The Modulation Effect of MoS₂ Monolayers on the Nucleation and Growth of Pd Clusters: First-Principles Study

Abstract

The geometries, electronic structures, adsorption, diffusion, and nucleation behaviors of Pd_n (n = 1–5) clusters on MoS₂ monolayers (MLs) were investigated using first principles calculations to elucidate the initial growth of metal on MoS₂. The results demonstrate that Pd clusters can chemically adsorb on MoS₂ MLs forming strong Pd–S covalent bonds with significant ionic character. We investigated the initial growth mode of Pd clusters on MoS₂ monolayers and found that Pd_n clusters tend to adopt pyramid-like structures for n = 4–5 and planar structures lying on MoS₂ substrates for n = 1–3. It can be explained by the competition between adsorbate–substrate and the intra-clusters’ interactions with the increasing coverage. Compared with pristine MoS₂ MLs, the work function was reduced from 5.01 eV upon adsorption of Pd monomer to 4.38 eV for the case of the Pd₅ clusters due to the charge transfer from Pd clusters to MoS₂ MLs. In addition, our calculations of the nucleation and diffusion behaviors of Pd clusters on MoS₂ MLs predicted that Pd is likely to agglomerate to metal nanotemplates on MoS₂ MLs during the epitaxial stacking process. These findings may provide useful guidance to extend the potential technological applications of MoS₂, including catalysts and production of metal thin films, and the fabrication of nanoelectronic devices.

1. Introduction

In recent years, two-dimensional (2D) layered transition metal dichalcogenides (TMDs), particularly MoS₂, exhibiting excellent electronic and optical properties, have drawn great attention due to their potential applications in flexible nanoelectronics, photonic devices, memory devices, etc. [1,2,3,4]. A series of experimental and theoretical studies have confirmed that MoS₂ monolayers (MLs) decorated with metal nanoparticles (NPs) could potentially extend its functionalities as novel catalysts, spintronic devices, and thermoelectric and photoelectric materials, which is owing to the unique size-dependent properties of metal nanoparticles [5,6,7,8]. For instance, Chen et al. [5] reported the metal clusters (Pd, Pt, and Ag) supported on MoS₂ MLs tend to display excellent electrocatalytic activity compared to those on graphene. Fu et al. [6] found that Au nanoparticles on two-dimensional MoS₂ nanosheets can be used to fabricate an attractive alternative photoanode for efficient photoelectron chemical miRNA detection. Recently, Burman and co-workers [7] successfully fabricated Pt decorated MoS₂ nanoflakes, and further confirmed its potential application as the sensing layer of an ultrasensitive resistive humidity sensor. Besides, Li et al. [9] reported that Au NPs imposed remarkable p-doping effects onMoS₂ transistors, which implied that a controllable method of metal NP decoration provides an effective way to design future optoelectronic devices. Furthermore, Guo et al. [10] used 2D MoS₂ effectively decorated with Au nanoparticles to improve the performance of flexible thermoelectric materials, which may become an alternative material for wearable thermoelectric devices. In addition, the MoS₂–Pd nanoparticle hybrid structure was used to engineer the oxide/electrode interface of hafnium oxide (HfO_x)-based metal oxide-based, resistive random-access memory, which has huge potential application in the field of data storage and wearable electronics [11].

Meanwhile, both experimental and theoretical studies have revealed that the surfaces of MoS₂ MLs with graphene-like structures can play an active role as a host surface for the clusterization and nucleation characteristics of transition metal atoms. Huang and co-workers [12] demonstrated that MoS₂ nanosheets can be used to direct the epitaxial growth of Pd, Pt, and Ag nanostructures by wet-chemical synthetic method under ambient conditions in experiments. Song et al. [13] studied the nucleation and growth dynamics of Au nanoparticles on MoS₂ nanoflakes by in situ liquid-cell transmission electron microscopy (TEM). In order to design more efficient and less expensive catalysts, the evolution of morphology and epitaxial growth of Pt NPs on MoS₂ (001) surfaces was systematically analyzed by density functional theory study [14]. Recently, Jiang and co-workers [15] proposed that 2D Fe/MoS₂ heterostructures constructed by deposition of Fe atoms on MoS₂ exhibits robust half-metallic magnetism and possesses robust ferromagnetic and half-metallic properties with 100% spin-filter efficiency based on first-principles calculations. Similarly, Cooley et al. [16] showed that graphene/MoS₂ heterostructures can be used as templates to grow stable clusters lying planar to the surface, as well as to prepare monoatomic layers of ordinary metals.

