First-Principles Investigations of Two-Sided Functionalised MoS₂ Monolayer

Abstract

In this computational study, we investigate two-sided functionalised MoS₂ with alkali metal atoms as donors and the organic acceptor molecule F₄TCNQ as an acceptor. Characterisation of functionalised MoS₂ involves first-principles calculations within the density functional theory (DFT) framework with a PBE+D3 scheme to investigate the electronic structure and quantify the charge transfer in the two-sided functionalised system in comparison to the one-sided functionalised counterpart. Within the two-sided functionalised systems, there is an increase in the overall charge on MoS₂ as a result of stronger electron transfer from the donor to the monolayer, additionally controlled by the ability of the acceptor to receive electrons.

1. Introduction

Over the past two decades, two-dimensional materials (2DMs) have garnered significant attention, owing to the versatile nature of their atomically thin crystalline layers obtained from the exfoliation of the bulk form [1,2,3]. These comprise an entire library of materials which are all beneficial in varied industrial applications, due to their excellent electronic and optical properties and the corresponding flexibility that originates from the modulation of such properties. Graphene is one of the most significant members of this class of compounds, however pristine graphene lacks an electronic band gap which limits its applications in a wide range of optoelectronic devices.

Transition metal dichalcogenides (TMDs) are another member of the family of 2DMs with the chemical formula MX₂, where M is a transition metal belonging to group IV (Ti, Hf), group V (Nb, Ta) or group VI (Mo, W) and X is a chalcogen (S, Se). Owing to their sizeable electronic band gaps [4,5], TMDs find a fascinating array of applications in optoelectronic devices [6], diodes [7], transistors [8], and semiconductor-integrated circuits [9]. MoS₂, in particular, undergoes a notable transition from an indirect to a direct electronic bandgap of 1.8 eV when moving from its bulk form to the thermodynamically stable 2H monolayer phase [10].

Research over the past two decades has shown that incorporating molecular functionalities into the system through covalent or non-covalent functionalisation schemes [11,12,13,14,15,16,17] allows for the control of the physicochemical and optoelectronic properties of the 2DMs. The phenomenon of doping, by means of surface adsorption of molecules, especially if they are strong electron donors or acceptors, has a direct impact on the electronic structure of the system as a result of changes in charge carrier density. Previous work in our group has extensively investigated this relationship, exploring the electronic and optical properties of both pristine and defective MoS₂ as a result of covalent functionalisation and effectively characterised the introduced adsorption states in the fundamental electronic band gap of MoS₂ [18,19]. The organic molecules 2,3,5,6-tetrafluoro-7,7’,8,8’-tetracyano-quinodimethane (F₄TCNQ) and 1,3,4,5,7,8-hexafluoro-tetra-cyano-napthoquinodimethane (F₆TCNNQ) are strong electron acceptors and pertinent examples in this regard. Former research has delved into the diverse adsorption phases involving F₄TCNQ as a molecular additive on coinage metals to modulate its work function [20,21,22], organic semiconducting polymers [23,24,25,26], graphene [27,28,29,30,31] and other 2DMs [32,33] to consequently influence the total charge carrier density of the pristine materials through controlled doping. The significance of the electronic nature of the substrate in determining the charge transfer mechanisms in van der Waals heterostructures comprising F₆TCNNQ and monolayer MoS₂ has been investigated in recent years through both experimental and computational methodologies [34,35]. Consequently, the charge transfer involving the molecular dopant in the heterostructure significantly influences the position of the Fermi level and the sample work function, with additional states induced by p-doping in the TMD. Furthermore, extensive research has been conducted in the past on the role of alkali metals [36,37] as suitable donors in graphite intercalation compounds (GIC) on account of flexible charge transfer from the intercalant to the host material [38,39,40].

