An efficient route to prepare suspended monolayer for feasible optical and electronic characterizations of two‐dimensional materials

Abstract

Two‐dimensional (2D) materials are highly sensitive to substrates, interfaces, and the surrounding environments. Suspended 2D materials are free from substrate‐induced effects, thus an ideal approach to study their intrinsic properties. However, it is very challenging to prepare large‐area suspended 2D materials with high efficiency. Here we report a universal method, based on pretreatments of densely patterned hole array substrates with either oxygen‐plasma or gold film deposition, to prepare large‐area suspended mono‐ and few‐layer 2D materials. Multiple structural, optical, and electrical characterization tools were used to fully evaluate the improved performance of various suspended 2D layers. Some of these observations reported in this study are: (1) Observation of a new Raman low frequency mode for the suspended MoS₂; (2) Significantly stronger photoluminescence (PL) and second harmonic generation (SHG) signals of suspended WSe₂, which enables the study of new optical transition processes; (3) The low energy electron diffraction pattern on suspended MoS₂ also exhibits much sharper spots than that on the supported area; and (4) The mobility of suspended graphene device approaches 300 000 cm² V⁻¹ s⁻¹, which is desirable to explore the intrinsic properties of graphene. This work provides an innovative and efficient route for fabricating suspended 2D materials, and we expect that it can be broadly used for studying intrinsic properties of 2D materials and in applications of hybrid active nanophotonic and electronic devices.

INTRODUCTION

Two-dimensional (2D) crystals were thought to be thermodynamically unstable since short-range thermal fluctuations lead to transverse atomic displacements comparable to their interatomic distances,^1,2 later known as the Mermin−Wagner theorem.^3,4 Since the first isolation of graphene, 2D crystals were usually prepared on solid substrates which suppress the transverse displacements and stabilize those crystals in 2D. While those substrate-supported 2D crystals yield properties strongly affected by the substrates, the substrate induced effects were well studied in the past 10 years. Moving carriers of, for example, graphene, were found strongly scattered by substrate charge traps in devices fabricated on SiO₂/Si substrate.⁵ In terms of optical properties, for example, photoluminescence (PL), a substrate, provides additional electronic screening that affects exciton properties of electron–hole pairs. Substrate effect also enhances the superconducting transition temperature (T_c) of FeSe, where T_c of its monolayer was recorded at 65 K on SrTiO₃^6,7 and only 8 K for its multilayer and bulk counterparts,⁸ however, the origin of this enhancement is still ambiguous so far.⁹

Intrinsic properties of 2D crystals are of fundamental interest; however, the presence of substrate can impact the properties of those 2D crystals. Suspended 2D materials can completely remove the influence of substrates, showing unique advantages in studying their intrinsic electronic, mechanical, and optical properties. Suspended graphene devices showed ultra-high mobility and ballistic transport behavior.^10,11 Most of the mechanical properties of graphene, MoS₂, WSe₂, and other 2D materials were investigated on the suspended structures, such as the Young's modulus and the spring constants.^12–15 The suspended samples also showed enhanced optical performances in metal dichalcogenides (MDCs) materials.^15,16 However, how to efficiently fabricate suspended samples of 2D materials is a significant challenge. Contamination and low yield ratio have been the two main obstacles for fabricating suspended 2D materials and devices. Suspended graphene devices were normally fabricated by the wet chemical etching strategy,^11,17 which cannot be used for chemically active 2D materials, and also presents a significant risk of etching away the metal electrodes. 2D materials can also be grown by chemical vapor deposition (CVD) on flat substrate and then transferred onto hole array substrate, but residue of organic molecules are inevitable in the transfer process.^18,19 The commonly used mechanical exfoliation method is sensitive to the morphology change of substrate, where the adhesion energy between layered materials and substrates with hole array structures dramatically decreases because of the reduced contact area compared with the integral flat substrate. Therefore, a highly efficient and contamination-free fabrication strategy is desirable and could open a vast new field in the study of 2D materials.