It is also known that the nature of metal–semiconductor interfaces plays a more important role than MoS₂ MLs themselves in MoS₂-based optoelectronics and nanoelectronics [17]. Motivated by the high work function of Pd and the small lattice mismatch of Pd and MoS₂, Pd can be used as the p-type metal contact on MoS₂ to modify the Schottky barrier height (SBH) and the charge carrier injection rates. Fontana et al. [18] have observed that MoS₂-based transistors show hole-doping and electron-doping behaviors when Pd and Au are used for source and drain contacts, respectively, and the formation of Schottky junctions at contact interfaces remarkably induced a clear photovoltaic effect. Later work highlighted an epitaxial growth mode of Pd deposition on MoS₂ bulk surface and a strong band bending effect and high contact resistance were observed for the Pd/MoS₂ interface [19]. Although metal contact engineering is a very useful avenue for building high-performance MoS₂-based devices, there is little research on how MoS₂ MLs modulate the nucleation and growth processes of Pd NPs and which further explores the nature of Pd_n/MoS₂ interfaces. Above all, it is crucial to explore the formation and diffusion properties of Pd clusters on MoS₂ MLs and to investigate the modulation effect of MoS₂ surfaces on the growth of Pd_n clusters for the sake of improving deposition technological applications at the device level.

In this work, we aim to systematically investigate the adsorption behaviors including geometries, relative stability, and electronic properties of Pd_n (n = 1–5) clusters on MoS₂ MLs, and the diffusion behaviors of Pd_n (n = 1–5) clusters on MoS₂ are discussed using density functional theory (DFT) calculations. The rest of the paper is organized as follows. In Section 2 we briefly describe the calculation method used. In Section 3 we report our results and discussions including the structures, relative stabilities, and the electronic properties of Pd clusters supported by MoS₂ MLs. Meanwhile, in order to better understand the role of MoS₂ surfaces during the nucleation of Pd clusters, the diffusion characteristics of Pd_n (n = 1–5) clusters are discussed in detail. The conclusions are given in the last section.

2. Computational Details

The geometries, electronic structures, and diffusion characters of Pd_n (n = 1–5) clusters absorbed at MoS₂ MLs were carried out with the first-principles calculations based on density functional theory (DFT) under the generalized gradient approximation (GGA) as implemented in the VASP code [20,21]. A plane wave basis set with the projector-augmented plane wave (PAW) was performed to describe the ion–electron interaction [22]. The plane-wave cutoff corresponding to a kinetic energy of 450 eV was adopted. The k-point meshes were generated according to the Monkhorst–Pack scheme [23] and 9× 9 × 1 mesh was used to sample the supercell which consisted of 4 × 4 MoS₂ units in the calculations. In order to prevent the interactions between neighboring slabs, a thick vacuum layer of more than 15Å was adopted in a direction perpendicular to the surface. During structural relaxation, all the atomic coordinates (including Mo, S, and Pd) were fully relaxed until the Hellmann–Feynman forces were smaller than 0.01 eV/Å.

To describe quantitatively the energetic trends of adsorbed Pd clusters on the MoS₂ ML and to further explore the modulation of MoS₂ substrate on the growth mechanism of Pd clusters, we introduce adsorption energy E_A, binding energy E_B, and intra-cluster binding energy E_IB, which are defined as the following:

(1)

The adsorption energies E_A,

$$E_A=\left[E_{{\mathrm{MoS}}_2}+E_{{\mathrm{Pd}}_n}-E_{tot}^{{\mathrm{Pd}}_n/{\mathrm{MoS}}_2}\right]/n,$$

(1)

where $E_{tot}^{{\mathrm{Pd}}_n/{\mathrm{MoS}}_2}$ and $E_{{\mathrm{MoS}}_2}$ are the total energies of the MoS₂ monolayer with and without Pd_n clusters, $E_{{\mathrm{Pd}}_n}$ is that of the floating Pd_n clusters consisting of n Palladium atoms. E_A can be used to describe quantitatively the strength of the adsorbate–substrate interaction.

(2)

The binding energy E_B,

$$E_B=\left[E_{{\mathrm{MoS}}_2}+n{E}_{\mathrm{Pd}}-E_{tot}^{{\mathrm{Pd}}_n/{\mathrm{MoS}}_2}\right]/n,$$

(2)

where $E_{\mathrm{Pd}}$ is the total energy of an isolated Palladium atom in a cubic supercell of 20 Å × 20Å × 20Å. The binding energy E_B reflects the relative stability of the Pd_n clusters supported by the MoS₂ ML.

(3)

The intra-cluster binding energy E_IB,

$$E_{IB}=E_B-E_A,$$

(3)

which could qualitatively reflect the strength of the Pd–Pd interactions. In order to compare directly, all considered energy terms were normalized with respect to the number of Pd atoms, given per adatom.

To get insight to the nucleation mechanism and growth mode of Pd clusters, we also calculated the diffusion properties of Pd_n (n = 1–5) clusters supported by the MoS₂ ML. The diffusion barrier and transition states were determined from the minimum energy pathway by employing the climbing-image nudged elastic band (NEB) method [24,25]. All geometries were optimized until the maximum force in every degree of freedom was less than 0.005 eV Å.