In this study, we aim to perform first-principles calculations to investigate the electronic structure of two-sided functionalised MoS₂ and eventually quantify a possible charge transfer through the MoS₂ monolayer, from the donor to the acceptor side. For such calculations, the donor atoms of choice are alkali metals while the fluorinated tetracyanoquinone derivative F₄TCNQ is the acceptor molecule. The choice of alkali metals as donor atoms in our work is guided by the fact that they offer flexibility in controlling the charge transfer to MoS₂ based on their concentration and coverage per TMD unit cell. In the past, surface adsorption studies involving alkali metals as simplest possible donors on MoS₂ have been performed, and the extent of preferential binding has been significant in comparison to elements of other groups, however, these do not include the combined effects of an appropriate donor-acceptor pair in the system [41,42]. Similarly, while studies exist on the charge transfer mechanisms involving F₆TCNNQ on MoS₂ [34,35], it is particularly interesting to investigate the electronic structure of a model comprising F₄TCNQ and MoS₂. This workflow is based on the premise that charge transfer occurs from the donor to the acceptor side through the MoS₂ monolayer and consequently alters the electronic structure of the the TMD as a result of a two-sided functionalisation scheme.

2. Materials and Methods

2.1. Computational Details

All spin-polarised DFT calculations were performed with the Vienna ab initio simulation package (VASP) [43]. The interactions between the valence electrons and core ions were described using the projector augmented wave (PAW) formalism [44,45]. Implementing the frozen-core approximation, the electrons in the 4d and 5s orbitals of molybdenum, the 3s and 3p orbitals of sulphur, the 3s orbital of sodium, and the 2s and 2p orbitals of carbon, fluorine, and nitrogen were treated as valence electrons, while the core electrons provided an implicit screening of the ionic potential. A plane-wave basis set associated with kinetic energy values up to 500 eV was chosen. To determine the lattice constant of the MoS₂ monolayer, structure relaxations were performed with a suitable generalised gradient approximations (GGA)-type functional such as Perdew-Burke-Ernzerhof (PBE) [46] and the Brillouin zone was sampled along a $\mathrm{\Gamma }$-centred mesh of 12 × 12 × 1. The atomic positions within the systems were allowed to relax until the energy convergence criterion of 10⁻⁵ eV was achieved, and the norms of all forces acting on the atoms became smaller than 0.01 eV Å⁻¹. The blocked-Davidson algorithm was implemented for the electronic minimisation step while ionic relaxations were performed using a conjugate-gradient algorithm, and a Gaussian smearing scheme with a smearing width of 0.05 eV was applied. Furthermore, dispersive interlayer interactions were accounted for using Grimme’s semi-empirical D3 correction scheme [47] along with Becke-Johnson damping [48].

To test the quality of the applied PBE+D3 functional for the electronic band gap, we additionally performed a calculation with the hybrid functional Heyd–Scuseria–Ernzerhof HSE06+D3 [49] for the MoS₂ monolayer. Whereas for PBE+D3 the band gap was 1.66 eV, it increased to 2.13 eV with the HSE06+D3 treatment. Although the accuracy of the PBE functional with respect to the band gap is not good, its accuracy is sufficient for the study we want to perform. As we have to move to larger supercells to adsorb the acceptor molecule, a PBE+D3 treatment is a sensible balance between accuracy and computing resources.

The total binding energy values $E_{\mathrm{bind}}$ in the one-sided functionalised systems were defined by the following expression:

$$E_{\mathrm{bind}}=E({\mathrm{MoS}}_2+\mathrm{X})-E\left({\mathrm{MoS}}_2\right)-n{\mathrm{E}}_{\mathrm{x}}$$

(1)

where $E({\mathrm{MoS}}_2+\mathrm{X})$ denoted the total energy of the one-sided functionalised MoS₂ monolayer, $E\left({\mathrm{MoS}}_2\right)$ was the energy of pristine MoS₂ monolayer as an adsorbent and ${\mathrm{E}}_{\mathrm{x}}$ was the energy of the isolated adsorbate species with n indicating the number of adsorbate groups.

To accurately evaluate the density of states (DOS), the tetrahedron method of smearing with Blöchl corrections was applied, along with a damped velocity friction algorithm for electronic minimisation. The atomic charges in the system were determined using a Bader charge analysis scheme, following the algorithm provided by Henkelman et al. [50].

