lowest unoccupied levels (HOL and LUL), respectively, as shown in Fig. 3. More importantly, the MoS₂/C₂₀ heterostructures is type II (see Fig. 3c), namely, with both the valence and conduction band edges of C₂₀ below the corresponding MoS₂ counterparts, which significantly lowers the effective band gap of the heterostructures and facilitates efficient electron–hole separation. Fig. 3(a) clearly displays that the HOL is only composed of the C 2p orbits, while (b) is compose of the Mo 4d, mixing with small S 3p orbits. In photocatalysis, such band alignment is not beneficial for the separation of electron–hole pairs. Thus, the fullerene (C₂₀) would be a sensitizer for MoS₂. These results indicate that choosing appropriate fullerene (such as C₂₀) is especially critical to obtain high efficiency of electron–hole separation in the monolayer MoS₂/fullerene heterostructures.

Fig. 3 Maps of the charge density distributions of the lowest unoccupied (upper panel) and highest occupied levels (lower panel). (a–c) are for the MoS₂/C₆₀, MoS₂/C₂₆, and MoS₂/C₂₀ heterostructures, respectively. The isovalue is 0.006 e Å⁻³.

3.3. Charge density difference and mechanism analysis

The interaction between MoS₂ and fullerene implies a substantial charge transfer between the involved constituents. This can be visualized (as shown in Fig. 4) by three-dimensional charge density difference Δρ = ρ_{MoS2/fullerene} − ρ_MoS2 − ρ_fullerene, where ρ_{MoS2/fullerene}, ρ_MoS2 and ρ_fullerene are the charge densities of the heterostructures, the monolayer MoS₂ and fullerene in the same configuration, respectively. Due to the interaction, a very interesting charge redistribution at the monolayer MoS₂/fullerene heterostructures can be obviously observed, which is quite different from those of TiO₂/GR and Ag₃PO₄(100)/GR heterostructures.^57,58 A strong charge accumulation (green part in Fig. 4), mainly from the bottom-most C atoms of the fullerene and some from the charge loosed by S atoms along the z axis just under the C atom rings, is found just above the top-most S atoms. Moreover, the charge redistribution at the bottom-most C atoms and the top-most S atoms becomes more significant as the carbon number is decreased (comparing Fig. 4(a) with (d)), which is consistent with the shorter interface distance and stronger interaction. Note that the electron losses of different C atoms in the bottom-most and of different S atoms vary with their positions, owing to the different atomic arrangement. Most importantly, closer inspection to Fig. 4(d) reveals that the slightly interaction results into the negatively charged Mo atoms in the monolayer MoS₂. This indicates that some Mo atoms at basal planes, initially catalytically inert, would turn out to be active sites, which are beneficial to the improved photocatalytic performance of the monolayer MoS₂/fullerene heterostructures.

Fig. 4 3D charge density differences for (a) MoS₂/C₆₀, (b) MoS₂/C₂₆, (d) MoS₂/C₂₀ heterostructures. The green and wine red represent charge accumulation and depletion, respectively. The isovalue is 0.002 e Å⁻³. (c) Profile of the planar averaged self-consistent electrostatic potential for the MoS₂/C₆₀ (C₂₆, C₂₀) as a function of position in the z-direction. (e) Profile of the planar averaged charge density difference for the MoS₂/C₆₀ (C₂₆, C₂₀) as a function of position in the z-direction. The horizontal black (pink) dashed line from up to down indicates the location of the bottom C atoms, the top of the S atoms respectively.