3. Results and Discussions

3.1. Geometries and Stabilities for Pd_n (n = 1–5) Adsorbed at MoS₂ ML

In order to understand the adsorption properties of Pd_n (n =1–5) clusters and explore the nucleation mechanism and initial growth of Pd nanoparticles on MoS₂ MLs, it is essential to identify the structural and electronic properties of pure MoS₂ ML for comparison. Figure 1a shows the top and side view of a 4 × 4 supercell of the MoS₂ ML; the calculated results show that the thickness of the MoS₂ ML was 3.14 Å and the bond length of the S–Mo was 2.84 Å, which is consistent with previous studies [26,27]. Besides, we calculated the band structures of the MoS₂ ML as shown in Figure 1b. The calculated results indicate that the MoS₂ ML presented semiconducting character with a direct gap of 1.75 eV at the K point, which is in good agreement with the previous theoretical results of 1.70 eV [28] and experimental results of 1.80 eV [29].

We first investigated the geometries and adsorption properties of a single Pd adatom on the MoS₂ ML. For the case of Pd monomer, we considered the binding of Pd on four high-symmetry sites: the hollow (H) site at the center of a hexagon, the top site directly above Mo (t-Mo) and S (t-S), and the bridge (B_S–S) site at midpoint of the S–S bond, as shown in Figure 1a. It is known that the larger the adsorption energy E_A, the stronger the interaction between the adsorbate and substrate.

Table 1. The structural parameters (Å) and calculated adsorption energies E_A (eV) for Pd monomer adsorbed at four high-symmetry sites of MoS₂ monolayer.

Site	dPd–Mo	dPd–S	dMo–S	hPd-sub	EA
t-Mo	2.83	2.34	2.40	1.33	2.16
H	3.64	2.42	2.43	1.59	1.79
t-S	4.18	2.18	2.43	2.19	1.59
BS-S	–	–	–	–	–

lists the structural parameters and adsorption energies for all considered adsorption configurations of Pd monomer adsorbed at the MoS₂ ML. The calculated results show that the t-Mo site with the adsorption energy of 2.16 eV was the most energetically favorable location, which is consistent with previous studies [26,30]. The Pd monomer adsorbed at the t-S and H sites were 0.57 and 0.37 eV, respectively, less stable than that of the t-Mo adsorption configuration. Our calculated results show that Pd monomer located at the B_S-S site finally relaxed to the t-Mo configuration, which indicates that Pd monomer adsorbed at the B_S-S site was unstable. As summarized in Table 1, Pd bonds to the surrounding S atoms with a bond length of 2.34, 2.42, and 2.18 Å for the considered adsorption configurations of t-Mo, t-S, and H, respectively, which are comparable with those in two types of PdS₂ monolayer with values of 2.34 and 2.40 Å [31]. The distances between Pd and nearest neighboring Mo are 2.34, 2.30, and 2.26 Å for three considered configurations, which are mainly resulting from the different adsorption sites. The Pd monomers located at 1.33, 1.59, and 2.19 Å higher than the underlying MoS₂ surface for three considered adsorption configurations, which is consistent with the decreased trend for the calculated adsorption energies from the t-Mo to t-S configuration.

We have chosen several initial configurations to search the most stable configurations of Pd_n (n = 2–5) clusters adsorbed at the MoS₂ ML, which is shown in Figure 2. The calculated structural parameters and adsorption, binding, and intra-cluster binding energies for the lowest energy configurations of Pd_n (n = 1–5) adsorbed on the MoS₂ ML are summarized in

Table 2. Calculated distance between Pd clusters and MoS₂ surface (d_Pd-substrate), bond length of Pd–S (d_Pd–S), Pd–Pd distance (d_Pd–Pd), adsorption energy E_A, binding energy E_B, and intra-cluster binding energy E_IB for the lowest energy Pd_n (n =1–5) configurations on the MoS₂ ML. The units of structural parameters and energies are Å and eV, respectively.

