Molecular beam epitaxy and other large-scale methods for producing monolayer transition metal dichalcogenides

Transition metal dichalcogenide (TMD/TMDC) monolayers have gained considerable attention in recent years for their unique properties. Some of these properties include direct bandgap emission and strong mechanical and electronic properties. For these reasons, monolayer TMDs have been considered a promising material for next-generation quantum technologies and optoelectronic devices. However, for the field to make more gainful advancements and be implemented in devices, high-quality TMD monolayers need to be produced at a larger scale with high quality. In this article, some of the current means to produce larger-scale semiconducting monolayer TMDs will be reviewed. An emphasis will be given to the technique of molecular beam epitaxy (MBE) for two main reasons: (1) there is a growing body of research using this technique to grow TMD monolayers and (2) there is yet to be a body of work that has summarized the current research for MBE monolayer growth of TMDs.


Introduction
Since the isolation of graphene, the field of 2D materials has gained wide interest for their unique optical, electronic, and flexible properties [1][2][3][4].In particular, one class of materials has gained considerable attraction for their remarkable Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.electronic potential and being a promising material in the rapidly growing field of quantum technology, are semiconducting transition metal dichalcogenides (TMDs).Monolayer TMDs have already been demonstrated in many electronic devices and have also been shown to be a viable platform for deterministic sources of single photon emitters which are the key component in quantum devices [5][6][7][8][9][10][11][12][13][14][15].However, despite having favorable characteristics for devices, being able to produce larger-scale monolayer TMDs remains a major engineering problem.
Much of the research to date that has utilized monolayer TMDs obtained their samples from mechanical exfoliation figure 1(a).Some of the shortcomings of this method are the generation of small crystal sizes ranging from ten to hundreds of microns and low yield.Despite several advances, this method uses scotch tape and resists which results in residue on the monolayers which limits the application of 2D TMD crystals even if the bulk growth method generated pristine samples [16][17][18].For these reasons, the process of exfoliation is not sufficient for practical device fabrication in an industry setting where monolayer TMDs would need to be produced reliably at a certain size with large throughput.For monolayer TMDs to become mainstream materials for devices in industry, research must be done to produce larger monolayer TMDs; this means that other techniques for obtaining monolayer TMDs must be explored.
In this review, we are going to discuss the current methods being implemented to produce large-scale semiconducting monolayer TMD samples with an emphasis on molecular beam epitaxy (MBE).So far, reviews on growing TMDs via MBE focused on multiple-layer growth [19].This review will begin by introducing the general structure and properties of TMDs section 1.1.From there, the growth of monolayer TMDs via MBE will serve as the bulk of the review section 2. Considerations for single crystal monolayer TMD growth will be then addressed along with how recent advances by CVD can advance the MBE field section 3. Lastly, gold exfoliation, another technique for obtaining large-scale monolayers, will be addressed section 4.

Crystal structure and properties of TMDs
The functional form for TMD crystals is MX 2 where the M is a transition metal atom (such as Mo or W) and the X is a chalcogen atom (such as S, Se, or Te).One monolayer of a TMD is formed from three atomic layers where metal atoms are sandwiched and covalently bonded between two identical chalcogen atoms.Monolayer materials can display drastically different optical and electrical properties than when they are in their bulk form.
One main property that changes at the monolayer limit is the bandgap.For example, in bulk MoS 2 , the material has an indirect bandgap.This changes to a direct bandgap as the layer number is reduced.Figure 1(b) is the calculated band dispersion using DFT displaying the layer-dependent transition from indirect (bulk) to direct (monolayer) [20].Other notable TMDs that exhibit a similar bandgap transition from bulk to monolayer are MoSe 2 , WS 2 , and WSe 2 .This is significant as direct bandgap semiconductors are more suitable for general optoelectronic devices as direct bandgap semiconductors have a higher probability for electron-hole radiative recombination [21].The properties of monolayer TMDs can also be dependent on the structural phase they exhibit (figure 1(c)).Most of the semiconductor TMDs find a stable configuration in the 2 H phase, but some monolayer TMDs when grown, such as MoTe 2 , can find a stable configuration in both the 2 H the 1 T ′ phases.The 1 T ′ phase is metastable and behaves as a semimetal; the topic of phases will be expanded upon further in section 2.2.