To further analyze the charge transfer, part e of Fig. 4 plots the planar averaged charge density difference along the direction perpendicular to the MoS₂, which offers quantitative results of charge redistribution. The positive values represent electron accumulation, and negative values indicate electron depletion. It is clear that the largest efficient electron accumulation localized above the top-most S atoms is about 0.90 × 10⁻⁴ e Å⁻³ in the MoS₂/C₆₀ heterostructures, the largest local efficient electron depletion at the bottom-most C atoms is about −0.38 × 10⁻⁴ e Å⁻³, while in the MoS₂/C₂₆(C₂₀) heterostructures, the largest efficient electron accumulation localized above the top-most C atoms is about 0.68 × 10⁻⁴ e Å⁻³(1.02 × 10⁻⁴ e Å⁻³), and the largest local efficient electron depletion at the bottom-most S atoms is about −1.0 × 10⁻⁴ e Å⁻³ (−0.53 × 10⁻⁴ e Å⁻³). This indicates that the charge transfer is related to the interface distance or vdW interaction.

To quantitatively analyze the charge variation at the interface, the Mulliken population analysis of the plane-wave pseudopotential calculations has been performed on the fullerene, isolated monolayer MoS₂, and monolayer MoS₂/fullerene heterostructures. Fig. 5 shows the results of the Mulliken charge on different atoms, in which several typical values are presented. For the isolated monolayer MoS₂, the S and Mo atoms have a Mulliken charge of 0.01 and −0.02, respectively. The interfacial interaction leads to a markedly change of Mulliken charge of each atom in the MoS₂ of the heterostructures, while the Mo atoms become −0.03, −0.02, and −0.01 in the MoS₂/C₆₀, MoS₂/C₂₆ and MoS₂/C₂₀ heterostructures, respectively, indicating that the electron of Mo atoms of monolayer MoS₂ is reduced due to the coupling of fullerene. The top-most S atoms of monolayer MoS₂ have a Mulliken charge of 0.01, 0.03 (MoS₂/C₆₀), 0.02, 0.03 (MoS₂/C₂₆, MoS₂/C₂₀), respectively. The charge variation demonstrates that the top-most S atoms of the MoS₂/C₂₆ (C₂₀) heterostructures would lose more electrons than those in isolated monolayer MoS₂. This would improve the stability of monolayer MoS₂/fullerene photocatalyst, just as the case of MoS₂/GR.^52,59 Although the C atom in the fullerene has a Mulliken charge of approach zero electrons, those C atoms in the MoS₂/fullerene heterostructures have different Mulliken charges because not only the arrangement of atoms under various C atoms is different, but also the interface interaction is varied. For example, Fig. 5(b) shows that, in the MoS₂/C₆₀ heterostructures, the C atom has a Mulliken charge of −0.02. Those C atoms at the corresponding to positions in the MoS₂/C₂₆ heterostructures have a Mulliken charge of −0.04, −0.02, and 0.01, respectively, it is similar to the case of MoS₂/C₂₀ heterostructures. As a result, the charge distribution fluctuations appear at the bottom-most C atoms due to the interactions between monolayer MoS₂ and fullerene.

Fig. 5 Charge distribution maps of (a) MoS₂, (b) MoS₂/C₆₀, (c) MoS₂/C₂₆, and (d) MoS₂/C₂₀, with an isovalue of 0.7 e Å⁻³. Gray, green and yellow spheres represent C, Mo and S atoms, respectively.

The effective net charge from one constituent to another in these composites can be analyzed on the basis of the Bader method, as listed in Table 1. The effective net charge from one constituent to another in these heterostructures can be analyzed on the basis of the Bader method, as listed in Table 1. Some electrons transfer from C₂₀ (C₆₀) to MoS₂ in the MoS₂/C₂₀ (C₆₀) heterostructures, but it is in the opposite direction in the MoS₂/C₂₆ heterostructures. Moreover, the number of electrons transferred from C₂₀ to MoS₂ is larger than that from MoS₂ to C₂₆ (or from C₆₀ to MoS₂). For example, 0.04 (0.007) electron transfers from C₂₀ to MoS₂, whereas 0.01 from MoS₂ to C₂₆. To understand the origin of such an interface electron transfer in these heterostructures, work functions for the fullerene and monolayer MoS₂ are calculated by aligning the Fermi level relative to the vacuum energy level. They are calculated to be 4.5, 5.58, 4.45, and 5.35 eV for C₆₀, C₂₆, C₂₀, and monolayer MoS₂, respectively. The spontaneous interfacial charge transfer in the monolayer MoS₂/fullerene heterostructures can be simply rationalized in terms of the difference of these work functions. Moreover, the larger difference in work functions, the more charge transfer. For instance, the work function difference (0.8 eV) between C₂₀ and monolayer MoS₂ is larger than that (0.75 (0.23) eV) between C₆₀ (C₂₆) and monolayer MoS₂; thus, the transfer amount of charge in the former is bigger than in the former (0.04 vs. 0.007(0.01)).

