A Predictive Model for Monolayer‐Selective Metal‐Mediated MoS2 Exfoliation Incorporating Electrostatics

The metal‐mediated exfoliation (MME) method enables monolayer‐selective exfoliation of van der Waals (vdW) crystals, improving the efficacy of large monolayer production. Previous physical models explaining monolayer‐selective MME propose that the main contributors to monolayer‐selectivity are vdW crystal/metal surface binding energy and/or vdW crystal layer strain resulting from lattice mismatch. However, the performance of some metals for MME is inconsistent with these models. Here, a new model is proposed using MoS2 as a representative vdW crystal. The model explains how the MoS2/metal interface electrostatics, in combination with strain, determines monolayer‐selectivity of MME by modulating the MoS2 interlayer energy. Monolayer MoS2/metal interfaces are characterized using in situ Raman spectroscopy and density functional theory calculations to estimate the electrostatics and strain of MoS2 in contact with different metals. The model successfully demonstrates the dependence of MME monolayer‐selectivity on the MoS2/metal interface electrostatics and highlights the significance of electrostatics in nanomaterial vdW interactions.


Introduction
[3] Especially in their DOI: 10.1002/admi.202300686monolayer form, they exhibit fundamental advantages over conventional bulk semiconductors. [4]Therefore, reliable preparation of large, damage-free, monolayer vdW crystals is an important manufacturing goal.7][8][9][10][11][12] Metal-mediated exfoliation (MME) enables the incorporation of pristine, millimetre-scale monolayer vdW crystals into electronic devices without the high temperatures needed for direct monolayer synthesis. [13]MME also avoids defects, common during solution exfoliation, that alter the vdW crystal electronic structure. [14][15][16][17] As the bulk vdW crystal is separated from the metal surface, vdW crystals are selectively exfoliated, leaving monolayers attached to the metal surface.Molybdenum disulfide (MoS 2 ), the most studied vdW crystal, is a model compound for exfoliation in the large family of TMDCs.[9]15,17] Other metals, including Pd, Ag, Pt, Ni, and Cu, have also been successfully used. [10,11,16]Despite its widespread use, the physical mechanism of monolayer-selective MME is still unclear, suggesting additional scope for fully exploiting MME.
A seminal model of MME proposed that monolayer-selectivity was due to the strong binding between the Au surface and S atoms on the surface of MoS 2 , comparable to covalent-like surface Au-thiol bonding. [5,7]Accordingly, efficient monolayerselectivity was due to the strength of the Au-MoS 2 bonds and the relative weakness of the MoS 2 vdW interlayer bonding.However, this model does not explain how cleaving preferentially occurs between the 1 st and 2 nd MoS 2 layers on the Au surface (MoS 2 (1), MoS 2 (2), respectively). [5,7]Cleaving occurs preferentially at interfaces with lower binding energy, yet the model does not suggest any difference in MoS 2 interlayer binding energy.To address this limitation, a second model proposed that lattice mismatch strain in MoS 2 (1) in contact with a metal surface is the main contributor to monolayer-selectivity in MME. [16,18]train reduces the atomic density of the MoS 2 (1) layer and/or increases the interlayer distance, reducing the attractive vdW interactions between MoS 2 (1) and MoS 2 (2).Indeed, Au applies a significant tensile strain to MoS 2 (up to 5.5%) [19] that may weaken the MoS 2 (1)/MoS 2 (2) interlayer binding energy and facilitate monolayer-selective MME. [16]However, this second model cannot explain observations by Johnston & Khondaker [10] concerning monolayer-selective MME on metal surfaces that apply negligible strain to MoS 2 , such as Pd. [10]The authors hypothesized that the large binding energy between MoS 2 and Pd facilitates monolayer-selectivity, similar to the first model, yet this does not explain the preferential cleavage at the MoS 2 (1)/MoS 2 (2) interface.Additionally, directly-deposited Al has a high binding energy and large lattice mismatch/applied strain, yet exhibits poor monolayer-selectivity, [10] inconsistent with the predictions of either model.The experimental results suggest that the current models are incomplete, and a new model is required that addresses the modulation of MoS 2 (1)/MoS 2 (2) interlayer binding energy in contact with different metal surfaces.