2.2. Model Construction

To investigate surface adsorption, a 4 × 4 supercell model of MoS₂ was relaxed using a 3 × 3 × 1 K-point sampling. The F₄TCNQ molecule, in its planar orientation, was placed 2.5 Å away from the 4 × 4 supercell of MoS₂ as a starting configuration. To prevent interactions within the periodic structure, a vacuum space of 20 Å perpendicular to the MoS₂ surface was maintained. Figure 1 illustrates the most stable configuration of the F₄TCNQ molecule adsorbed on MoS₂, with an associated binding energy of −1.14 eV at a distance of 3.35 Å from the monolayer.

Subsequently, a second model was constructed comprising an F₄TCNQ molecule with an identical planar orientation to a 6 × 6 supercell of MoS₂ and subjected to structural relaxations with a 3 × 3 × 1 K-point sampling. The modification in the size of the MoS₂ supercell resulted in a binding energy of −1.09 eV at a distance of 3.30 Å, therefore, demonstrating no significant impact of the size of the supercell on the characteristics of acceptor binding within the one-sided functionalised system.

3. Results and Discussion

3.1. One-Sided Functionalisation with Only Donors

In this subsection, we aim to explore the influence of alkali metal atoms on the electronic structure of the TMD monolayer. To find the most stable adsorption site of the donor atom, we determined the adsorption energy of a Na atom at various sites on a monolayer of MoS₂ (for optimised structures, see Figure 2).

The negative binding energy values presented in

Table 1. Calculated properties of one-sided functionalised MoS₂ with different alkali metal atoms: adsorption site on MoS₂, total binding energy (E_bind) in eV, distance between the alkali metal atom and the MoS₂ monolayer (d_(metal-ML)) in Å and charge transfer occurring from the alkali metal to MoS₂ in electrons.

System	Adsorption Site	Ebind (eV)	d(metal-ML) (Å)	Charge Transfer (e)
1Na-MoS2	M	−1.46	2.73	0.85
1Na-MoS2	S	−1.05	2.60	0.79
1Na-MoS2	H	−1.44	2.74	0.84
1Na-MoS2	B	−1.46	2.74	0.84
1Li-MoS2	M	−1.97	2.35	0.87
1K-MoS2	M	−1.84	3.08	0.89
1Rb-MoS2	M	−1.87	3.23	0.90
1Cs-MoS2	M	−1.90	3.40	0.90

are all greater than 1 eV in magnitude, and therefore, representative of chemisorption. The hollow site above a Mo atom, denoted as the M site, was identified as the most favoured adsorption site. The donor ability of a sodium atom in comparison to other alkali metals, is shown in Figure 3 and Table 1. The charge transfer in the system was quantified by a two-step approach. The systematic Bader partitioning technique of dividing the charge density grid into Bader volumes by zero-flux surfaces, returns values for constituent atomic charges enclosed within these Bader volumes. These atomic charges are then subtracted from the number of valence electrons in the corresponding neutral atoms to yield net atomic charges as listed in Table 1.

The coverage of the donor atoms was then systematically increased with respect to the MoS₂ monolayer (Figure 4), and the outcomes are presented in

Table 2. Calculated properties of one-sided functionalised MoS₂ with a varied coverage of donor atoms: total binding energy (E_bind) in eV, the binding energy per Na atom (E_bind/Na) in eV, the average distance between the Na atom and the MoS₂ monolayer (d_(Na-ML)) in Å and average charge transfer occurring from each Na atom to MoS₂ in electrons.

System	Ebind (eV)	Ebind/Na (eV)	d(Na-ML) (Å)	Charge Transfer (e)
1Na-MoS2	−1.46	−1.46	2.73	0.85
2Na-MoS2	−2.62	−1.31	2.74	0.67
4Na-MoS2(a) *	−4.60	−1.15	2.80	0.51
4Na-MoS2(b) †	−4.92	−1.23	2.67	0.79
8Na-MoS2	−10.24	−1.28	2.82	0.46
16Na-MoS2	−20.64	−1.29	2.93	0.36
32Na-MoS2	−39.36	−1.23	2.88	0.18

* The average distance between two Na atoms is 3.16 Å; ^† The average distance between two Na atoms is 6.36 Å.