Configurations	Pd	Pd2	Pd3	Pd4	Pd5
	t-Mo	t-(Mo)2	t-(Mo)3-S	t-(Mo)4-S	t-(Mo)5-h
dPd-substrate	1.33	1.42	1.49	1.46	1.44
dPd-S	2.34	2.31, 2.35, 2.42	2.28, 2.46	2.43, 3.49	2.33, 2.42, 2.47, 2.51
dPd-Pd	–	3.05	2.94	2.67, 3.02	2.63, 2.74, 3.05, 3.20
EA	2.16	1.84	1.44	0.93	0.86
EB	–	2.21	2.29	2.36	2.38
EIB	–	0.37	0.85	1.43	1.52

. The most preferential configuration of Pd dimer adsorbed at the MoS₂ ML was that two Pd atoms both adsorbed at the top of Mo, and they were separated by 3.05 Å, which was smaller than the calculated lattice constant of MoS₂ ML, as shown in Figure 3a. For the cases of Pd₃ cluster adsorbed at MoS₂ ML, the calculated results show that the t-(Mo)₃-S configuration with the largest adsorption energy of 1.44 eV presents higher stability than the t-(Mo)₃-h configuration due to the extra binding of S1 atom, in which Pd trimer stands in a plane parallel to the MoS₂ surface. Besides, it is not surprising that the considered t-(Mo)₃-L with three Pd atoms in a line adsorbed at the top of Mo is higher in energy than the triangular islands because of the decrease in the number of intra Pd–Pd bonds. The average bond length of Pd–Pd and the height of Pd₃ cluster above the MoS₂ surface are 2.94 and 1.49 Å, respectively. The Δ–(Mo)₃ structure where two Pd atoms were located at the t-Mo sites and the third one was located at the bridge site of the two Pd atoms was also considered for the case of the Pd₃ cluster. However, different from the case of Pt₃ on MoS₂ ML, such vertical configuration is unstable as it is about 0.65 eV less stable than the t-(Mo)₃-S configuration. For the case of Pd tetramers adsorbed at MoS₂ surface, we considered three possible configurations, including aplanar-(Mo)₄ (four Pd atoms located at the t-Mo site, not shown here), pyramid-like t-(Mo)₄-h, and t-(Mo)₄-S configurations. The computed results show that the most favorable structure is t-(Mo)₄-h (shown in Figure 2c) for Pd tetramer adsorbed at the MoS₂ ML, implying the growth mechanism transitions from a two-dimensional (2D) to a three-dimensional (3D) mode from the formation of Pd₄ cluster. Based on the most stable configuration of Pd₄ tetramers supported by the MoS₂ ML, we considered three initial geometries for Pd pentamer. After full structural optimization, the most stable structure was asquare pyramid t-(Mo)₅, shown in Figure 2d, which could be obtained by adding one additional Pd atom adsorbed at a neighboring t-Mo site with respect to the t-Pd₄-h configuration.

From the above calculations, it is clear that the palladium clusters are energetically preferred to lying planar to the surface for the initial growth of Pd_n clusters on MoS₂ ML at very low coverage (from Pd₁ to Pd₃). With increasing the coverage, the Pd_n clusters immediately form islands clusters, such that the morphology of t-(Mo)₄-h and t-(Mo)₅-h are the most stable configurations for Pd tetramer and pentamer, respectively. Therefore, under situations dominated by the thermodynamic effects, the clusters with planar structures may be expected to only appear in the very early growth stage and the size of these clusters are very small (e.g., Pd₂ and Pd₃), which is immediately followed by the Vomler–Weber growth mechanism.

In our previous study on the initial growth of Pd_n/NiAl(110) [32], we reported that small-size Pd_n (n = 1–5) clusters favor the planar structures on the NiAl(110) surface, which was explained by the stronger interaction between Pd_n clusters and NiAl substrate than the interaction among Pd adatoms in clusters. In order to explore the modulation of MoS₂ substrate on the growth mechanism of Pd_n clusters, it is crucial to understand the evolutions of the metal–metal and metal–slab interactions with the increase of cluster size. We summarize the adsorption, binding, and intra-cluster binding energies as well as structural parameters for the most stable structures of Pd_n (n = 1–5) adsorbed on the MoS₂ ML in Table 2. It was found that the adsorption energies, E_A, decreased from 2.16 to 0.86 eV when the Pd coverage increased from Pd₁ to Pd₅ clusters, which indicates the strength of the interactions between the Pd_n (n = 1–5) clusters and MoS₂ gradually weakened. The results are reasonable since the height of Pd clusters above MoS₂ increases from Pd monomer to Pd₃ cluster with planar structures. For the case of pyramid-like structures, Pd₅ waslocated at 0.03 Å higher than that of Pd₄ above the MoS₂ ML as listed in Table 2; however, the additional Pd–Pd bonds weakened the Pd–S bonds resulting in less stability of Pd₅ cluster. The binding energy, E_B, that reflects the relative stability of the Pd_n (n = 1–5)/MoS₂ system, gradually increased from 2.21 eV for Pd₂ to 2.38 eV for Pd₅, which indicates the relative stability of larger Pd clusters adsorbed at the MoS₂ ML was higher than that of smaller ones. With the increase of Pd coverage (from Pd₂ to Pd₅), the intra-cluster binding energy E_IB rapidly increased from 0.37 to 1.52 eV, which suggests that the interaction among the Pd adatoms in the Pd₅ cluster was stronger than those of smaller ones. Besides, it was noticeable that the E_IB was larger than E_A for Pd₄ and Pd₅, which indicated that intermetallic Pd–Pd bonds in clusters were stronger than the bonds between Pd and surrounding S or Mo. This can be used to explain the fact that the most stable structures for Pd₄ and Pd₅ started to appear around the three-dimensional structures with smaller Pd–Pd bond lengths (about 2.63 Å). Compared with a previous study on Pd_n cluster/graphene [33], in which size-selected monodisperse nanoclusters were identified by scanning tunneling microscopy, Pd_n clusters supported by MoS₂ are more stable due to larger binding energies and shorter distance between Pd_n and MoS₂ substrate, which indicated that the MoS₂ ML was inert and an ideal template for deposition of the metal NPs to some extent.