Large scale growth of monolayer TMDs via MBE
MBE is a desirable platform for growing 2D materials given that it is known for being an ultra-high vacuum growth technique (<1 × 10 −8 Torr) which can grow conventional materials with high purity and excellent crystal quality [23,24].Unlike other growth techniques, MBE's slow growth rate (few hundred nm hr −1 ) allows for highly controlled growth, resulting in very smooth thin films [23,25].Embedded in MBEs, reflection high-energy electron diffraction (RHEED) systems also allow for the monitoring of structure and composition during growth [25].While techniques like chemical vapor deposition (CVD) have made great strides in growing monolayer TMDs at wafer scale, a limit has been reached in terms of minimizing defects in their 2D semiconducting monolayers [26].Obtaining low-defect 2D semiconductors is a primary objective in the community, and currently, the point defect density in CVD-grown 2D semiconductor TMDs is about 10 12 -10 13 cm 2 [26].To be more useful for industry purposes, it has been stated that this point defect density should be reduced by an order of three magnitudes [26].For these reasons, it is worth investing more research into techniques like MBE for 2D materials growth as this is a platform known for growing the highest quality conventional materials.
The typical MBE consists of a stainless steel main chamber, multiple pumps to maintain an ultra-high vacuum, a substrate heater, effusion cells (or Knudsen cells), and multiple other components (figure 2) [25].Inside the MBE vacuum system, crucibles heat elemental sources with ultra-high purity (99.99%)where the materials evaporate through a small aperture pointed toward a substrate.The heated metal vapor will then diffuse to an energetically favorable location on the substrate where atoms can grow into a film.For TMDs, the transition metals (such as Mo or W) are heated in an electron beam evaporator which is the standard tool on MBE when working with refractory metals that exhibit high melting points.The chalcogen elements (such as Se, S, or Te) can be heated in standard MBE effusion cells.At this current date, MBE has not had as much development in growing monolayer TMDs as other techniques.This may be attributed to the limited number of groups growing chalcogenides plus the challenges of using electron beam sources for evaporating refractory metals.The following subsections will review the current efforts to grow large-scale semiconducting monolayer TMD diselenides, disulfides, and ditellurides via MBE For information on the growth of multi-layer TMDs via MBE Singh and Gupta is recommended [19].

