Nonmetal‐Mediated Atomic Spalling of Large‐Area Monolayer Transition Metal Dichalcogenide

Transition metal dichalcogenides (TMDCs) have attracted intense interest; however, despite the considerable effort of researchers, a universal manufacturing method that can guarantee both high material quality and throughput has not been realized to date. Herein, a universal approach to producing high‐quality monolayer TMDCs on a large scale via germanium (Ge)‐mediated atomic spalling is presented. Through the modified analytic model, the study verifies that the thin Ge film could be a suitable stressor that effectively reduces the crack propagation depth at the sub‐nanometer range. In particular, an acid‐etching process is not required in the overall atomic spalling process due to the water‐soluble nature of the Ge, enabling it widely applicable to various TMDCs. Under the optimized spalling conditions, a millimeter‐sized monolayer of stable MoS2, as well as unstable MoTe2, is successfully achieved. Through detailed spectroscopic and electrical characterizations, it is confirmed that the proposed methodology for obtaining large‐area atomic layers does not introduce any significant structural defects or chemical contaminations.


Introduction
8][9][10] Although a proof of concept of functional devices based on TMDCs has been demonstrated, there is yet to be a known scalable materials production method that can achieve both high material quality and throughput production.
13] Nevertheless, the formation of structural defects during the growth process is inevitable during CVD, thus degrading the inherent properties of TMDCs and the overall device performance. [14,15]eanwhile, mechanical cleavage approaches have emerged as the simplest way to obtain the best-quality monolayer TMDCs to date.However, the size of isolated monolayer flakes obtained using such an approach is generally limited to tens of micrometers, and the yield is very poor, which restricts its usage for academic purposes. [16,17][23][24][25][26][27][28] For example, Huang et al. achieved monolayer TMDCs from bulk crystals by leveraging the strong affinity between Au atoms and chalcogen atoms. [21]In another study, Moon et al. reported an atomic spalling method, known as the controlled crack propagation technique, by adjusting the interfacial toughness and the internal stress of the metal film. [28,29]However, according to the conventional process of modified exfoliation techniques, a wet-etching process based on strong acids or iodine to remove the top or bottom metal layers (Au or Ni) is needed, which is environmentally harmful and cannot be applied to chemically unstable TMDCs (e.g., MoTe 2 ). [30]ere, an effective and universal TMDCs monolayer manufacturing method, on a macroscopic scale, is presented.Using Ge as a stressor film, controlled atomic spalling of monolayer TMDCs from bulk van der Waals (vdW) crystals is induced.Ge can serve as a suitable stressor material for atomic spalling because of its small interfacial toughness (γ) with vdW materials (γ Ge-vdW = 32 meV atom À1 ), which is similar to the interfacial toughness within vdW materials (γ vdW-vdW = 25 meV atom À1 ), which could effectively reduce the spalling depth of 2DMs to a few atoms thick. [31,32]Above all, the water-soluble nature of Ge means it does not require a wet chemical etching process, thus making it widely applicable to various TMDCs.By utilizing a 70 nm-thick Ge stressor, millimeter-scale monolayer TMDCs (MoS 2 and MoTe 2 ) were successfully separated from the crystals.The spalled monolayer does not exhibit any intrinsic defects or chemical contamination, as confirmed by spectroscopic and electrical characterization.It is believed that the Ge-mediated atomic spalling approach to achieve high-quality and large-scale monolayer TMDCs will pave the way for scaling up the production of 2DMs and accelerate both their fundamental research and industrial applications.