. While comparing the observations from a Bader charge analysis across different models, it was evident that the system denoted as 4Na-MoS₂(b), comprising the spaced-out arrangement of four donor atoms on MoS₂ demonstrated the most substantial average charge transfer per donor atom. In this system, each Na atom donated 0.79 electrons, resulting in a total transfer of 3.16 electrons to the monolayer. As the donor coverage was further increased, there was favourable adsorption indicated by the binding energy per Na atom, however, there was a decrease in the average charge transfer from each donor atom. Furthermore, an additional layer of Na atoms was introduced into the 16Na-MoS₂ system, resulting in donor atoms being distributed across two layers in both the M and H sites in the 32Na-MoS₂ system. Concerning the initial layer of Na atoms, the second layer showed a reduced binding affinity of −1.17 eV per Na atom and a nominal average charge transfer of 0.18 electrons per Na atom to MoS₂. The interlayer distance of 3.65 Å between the Na atoms in 32Na-MoS₂ is close to the nearest neighbour distance of 3.71 Å for Na metal crystallising in a BCC lattice [51]. This is an indication that the second layer contributed to a minimal charge transfer to MoS₂ and retained an essentially metallic character. The reduced binding affinity and charge transfer in 32Na-MoS₂ indicate that the extent of donor functionalisation is reliant on both the electron-donating capacity of the Na atoms and the acceptor characteristics of MoS₂.

For a more comprehensive understanding of the electronic structure of the functionalised systems, the projected DOS along elements is illustrated in Figure 5 and compared to that of pristine MoS₂. Upon donor functionalisation, the DOS was altered, and there was an upward shift in the Fermi level towards the conduction band of MoS₂. This was due to the generation of electronic states within the fundamental band gap of the TMD. These donor states, attributed to mobile charge carriers, emerged at the edge of the conduction band as a result of n-doping in the system. Upon the adsorption of a single Na atom, the Fermi level shifted to the bottom of the conduction band with gradual filling of the conduction band as the donor coverage was increased to accommodate up to 32 Na atoms. The intrinsic direct band gap nature of MoS₂ remained unaffected. However, it was evident that electrons were transferred from the valence 3s orbitals of the Na atom to the 4d orbitals of Mo, making them suitable donors in this case. With a higher coverage of donor atoms as in 8Na-MoS₂ and 16Na-MoS₂, the DOS became asymmetric in alpha and beta spins. This was further observed in small magnetic moment values of approximately −0.1 ${\mathsf{\mu }}_B$ and −0.01 ${\mathsf{\mu }}_B$ on Mo and S respectively, while the values ranged between 0.01 ${\mathsf{\mu }}_B$ and 0.05 ${\mathsf{\mu }}_B$ for the Na atoms in 16Na-MoS₂. Additionally, the metallic character of the second layer of the Na atoms in 32Na-MoS₂ was observed in its corresponding DOS.

3.2. Two-Sided Functionalisation with Both Donor and Acceptor

This section presents an analysis of the characteristics of a model consisting of two-sided functionalised MoS₂, aiming for a precise comparative evaluation with its one-sided functionalised counterpart. Figure 6 depicts the most stable configuration of a 4 × 4 MoS₂ supercell with two-sided functionalisation. The system, denoted as F₄TCNQ-MoS₂-4Na, in the upper section of Figure 6 comprises the organic acceptor molecule F₄TCNQ on one side and 4 Na atoms on the other side in their spaced-out arrangement, with the same starting configuration as in the system denoted as 4Na-MoS₂(b). In the lower section of Figure 6, the extent of donor atom coverage was increased to accommodate 8 Na atoms to build a two-sided functionalised model denoted as F₄TCNQ-MoS₂-8Na.

To evaluate the adsorption behaviour in the two-sided functionalised models, the binding energy $E_{\mathrm{bind}}$ was calculated using the following expression:

$$E_{\mathrm{bind}}=E\left({\mathrm{F}}_4\mathrm{TCNQ-Mo}{\mathrm{S}}_2\mathrm{-xNa}\right)-\left(E(\mathrm{xNa-Mo}{\mathrm{S}}_2)+E({\mathrm{F}}_4\mathrm{TCNQ})\right)$$

(2)

where $E\left({\mathrm{F}}_4\mathrm{TCNQ-Mo}{\mathrm{S}}_2\mathrm{-xNa}\right)$ was the energy of the two-sided functionalised system with x denoting the number of Na atoms, the energy of the one-sided functionalised MoS₂ with x Na atoms was denoted as $E\left(\mathrm{xNa-Mo}{\mathrm{S}}_2\right)$ and $E\left({\mathrm{F}}_4\mathrm{TCNQ}\right)$ was the energy of the isolated F₄TCNQ molecule. Thus, the value of $E_{\mathrm{bind}}$ in this case, particularly elucidated the binding affinity of the one-sided donor functionalised MoS₂ with 4 or 8 Na atoms to the acceptor molecule F₄TCNQ.