The interface charge redistribution would surely alter the electrostatic potential distribution in whole system. To conduct quantitative analysis, the profile of the planar averaged self-consistent electrostatic potential for the monolayer MoS₂/fullerene heterostructures as a function of position in the z-direction is displayed in Fig. 4(c). Surprisingly, the electrostatic potential at the middle region of the interface is close to zero, due to charge redistribution. One can see that the monolayer MoS₂ is a typical S–Mo–S sandwich structure. The potential at the Mo atomic plane is higher than that at the fullerene, resulting into a large potential difference between the two constituents. The built-in potential would be one of the important factors for improving the photocatalytic activity and stability of monolayer MoS₂/fullerene photocatalyst. Under light irradiation, the separation and migration of photogenerated carriers at the interface will be affected by this built-in potential, i.e., the existence of a potential well can effectively hinder the recombination of photogenerated charge carriers in the monolayer MoS₂/fullerene heterostructures. Therefore, the photocatalytic activity and stability of MoS₂ photocatalyst could be improved by coupling fullerene.

3.4. Optical properties and photocatalytic water splitting

For many semiconductors (for example, TiO₂,^6,60 CeO₂,⁴⁶ SrTiO₃,⁴⁷ Ag₃PO₄ (ref. 61), and g-C₃N₄ (ref. 62)) with wide band gap, the incorporated GR sheet can extend their absorption edge to the vis-light region. Similarly, coupling fullerene with wide-band-gap semiconductors is also an effective strategy to extend the absorption edge and enhance the photocatalytic activity. To explore the influence of the coupled fullerene on the light absorption and photocatalytic performance of MoS₂, the imaginary part of the dielectric function and UV-vis absorption spectra of monolayer MoS₂ and the monolayer MoS₂/fullerene heterostructures are calculated, as shown in Fig. 6. For the monolayer MoS₂, the optical absorption occurs at about 1.89 eV,⁴⁴ which is attributed to the intrinsic transition from the Mo 4d to S 3p orbitals. As can be clearly seen from Fig. 6, the absorption intensity of MoS₂/fullerene heterostructures is enhanced significantly in the UV-vis light region. Miraculously the shape of absorption curve of the monolayer MoS₂/fullerene heterostructures depends on the carbon number of the fullerene (see Fig. 6(b)), indicating that the electronic transitions are different. In the region from 400 to 420 nm, the absorption of MoS₂/C₆₀ heterostructures is much higher than that of MoS₂/C₂₆ (C₂₀) heterostructures; whereas for the latter, interestingly, in the region from 530 to 700 nm, the absorption is much higher than that of MoS₂/C₆₀ heterostructures. These distinctions can be attributed to the difference of electronic structures, especially those near the band gap (Fig. 2 and 3). Thus, it is reasonable to conclude that coupling fullerene on the MoS₂ semiconductor would lead to the enhanced absorption in the UV-vis region, which is one of the most important factors to improve the photocatalytic activity of MoS₂.

Fig. 6 Calculated (a) imaginary part of the dielectric function and (b) absorption spectra of the MoS₂ (blue solid line), MoS₂/C₆₀ (red solid line), MoS₂/C₂₆ (rose red solid line) and MoS₂/C₂₀ (green solid line) heterostructures, respectively.