In this work, we present a universal method based on substrate pretreatments that can efficiently suspend various 2D materials with size up to several millimeter. Depending on 2D material of interest, we pretreat the densely patterned hole array SiO₂/Si substrates with either oxygen plasma or Au film deposition. For graphene and high temperature cuprate superconductor Bi₂Sr₂CaCu₂O₈ (Bi2212), oxygen plasma treatment was applied to clean the substrate with hole arrays before flake exfoliation. The suspended graphene device shows ultra-high mobility, which is much higher than that supported on SiO₂. For MDC material (MoS₂, WSe₂, SnS₂, etc.) and black phosphorus (BP), a thin layer of Au/Ti metal was first deposited on the substrates with hole arrays to enhance the interaction between the 2D materials and the substrates. In both strategies, there are no organic molecules involved in the entire process, which guarantees the surface to be free of organic contamination, this ultra-clean surface enables the preservation of the 2D material's intrinsic properties. From the suspended samples, we observed more Raman modes, more intense PL, enhanced second harmonic generation (SHG), and sharpened low-energy electron diffraction (LEED) patterns. All these experimental results demonstrate that suspended samples would be valuable for studying the intrinsic properties of 2D materials.

RESULTS AND DISCUSSION

Figure 1A illustrates two different strategies for fabricating suspended 2D materials. SiO₂/Si substrate with hole arrays was prepared by optical lithography patterning and plasma etching with SF₆. The depth of the holes can be varied in the range between 100 nm and 10 μm by controlling the etching time. Since the interaction between the layered materials and the substrates plays a critical role in the exfoliation process, two surface treatment methods were used. For graphene and cuprate superconductors (e.g., Bi2212 or Bi₂Sr₂CuO₆ [Bi2201]), the substrates can facilitate exfoliating large area 2D flakes with high efficiency when applying oxygen plasma treatment.²⁰ Hence, we first applied oxygen plasma to clean the surface of SiO₂/Si substrate with hole arrays, and then apply the tape with freshly cleaved graphite onto the substrate, followed by baking the substrate together with graphite/tape at 100°C for 1 min. After cooling down to room temperature, the tape was peeled off from the hole-array substrate. Suspended graphene flakes can be observed by optical microscopy (Figure S1). Similar process can be applied to prepare suspended Bi2212 samples, as shown in Figure S2. For MDC materials or BP, the interaction between the substrates and the materials is not strong enough to facilitate exfoliation of large size monolayer flakes, and the production yield is extremely low. It has been reported that the interaction between MDC and gold is strong, which provides a feasible method to exfoliate large size samples.^21–24 Layered materials, especially for those which contain S, Se, Te, P, and Cl, can be exfoliated onto the hole-array substrate by the gold-assisted method. In this approach, a thin layer of Au/Ti (5 nm/2 nm) was deposited onto the substrate with hole arrays before the freshly cleaved crystal was put on. This technical approach is effective for preparing MDC materials (e.g., MoS₂, WSe₂, SnS₂), BP, RuCl₃, and so on. The suspended 2D materials can be exfoliated on hole arrays with various geometrical structures, such as rectangle, Hall bar, and circle, as shown in Figure 1B–D. For MDC materials, such as MoS₂ and WSe₂, millimeter sized flakes can be exfoliated onto hole-array substrate. Few layer samples can also be prepared with this method. The layer number of MoS₂ and WSe₂ in Figure 1C,D can be clearly distinguished. Figure 1E presents a typical PL mapping image of monolayer WSe₂, the suspended area shows high PL intensity while the supported area is dark because underneath gold quenches the PL signal. More optical images of suspended 2D crystals are presented in Figures S1–S3, including related PL and Raman measurements