Analytic Model for Ge-Mediated Atomic Spalling
To investigate critical spalling conditions in the Ge/TMDCs bilayer system, theoretical studies were first conducted based on the modified Suo-Hutchinson (S-H) model. [33,34]The intrinsic, well-known properties (i.e., Young's modulus and Poisson's ratio) of MoS 2 crystal were used to determine whether and how spalling depth (d spall ) is dependent on the internal stress of the Ge stressor (Figure 1a and Notes S1 and S2, Supporting Information).The estimated process window for controlled spalling of the MoS 2 crystal is depicted in Figure 1b.When the controlled spalling condition is satisfied, a crack initiates from the edge of the MoS 2 crystals upon the application of a gentle external force to the Ge stressor.This crack then propagates downward due to the mixed-mode fracture of K I (vertical stress direction) and K II (lateral stress direction). [33,34]Under thermodynamic equilibrium conditions, where K II becomes zero, the total accumulated strain energy of the Ge/MoS 2 bilayer system reaches an equilibrium with the binding energy of MoS 2 , at which point the crack no longer propagates downward but grows parallel to the interface between MoS 2 and the Ge stressor.Consequently, the top MoS 2 layers can be selectively separated from the crystals.The relationship between the d spall of MoS 2 and the internal stress (σ f ) of Ge can be expressed as follows. [28] where ν s , Y s , t s , t f , ν f , and Y f are Poisson's ratio of MoS 2 , Young's modulus of MoS 2 , the thickness of MoS 2 , the thickness of the Ge film, Poisson's ratio of Ge, and Young's modulus of Ge, respectively.In the deposition system, it was experimentally confirmed that the σ f of the Ge film with a thickness of 70 nm is about 262 AE 10 MPa, which is within the controlled spalling region criteria (blue star symbol in Figure 1b).Therefore, when the t f is 70 nm, it is expected that the value of d spall -which is the point at which the binding energy of MoS 2 is balanced with the total accumulated strain energy-is within a range of monolayer MoS 2 thickness when t s is between 170 and 230 nm (Figure 1c).

Atomic Spalling of Monolayer MoS 2
Based on the theoretical predictions, atomic spalling of the topmost monolayer of MoS 2 from the thick MoS 2 crystal was conducted.Figure 2a shows the detailed process of Ge-mediated  Figure 2b shows a photograph of spalled monolayer MoS 2 on the 300 nm SiO 2 /Si substrate.A continuous MoS 2 monolayer with a lateral size of a few millimeters was successfully separated from the thick MoS 2 crystal without physical or chemical damage (Figure 2c,d, and S3, Supporting Information).
The quality of the spalled monolayer MoS 2 samples was verified through Raman and photoluminescence (PL) spectroscopy analysis.Figure 2e-g shows the representative Raman spectra and histogram for the spalled monolayer MoS 2 .The strong E 2g and A 1g peaks, which are associated with the out-of-plane and in-plane vibration modes of MoS 2 , respectively, are located at the nearly fixed positions of %381.2 and %401.5 cm À1 , respectively, with a position difference of around %20 cm À1 . [35,36]The E 2g peak position in the spalled sample was found to be slightly redshifted compared to the tape-exfoliated monolayer MoS 2 (Figure S4, Supporting Information).This observation indicates that the spalled monolayer is under tensile strain, which is a typical feature of spalled materials. [29]The intensity of the defectrelated peaks at %227 cm À1 in spalled monolayer MoS 2 was negligible (Figure S5, Supporting Information). [37]Moreover, strong PL intensity was acquired at 77 K and observed at 1.90 eV, as shown in Figure 2h and S6, Supporting Information. [38,39]The full width at half maximum (FWHM) of the E 2g peak and PL peak were 4.8 AE 0.54 cm À1 and 0.12 AE 0.016 eV, respectively, which were comparable values with those of the tape-exfoliated monolayer MoS 2 (Figure S7, Supporting Information).The above results suggest the thickness uniformity and high crystallinity of spalled MoS 2 and support that the study's Ge-assisted spalling approach is an effective method for obtaining high-quality monolayer TMDCs on a large scale. [40,41]