Growth of monolayer diselenides
In this section of the review paper, we will discuss some of the works looking into growing MBE monolayer MoSe 2 and WSe 2 .Some of the first works relating to growing monolayer/few-layer TMDs using MBE were selenides in 2014 and 2015 by Zhang et al, Liu et al and Jiao et al [27][28][29][30][31]; all of the studies used MBE to grow MoSe 2 using graphene or highly ordered pyrolytic graphite (HOPG).In particular,  Jiao et al investigated the growth and boundary formation of MoSe 2 on graphene and HOPG; they demonstrated that when using these substrates, MoSe 2 growth occurs over a wide range of growth conditions by the nucleation of 2D islands on the surface [31].The size of the grown monolayer MoSe 2 flakes was not reported, but an epitaxy relationship of monolayer MoSe 2 on HOPG was established; in particular, it was noted that the step edges of the substrate can act as nucleation sites along with various growth conditions that can impact defect formation during growth.
In 2017, Chen et al grew monolayer MoSe 2 on GaAs(111)B to demonstrate large-scale monolayer TMDs grown via MBE can be used for device application.GaAs(111)B was chosen as the growth substrate for this experiment because it allowed for a large degree of freedom of control over lattice orientation as the two materials share a similar symmetry [6,31].The electrical properties of MBE-grown monolayer MoSe 2 were probed via transistor applications.They found that their charge mobility values (see table 1) were significantly lower than those of CVD-grown MoSe 2 ; this indicated to them that the charge carrier transport was strongly influenced by disorder in the monolayer [6].The photoluminescence (PL) spectra of the MBE-grown monolayer MoSe 2 from this work displayed broader emission relative to the PL of exfoliated monolayer flakes.The spectral broadening and lower optical qualities exhibited by MBE grown monolayers [6,29,30,[33][34][35][36][37][38] has given rise to the claim that the optical qualities of monolayers grown via MBE are worse than exfoliated flakes [39].
In 2020, research was conducted to counter the effects of spectral broadening that seems to occur in MBE-grown monolayer samples.To improve the PL linewidth of MBEgrown monolayer samples, Packuski et al utilized exfoliated hexagonal boron nitride (hBN) as a substrate; hBN is commonly used with semiconducting TMDs to improve electronic and optical qualities [39][40][41][42][43].By using hBN as a substrate, they demonstrated that MBE-grown TMDs can be comparable optically to exfoliated TMDs.They grew on samples of 1 cm 2 wafer of Si(100) with a 90 nm thick layer of SiO 2 which was then covered by a large number of exfoliated hBN flakes.MoSe 2 was then deposited on the entire wafer via MBE; a scheme of the sample is displayed in figure 3. Using a variety of growth times, the best monolayer areas were acquired when using a slow growth rate (12 hours of growth) and annealing at 750 • C.
In 2023, Xia et al claimed 2 in wafer-scale singlecrystalline MoSe 2 and WSe 2 monolayers grown by molecularbeam epitaxy at low temperatures [44].The substrate of choice in this experiment was an Au(111) film on an Al 2 O 3 or Mica substrate.The choice of the crystalline Au substrate was attributed to its stability in a chalcogen-rich environment [45][46][47] and that it had been adopted successfully for CVD growth of metal-disulfides [48][49][50][51].To start this growth process, the Au surface is cleaned via Ar + sputtering followed by thermal annealing to obtain a flat and threefold symmetrical surface.The surface is then exposed to selenium before and during MSe 2 (M = W or Mo) deposition at 200 • C-400 • C. The surface of the substrate before and after the Se deposition is shown in figure 4(a).The growth pattern during the initial growth is shown in figure 4(b) where triangular islands seem to grow in random areas with the same orientation rather than grow at the Au steps.As the growth continues, the triangular islands grow and merge seamlessly (figures 4(c) and (d)).A schematic (upper panel) and scanning electron microscope images (lower panel) of the growth stages at different times are shown in figures 4(e)-(g).

Growth of monolayer disulfides
While there is not a lot of literature on the MBE growth of monolayer sulfides, much work has been done in recent years in growing MoS 2 .As of recently, epitaxial techniques like CVD/MOCVD have been the most promising techniques for growing monolayer TMD sulfides having demonstrated MoS 2 [52][53][54][55][56] and WS 2 [57][58][59][60] monolayer samples using a variety of different substrates.In 2017, Fu et al wanted to address the issues of grain orientation by using MBE which allows more precise tuning of growth flux and substrate orientation [61].This study demonstrated MBE growth of epitaxially aligned monolayer MoS 2 on exfoliated hBN.
This study obtained uniform MoS 2 growth via MBE using a two-step nucleation process: (1) The first step involved heating the substrate to 750 • C while Mo and S fluxes were introduced and allowed to interact with the surface for 3 to 4 hrs.This step would produce individually small triangles of MoS 2 to form.
(2) In the second step, the substrate temperature was increased to 900 • C, and the Mo flux decreased.The initial triangular MoS 2 nucleation domains transformed into well-aligned hexagonal crystals; this growth step would continue for 6 to 7 hrs until MoS 2 covered the entire hBN flake.The characteristics of the MoS 2 and AFM images depicting this two-step nucleation are displayed in figure 5.In a previous study where MoS 2 was grown on hBN using CVD, the film was covered equally by two different grain orientations, 0 • and 60 • [62].When using MBE by controlling the growth temperature and precursor flux, Fu et al got only the 0 • orientation leading to a smooth film.