The results listed in

Table 3. Calculated properties of two-sided functionalised MoS₂: binding energy (E_bind) in eV, the average distance between the F₄TCNQ molecule and the MoS₂ monolayer (d_(F4TCNQ-ML)) in Å and the average charge transfer occurring from F₄TCNQ in electrons.

System	Ebind (eV)	d(F4TCNQ-ML) (Å)	Charge Transfer (e)
F4TCNQ-MoS2	−1.14	3.35	−1.07
F4TCNQ-MoS2-4Na	−2.05	3.24	−1.22
F4TCNQ-MoS2-8Na	−1.77	3.21	−1.22

suggest preferential binding of one-sided donor functionalised MoS₂ with varying donor coverage to the acceptor molecule. The value of $E_{\mathrm{bind}}$ in the two-sided functionalised MoS₂ increased to −2.05 eV from −1.14 eV, as in the one-sided acceptor functionalised system, which is further corroborated by the reduced distance between the TMD and the F₄TCNQ molecule. On the addition of 8 Na atoms in the two-sided functionalised model, the value of $E_{\mathrm{bind}}$ was reduced to −1.77 eV. The acceptor molecule moved slightly closer to MoS₂ while the nearest Na atom moved farther away to 2.82 Å away from the monolayer in F₄TCNQ-MoS₂-8Na, in comparison to 2.69 Å in F₄TCNQ-MoS₂-4Na. The electron transfer in the two-sided functionalised MoS₂ was only slightly higher as compared to the acceptor functionalised MoS₂ which indicated that the acceptor ability of F₄TCNQ constrained the extent of charge transfer in the system. The overall charge on the MoS₂ monolayer in the F₄TCNQ-MoS₂ system was 1.07 holes due to the acceptor properties of F₄TCNQ. With the incorporation of 4 donor atoms as in the two-sided functionalised system, the total charge transferred from the 4 Na atoms amounted to 3.12 electrons, consequently increasing the overall charge on MoS₂ to 1.90 electrons and switching it from a p-doped to an n-doped material. Furthermore, with an increased coverage of donor atoms as in F₄TCNQ-MoS₂-8Na, the charge transfer from each Na atom was reduced to 0.50 electrons, amounting to a total charge transfer of 4 electrons from 8 Na atoms to MoS₂. Thus, the overall charge on MoS₂ in this system increased to 2.78 electrons. This confirmed the role of the Na atoms in facilitating additional charge transfer from MoS₂ to F₄TCNQ, however, only to a small extent as it is limited by the acceptor ability of F₄TCNQ.

Figure 7 depicts a contour plot of charge density difference $\mathrm{\Delta }\rho$ in the two-sided functionalised systems. The value of $\mathrm{\Delta }\rho$ in the two-sided functionalised systems was calculated with the following approach:

$$\mathrm{\Delta }\rho =\rho \left({\mathrm{F}}_4\mathrm{TCNQ-Mo}{\mathrm{S}}_2\mathrm{-xNa}\right)-(\rho \left(\mathrm{Mo}{\mathrm{S}}_2\right)+\rho \left(\mathrm{xNa}\right)+\rho \left({\mathrm{F}}_4\mathrm{TCNQ}\right))$$

(3)

where $\rho \left({\mathrm{F}}_4\mathrm{TCNQ-Mo}{\mathrm{S}}_2\mathrm{-xNa}\right)$ referred to the charge density of the two-sided functionalised systems, $\rho \left(\mathrm{Mo}{\mathrm{S}}_2\right)$ was the charge density of pristine MoS₂, $\rho \left(\mathrm{xNa}\right)$ and $\rho \left({\mathrm{F}}_4\mathrm{TCNQ}\right)$ referred to that of the individual donor and acceptor components, respectively with x denoting 4 or 8 Na atoms.