Here, we present such a model that elucidates how the electrostatics of the MoS 2 (1)/metal interface, in combination with strain from lattice mismatch, modulates the monolayer-selectivity of MME by directly modulating the MoS 2 (1)/MoS 2 (2) interlayer energy.This model lays the foundation for a theory that can predict monolayer selectivity of MME, enabling highly efficient and fully controlled production of large monolayer vdW structures.The model also has important implications for understanding electrostatic modulation of vdW interactions and its impact on manipulation of nanomaterials.The model has resulted from a thorough investigation of the electrostatics of the MoS 2 /metal interface.In situ characterization of these interfaces is experimentally challenging so data in the literature is sparse, and indirect electronic methods can perturb the interface. [20]Fortunately, modulation of electron density and strain in monolayer MoS 2 (1L-MoS 2 ) can be measured by changes in Raman spectra, allowing direct in situ characterization of 1L-MoS 2 in contact with metals, with negligible interference to the MoS 2 /metal interface. [9,17,21]oS 2 /metal interface properties such as the built-in potential and lattice mismatch strain can then be derived from measured 1L-MoS 2 properties.Here, we report experimental in situ Ra-man spectroscopy characterization of 1L-MoS 2 /metal interfaces for a variety of metals.Changes in the 1L-MoS 2 electron density and strain are used to derive the built-in potential and strain at the MoS 2 surface of MoS 2 /metal interfaces.This elucidates the mechanism of monolayer-selective MME of MoS 2 .Density functional theory (DFT) calculations of MoS 2 /metal interfaces support the experimental measurements of the interface electrostatics and determine how the modulation of MoS 2 interlayer energy from electric fields depends on the structure and electron distribution of the material.

Raman Analysis of 1L-MoS 2 in Contact with Metals
The Raman spectrum of MoS 2 has two distinct modes, A 1 ′ and E′, corresponding to out-of-plane and in-plane Raman-active vibrational modes (Figure 1A).The Raman shift of both modes is dependent on the electron density and strain in the MoS 2 sample. [22][26][27] The relationship between A 1 ′ and E′ Raman shifts and electron density and strain can be expressed as, [21] ][27] The electron density constants k A ′ 1 = −2.2× 10 13 cm −2 and k E′ = −0.33 × 10 13 cm −2 have been found previously by fitting experimental data. [21,23]Suspended 1L-MoS 2 , with no contact with any other material (aside from ambient air), was used as the reference, with ɛ = 0% and Δn e = 0. Lloyd et al. [28] measured the E′ Raman mode peak at 385 cm −1 and the A 1 ′ Raman mode peak at 405 cm −1 for suspended 1L-MoS 2 , which we use as the reference (Figure 1A) .The different characteristic Raman vibrational mode peaks that were fitted on the Raman spectra of 1L-MoS 2 /metal interfaces are listed in Table 1.
Here, metal films (except Al) were deposited via thermal or electron-beam evaporation physical vapor deposition (PVD) directly onto a bulk MoS 2 crystal, followed by monolayer-selective MME of the bulk MoS 2 to reveal the 1L-MoS 2 /metal interface (details in Experimental Section; Section S1 and Figure S1, Supporting Information).Here, direct deposition of the metal film on to bulk MoS 2 via PVD was preferred to the transfer method, [32] as the PVD approach ensured no oxidation of the metal surface [16] or impurity contamination [6] occurred at the 1L-MoS 2 /metal interface.While some damage to MoS 2 may occur during PVD metal deposition, [32,33] it can be accounted for by fitting the disorder activated LA(M), LO(M), and TO(M) modes if they appear in the Raman spectra (Table 1).Al films could not achieve monolayerselectivity, so MoS 2 was directly exfoliated onto a freshly deposited Al film on a Si/SiO 2 substrate under inert atmosphere (glovebox) and a small 1L-MoS 2 flake was used to characterize the 1L-MoS 2 /Al interface.Figure 1B-H   Fundamental lateral vibrational mode.Red shifts under tensile strain and blue shifts under compressive strain. [ 21,27]− and E + <385 Split E′ vibrational modes due to strain-induced lattice symmetry breaking.
A 1 ′ 405 Fundamental vertical vibrational mode.Red shifts when electron density increases and blue shifts when electron density decreases. [ 21,27]A(M) 450 Second order longitudinal acoustic mode at M point.Weak intensity. [ 27,29](≈K)+ TA(≈K) 428 Linear combination of the longitudinal acoustic mode and transverse acoustic mode at K point.Very weak intensity. [ 27,30](M) 227 Longitudinal acoustic mode at M point.Significant disorder-activated and intensity proportional to defect density in 1L-MoS 2 . [31](M) 377 Longitudinal optical mode at M point.Only activated from significant crystal lattice disorder. [31](M) 358 Transverse optical mode at M point.Only activated from significant crystal lattice disorder. [31]tted with Voight spectral profiles to incorporate the intrinsic Lorentzian peak profile and the instrumental-dependant Gaussian peak profile. [22,26,28]All Raman spectra shown in Figure 1B-H represent an average of >4 points across the 1L-MoS 2 /metal interface and are normalized to the maximum peak intensity of each spectrum (only relative intensity between peaks of the same spectrum is considered).Figure 1I (Supporting Information) plots  and Δn e of each 1L-MoS 2 /metal interface, calculated from the E ′ (or E − ) and A 1 ′ mode Raman peaks.Figure S2 (Section S2, Supporting Information) also plots E ′ (or E − ) against A 1 ′ mode Raman peak positions for each 1L-MoS 2 /metal interface with reference lines to visualise the change of  and Δn e .The fitted peak data and resulting calculated 1L-MoS 2  and Δn e from all samples are summarized in Table 2. 