3.2. Electronic Properties of Pd_n (n=1–5)/MoS₂ Monolayer

In order to better understand and control how the deposition of Pd clusters affect the structure and electronic properties of MoS₂, we calculated the density of states (DOS) of MoS₂ ML with and without the adsorption of Pd_n (n = 1–5) clusters shown in Figure 3. It is clear that the 4d states of isolated Pd atom was very sharp at 0.35eV, while 4d states of Mo hybrids with the 3p states of neighboring S atoms for pure MoS₂ ML. Upon the adsorption of Pd monomer on MoS₂ (Figure 3b), the band gap decreased to about 1.09 eV, which is mainly attributed to the hybridization of the 4d states of Pd atoms with 4d states of underlying Mo and 3p states of the nearest surrounding S at 0.50 eV below Fermi level. For the case of Pd dimmer adsorbed at MoS₂ ML (Figure 3c), a gap state emerged at the 0.80 eV above the Fermi level, which resulted from the hybridizations between Pd atoms and the nearest-neighboring Mo and S atoms. For the case of Pd₃ cluster, the partial density of states (PDOS) of three Pd adtoms were similar due to the identical atomic environments as shown in Figure 3d. We found that Pd adatoms hybridize more strongly with the S atom located at the hollow site of the Pd trimer (labeled by S1 in Figure 2b) than the nearest-surrounding S atoms (labeled by S2 in Figure 2b) at −0.80 eV. For the case of the Pd₄ and Pd₅ clusters with pyramid-like geometries (Figure 3e–f), the DOS of the topmost Pd adatoms labeled as Pd₄-1 and Pd₅-1 (located at the second layer of clusters) in Figure 2c were relatively localized compared with those of the underlying Pd (labeled by Pd₄-2 and Pd₅-2 in Figure 2d, which were located at the first layer of the clusters), which indicated that the electronic properties of the topmost Pd were hardly affected by the MoS₂ substrate. The calculated results also show that the gap state located above the E_F was shifting close to 0 eV from the Pd₃ to Pd₅ clusters, which caused the band gap to decrease from 0.70 eV of the Pd₃/MoS₂ system to 0.19 eV of the Pd₅/MoS₂ system.

3.3. Charge Redistribution and Work Functions

In order to analyze the character of bonds between adsorbates and MoS₂ substrate as well as the charge redistribution of MoS₂ upon the adsorption of Pd clusters, we calculated and analyzed the electron density difference, which is defined as $\Delta \rho ={\rho }_{{\mathrm{Pd}}_n-{\mathrm{MoS}}_2}-{\rho }_{{\mathrm{MoS}}_2}-{\rho }_{{\mathrm{Pd}}_n}$, where ${\rho }_{{\mathrm{Pd}}_n-{\mathrm{MoS}}_2}$ is the charge density of total system, ${\rho }_{{\mathrm{MoS}}_2}$ and ${\rho }_{{\mathrm{Pd}}_n}$ are the charge densities of pristine MoS₂ ML and the free-floating Pd clusters in the frozen geometry they adopted on the Pd_n/MoS₂ system, respectively. Figure 4 shows the corresponding difference in electron densities for all considered optimized stable configurations, yellow and blue region represent charge accumulation and charge loss, respectively. As shown in Figure 4, the charge redistributions upon the deposition of Pd_n cluster mainly involved Pd clusters and surrounding S and Mo atoms, which imply strong charge transfers between the Pd_n (n = 1–5) clusters and MoS₂ substrate. It is clear that there was strong electron density accumulation between Pd atoms and nearest-neighboring S atoms, which indicates that the bonds between Pd adatoms and surface S atoms present a covalent bond with partial ionic features. There are depletion regions close to the Pd atoms along the bond directions of Pd–S, which can be explained by the stronger electronegativity of S than Pd. For the cases of Pd₂ and Pd₃ clusters, the Pd atoms highly hybrid with the center-S (labeled as S1 in Figure 2). It is also observed that the characteristics of Pd–Pd bond remain strong metallic upon Pd clusters supported by MoS₂ ML. However, for the cases of the Pd₄ and Pd₅ clusters (Figure 4d,e), it is surprising that strong electron density accumulation was found for the topmost Pd atoms (such as Pd₄-1 and Pd₅-1), which indicates that the top Pd atoms directly receive charge from the underling Pd layers rather than losing charge to the MoS₂ substrate.