Growth of monolayer ditellurides
For the most commonly studied semiconducting TMDs such as MoSe 2 , WSe 2 , MoS 2 , and WS 2 , the 2 H hexagonal phase is most energetically favorable.This is not the case for ditellurides such as WTe 2 and MoTe 2 ; for WTe 2 , the 1 T ′ phase is more energetically favorable than the other phases, and for MoTe 2 , there is little preference in phase as the energy difference between the 2 H and 1 T ′ (<0.05 eV per formula unit) [63][64][65].While the 1 T ′ phase has been shown to behave as a semi-metal and has gained particular interest for its topological properties, only the 2 H phase behaves as a direct bandgap semiconductor [65,66].Given that the goal of this paper is to discuss the current MBE methods to grow semiconducting TMDs, we will focus on the current efforts that have been made to control the phase and growth of 2 H-MoTe 2 .In 2020, Seredyński et al used MBE to grow MoTe 2 on a 1 cm exfoliated hBN structure similar to that in figure 11 [67].They recorded different growth processes with varying growth temperatures, growth times, and Te flux.While they did display the varying growth conditions that led to the formation of quasi-1D structures, they did not obtain large continuous monolayers of a single phase.In 2022, Ohtake et al grew MoTe 2 on GaAs(111)B to investigate the behavior of certain growth phases under different conditions for large-scale applications [63].They found that with annealing in a Te-rich environment, they could obtain a film mostly composed of the 2 H phase.While they only grew small samples (mm size), they claim there is no reason that their growth recipe could not be used on larger 2-inch wafers.

Considerations for single crystal growth as informed by recent CVD developments
In this section, considerations for how single crystal monolayer TMDs will be examined along with how recent research done using CVD can inform advanced single crystal growth in MBE Before growth even begins, the choice of substrate is a critical consideration.In 2020, Dong et al published work on a theoretical framework for the epitaxial growth of 2D materials and their interplay with substrates [68].Based on DFT calculations, they noted that the high symmetry direction of the 2D material tends to align along a high symmetry direction of the substrate.They composed a table of the different possible alignments of 2D materials on different substrates; a comparison of their theoretical predictions with experimental work for the growth of TMDs on substrates is shown in figure 6.In another report the same year, Ohtake and Sakuma grew monolayer MoSe 2 films on three differently oriented GaAs substrates (figure 7); they found that MoSe 2 would align with its direction having the highest linear atomic density parallel with the GaAs substrate and they noted the lattice mismatch was not a significant factor in forming an epitaxial relationship [32].
Having a stable surface energy, atomic flatness, and no dangling bonds is ideal for 2D growth systems as this allows for only vdW interactions between the substrate and the 2D material [76][77][78].This is most likely one of the reasons why much of the research cited in this review on monolayer growth had some form of treatment process for their substrates before growth [6,32,44,63].While this can be an important consideration for a given substrate, it is also important to consider the surface of the substrate and if any techniques can be implemented to grow 2D materials rather than just thinking about symmetry and the reduction of dangling bonds.In this regard, recent research in CVD could be a good guide on growing monolayer TMDs for MBE CVD is arguably one of the most popular techniques for growing 2D monolayers featuring many publications [79][80][81][82] and reviews [83][84][85][86].Recent publications using CVD have made great strides in growing large-area monolayer TMDs on C-plane sapphire ((0001)α-Al 2 O 3 ) which we think would be useful to MBE users.α-Al 2 O 3 is a popular substrate to grow on because of its commercial availability, thermal stability, and similar symmetry to TMD materials.Multiple studies using CVD techniques to grow monolayer TMDs on α-Al 2 O 3 reported that the grains of the TMD would align themselves with the steps on the sapphire surface.By tuning the growth parameters, multiple studies have obtained mostly uniform monolayer TMD coverage [81,87,88].This type of epitaxial growth has been termed 'step-guided epitaxy' as the steps on the substrate would help guide the unidirectional alignment of the 2D material [78].
We choose to focus on step-guided epitaxy as we think it could apply to MBE both in terms of trying to replicate it and also demonstrating that multiple techniques have been implemented by researchers via CVD but have not been demonstrated in MBE In 2023, research was published by Fu et al demonstrating that the step edges on α-Al 2 O 3 were not the main driver for allowing uniformly oriented monolayer growth.By performing cross-sectional dark field (DF) scanning transmission electron microscopy (STEM), they were able to confirm that the step edges of α-Al 2 O 3 are made up of crystal slabs with the same termination, but the two slabs are mirror-reflected (figure 8).By annealing in the presence of oxygen at > 1400 • C the surface steps of α-Al 2 O 3 could be reconstructed such that only one type of slab would be exposed to the surface which was favorable for monolayer growth (figure 9).A technique like this could easily be replicated in MBE possibly providing new insights into growth and defect formation.For more information on different various growth modes like step-guided epitaxy, Zhang et al published a review on the epitaxy of 2D materials towards single crystals for CVD systems [78].Reprinted with permission from [32].Copyright (2020) American Chemical Society.