1L-MoS 2 in contact with directly deposited Au, Ag, and Ni films exhibited measurable splitting of the E′ mode peak (Figure 1B,D,F).This splitting has been reported previously in 1L-MoS 2 with >1% uniform uniaxial tensile strain and likely occurs at lower , although the split peaks are challenging to distinguish clearly. [24]E′ mode peak splitting is due to symmetry breaking under uniaxial tensile strain that changes the crystallographic point group from D3h to Cs. [24,35,36] Lateral E′ mode lat-tice vibrations parallel (E − ) and perpendicular (E + ) to the applied strain are no longer degenerate.This indicates that 1L-MoS 2 is under uniaxial tensile strain when in contact with these metal films due to lattice mismatch.The Grüneisen parameters for the change of E′ mode Raman shift due to , are calibrated on the split E′ mode that correlates with the  direction.Thus, the E − mode peak is used to determine 1L-MoS 2  and Δn e from the Raman spectra with split E − mode peaks.The E − mode peaks for the measured samples are lower in intensity than the E + mode peaks, in contrast to previous observations of uniaxially strained MoS 2 . [24]However, in these samples  was applied via lattice mismatch of a strongly interacting metal film.Thus, the metal film will interfere with the 1L-MoS 2 vibrational modes and suppress the E′ mode peaks. [19]L-MoS 2 /Au also exhibits splitting of the A 1 ′ mode peak, with an observable small shoulder (A 1 1 ) at 399.2 cm −1 on the peak (A 1 2 ) at 406.7 cm −1 (Figure 1B).This has been observed previously in heterogeneous MoS 2 /metal interfaces where the metal did not contact the whole MoS 2 surface, or regions of the interface varied. [9,36]Inhomogeneous distribution of Au directly deposited on MoS 2 by PVD may cluster into non-uniform Au nanostructures on the MoS 2 surface (island growth kinetics), [37] Table 2. Voight profile peaks fitted to the 1L-MoS 2 /metal Raman spectra for the E′ (or split E − and E + ) and A 1 ′ Raman modes, electron density change (Δn e ) and strain () calculated from the Raman peaks, metal work function (Φ m ), [34] ideal (Φ i ) and measured (Φ Δ ) built-in potential for the 1L-MoS 2 /metal interface, and the DFT-calculated charge transfer (negative for electron depletion and positive for electron accumulation in the metal substrate) and binding energy of the 1L-MoS 2 /metal interface.
Δn e (10 13 cm −2 ) interfacing with 1L-MoS 2 may also create moiré superstructures that result in heterogeneous 1L-MoS 2 /Au interfaces and different regions with varying interactions. [38]These result in a heterogenous metal-MoS 2 interface that will cause additional splitting of the A 1 ′ and E′ mode peaks, corresponding to the different regions that cause distinct  and Δn e . [9]A lower intensity A 1 1 mode peak compared to the A 1 2 mode peak may indicate intimate MoS 2 /metal contact or high  causing severe Raman intensity suppression. [19]The split E ′ mode peaks corresponding to A 1 1 will also have low intensities that make it difficult to observe in the Raman spectrum.The reduced intensity of the E ′ modes corresponding to A 1 1 can obscure them under other E′ modes and previous literature may have overlooked the additional splitting of E′ mode peaks for this reason. [20]A small Raman peak in the deconvoluted Raman spectra at 361.6 cm −1 was assigned to the E − mode corresponding to A 1 1 Using the A 1 1 and cor-E − mode peaks (Table 2) to define the primary 1L-MoS 2 /Au interface region allowed estimation of  = 4.5% and Δn e = −0.85× 10 13 cm −2 , consistent with recent experimental reports and theoretical  from the Au-MoS 2 lattice mismatch (6.3%). [17,19,20,39]or the 1L-MoS 2 /Pd interface, the A 1 ′ mode peak is split into two large prominent peaks at 407.8 and 420.4 cm −1 (Figure 1C).The peak at 420.4 cm −1 , although having a large Raman shift, is not due to the LA(≈K)+ TA(≈K) modes because its FWHM of 9.9 cm −1 is too small for these phonon modes in non-resonance Raman. [30]Additionally, the 2LA(M) mode peak should be more intense than the LA(≈K)+TA(≈K) mode peak for 1L-MoS 2 in non-resonant or resonant Raman spectra. [29]However, in the 1L-MoS 2 /Pd interface Raman spectrum, the 420.4 cm −1 peak is more intense than the 2LA(M) mode peak.Further, the peak observed at 428.0 cm −1 is less intense and possesses a much larger FWHM of 24.0 cm −1 and is thus identified here as the LA(≈K)+TA(≈K) combination peak.Pd deposition on MoS 2 has been reported to exhibit island growth with very small atomic clusters with ⟨111⟩ direction interfacing with the MoS 2 . [40]This creates a heterogeneous interface, similar to the1L-MoS 2 /Au interface, and can explain the A 1 ′ mode peak splitting.The Pd islands are preferentially limited to very small 7 atom clusters, so the Pd film surface still has very low roughness. [40]The interface region between the islands will have increased interface distance and reduced binding energy, and will thus have different  and Δn e values.The primary 1L-MoS 2 /Pd regions (Pd < 111 > island face on MoS 2 ) have a measured  = 0.02%, expected from the small lattice mismatch between 1L-MoS 2 and Pd (≈0.5%) [37] and similar to previous reports. [40]aman peaks that are assigned to the secondary interface region for the 1L-MoS 2 /Au and 1L-MoS 2 /Pd samples along with their calculated Δn e and  are presented in Section S2 (Supporting Information).1L-MoS 2 /Ag exhibited similar splitting of the A 1 ′ mode peak.A small secondary A 1 ′ mode peak at 396.8 cm −1 was observable indicating a secondary 1L-MoS 2 /Ag interface, as previously reported for this interface. [36,37,41]However, we found that the corresponding E − mode peak for the secondary 1L-MoS 2 /Ag interface was too small to be accurately deconvoluted from the obtained Raman spectra, so the secondary interface region could not be measured for the 1L-MoS 2 /Ag sample.