To further give a detailed insight into the charge transfer, we also calculated the atomic populations for the most favorable configurations of Pd clusters adsorbed at the MoS₂ ML, as summarized in

Table 3. Bader charge analysis for the lowest energy configurations of Pd_n (n = 1–5) clusters supported by the MoS₂ ML.

Configurations	Pd1	Pd2	Pd3	Pd4	Pd5
first layer	9.74	9.80(2)	9.82(3)	9.80(2), 9.82	9.78(2), 9.79, 9.89
second layer	–	–	–	10.14	10.15
Bader charge	0.26	0.40	0.54	0.44	0.61

. Upon Pd adatoms adsorbed at the t-Mo site, Pd adatoms lost about 0.26e to the MoS₂ ML by Bader analysis, which suggested Pd–S bonds exhibited a relatively significant ionic bonding component, as illustrated by the substantial charge density difference between Pd and neighboring S atoms shown in Figure 3a. Similarly, Pd adatoms in dimer and trimer averagely contributed about 0.20 and 0.18e to the MoS₂ ML, respectively. However, in the cases of Pd₄ and Pd₅ clusters with pyramid-like geometry, Pd atoms in the first layer and second layer of the clusters behave in a different way. The Pd atoms in the second layer of the cluster (Pd₄-1 and Pd₅-1) obtained charge, while the Pd atoms of the first layer lost charge. This result is in good agreement with the phenomenon of charge accumulation near the topmost Pd atoms as shown in Figure 4d,e. Therefore, it is not surprising that the MoS₂ slabs obtained less charge from Pd₄ and Pd₅ clusters than that of the Pd₃ cluster.

Figure 5 shows the in-plane averaged electrostatic potential (ESP) for the MoS₂ surface with Pd monomer (solid line) and that of the pristine MoS₂ surface (dotted line), respectively. The same were done for other Pd clusters, which are not shown here. Ionization energy (IE), defined as the energy difference between the vacuum level and valence band maximum (VBM), was determined to be 5.48 eV for the clean MoS₂ ML. Upon the Pd_n (n = 1–5) clusters adsorption, the increase of ionization energy (ΔI) was observed, which can be quantificationally given by the energy difference between the vacuum levels. In addition, the work function is described as the following equation: W = E_vac−E_F, where E_vac is the electrostatic potential in the vacuum region of the adsorbate side of the MoS₂ surface, while E_F refers to Fermi energy. The work function of pristine the MoS₂ ML was estimated to be 5.26 eV, which is slightly higher than the experimental result of 5.03 eV [34].

As indicated in Figure 5, we also defined the energy difference between Fermi level (E_F) and the CBM of the MoS₂ ML as p-SBH (Φ_P) for convenience, although the well-defined Schottky barrier contact had not formed yet in our considered initial growth stage of Pd clusters. In

Table 4. Calculated work function (W), p-SBH (Φ_P), dipole moment (D_i), and variations of ionization energy (ΔI) upon the adsorption of the lowest energy Pd_n (n = 1–5) clusters on the MoS₂ ML.

Configurations	Pd1	Pd2	Pd3	Pd4	Pd5
W (eV)	5.01	4.73	4.62	4.46	4.38
ΦP (eV)	0.52	0.82	1.00	1.18	1.27
ΔI (eV)	0.17	0.16	0.08	0.06	0.05
Di (eÅ−1)	0.35	0.57	0.80	0.64	0.88

we summarized the calculated work function (W), p-SBH (Φ_P), dipole moments (D_i), and the variation of ionization energy (ΔI) for the adsorption of Pd clusters. It became clear that the increasing of Pd coverage leads to decreases in the work function from 5.01 eV of Pd adatom to 4.38 eV of Pd₅ cluster, which may result from the larger amount of CT from Pd_n cluster to MoS₂ as listed in Table 3. We think the variations of p-SBH are mainly attributed to the gap states caused by Pd adatoms (as shown in PDOS in Figure 3) and the partial charge transfer from 1stlayers to the second layer Pd atoms. The trend for the variations of ionization energy is obvious: as the cluster size increases (from Pd₁ to Pd₅), ΔI reduces rapidly, while ΔI rises in the initial growth stage of Ni clusters supported by MgO (001) [35]. In addition, the dipole moments (D_i) were calculated by the product of transfer charge and the distance of adsorbate-substrate. The calculated dipole moments of Pd_n/MoS₂ were not in a monotonic variation, which is different from the monotonic increase of D_i with the increase of Ni coverage on MgO (001).We think that the main reason for these distinct phenomena of the two systems is that the Pd_n clusters injected electrons into the VBM of the MoS₂ substrate while the Ni_n clusters extracted electrons from the MgO (001) surface. Besides, Pd adatom, Pd₂, and Pd₃ clusters prefer the planar structures as discussed above, and there is only the interface dipole contribution in such systems. For the cases of Pd₄ and Pd₅ clusters with pyramid-like structures, intra-cluster dipoles due to the CT between the topmost layer and the lower part of the cluster also contribute to the dipole moments. Since these two dipoles have opposite directions, the dipole interactions between Pd₄ or Pd₅ clusters and MoS₂ substrate can be cancelled to some extent.