FIGURE 1. Fabrication process and characterization of suspended 2D materials. (A) Schematic images for preparing suspended samples. (B–D) Optical images of exfoliated graphene, MoS2, and WSe2 on different patterned substrates, including rectangle, Hall bar, and circular hole structures. (E) PL mapping image of suspended monolayer WSe2. (F) PL mapping images of Chinese zodiac signs, which were collected on suspended WSe2 flakes. Some details are added artificially, such as eyes and mouths. The scale bar is 4 μm. PL, photoluminescence

The suspended 2D materials not only show advantages in fundamental studies, but also have great potential in many applications. Figure S1A shows an exfoliated monolayer WSe₂ with an area of 2 mm². The PL image in Figure S1B demonstrates that the suspended monolayer WSe₂ area is highly uniform. Figure 1F shows PL of suspended WSe₂ with Chinese zodiac sign structures, indicating that the suspended flakes can be successfully prepared with irregular shapes. Hole-array and groove-array meta-surfaces are of high interest in topological photonics,^25,26 photonic crystal,^27–29 meta-lenses,³⁰ and valleytronics.³¹ Integration 2D material with meta-surfaces would enable active light-emitting structures with opportunities for new types of light sources³¹ and nanolasers.^28,32 In contrast, traditional polymer-assisted dry transfer technique shows extremely low efficiency in device fabrication, and the devices made by wet transfer process typically suffer the poor-quality of CVD grown 2D materials. This method would be useful in research and applications of hybrid nanophotonic and 2D electronic devices.

Raman spectroscopy is a nondestructive characterization tool widely used for detecting defects, identifying strain and layer numbers for 2D materials.^33–38 Recently, ultra-low frequency (ULF) Raman spectroscopy has been used to study the interlayer vibrational modes of graphene and MDCs materials.^39–41 For MoS₂, the ULF Raman peaks originate from the in-plane (shear) and out-of-plane (breathing) vibrations of MoS₂, which can be used to identify the number of MoS₂ layers precisely.^39,41 On the suspended few-layer (1–5 layers) MoS₂, we observed much stronger ULF Raman modes. The sharp peak at ~30 cm⁻¹ is denoted as a shear mode (S1), while the broad peaks at 40 cm⁻¹ for 2 L, 21 cm⁻² for 4 L, and 17 cm⁻¹ for 5 L are assigned as breathing modes (B1), as shown in Figure 2A. It can be seen that the intensities of the Raman peaks, especially the ULF Raman peaks, of suspended MoS₂ are much higher than that of the supported MoS₂, and more detailed spectral information can be detected as a result. There is only one S1 mode observed on 3–5 layer MoS₂ for the sample supported on Au/SiO₂/Si substrate. No clear feature can be detected on 2 L supported MoS₂. In contrast, both the S1 and B1 modes can be observed clearly on suspended 2–5 L MoS₂, and the layer dependence trend of these two modes are marked in Figure 2A by dashed blue and dashed red lines. The breathing mode (B1) for suspended 2 L MoS₂ can also be clearly observed at 40 cm⁻¹. Since the ULF modes originate from the interlayer vibration, they are more sensitive to the interface between MoS₂ and the substrate. The breathing modes B1, which correspond to a rigid-layer displacement parallel to the c axis, is even more sensitive for the pinning-effect induced by the substrate. The disappearance of breathing mode in 1–5 L supported MoS₂ is mainly due to the gold atom induced pinning-effect, which provide a convincing evidence for the formation of covalent-like quasi-bonding between MoS₂ and gold interface.⁴² The enhanced Raman signal of the suspended MoS₂, especially in the ULF region, can be attributed to excitation of all the vibration modes, which was not easily detectable on supported samples.⁴³ The suspended 2D materials present the most intrinsic vibrational modes and prevent all the phonon-coupling and pinning-effect from the substrates.