Gold exfoliation techniques
As mentioned earlier, since the exfoliation of graphene in 2004, exfoliation has been the main method for preparing monolayer samples for research purposes.In 2015, Fu et al wanted to address the low-yield and small-size monolayers obtained from normal exfoliation by introducing a gold exfoliation technique [89].They used gold to exfoliate monolayer flakes of MoS 2 and WSe 2 that were hundreds of microns.Chalcogenide atoms have a strong chemical affinity to gold and the two materials can bond strongly together making it easier to obtain large flakes [90][91][92][93][94]. Since 2015, many other works have used gold tapes to obtain large-area monolayers, and it has been demonstrated to obtain monolayer TMDs that reach centimeter-scale sizes [92,[94][95][96].Many of these different gold exfoliation techniques are reviewed by Heyl et al [97], but since then, research has been done that we would like to address in this review.Monolayers obtained using gold tape methods suffer from broad exciton linewidths, poor quantum efficiency, and large inhomogeneity across the sample [84,88,89].While there has been research to address this issue, to do so, the large area monolayer flakes were broken down to micron sizes to be encapsulated with exfoliated hBN [84].
In 2023, Li et al published research on an encapsulation technique that allowed for high-quality exciton linewidths while maintaining the large-area monolayers provided by gold exfoliation [94].First, to create the 'gold tape' to exfoliate large monolayers, they used a method from Liu et al (figure 10) [92].To address the problems that normally come     After studying different variations of this encapsulation method, the data suggested that the bottom layer of dodecanol protects the monolayer from charge disorders on the substrate surface; this suppresses non-radiative decay and increases the intensity of PL emission.The top dodecanol layer also improves the PL as it appears to help passivate defects on the monolayer surface.The PL spectra along with reflective contrast spectra (RC) of the large-scale MoSe 2 with and without this encapsulation method are displayed in figures 11 (c) and (d).

Summary and future outlook
is the first review to summarize the current research on obtaining large-scale semiconducting monolayer TMDs via various methods.In particular, we have reviewed multiple research publications for different MBE growth techniques for the most common semiconducting monolayer diselenides, disulfides, and ditellurides.With Moore's law reaching a plateau and the rapid development of quantum technologies, it is important to look to new materials to help advance these technologies and 2D TMDs are an excellent candidate.However, until 2D TMDs can be fabricated at large sizes with high quality, industrial uses for these materials will remain unlivable.
The field of monolayer TMD growth would benefit from more research regarding 2D material and substrate interaction as there are still new developments on substrate processes that can be done before growth.Regarding monolayer growth with MBE we think it is important to prioritize various substrate interactions and symmetry interplay before growth when attempting to develop a monolayer single-crystal film.Growth parameters such as growth rate, temperatures, and flux are also important when developing a monolayer single-crystal film and should be thoroughly examined.Lastly, the field of monolayer TMD growth on MBE can learn from the processes and developments that are being done through CVD and other methods.Using MBE to replicate and confirm techniques that have succeeded through other growth methods can help further our understanding of not only monolayer TMD growth but also the field of 2D materials.