This diagram illustrates a region of pronounced charge depletion around the Na atoms and a charge accumulation over the F₄TCNQ molecule with a dependence of $\mathrm{\Delta }\rho$ on the coverage and arrangement of sodium atoms on MoS₂. In F₄TCNQ-MoS₂-4Na, the charge transfer with respect to the acceptor molecule was located more uniformly at the centre of the monolayer while in F₄TCNQ-MoS₂-8Na the charge was transferred across different regions of MoS₂. Thus, the S atoms in the monolayer proximal to F₄TCNQ had different charge densities in both of the two-sided functionalised models which led to an overall larger positive charge on MoS₂ in F₄TCNQ-MoS₂-8Na. Furthermore, in the presence of 4 Na atoms, a larger extent of negative charge transfer to the $\pi$-system and positive charge transfer to the $\sigma$-system in the acceptor molecule was observed, in comparison to the system with 8 Na atoms. This indicated that the different coverage and arrangement of the Na atoms is able to influence both the extent and position of charge transfer between MoS₂ and F₄TCNQ. Further investigations, including a detailed analysis of the occupied and unoccupied orbitals of isolated F₄TCNQ and their changes induced by adsorption, will be necessary to elucidate the intricate interplay between donor coverage and arrangement and the resultant charge distribution within the acceptor molecule.

Figure 8 illustrates the projected DOS in the one-sided and two-sided functionalised systems. As a result of electron transfer from MoS₂ to F₄TCNQ, additional acceptor states belonging to the C atom appeared within the intrinsic band gap of the system above the valence band edge. This further corroborated electrons being transferred from MoS₂ to the unoccupied orbitals of F₄TCNQ. In the two-sided functionalised systems, additional donor states appeared at the lower edge of the conduction band due to the presence of the Na atoms in the systems. With up to 8 Na atoms in the system, more donor states were introduced into the electronic band gap of MoS₂ and the Fermi energy shifted further up to the conduction band by about 0.2 eV. This demonstrated the change in electronic properties of the TMD monolayer on functionalisation, since MoS₂ was p-doped in the acceptor functionalised system and n-doped on two-sided functionalisation. The DOS in the two-sided functionalised systems displayed an antisymmetry in states belonging to the C atom. To explain this behaviour, we performed spin-restricted DFT calculations on F₄TCNQ-MoS₂-4Na and the total energy in this case was higher by 50 meV than that of the spin-unrestricted calculations (Figure 8d). Furthermore, the spin-projected DOS in F₄TCNQ-MoS₂-4Na was visualised to indicate a more prominent $\alpha$-spin character on F₄TCNQ as compared to the $\beta$-spin. The antisymmetric characteristic of the DOS for both of the two-sided functionalised systems was represented by varying values of positive and negative magnetic moments on the C atoms in the acceptor molecule. Finite values of magnetic moments on F₄TCNQ were observed in these systems, however, further investigation is required to characterise these effects.

4. Conclusions

Our first-principles calculations indicated a reasonably large extent of charge transfer to both one-sided and two-sided functionalised MoS₂ on account of n-doping due to donor adsorption. This was investigated by increasing the coverage of Na atoms on the MoS₂ monolayer and comparing the preferential binding in each system. The charge transfer in such one-sided donor functionalised systems was dependent on both donor coverage and the electron accepting properties of MoS₂. Our study was then extended to two-sided functionalised MoS₂ with F₄TCNQ as acceptor and two differing coverages of donor atoms in the systems. The overall charge transfer to the acceptor molecule increased from 1.07 holes to 1.22 holes, with the addition of Na atoms in the system. However, this was limited by the acceptor capacity of F₄TCNQ, as an increased incorporation of Na atoms elevated the electronic charge within the MoS₂ monolayer without affecting the charge on the acceptor. These investigations additionally demonstrated that the charge density on F₄TCNQ could be modulated by varying the coverage and arrangement of donor atoms in the two-sided functionalised systems. To summarise, the overall charge on the MoS₂ monolayer was increased as a result of stronger electron transfer from the donor to the acceptor side within a two-sided functionalisation scheme.