FIGURE 2. Raman spectra of suspended MoS2 and supported MoS2. (A) Raman spectra of 1–5 layer supported (top) and suspended (bottom) MoS2 at low frequency (−45 to 45 cm−1). The dashed blue and red lines show the trend of B1 and S1. (B) Two dominant Raman peaks of supported (top) and suspended (bottom) MoS2 at higher wave frequency (360–430 cm−1). The insets show atomic displacements of the two Raman-active modes E2g1 and A1g

Two high frequency ${\mathrm{E}}_{2\mathrm{g}}^1$ and A_1g modes at around 380 cm⁻¹ and 405 cm⁻¹ are detected on both supported and suspended 1–5 L MoS₂. The ${\mathrm{E}}_{2\mathrm{g}}^1$ and A_1g modes originate from in-plane and out-of-plane vibrations, respectively (insets in Figure 2B). The intensity of the two Raman peaks is higher on suspended MoS₂ than on supported substrate, which is more pronounced for monolayer samples. Both low frequency and high frequency Raman results suggest that the suspended samples have higher Raman intensity and can be used to study some fine Raman modes.

In 2D semiconductor materials, PL is sensitive to doping, strain, and dielectric environments. The substrate itself and a trace amount of moisture on the substrate can dope the material, thus affect the spectral weights of excitons and trions.^15,44 The inhomogeneities of substrate can bring strain on 2D materials, which is another factor that influences the PL of the material.^45,46 Also, the multiple-beam interference of oxide coated substrate can enhance or weaken the PL intensity.⁴⁷ Therefore, it is essential to eliminate the influence from the substrate in order to study the intrinsic PL and other optical properties of 2D materials.

As one of the most well-studied 2D semiconductor, WSe₂ exhibits many interesting optical properties, such as valley excitons⁴⁸ and biexcitons.⁴⁹ Shown in Figure 3A, the PL intensity of suspended 1 L WSe₂ is one order of magnitude (≈14 times) stronger than that from the supported samples, which is similar to other reports.¹⁵ The enhanced PL efficiency on the suspended WSe₂ sample is partly due to suspended clean surface, which avoid doping effect from the substrate. Also, it is proposed that the higher exciton-exciton annihilation rate in the suspended sample can compete with the defect-assisted recombination, thus generating higher PL efficiency.⁴⁴ The interference effect can influence the intensity as well, but it is not the main factor which enhances the PL intensity in suspended area. In previous reports, Liu et al. found that both Raman and PL intensity of WS₂ on suspended area is higher than the supported area.⁵⁰ Even the lowest intensity on suspended area due to interference effect is still higher than the one on supported area.⁵⁰ To completely remove the interference, we transfer monolayer MoS₂ onto the substrate with through-hole. In this case, the interference effect can be completely excluded. As shown in Figure S7, the PL intensity of MoS₂ on through-hole is still higher than the supported area. The small PL peak redshift (~0.04 eV) of suspended WSe₂ in Figure 3A is mainly due to the strain effect.^51,52 Due to the small local difference of internal and external air pressure on the suspended sample, the suspended material can be a little convex or concave (see Figure S5 and Section 4). Since the SiO₂ substrate is not atomic level flat and exhibits many scattering centers on the surface, the lattice structure and PL generation process of WSe₂ can be also affected. As the result, PL peak width is broader on supported area than the suspended area.

FIGURE 3. PL spectra of WSe2 and SHG mapping of WS2. (A) PL spectra of supported (red curve) and suspended (blue curve) WSe2, which were excited by 532 nm laser with 0.5 mW power. (B) PL spectra of 1–3 layer WSe2, the blue curves are measured on suspended area, while the pink curves are measured on supported WSe2. The inset in monolayer PL spectra is an optical image of 1–3 L WSe2 on hole array substrate. Another inset shows the schematic PL transitions of trilayer WSe2. (C) SHG mapping image of monolayer WS2 and the intensity profile across the suspended area. The average SHG intensity of suspended WS2 is ≈25 000, while the SHG intensity of supported WS2 around the edge of hole is ≈230. PL, photoluminescence; SHG, second harmonic generation