Figure 1 .
Figure 1.(a) Schematic of mechanical exfoliation: (I) Scotch tape is attached to the top van der Waals (vdW) crystal.(II) Tape is peeled off of the top of bulk sample so that only few layers are on the tape.(III) The tape with few layers is then pressed against a desired substrate.(IV) The tape is then peeled from the substrate leaving the bottom layer of material.Reproduced from [22].© IOP Publishing Ltd.All rights reserved.(b) Bandgap of MoS 2 as the number of layers varies: (I) Bulk MoS 2 , (II) Four layer MoS 2 , (III) Bilayer MoS 2 , and (IV) Monolayer MoS 2 .Reprinted with permission from [20].Copyright (2010) American Chemical Society.(c) Table of the three different TMD phases with 2 H being the structural phase in TMD semiconductors.

Figure 2 .
Figure 2. Schematic diagram displaying the multiple components that make up an MBE system.

Figure 3 .
Figure 3. Depiction of MoSe 2 samples grown by MBE on SiO 2 covered partially by hBN flakes.The typical dimensions of the Si (100) wafers were 1 cm 2 .The lateral size of flat hBN flakes is up to 200 µm [39].

Figure 4 .
Figure 4. (a) The Au(111) substrate before and after the Se deposition.(b) The growth pattern during the initial growth is shown where triangular islands seem to grow in random areas with the same orientation.(c)-(d) As the growth continues, the triangular islands merge into a single crystalline film.(e)-(g) A schematic (upper panel) and scanning electron microscope images (lower panel) of the growth stages at different times.Reproduced from [44].CC BY 4.0.

Figure 5 .
Figure 5. Two-step nucleation process for MoS 2 film.(a) Photoluminescence and (b) Raman spectra of a grown monolayer MoS 2 film on hBN (red curves) compared with results from exfoliated single crystalline MoS 2 monolayers on hBN (blue curves).(c)-(f) AFM scans at different growth stages: (c) nucleation of triangular grains, (d) enlarged grains with hexagonal shape (transformed from triangular grains), (e) The hexagonal grains have expanded to almost all of the film, (f) uniform monolayer film.The height profile along the dashed line in (d) Reprinted with permission from [61].Copyright (2017) American Chemical Society.

Figure 6 .
Figure 6.Alignment of TMDs on commonly used low-index substrates: experimental results from TMDs grown via CVD are compared with theoretical predictions.N represents the number of possible alignments and θ represents the misorientation angle of TMD grains.ZZ represents zigzag edge of the TMD.Reproduced from [68].CC BY 4.0.

Figure 8 .
Figure 8.(a) A and B slab that form α-Al 2 O 3 steps with a mirror-symmetric and threefold atomic arrangement.The surfaces of the A and B slabs stack in alternating order along the [1120] direction.(b) Cross-sectional DF-STEM displays the atomic arrangement of the A and B slabs.Reproduced from [89], with permission from Springer Nature.

Figure 9 .
Figure 9. (a) Schematic and corresponding AFM images of antiparallel triangular MoS 2 domains (marked by blue and yellow triangles) appear alternatively on slabs A and B along the [1120] direction.(b) The presence of a single-type slab is the main driver for obtaining uniform orientation of MoS 2 flakes.Reproduced from [89], with permission from Springer Nature.
Figure 10(a) displays atomic force microscopy (AFM) of a large-scale MoSe 2 monolayer encapsulated in 1-dodecanol over a 5 × 5 µm 2 area.The height of the highlighted area in figure 11(a) is represented in figure 11(b) where the encapsulation method can be seen more clearly.

Figure 10 .
Figure 10.Gold exfoliation method used to obtain large-scale TMD monolayer from Liu et al in 2020.Reproduced with permission from [92].