Previous studies have confirmed that the coverage-dependent depolarization effects play a non-negligible role in metal–organic interfaces [36,37,38]. In order to get insight into the coverage-dependent depolarization effects caused by the interaction between the adjacent supercells, we also used a (6 × 6) supercell to study the adsorption of Pd_n clusters at the MoS₂ substrate. We found that the CT and work function of Pd_n (n = 1–3)/MoS₂ systems have no significant change, while the variation on CT and work function for Pd₄/MoS₂ and Pd₅/MoS₂ were less than 0.04 and 0.01 eV, respectively. Therefore, the interactions between Pd_n (n = 1–5) clusters within adjacent supercells is ignorable, and thus the coverage-dependent depolarization effects can be ignored in Pd_n/MoS₂ considered in this work. The discrepancy between metal–organic interfaces [36,37,38] and Pd_n/MoS₂ interface maybe explained by different interactions between adsorbates and substrate and different sizes of adsorbates, such as non-specific bonding between organic molecules and substrates versus the covalent Pd–S chemical bonds in our study, and larger diameters of organic molecules than that of metal clusters.

3.4. Diffusion of Pd Clusters on an MoS₂ Monolayer

In order to investigate the nucleation mechanism and diffusion properties of Pd clusters on the MoS₂ ML, we analyzed the diffusion and surface mobility of Pd_n (n = 1–5) clusters on the MoS₂ ML from the most favorable adsorption configurations. We defined the reaction rate k as the following:

$$k=v_0\exp (-\frac{\Delta E_a}{k_{B}T}),$$

(4)

where $v_0={10}^{13}{s}^{-1}$ is the rate pre-factor, assumed to be irrelevant to the reaction or the hopping events, and k_B and T are the Boltzmann constant and temperature, respectively. The equation indicated that reaction rate k is proportional to temperature T, while k is inversely related to the activation energy barrier $\Delta E_a$. In here, the activation energy barrier $\Delta E_a$ is computed from the total energy difference between the initial configuration and the saddle points of the minimum energy pathway between two adsorption configurations. The k value is usually used to measure the possibility of nucleation and diffusion by overcoming the energy barrier at the low Pd coverage. The energy diagrams of Pd_n (n = 1–5) clusters nucleated or diffused on the MoS₂ ML are shown in Figure 6. As shown in Figure 6a, the calculated activation energies were 0.12 and 0.02 eV for the on-surface diffusion of Pd monomer along the two paths of t-S→t-Mo and H→t-Mo, respectively, which indicates the diffusion of Pd monomer on the MoS₂ surface show remarkably anisotropy. The activation energy barrier was much smaller than the value of 0.34eV for Pd monomer diffusion on MgO (100) via single atom hops between oxygen sites [39], implying the Pd adatom on the MoS₂ surface was mobile during the in situ growth by deposition. According to Equation (4), the number of hopping events per second between two T_Mo sites was estimated to be 10³ s⁻¹ along the Mo–H–Mo path and 10 s⁻¹ along the Mo–S–Mo path at room temperature, respectively. The results indicated that the Pd adatoms are more likely to be mobile for coarsening and growth of large clusters rather than a random dispersion during the deposition. We also found that a newly deposited Pd atom prefers to bond to existing Pd adatoms located at t-Mo sites by possible diffusion, which is illustrated in Figure 6b. The energy barrier for the attachment of a Pd adatom to an existing Pd monomer to form Pd dimer is 0.32 eV, and the process is downhill by 0.48 eV. In other words, the deposited Pd adatoms are expected to bond to Pd monomer adsorbed at MoS₂ rather than adsorb at a remote site. According to Equation (4), the higher the reaction temperature is, the easier the reaction occurs. For instance, the reaction rates k for the nucleation of Pd dimer from two Pd adatoms on MoS₂ surface will increase about 140 and 485 times compared to that of room temperature (RT)under T = 500 and 600 K, respectively.