The E′ mode peak in the 1L-MoS 2 /Cu interface Raman spectrum has a greater intensity than the A 1 ′ mode peak, in contrast to the greater intensity A 1 ′ mode peak for every other metal.Additionally, there is no splitting of the E′ mode peak.More intense, non-split E′ mode peak is indicative of a uniform biaxial strain experienced by the 1L-MoS 2 at the 1L-MoS 2 /Cu interface. [28]Small Δn e and strain were measured from the transferred 1L-MoS 2 /Al interface.Small strain is expected for transferred contacts as the larger gap between the MoS 2 and metal layers inevitably results in a weaker interaction and between the layers and less possible total strain being applied. [17]ntroducing significant defects in the 1L-MoS 2 crystal lattice causes the appearance of the LA(M) mode peak at ≈227 cm −1 , and the intensity is proportional to the defect density. [31]LA(M) mode peak is only observable in the 1L-MoS 2 /Pt Raman spectra which indicates that only this interface has significant defects introduced to the 1L-MoS 2 .Broadening of E′ and A′ 1 mode peaks in 1L-MoS 2 /Pt Raman spectra is also characteristic of damage defects. [31]Pt deposition may have caused damage to MoS 2 due to the high energy required for electron beam PVD.The Raman peaks at 379.3 and 358.1 cm −1 are assigned as the disorderactivated LO(M) and TO(M), respectively, leaving the Raman peak at 370.7 cm −1 assigned as the E′ mode peak.The 2LA(M) mode peak at ≈450 cm −1 is observable in most of the 1L-MoS 2 /metal spectra. [29,42]he measured  and Δn e were then used to derive the Schottky junction built-in potential (Φ Δ ) and the interfacial charge transfer.

Schottky Junction Formation, Charge Transfer, and Induced Strain During MME
When the metal work function (Φ M ) is larger than the Fermi energy (E F ) of the semiconductor, electrons transfer from the MoS 2 semiconductor to the metal and Schottky junctions can form at the MoS 2 /metal interface (Figure 2A).This causes electron depletion in the semiconducting MoS 2 layer (see further discussion in Section S3, Supporting Information). [43,44]Indeed, the 1L-MoS 2 /metal interfaces reduced the electron density (Δn e < 0) of the 1L-MoS 2 (Figure 1I), suggesting formation of Schottky junctions. [39]A correlation is observed between the ideal built-in potential (Φ i ) and Δn e , where Φ i is calculated as follows: where X MoS 2 is the 1L-MoS 2 electron affinity, and E F and E C are the Fermi level and conduction band minimum, respectively.The effects of 1L-MoS 2 strain are also important.The X MoS 2 of 4.33 eV can be increased by ∼0.14 eV per 1% tensile strain, resulting in a reduced Φ i and consequently reduced Δn e in the MoS 2 . [45,46][49] N d is highest (∼10 19 cm −3 ) on ambient exposed surfaces of MoS 2 , constituting highly n-doped 1L-MoS 2 . [50]PVD deposition of metal films also creates additional V S in the MoS 2 surface relative to the suspended 1L-MoS 2 reference.V S for the 1L-MoS 2 sample used was confirmed by energy dispersive X-ray spectroscopy (EDX) measurements.This indicated a ∼1:1.7 Mo:S stoichiometry pared to 1:2 for pristine MoS 2 (Section S4, Supporting Information).Due to this high defect density on the MoS 2 surfaces we estimate that E F -E C ≈ 0. [50,51] Consequently, Φ i for these samples can be calculated as, Figure 2B plots the Raman spectra-determined Δn e against Φ i .The Φ M of the < 111> surface was used for each metal (Table 2), except for Au where the Φ M of a polycrystalline surface was used due to its island growth on MoS 2 surface producing an inhomogeneous interface (See Section S2, Supporting Information). [34,37,40]A linear correlation was observed between Δn e and Φ i , consistent with Schottky-Mott theory that states larger Φ i values increase electron depletion.The actual built-in potentials (Φ Δ ) at the MoS 2 surface in contact with the metals were calculated from Δn e (Table 2; and Section S5, Supporting Information).The calculated pinning factor S was ≈0.64, suggesting that only partial Fermi level pinning has occurred for these 1L-MoS 2 /metal interfaces, similar to that predicted by Gong et al (S = 0.71). [39,52]A Δn e value of −3.9 ± 0.98 × 10 13 cm −2 per 1 eV Φ i was measured.The 1L-MoS 2 /Au interface induced only a small reduction in electron density, indicative of a small built-in potential and Schottky barrier.This correlates well to the lower measured contact resistivity for Au/MoS 2 reported in the literature, [53] and demonstrates the impact of the large strain of the Au/MoS 2 interface reducing the built-in potential.