Besides large area suspended monolayer, many flakes with different layer numbers can also be efficiently prepared with our method, as shown in Figure 1A. The suspended structure provides an ideal model for carrying out some layer-dependent optical measurements. As shown in Figure 3B, the PL spectra of suspended WSe₂ show clear layer dependence at room temperature. On the suspended areas, one PL peak is observed on monolayer WSe₂, which is consistent with previous measurements on supported monolayer WSe₂.⁵³ For suspended bilayer WSe₂, two PL peaks can be clearly seen. In previous studies, even though two peaks on bilayer WSe₂ were detected, the two peaks at 1.55 and 1.63 eV were not well understood.⁵⁴ More importantly, three peaks were detected on suspended trilayer WSe₂ for the first time in this study. Theoretically, three PL transition modes can be expected, as known from the band structure of trilayer WSe₂, K_conduction → K_valence, K_conduction → Γ_valence, and Λ_conduction → Γ_valence. However, only two broad PL peaks were observed on trilayer WSe₂ in previous studies.^54,55 The reason is mainly attributed to the quality of supported samples that reduced the PL resolution. In order to directly compare the PL spectral difference between supported and suspended samples, we also measured the PL spectra of 1–3 L WSe₂ on SiO₂/Si substrate (Figure 3B, pink curves), which is similar to the previous reports. The layer-dependent PL measurements on WSe₂ demonstrate that suspended structure facilitates to extract fine transition modes which could not be observed on supported samples. Therefore, our new exfoliation method for preparing suspended structures will open a vast field in PL studies of many 2D materials.

Nonlinear optical properties of MDC are fascinating both from the fundamental understanding of the materials and also for various potential applications.^56–60 SHG can reveal diverse properties associated with structural symmetries such as crystal orientation, grain boundary, thickness, twist angle and stacking order,^57,61–63 and can be applied to probe valley polarization,⁶⁴ carrier dynamics^65,66 and charge transfer in the heterostructures.⁶⁷ We observed that simply suspending the monolayer MDC can get a more than 100 times SHG intensity enhancement compared to that supported on the silicon substrate, as shown in the SHG mapping image in Figure 3C. This enhancement can be explained by the refractive index-dependent relationship between the fundamental excitation power P1 and the SHG signal power $P\left(2\omega \right)$. By solving the Green's function with the nonlinear sheet source, the relationship is estimated as^68,69:[Image Omitted. See PDF]where S is the shape factor for Gaussian pulses, τ is the temporal pulse width, $P\left(\omega \right)$ is the incident average power of the pump beam, f is the repetition rate, n is the refractive index of the substrate at the pump wavelength, and ω is the angular frequency of the pump. For the pump wavelength at 830 nm, the refractive index of silicon is 3.65. The enhancement factor of suspended sample compared to supported one is $\frac{{\left(1+n_{\text{silicon}}\right)}^6}{{\left(1+n_{\mathrm{air}}\right)}^6}\approx 157$, which is in good agreement with our experiment. It should be noted that the enhancement of SHG did not originate from change of ${\chi }^{\left(2\right)}$, it is an apparent increase related to the dielectric environment. In addition to the SHG, other nonlinear optical responses can also be enhanced in the suspended samples since the mechanism is the same. Thus, suspended sample is likely to be a considerable strategy to enhance the nonlinear optical signal in nanophotonic devices.