The three flat trimers t-(Mo)3-123°, t-(Mo)₃-h, and t-(Mo)₃-S shown in Figure 6b are easily accessible during metal deposition, which can be formed by the low-energy diffusion of Pd monomer on MoS₂ surfaces to reach a Pd dimer. As shown in Figure 6b, although the total energies of the initial states of t-(Mo)3-123° and t-(Mo)₃-h configurations were about 0.21 and 0.06 eV higher than that of the most stable configuration of t-(Mo)₃-S due to the extra binding of the S1 atom, the energy barriers for transforming the flat t-(Mo)3-123° and t-(Mo)₃-h configurations to t-(Mo)₃-S were 1.31 and 0.92 eV, while the reverse processes were examined to surmount the energy barriers of 1.52 and 0.98 eV, respectively. We found that the transition state from t-(Mo)₃-h to t-(Mo)₃-S was Δ-(Mo)₃, which was0.96 and 0.98 eV energetically higher than that of the initial and final states. However, the identical Δ-(Mo)₃ configuration was predicted as the intermediate state with the lowest energy during the transformation between t-(Mo)₃-h and t-(Mo)₃-S configurations of Pt₃ clusters on MoS₂ ML as reported in Reference [14]. Such discrepancy may be due to the larger cohesive energy of Pt than that of Pd, which makes it is more likely to form islands for Pt NPs than Pd NPs.

We have considered various possible structures of palladium tetramer_, which is formed by the simple extension from t-(Mo)₃-S and t-(Mo)₃-h via the attachment of Pd monomer to Pd₃ clusters. The computed results show three-dimensional t-(Mo) ₄-S was favored over t-(Mo) ₄-h only by 0.10 eV in total energy, both of which can be nucleated on the MoS₂ ML. It was clearly observed that transition from t-(Mo) ₄-h to t-(Mo) ₄-S should overcome the energy barrier of 0.83 eV, which is twice that of the transformation barrier of Pt₄ clusters with the identical structures on the MoS₂ ML [14]. It indicated that the diffusion of Pt₄ clusters was likely to be much more accessible compared with Pd₄ clusters on MoS₂ MLs. Similarly, the most preferable configuration can be accessed from configurations t-(Mo₄)-h and t-(Mo₄)-S by deposition of new Pd atoms or diffusion of Pd monomers to the nearest-neighboring T_Mo site. The two pyramid-like Pd₅ clusters labeled as t-(Mo)₅-h and t-(Mo)₅-S are shown in Figure 6e, respectively, which were found to be stable and have a slight energy difference of about 0.03 eV. The computed results show that the transformation of t-(Mo)₅-h and t-(Mo)₅-S was almost barrier less with E_a about 0.13 eV.

The diffusion of Pd atoms from the topmost site of a pyramid-like structure to the MoS₂ substrate was a key factor to decide the growth mode of the Pd_n cluster on the MoS₂ monolayer. Therefore, we also calculated the diffusion behaviors of Pd atoms from topmost sites of Pd₄ and Pd₅ clusters to the MoS₂ substrate. The calculated results show the topmost Pd atoms moving to the nearest-neighboring t-Mo sites of the MoS₂ substrate needed to overcome the energy barriers of 0.73 and 1.13 eV for Pd₄/MoS₂ and Pd₅/MoS₂ systems, respectively. The relative high energy barriers imply that the Pd atoms prefer to form a sheet-supported metal nanotemplate on MoS₂ in the initial growth stage, which is in conformity with the previous experimental study reported by Gong et al. [40] that Pd forms a uniform contact by physical vapor deposited on MoS₂ monolayers.

4. Conclusions

In summary, we investigated theoretically the stable configurations, electronic structures, and surface mobility of Pd_n (n = 1–5) clusters on MoS₂ monolayers using first principles density functional theory calculations. The results demonstrate that Pd clusters can chemically adsorb on MoS₂ MLs and Pd adatoms are strongly bound to the surface S atoms, which exhibit covalent bonds with significant ionic character. The geometries of Pd_n cluster varies from a planar structure to a pyramidal morphology when the cluster size increases due to the relative strengths between Pd_n–MoS₂ and Pd–Pd interactions. Upon the deposition of Pd clusters, the band gaps of MoS₂ weretunable due to the hybridization between 4d electrons of Pd and 3s electrons of S. The work function was modulated from 5.01 to 4.38 eV with the increase of Pd coverage, which resulted from the charge transfer from Pd clusters to MoS₂ ML.

In addition, we investigated the nucleation and diffusion properties of Pd_n (n = 1–5) clusters on MoS₂ ML, e.g., the distant isolated Pd atoms or additional adatoms favor migrating to nearby Pd_n clusters, which indicated that Pd is likely to agglomerate to metal nanotemplates on the MoS₂ ML during the epitaxial stacking process. These findings may provide useful guidance to extend the potential technological applications of MoS₂, including catalysts and production of metal thin films, and the fabrication of nanoelectronic devices.