Corroboration from Density Functional Theory Calculations
DFT calculations using a vdW correlation-corrected GGA functional were performed to validate the charge transfer at the 1L-MoS 2 /metal interfaces (Figure 2C).1L-MoS 2 /metal interfaces were chosen to be studied via DFT (rather than 2L-MoS 2 /metal or periodic MoS 2 /metal interfaces) to enable direct comparison with the samples measured by Raman spectroscopy.From these DFT 1L-MoS 2 /metal interfaces, the net charge transfer along the z-direction was calculated with respect to the x-y plane located at the interface.The calculated values correlate well with the experimental Δn e values and are approximately linearly related to Φ i (Figure 2B and Table 2).This suggests that the charge redistribution is mainly driven by the Schottky junction and that the Schottky-Mott rule holds at the atomic scale for the 1L-MoS 2 /metal interface.The 1L-MoS 2 /Au interface was calculated to have the smallest electron transfer from the 1L-MoS 2 to a metal film.This small electron transfer matches the small negative Δn e measured experimentally from the primary 1L-MoS 2 /Au interface region.The calculations showed that, in 1L-MoS 2 /Al, there was a net transfer of electrons into MoS 2 (Δn e > 0), opposite to the other metals.This is due to the smaller Φ M of Al compared to 1L-MoS 2 E F that drives electron accumulation in 1L-MoS 2 (Figure 2C).The Δn e and  values from Raman spectra and DFT calculations were used to determine Φ Δ for the MoS 2 /metal interfaces.The change in MoS 2 (1)/MoS 2 (2) interlayer energy as a function of Φ Δ and  could then be determined.

Model for Electrostatics-Enabled, Monolayer-Selective MME
We propose that metal surfaces in contact with bulk MoS 2 and other semiconductor TMDCs enable monolayer-selective MME by reducing electron density in MoS 2 (1) and shifting electron distribution away from the interlayer through electric fields.This reduces attractive vdW interactions at the MoS 2 (1)/MoS 2 (2) interface (Figure 3A) and works in combination with with reduced attractive vdW interactions caused by strain.Electric fields have been shown previously to reduce attractive vdW interactions in MoS 2 and other molecules by removing electron density from the interlayer and increasing effective interlayer distance. [54,55]etal surfaces can reduce electron density in bulk MoS 2 and form an electric field that increases effective MoS 2 (1)/MoS 2 (2)  interlayer distances by forming a Schottky junction that redistributes charge in the bulk MoS 2 (Figure 3B).The resulting interlayer binding energy (E Int ) can be written as, The initial interlayer energy (E Int0 ) is modulated by the strain-induced change in MoS 2 (1) atomic density and the MoS 2 (1)/MoS 2 (2) interlayer distance (ΔE Int ()), the Schottky electric field-induced change in effective MoS 2 (1)/MoS 2 (2) interlayer distance (ΔE Int (E)), and the electron density-induced change in polarizability (ΔE Int (n)).
It is well known that atomic registry mismatch strain increases interlayer distance and the distance for minimum energy, depending on the structure of the vdW crystal. [18]Sun et al. [18] calculated a reduction in E Int for bilayer MoS 2 of ≈0.0025 eV Å −2 for  = 5% in the MoS 2 top layer, which is used to estimate a linear E Int (), To determine the structure-dependent ΔE Int (E), geometryoptimized calculations of bilayer MoS 2 with applied electric fields were performed with the vdW correlation-corrected GGA functional to model the effect of the Schottky-induced electric field at the MoS 2 (1)/MoS 2 (2) interlayer (Section S6, Supporting Information).An ΔE Int (E) of ≈0.001 eV Å −2 for an out-of-plane applied field of 0.016 eV Å −1 or 1.6 × 10 6 V cm −1 was calculated.