It is well known that the enhanced photocatalytic activity mainly derives from the efficient generation, separation and transfer process of the photoinduced electron–hole pairs, which strongly depends on the band structure of the composite photocatalyst. The redox ability of MoS₂/C₂₆ (C₂₀) heterostructures is assessed by determining the energy positions of valence and conduction bands with respect to the water oxidation/reduction potential level. However, the band edge energies of the CB could not be determined directly by electrochemical analysis. To give direct analysis, the CBM and VBM of MoS₂/C₂₀ compound can be estimated from the absolute electronegativity of the atoms and the band gap of the semiconductors by the following equations:^63,64

E_VB = X − E_e + 0.5E_g (4)

E_CB = E_VB + E_g (5)

here E_VB and E_CB are the VB and CB edge potentials, X is the electronegativity of the semiconductor (the geometric mean of the electronegativities of the constituent atoms), E_e is the standard electrode potential on the hydrogen scale (∼4.5 eV), and E_g is the band gap. The X values for monolayer MoS₂ and C₂₀ were 5.324 and 6.27 eV, respectively.

Fig. 7 displays the charge transfer pathway of the MoS₂/C₂₀ heterostructures under visible light irradiation. Clearly, the interactive band structure of the MoS₂/C₂₀ is favorable for the transfer of photogenerated charge carriers. The photoinduced electrons can transfer easily from the CB bottom of MoS₂ to that of C₂₀, while the holes left on the VB top of C₂₀ move in the opposite direction to the VB top of MoS₂. Thus, the photoinduced electrons and holes are separated efficiently, resulting in enhanced photocatalytic activity. Furthermore, the calculated VB and CB edge potentials are also shown in Fig. 7. In the monolayer MoS₂ the CB edge potential is −0.12 V, which is lower than that of H⁺/H₂ (0 eV), and the VB edge potential is 1.77 eV, which is higher than that of O₂/H₂O (1.23 V). Therefore, the monolayer MoS₂ has the ability to oxidize H₂O to produce O₂ or oxidation pollutants and can reduce H⁺ to H₂. The calculations consistent with theoretical results.^65,66 Whereas, in the MoS₂/C₂₀ heterostructures, the VB edge potential is 1.674 eV, the CB edge potential is 0.82 eV. Therefore, the MoS₂/C₂₀ heterostructures has the ability to oxidize H₂O to produce O₂ or oxidation pollutants but cannot reduce H⁺ to H₂. This indicates that the MoS₂/C₂₀ heterostructure would be a potential substitute for these expensive metal oxide photocatalysts, such as Ag₃PO₄,⁶⁷ to harness visible light to oxidize water as well as decompose organic contaminants.

Fig. 7 Calculated VB and CB potentials versus normal hydrogen electrode of monolayer MoS₂ and MoS₂/C₂₀ heterostructures. The carrier transfer and separation in the MoS₂/C₂₀ heterostructures is displayed.

4. Summary

In summary, using first-principles DFT calculations, we have studied changes in the electronic structure, charge transfer and photoactivity activity of MoS₂ in the presence of various non-covalently bound fullerenes. It is unveiled that the fullerene C₂₀ can act as a sensitizer in MoS₂ nanocomposites to improve the photocatalytic activity. Compared to monolayer MoS₂, the monolayer MoS₂/fullerene heterostructures has a smaller band gap (1.75, 0.41 and 0.85 eV), thus extending the absorption spectrum covering the entire visible region. The type-II, staggered, band alignment existing between monolayer MoS₂ and C₂₀ can promote the separation of photoinduced carriers, thus enhancing the photocatalytic activity. It is expected that C₂₀ acts as a sensitizer in other fullerene–MoS₂ nanocomposites. This strongly suggests possible applications in photocatalysis. These findings provide a theoretical basis for developing highly efficient MoS₂-based or fullerene-based photocatalysts.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 51471068 and 51271075).

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