Low energy electron microscopy (LEEM) is a powerful surface analysis technique, which has been widely applied in the characterization of 2D materials.^70–72 Apart from real-time imaging in spatial resolution down to several nanometers, microanalysis, such as microprobe low energy electron diffraction (μLEED), can provide important reciprocal space information of 2D materials by selecting micrometer-sized zones on the surface.⁷³ Both LEEM and LEED show ultra-high sensitivity for surface and substrate changes. Figure 4A shows a LEEM image of a few-layer MoS₂ flake exfoliated on the hole-array substrate with Au (5 nm)/Ti (2 nm) film underneath. In this LEEM image, suspended MoS₂ on the hole appears as a bright area while supported MoS₂ looks relatively dark. As shown in Figure 4B,C, a sharp μLEED pattern was obtained from the central part of suspended MoS₂, whereas the pattern of supported MoS₂ is more diffused. In Figure 4D, the normalized intensity profiles across the (00) diffraction spots of both patterns were compared, and the extracted Gaussian width of the diffused pattern (0.09 Å⁻¹) is three times as large as the sharp one (0.03 Å⁻¹). This implies a microscopically corrugated surface of supported MoS₂ compared with the suspended one, which is generally attributed to the conformation of atomically thin 2D layer to the undulating substrate surface. We note that the corrugation of the observed supported MoS₂ here is already alleviated because of its few-layer thickness, for monolayer, the expected difference will be even more pronounced (not shown in this article). Assuming a random surface corrugation of the supported MoS₂ and a Gaussian distribution of local surface normal, the SD of the angular spread of the (00) diffraction beam, $∆\theta$, can be obtained according to the following relation⁷⁴:[Image Omitted. See PDF]where $k_{\parallel }$ is the Gaussian width of (00) spot and $E_{\mathrm{kin}}$ is the incident electron energy. This gives $∆\theta$ of 0.1° and 0.3° for suspended and supported MoS₂, respectively. The above results demonstrate that the substrate-induced roughness in 2D layers can be greatly alleviated by suspending the material on a hole. It is worth noting that our newly developed exfoliation method is high compatible with many surface characterization techniques requiring conductive substrates, such as scan tunneling microscopy, LEEM, LEED, and angle-resolved photoemission spectroscopy since there is already a metallic layer underneath the 2D materials.

FIGURE 4. Low energy electron diffraction (LEED) patterns of MoS2 and electrical transport measurements of graphene devices. (A) Low energy electron microscopy image of MoS2 flake on hole array substrate with Au (5 nm)/Ti (2 nm) underneath. (B, C) are μLEED patterns of suspended and supported MoS2, respectively. (D) Normalized intensity profiles along the (0, 0) spots of (B) and (C). Gaussian width of the (00) spots for the suspended and supported MoS2 in (B) and (C) are 0.03 Å−1 and 0.09 Å−1, respectively. (E) Typical resistivity of three types of devices as the functions of back-gate voltage. Field sweeps were repeated to verify reproducibility. The inset is an optical image of suspended graphene device. μLEED, microprobe low energy electron diffraction

The intrinsic optical and electrical properties of 2D materials can be more or less affected no matter what substrates are underneath (e.g., SiO₂, h-BN). Both theoretical and experimental results have proved that the SiO₂/Si substrate can reduce the mobility of graphene because of charge and phonon scattering.⁷⁵ Although h-BN-graphene heterostructures provide another strategy to get high mobility devices, the periodical atomic potential of B and N atoms also influences the band structure of graphene.⁷⁶ Therefore, suspended samples might be the most ideal candidate for studying the intrinsic electrical properties of 2D materials. During the last decades, high mobility devices are mainly reported on h-BN-based heterostructures, while suspended devices are rarely used due to the high fracture rate of traditional fabrication procedures, where wet chemistry and critical point drying were involved.¹¹ Here we first prepare suspended 2D materials on special hole structures, such as Hall bar and cross, and then fabricate devices after exfoliation, which results in a higher success rate of suspended devices. Figure 4E is the resistivity as the function of back gate voltages of supported and suspended graphene devices, which are made by electron-beam lithography. The two devices exhibit near symmetric feature with respect to the resistivity maximum. From the two curves, it is immediately found that the charge neutral points (CNPs), indicated by the maximum in the resistivity, for the suspended graphene device is 1.7 V, lower than the graphene on SiO₂/Si substrate (8.2 V). The full width at half maximum (FWHM, ~2.5 V in terms of V_g) of transfer curve is also much narrower than those of the supported ones (~8 V). Both the position of CNPs and the FWHM of the transfer curves are associated with the charged impurity level and therefore correspond to the quality of devices.⁷⁷ Due to removal of the substrate, our suspended device showed substantial improvement in electrical quality. The field-effect mobility has been calculated using the following equation:[Image Omitted. See PDF]where σ is the conductivity of graphene device, V_g is the gate voltage, and L and W are the length and width of the device, respectively. The capacitance value of the 300 nm SiO₂ layer is C(SiO₂) = 11.6 nF cm⁻².⁷⁸ For suspended graphene device, this value is C(suspended) = 0.6 nF cm⁻².¹¹ The calculated field effect electron mobility are ~7000 cm² V⁻¹ s⁻¹ and ~320 000 cm² V⁻¹ s⁻¹ for graphene on SiO₂/Si substrate and suspended graphene, respectively. The high mobility of suspended graphene device is consistent with previous reports about suspended and h-BN-based graphene devices.⁷⁹ The results unambiguously demonstrate our suspended device has better electrical quality.