To calculate the Schottky junction-induced electric field at the MoS 2 (1)/MoS 2 (2) interface, the depletion region width in MoS 2 is first calculated using the full depletion approximation as [56] x qN d (7)   where N d is the defect density, and V a is applied bias across the interface.Using N d = ∼10 19 cm −3 , [50] and dielectric constant of MoS 2 as ∼4, [54] no applied bias, and using our calculated Φ Δ from the measured Δn e in 1L-MoS 2 (Table 2) we can obtain, Schottky junction-induced electric field at the MoS 2 (1)/MoS 2 (2) interface is then calculated as, [56] where x t is the distance from the MoS 2 /metal interface to the MoS 2 (1)/MoS 2 (2) interface, which is the 1L-MoS 2 thickness (0.7 nm). [57]Equation 9 can then be expanded using Equation 8as, Thus, the relationship of ΔE Int (E) at the MoS 2 (1)/MoS 2 (2) interface due to Φ Δ is, Equation 7 shows that applying a bias across the MoS 2 /metal interface can modulate x d and consequently E(x) and ΔE Int (E).This suggests that the interlayer vdW attraction of the MoS 2 (1)/MoS 2 (2) interface can be precisely controlled via an applied bias.This presents a great opportunity for applications involving precise exfoliation or manipulation of monolayer vdW crystals.These equations also highlight that x d and thus the electric field extends 2.4-7 nm into the MoS 2 for Φ Δ between 0.13-1.11eV, reducing E Int for a few MoS 2 interlayers.However, the electric field is still strongest nearest the MoS 2 /metal interface and the MoS 2 (1)/MoS 2 (2) interface will have the greatest reduction in E Int to enhance monolayer-selective MME efficacy.
ΔE Int (n) is a highly complex function that depends on the change of polarizability of the MoS 2 layers due to changes in Figure 3. A) Simplified schematic of the MoS 2 /metal Schottky junction causing reduced interlayer energy/vdW interactions.The Schottky-induced electric field distorts the electron distribution and increases the effective interlayer distance (D), consequently reducing vdW interactions.The electron depletion/reduced electron density (n e ) results in reduced polarizability that reduces vdW interactions.B) Electrostatics of the MoS 2 /metal Schottky junction using the full depletion approximation.Electron density (n e ) (green dashes) is reduced in the MoS 2 (right side) and equally increased in the metal (left side).An electric field (blue dashes) is established in the MoS 2 depletion width (x d ), with maximum strength near the interface.The y-axis is the change in electron density (Δn e ) or electric field strength, and the x axis is the distance from the interface with the x = 0 as the MoS 2 /metal interfacial plane.C) Comparison of the properties of 1L-MoS 2 /metal interfaces that are predicted to enable monolayer-selective MME and the experimental attempts with different 1L-MoS 2 /metal interfaces.Square data points are from this study and diamond data points are derived from the literature. [11,16]l could not enable monolayer-selective MME in this study similar to that reported in the literature, so the transferred 1L-MoS 2 on Al film is displayed instead labelled "Al (T)".The dashed grey lines show the 1L-MoS 2 /metal interface properties that result in 5% or 10% reduction in interlayer binding energy (E Int ) at the MoS 2 (1)/MoS 2 (2) interface according to the proposed model from Equation 14. Dotted grey lines show 5% or 10% reduction in E Int from strain effects only (ΔE Int ()).
the electron density and is dependent on the band structure and geometry of the crystals (Section S7, Supporting Information).Mannebach et al. [58] proposed a simplified model based on Lifshitz theory that estimates ΔE Int (n) in TMDCs by the Casimir force.The TMDCs layers are assumed to fit the Drude model (resistivity due to scattering of electrons by metal ions) for their dielectric function when they have high free electron density.[60] It is applicable to surface MoS 2 because the high surface doping causes large free electron density.This model calculates ΔE Int (n) from the change of volumetric charge carrier density (Δn) as, where m is the effective electron mass, e is the elementary charge, and l is the Mo-Mo interlayer distance.Larger n increases attractive interlayer vdW interactions.Using the full depletion approximation (Δn e = N d = 10 19 cm −3 ) , [50] m of MoS 2 of 0.45, l of ≈6.2 Å, [58] and assuming a Schottky junction on MoS 2 (1), ΔE Int (n) of the MoS 2 (1)/MoS 2 (2) interface can be obtained as (full derivation in Section S8, Supporting Information), The Casimir force change in ΔE Int (n) at the MoS 2 (1)/MoS 2 (2) interface is likely stronger than estimated by Equation 13, because the highly-doped, metal-like, surface MoS 2 can transition to a poor conductor (low free electron density) after electron depletion from the Schottky junction, however we do not account for that change here. [51,60,61]quations 6, 11, and 13 can be substituted into Equation 5to obtain an estimate of E Int at the MoS 2 (1)/MoS 2 (2) interface based on the Φ Δ and  in MoS 2 (1), Figure 3C plots the measured Φ Δ and  for the 1L-MoS 2 /metal interfaces from this study and from the literature for comparison (see Section S9, Supporting Information for all values). [11,16]Dashed lines denoting a 5% and 10% reduction in the MoS 2 (1)/MoS 2 (2) E Int are based on Equation 14. E Int0 = −0.01936 eV Å −2 was calculated from the MoS 2 bilayer calculation (Section S6, Supporting Information).