Atomic Spalling of Unstable Monolayer MoTe 2
One of the key benefits of the study's approach is that it does not require a chemical-based wet etching process.While a diverse range of vdW materials has been discovered, and although its large-area monolayers have been successfully obtained through a modified exfoliation approach, chemically unstable TMDCs still pose difficulties in achieving large monolayers because unavoidable surface oxidation and physical damage occur during the metal film removal process.For example, monolayer MoTe 2 , which has a rich phase structure with important application potential, has not been realized in a large area or freestanding form using a recently modified exfoliation method.To this point, it has only been implemented on a metal substrate, and subsequent metal removal steps were needed for transfer onto the target substrate.Here, the study spalled chemically unstable MoTe 2 via a water-soluble Ge-mediated spalling method.The entire spalling process only involves DI water, which prevents degradation of the intrinsic properties of MoTe 2 throughout the procedure (Figure S8 and S9, Supporting Information). [30,42]ince the mechanical properties of MoTe 2 are similar to those of MoS 2 , depositing a 70 nm Ge film enabled the peeling off of the topmost MoTe 2 monolayer from the bulk crystal, thus yielding a monolayer of MoTe 2 with a lateral dimension of 1.2 mm, which is determined by the starting crystal (Figure 3a). [43,44]Microscopy and spectroscopy analyses confirmed the cleanliness and lack of surface damage to the monolayer MoTe 2 after the DI water dipping process.Atomic force microscopy (AFM) images of the spalled MoTe 2 on a 300 nm SiO 2 /Si substrate showed a uniform and smooth surface without any polymeric residue or physical defects such as cracks, tearing, and folding (Figure 3b). [45]The root mean square roughness further supported that the flatness of MoTe 2 is similar to that of exfoliated 2D materials on a SiO 2 /Si substrate. [46]he study next conducted Raman and PL spectroscopy measurements for spalled MoTe 2 .A strong E 2g mode (236 cm À1 ) and a clear single peak in the A 1g mode (169 cm À1 ) were observed, without Davydov splitting generated by interlayer interactions (Figure 3c). [47,48]Moreover, the absence of B 2g phonon modes, which result from translational symmetry breaking, proves that the spalled MoTe 2 is a monolayer. [49]It should be noted that no Ge-related peak was observed, thus indicating that the water-soluble Ge film was completely removed and that the spalled monolayer preserved its clean surface without any chemical contaminants (Figure S10 and S11, Supporting Information). [50,51]he Raman maps performed on 50 μm Â 50 μm areas highlight the uniformity of the intensity of the A 1g , E 2g , and B 2g peaks (Figure 3d-f ).Moreover, a strong PL peak was observed at 1.08 eV, as shown in Figure 3g. [49]

Electrical Properties in Spalled Monolayer MoTe 2
Electrical measurements are one of the most effective methods for assessing the quality of layers.Therefore, by connecting the gate to the silicon, the field-effect transistor (FET) properties of monolayer MoTe 2 and MoS 2 were investigated (Figure S12, Supporting Information).Figure 4a demonstrates a schematic of back-gated monolayer MoTe 2 FETs, which is fabricated with an Au/Cr source and drain contacts on 300 nm SiO 2 /Si substrates.
The detailed device fabrication process is described in the Experimental Section. Figure 4b shows that the results of source-drain current (I ds ) vs source-drain voltage (V ds ) (I ds -V ds ) indicate the existence of Schottky contact between monolayer MoTe 2 and metal electrodes, which is consistent with previous reports. [52]The band alignment of the MoTe 2 Schottky junction with a metal contact is illustrated in the inset of Figure 4b, providing an explanation for the Schottky contact in the I ds -V ds results.Furthermore, Figure 4c shows the transfer characteristics of the monolayer MoTe 2 FET device.The logarithmic plot of gate voltage (V g ) in the inset in Figure 4c reveals the ambipolar behavior of monolayer MoTe 2 devices. [53,54]These findings collectively suggest that the spalling process did not introduce chemical attack and contamination into the spalled monolayer MoTe 2 .By referring to the transfer plot, it is possible to calculate the field-effect carrier mobility of a MoTe 2 flake using μ FE ¼ L W dI ds C ox V ds dV g , where L and W are the length and width of the channel (here, we used L = 7.5 μm and W = 4 μm), and C ox is the gate oxide capacitance of 300 nm SiO 2 .7][58]

Conclusions
This study presents a water-soluble nonmetal Ge-mediated atomic spalling approach that is a simple and facile method for obtaining large-area monolayer TMDCs.A modified analytic model was used to calculate the effectiveness of the Ge stressor for selectively separating monolayer TMDC from bulk crystal.MoS 2 and MoTe 2 monolayers with lateral sizes of several millimeters were successfully achieved without needing to use an acid-based wet-etching process.Moreover, the study obtained a monolayer of graphene and other TMDCs (MoSe 2 and WSe 2 ) by applying the Ge-mediated atomic spalling approach (Figure S13, Supporting Information).Detailed spectroscopic and electrical characterizations were conducted, that supported the high crystallinity of spalled monolayer TMDCs.These results have the potential to be widely employed for the high-throughput manufacture of high-quality monolayer TMDCs.