CONCLUSION

In summary, we have developed a universal method to exfoliate various 2D materials to suspended samples with high efficiency, including graphene, Bi2212, MoS₂, WSe₂, and BP. The Raman results demonstrate that low frequency modes of 2D materials can be easily observed on suspended samples. The PL and SHG signals are strongly enhanced on suspended 2D materials when compared with the samples supported on SiO₂/Si substrate. An additional PL transition mode is observed on suspended 3 L WSe₂, which have not been reported on supported samples. Both LEEM and LEED results show that the suspended 2D material area present sharper signals, which indicate that the suspended structure of 2D materials can facilitate many other surface characterizations. The high mobility of suspended graphene field-effect transistor (FET) device prove that removing substrate induced charge and phonon scattering are crucial for reaching the intrinsic limits of the material. This work could open a vast field for preparing suspended 2D materials and studying their intrinsic optical, electrical, and surface related properties. We also expect this method to be useful in research and applications of hybrid nanophotonic and 2D electronic devices.

EXPERIMENTAL SECTION Preparation of suspended 2D materials

First, the SiO₂/Si substrate with hole array was patterned by optical lithography and plasma etching. For graphene and Bi2212, the substrate with hole array was cleaned by oxygen plasma, after that a new cleaved surface of graphite or bulk Bi2212 was put onto the substrate, and then peeled off the tape with bulk flakes. For MDC materials (MoS₂, WSe₂, TaSe₂, etc.) and BP, a thin layer of metal (Au/Ti: 5 nm/2 nm) was deposited onto the substrate with hole array. Cleave a new surface of layered crystal by tape and put onto the substrate surface. Large area of suspended 2D materials can be exfoliated onto hole-array substrate. The success rate is higher than 99%. The size of suspended monolayer and few layer samples mainly depends on the size of their bulk crystal. It is difficult to get large-area suspended flakes on hole-array substrate if the bulk crystal is too small. The diameter of holes and the distance between holes are also key parameters to prepare large-area suspended 2D materials. Once the diameter of holes is larger than 5 μm, the yield ratio of suspended zones will start to decrease. On the other hand, it is difficult to fabricate holes with diameter smaller than 1 μm.

The fabrication was carried out at room temperature and 1 atm pressure. However, due to the small local difference of internal and external air pressure on the sample, the suspended material can have a slightly convex or concave profile (Figure S5). The biaxial strain in typical sample is as low as 0.014%, which should not produce notable influence to the properties of 2D materials. However, we do observe that very few suspended samples have relatively large strain (up to 0.5%). For this kind of sample, one can burn a small hole on the edge of suspended area by tightly focused laser to balance the difference of air pressure between inside and outside the hole.

The Raman and PL measurements

These measurements were performed on WITec alpha 300R and JY Horiba HR800 system with a wavelength of 532 nm and power at 0.6 mW. Figure S4 shows the Raman peak difference of ${\mathrm{E}}_{2\mathrm{g}}^1$ and A_1g for both supported and suspended MoS₂ film.