The effective monolayer-selective MME of bulk MoS 2 with Pd demonstrates that monolayer-selectivity is not solely due to ΔE Int (), as MoS 2 /Pd interfaces have small strain ( < 0.5%) that causes negligible ΔE Int ().Rather the positive ΔE Int (E) and ΔE Int (n) values explain the effective monolayer-selective MME using Pd surfaces.The ineffectiveness of monolayer-selective MME of bulk MoS 2 using directly-deposited Al is also not solely explained by ΔE Int (), as the large lattice mismatch between Al < 111 > and 1L-MoS 2 (≈5%) should produce a large  that reduces E Int . [39]Additionally, the binding/adsorption energy for 1L-MoS 2 /Al interfaces is high (−0.20 eV Å −2 ), which was previously proposed to increase monolayer-selective MME effectiveness. [10]nstead, the negative ΔE Int (E) and ΔE Int (n) of the MoS 2 /Al interface from the model offset the effect of ΔE Int (), resulting in unchanged or greater E Int .This is in contrast to prior literature models that propose that the binding energy and strain between the 1L-MoS 2 /metal interface are the only factors reducing attractive interlayer vdW interactions. [10]he examples of Pd and Al exemplify how the Schottky junction-induced electron depletion and electric fields in MoS 2 /metal interfaces reduce E Int and facilitate monolayerselective MME, in synergy with strain effects from lattice mismatch.The trends we observed are consistent with reports of metal MME in literature (Table S3, Supporting Information).The proposed model can effectively estimate the reduction in E Int due to the MoS 2 /metal interface properties.The model further suggests that E Int could be precisely controlled by an applied bias across the MoS 2 /metal interface, increasing monolayerselectivity and allowing switching from adhesion to exfoliation regimes.Electronic control of the vdW crystal E Int could vastly improve the effectiveness and efficiency of monolayer-selective MME and/or manipulation of monolayer vdW crystals towards device fabrication.

Conclusion
Different 1L-MoS 2/ metal interfaces were characterized in situ using Raman spectroscopy and DFT calculations to estimate the electrostatics and strain of MoS 2 in contact with metals.Schottky junctions at the 1L-MoS 2 /metal interfaces caused electron depletion/accumulation in 1L-MoS 2 and a built-in potential.A model is proposed that explains how the electrostatics of the MoS 2 /metal interface acts synergistically with applied strain to determine monolayer-selectivity of MME by modulating the MoS 2 interlayer vdW interactions.The model estimates a change in MoS 2 interlayer energy from the measured MoS 2 /metal interface electrostatics and strain that correlates with the monolayerselectivity of metals for bulk MoS 2 MME.The model demonstrates the significance of electrostatics in modulating nanomaterial vdW interactions and the potential for precise electronic control of vdW interactions for nanomaterial exfoliation and manipulation.The principles underlying the model will provide significant impact beyond MME, including understanding the impact of electrostatics on vdW interactions in materials, and designing ohmic contacts for optoelectronic devices, sensing systems, and vdW heterostructures.

Experimental Section
Fabrication of 1L-MoS 2 /Metal Interfaces (Direct Deposition Method): Bulk MoS 2 crystal, naturally sourced and purified, was supplied by 2D Semiconductors (AZ, USA).The bulk MoS 2 crystal was adhered to low-tack clean room tape.100 nm of either Au, Pd, Ag, Pt, Ni, Cu, or Al was directly deposited onto the exposed face of the bulk MoS 2 by PVD at <10 −6 torr.Pd, Ag, Pt, Ni, and Al metals were deposited using an Angstrom Engineering Thin Film Deposition System and Au and Cu were deposited using a Thermionics e-Beam +D5:D27 Evaporator system.Au, Pd, Pt, and Cu were evaporated with an electron beam and Ag, Ni, and Al were thermally evaporated.Deposition rate was 0.1 Å s −1 for the first 5 nm and then ≈1 Å s −1 thereafter to reduce damage to the MoS 2 .MME was then performed; thermal release tape was applied and adhered to the deposited metal film face (of the tape/MoS 2 /metal sample) and pulled off, thereby monolayer-selectively exfoliating the MoS 2 and resulting in a large yield of 1L-MoS 2 on the metal adhered to the thermal release tape (except for Al).The exposed 1L-MoS 2 on the metal film was then characterized.
Fabrication of 1L-MoS 2 /Al Interface (Transfer Method): 100 nm of Al was directly deposited onto a Si/SiO 2 wafer substrate by PVD at <10 −7 torr using an Angstrom Engineering Thin Film Deposition System.Immediately after deposition and opening of the deposition chamber (<20 s), bulk MoS 2 was applied to the fresh Al film surface and firmly pressed for 1 min to exfoliate the bulk MoS 2 onto the Al film.The deposition chamber opens into a controlled atmosphere glovebox (<100 ppm O 2 , ≈0 ppm H 2 O) preventing exposure of the Al film surface to ambient atmosphere and reducing any potential oxidation.The bulk MoS 2 crystal was then slowly removed, with exfoliated MoS 2 flakes remaining on the Al film.The proportion of 1L-MoS 2 exfoliated was extremely low; almost all exfoliated MoS 2 flakes on the Al film were multilayer.