Experimental Section
Ge-Mediated Spalling Process: Tightly fixed TMDC crystals (MoS 2 and MoTe 2 , 2D semiconductors) with epoxy resin (Officeahn) were prepared.Next, 70 nm Ge film was deposited on the fresh surface of TMDC using ebeam deposition.The deposition rate was set to 0.1 Å s À1 for the initial 5 nm of Ge to minimize physical damage and then increased to 1.1 Å s À1 for the remaining 65 nm of Ge film.Subsequently, poly(methyl methacrylate) (PMMA) was spin coated at 2000 rpm for 1 min.Thermal release tape (Revalpha 3196, Nitto Denko, TRT) was attached to the top of the PMMA/Ge/TMDC, and gentle force was applied to exfoliate the monolayer TMDC from the bulk TMDC and transfer it to the target substrate.The TRT lost its adhesive force at 110 °C and was removed from the substrate.The PMMA was removed by immersing the sample in acetone, after which the Ge film was removed in a deionized water bath at 60 °C.
Characterization: The surface morphology-spalled samples were analyzed using bright-field optical microscopy (BF-OM, Olympus) and AFM (MFP-3D Origin, Oxford Instruments).For the average roughness analysis of the surface (R q ), tapping mode was performed at a slow scanning speed of 0.1 Hz, and the acquired AFM images were analyzed using Gwyddion software.Raman/PL spectroscopy (Renishaw Raman system) with excitation laser lines of 532 nm was used to characterize the crystallinity and quality of spalled monolayer.To prevent the heating effect of spalled monolayer, the power of the excitation laser line was kept below 0.1 mW.The intrinsic peak of Si, 520 cm À1 , was used as a reference for the wave number calibration.The internal stress of Ge film (σ Ge ) was calculated using the Stoney formula, σ Ge ¼ 1 Þt , where R is the measured curvature of Si after Ge film deposition, R 0 is the measured curvature of the Si before Ge film deposition, Y s is Young's modulus of the Si wafer, ν s is Poisson's ratio of Si wafer, t s is the thickness of Si wafer, and t is thickness of Ge film.We used a standard H-terminated Si wafer to measure the internal stress of Ge film.
Device Fabrication and Characterization: MoTe 2 FET was fabricated using a typical photolithography process.First, the metal electrode was patterned on transferred MoTe 2 , followed by the deposition of Cr/Au 5/45 nm using an e-beam evaporator.After the lift-off process, the channel was defined by reactive ion etching (SF 6 /Ar, 40/40 sccm, 100 W, 60 s).The electrical characteristics of the devices were investigated using a Keithley SCS-4200 system and a probe station (MSTECH, MST5000) under ambient conditions.

Figure 1 .
Figure 1.a) Schematic illustration of the controlled spalling process.b) Plot of the stressor thickness versus internal stress of the Ge stressor.The study confirmed that the internal stress of the 70 nm-thick Ge film is in the controlled spalling window (blue star).c) Plot of the accumulated strain energy in the Ge/MoS 2 bilayer system versus spalling depth.The spalling depth is determined by the MoS 2 thickness in the fixed thickness of a 70 nm Ge stressor.
atomic spalling.First, a cleaved MoS 2 substrate with a thickness of 192 AE 27 nm was prepared, and a 70 nm-thick Ge film was deposited onto a fresh MoS 2 surface (FigureS1, Supporting Information).It was confirmed that the internal stress of the as-deposited Ge film is in the range of 262 AE 10 MPa, which allows for the crack propagation depth within MoS 2 monolayer thickness to be controlled.Spalled monolayer MoS 2 is then transferred onto a target substrate (e.g., rigid SiO 2 /Si substrate and transparent flexible substrate), and the Ge film is subsequently completely washed away by dipping the sample in a clean deionized (DI) water bath (Figure2band S2, Supporting Information).

Figure 2 .
Figure 2. a) Schematic illustration of the Ge-mediated atomic spalling process.b) Photograph of spalled monolayer MoS 2 on 300 nm SiO 2 /Si substrate.The scale bar is 5 mm.c,d) Low-and high-magnification OM images of large-scale spalled monolayer MoS 2 .The scale bars are 1 mm and 100 μm, respectively.e) Representative Raman spectra of spalled monolayer MoS 2 .f,g) Histogram of the Raman peak position map for the E 2g peak and A 1g peak, and Raman peak position difference Pos (A 1g -E 2g ) maps for monolayer MoS 2 .h) PL intensity maps at fixed positions of 1.90 eV for monolayer MoS 2 .Inset shows representative PL spectra of monolayer MoS 2 .Scale bar: 10 μm.

Figure 4 .
Figure 4. a) Schematic illustration of back-gate monolayer MoTe 2 FET.b) Output characteristics of spalled monolayer MoTe 2 FET.An optical image of the device is shown in the inset.The scale bar is 10 μm.c) Transfer characteristics of spalled monolayer MoTe 2 FET (V ds = 0.5 V).The inset shows the logarithmic scale plot of the transfer curve.