SHG measurement

To avoid the interference effects, the monolayer sample was suspended on a through hole. The SHG image was collected by a homemade stage scanning microscope system with a reflection geometry at room temperature. The fundamental laser field was provided by a Ti:Sapphire oscillator (Coherent Verdi V-10, Mira-HP) pump at 830 nm, with a pulse width of ~200 fs and a repetition rate of 76 MHz. The average laser power was kept at 3 mW. The laser is directed to an inverted microscope equipped with a scanning stage (Princeton Instruments). The laser spot was focused to ~500 nm diameter by an objective lens (×40, numerical aperture (NA) = 0.6). The reflected SHG signal is collected by the same lens and directed to a 450 nm short-pass filter (FESH450, Thorlabs) and a 360–580 nm band-pass filter (BG39, Thorlabs) to eliminate the reflected pump beam. The SHG signal is detected using a photomultiplier tube (Hamamatsu).

LEEM and LEED

Here, we characterized the structure and surface morphology of MoS₂ on the Au (5 nm)/Ti (2 nm)-covered hole-array substrate with the XPEEM endstation (BL09U, Dreamline)⁷⁷ of Shanghai Synchrotron Radiation Facility (SSRF). For μLEED measurements, a micro area sample of 1.5 mm diameter on the surface was selected. Before LEEM measurements, the sample was cleaned by annealing at about 250°C for 3 h in ultrahigh vacuum (base pressure ~ 1 × 10⁻¹⁰ Torr).

FET device and electrical measurements

The electrical transport properties of graphene were measured using microfabricated FETs. After exfoliating graphene flakes onto 300 nm SiO₂/Si with and without hole arrays, we fabricated test devices using standard optical lithography and deposited Ti/Au (5 nm/50 nm) as contact electrodes using electron-beam evaporation. The final devices were annealed in high vacuum (10⁻⁸ Torr) at 300°C for 1 h in order to remove resist residues and enhance the metallic contacts. All the devices are measured in low-pressure Helium vapor cryostat at 7 K. The degenerately doped silicon substrate serves as a gate electrode with silicon oxide acting as the gate dielectric, and a lock-in amplifier was used to pass current between the two outer electrodes at I = 100 nA, and record the voltage difference V_sd between two inner electrodes. The ratio of width (W) to length (L) of samples between voltage probes has been estimated to eliminate the effect of sample geometry. The suspended graphene devices are also measured under the same condition except limiting the gate voltage within ±8 V, in order to avoid the electrostatic induced collapse of graphene. All the measured curves are repeated to guarantee the data consistency.

ACKNOWLEDGMENTS

The authors thank Dr. Norman N. Shi for helpful discussions. This work is supported by the National Key Research and Development Program of China (Grant No. 2019YFA0308000, 2018YFA0306302, 2018YFA0305800, 2018YFA0704201), the Youth Innovation Promotion Association of CAS (2019007, 2018013), the National Natural Science Foundation of China (NNSFC, Grant No. 62022089, 11874405, 61725107, 61971035, 61725107, 92163206), the National Basic Research Program of China (Grant No. 2015CB921300), and the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB07020300, XDB30000000), the Research Program of Beijing Academy of Quantum Information Sciences (Grant No. Y18G06). Work at Nanjing University acknowledges support from the NNSFC (Grant No. 51772145), Natural Science Foundation of Jiangsu Province (Grant No. BK20180003), 333 high level talent training project of JiangSu and JiangHai talent program of NanTong. One Chinese patent was filed (2019105297962) by the Institute of Physics, Chinese Academy of Sciences, along with their researchers (Y.H., Lin Zhao, and Xing-Jiang Zhou).

CONFLICT OF INTEREST

The authors declare the following competing interests that three Chinese patents were filed (201910529796.2; 201910529623.0) by the Institute of Physics, Chinese Academy of Sciences, and their researchers (Y.H., L.Z., and X.J.Z).