Raman Spectroscopy Characterization and Analysis of 1L-MoS 2 /Metal Interfaces: Raman spectroscopy characterization of the 1L-MoS 2 in contact with metal films was performed using a Renishaw InVia Raman Spectroscopy Microscope.Excitation was at 532 nm with a typical 1% power.Spectra were accumulated at single points on the 1L-MoS 2 samples for 10 s and 20 repetitions using 1800 cm −1 grating.Raman spectra were obtained from 4-10 different locations on a 1L-MoS 2 /metal sample and averaged to produce the 1L-MoS 2 /metal interface Raman spectra, displayed in Figure 1, and used for analysis.Averaging was necessary to reduce noise in the spectra due to the low intensity of the peaks and to reduce errors from interface defects generated during fabrication.Raman spectra were normalized to the maximum peak intensity of each spectrum.Voight peak profiles were fitted to the Raman spectra to obtain the Raman mode peaks.
[64] A van der Waals correlation correction was applied using the method of Grimme, with Becke-Jonson damping. [65,66]Projector augmented-wave (PAW) potentials were used to describe the core-valence interaction with the valence electrons described by periodic plane waves with cut-off energy of 520 eV.The convergence criteria used for energy and forces on each atom was 10 −6 eV and 10 −2 eV Å −1 , respectively.The charge transfer, from and to the metallic substrate, had been calculated considering the charge included within the Wigner-Seitz atomic radius.
Optical Microscopy and X-ray Spectroscopy of 1L-MoS 2 /Metal Interfaces: Optical microscope images of the 1L-MoS 2 /metal samples were obtained using an Olympus BH2-UMA optical microscope with 50x objective and NIS Elements acquisition software.
Energy dispersive X-ray spectroscopy of the 1L-MoS 2 /Pd interface sample was obtained with a Hitachi FlexSEM 1000 using the EDX mode with a XFlash 5010 detector.Data was acquired with 15 keV beam energy at 30°take-off angle, 25 s acquisition time, 10.5 mm working distance, and ≈150 μm x 200 μm scan area.

Figure 1 .
Figure 1.A) In-plane, E′, and out-of-plane, A 1 ′, Raman-active fundamental vibrational modes of 1L-MoS 2 that have intrinsic (unmodulated) Raman shifts of 385 and 405 cm −1 , respectively.B-G) Non-resonant Raman spectra of 1L-MoS 2 contacting Au, Pd, Ag, Pt, Ni, or Cu films, respectively, prepared by direct PVD of metals on bulk MoS 2 , and performing MME.H) Non-resonant Raman spectra of 1L-MoS 2 contacting Al film obtained by standard mechanical exfoliation on an Al film, labelled as Al (T).Spectra were obtained with a 532 nm excitation wavelength.A 1 ′ mode peaks and E′ mode peaks are blue and red, respectively.Peaks marked with dashes are from a secondary region of the 1L-MoS 2 /metal interface.Other Raman-active vibrational mode peaks are grey.Raman spectra are normalized to the maximum intensity peak within each spectrum.I) Δn e versus percentage ɛ of the 1L-MoS 2 at the various 1L-MoS 2 /metal interfaces, calculated from the respective measured Raman spectra peaks.
(Supporting Information) shows the Raman spectra obtained from 1L-MoS 2 samples in contact with different metal films and the Voigt profile-fitted characteristic Raman vibrational mode peaks.MoS 2 Raman peaks are

Figure 2 .
Figure 2. A) Schematic of the band structure of typical n-type MoS 2 and a metal surface, before and after contact, showing the formation of a Schottky junction.Electrons are depleted from the MoS 2 and transfer to the metal to maintain a constant electrochemical potential across the interface, resulting in band bending at the interface and an in-built potential at the MoS 2 surface.B) Raman spectra-determined Δn e for the different 1L-MoS 2 /metal interfaces against their ideal built-in potential (Φ i ) (filled squares), showing increased electron depletion with greater Φ i .The interfacial electron transfer obtained by DFT calculations is also plotted against Φ i , showing a similar trend.C) 3D rendering of the DFT calculations of the 1L-MoS 2 /metal interfaces and visualization of the electron redistribution at the interface.1L-MoS 2 /Au, 1L-MoS 2 /Pd, and 1L-MoS 2 /Al interfaces are exhibited left to right.Blue and magenta volumes indicate electron depletion and accumulation, respectively (brightness does not indicate depletion/accumulation magnitude).

Table 1 .
Peak positions and descriptions of the Raman mode peaks of interest for characterizing the 1L-MoS 2 /metal interfaces.