
==== Front
Natl Sci Rev
Natl Sci Rev
nsr
National Science Review
2095-5138
2053-714X
Oxford University Press

10.1093/nsr/nwae248
nwae248
Research Article
Information Science
Nsr/3
AcademicSubjects/MED00010
AcademicSubjects/SCI00010
Investigating thermal properties of 2D non-layered material using a NEMS-based 2-DOF approach towards ultrahigh-performance bolometer
https://orcid.org/0000-0002-6220-6106
Wang Luming Data curation Formal analysis Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China

https://orcid.org/0000-0002-3104-1855
Wu Song Data curation Formal analysis Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China

https://orcid.org/0009-0001-7437-2363
Zhang Zejuan Data curation Formal analysis Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China

https://orcid.org/0000-0002-5495-7612
Zhu Jiankai Conceptualization Data curation Formal analysis Investigation Methodology Writing - original draft Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China

https://orcid.org/0009-0002-8355-3593
Zou Luwei Methodology School of Physics, Hunan Key Laboratory of Nanophotonics and Devices, Central South University, Changsha 410083, China

https://orcid.org/0000-0003-0262-2017
Xu Bo Investigation Methodology Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China

https://orcid.org/0009-0003-5309-5592
Wu Jiaqi Data curation Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China

Zhu Junzhi Data curation Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China

https://orcid.org/0000-0003-1441-9139
Xiao Fei Data curation Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China

https://orcid.org/0000-0002-1658-5459
Jiao Chenyin Investigation Writing - review & editing Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China

https://orcid.org/0000-0002-0760-8700
Pei Shenghai Investigation Writing - review & editing Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China

https://orcid.org/0009-0008-4311-8961
Qin Jiaze Formal analysis Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China

https://orcid.org/0000-0003-0258-6212
Zhou Yu Project administration School of Physics, Hunan Key Laboratory of Nanophotonics and Devices, Central South University, Changsha 410083, China

https://orcid.org/0000-0002-8558-6850
Xia Juan Funding acquisition Project administration Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China

https://orcid.org/0000-0003-3743-7567
Wang Zenghui Conceptualization Funding acquisition Methodology Project administration Writing - review & editing Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China
State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu 611731, China

Corresponding authors. E-mails: zhujiankai@uestc.edu.cn
Corresponding authors. E-mails: yu.zhou@csu.edu.cn
Corresponding authors. E-mails: juanxia@uestc.edu.cn
Corresponding authors. E-mails: zenghui.wang@uestc.edu.cn
Equally contributed to this work.

10 2024
17 7 2024
17 7 2024
11 10 nwae24824 12 2023
15 4 2024
13 5 2024
27 8 2024
© The Author(s) 2024. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd.
2024
https://creativecommons.org/licenses/by/4.0/ This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

ABSTRACT

Two-dimensional (2D) non-layered materials in many aspects differ from their layered counterparts, and the exploration of their physical properties has produced many intriguing findings. However, due to challenges in applying existing experimental techniques to such nanoscale samples, their thermal properties have remained largely uncharacterized, hindering further exploration and device application using this promising material system. Here, we demonstrate an experimental study of thermal conduction in β-In2S3, a typical non-layered 2D material, using a resonant nanoelectromechanical systems (NEMS) platform. We devise a new two-degrees-of-freedom technique, more responsive and sensitive than Raman spectroscopy, to simultaneously determine both the thermal conductivity to be 3.7 W m−1 K−1 and its interfacial thermal conductance with SiO2 as 6.4 MW m−2 K−1. Leveraging such unique thermal properties, we further demonstrate a record-high power-to-frequency responsivity of −447 ppm/μW in β-In2S3 NEMS sensors, the best among drumhead NEMS-based bolometers. Our findings offer an effective approach for studying thermal properties and exploring potential thermal applications of 2D non-layered materials.

This work employs a NEMS platform to probe the thermal conduction at the nanoscale, offering a new approach for extracting thermal properties in ultrathin crystals.

thermal properties
non-layered material
resonant NEMS
nanoscale motion
bolometer
National Key Research and Development Program of China 10.13039/501100012166 2022YFB3203600 National Natural Science Foundation of China 10.13039/501100001809 T2325007 62450003 62250073 U21A20459 62004026 61774029 Sichuan Science and Technology Program 2021JDTD0028 China Postdoctoral Science Foundation 10.13039/501100002858 GZB20230107 GZB20240109 Natural Science Foundation of Sichuan Province 10.13039/501100018542 2024NSFSC1430 2024NSFSC1408 Science and Technology Innovation Program of Hunan Province 2021RC3021
==== Body
pmcINTRODUCTION

Thermal conduction plays a critical role in the performance of semiconductor devices, as noise figure, power consumption and reliability of devices are all sensitive to temperature and thus thermal conduction [1–3]. The introduction of two-dimensional (2D) semiconductors [4] and their heterostructures [5] offers new opportunities for designing nanoscale devices with unique performance, accompanied by the average phonon mean-free path exceeding or equaling device thickness, making collective phonon excitations the main heat carriers and thermal conductivity tunable by device size [6–8]. This also introduces a plethora of intriguing thermal behavior in 2D devices, including enhanced phonon-boundary scattering at the atomically sharp interfaces between the 2D materials and their immediate environment [9,10], alterations in thermal scattering rates due to changes in crystal symmetry [11], localized temperature rise effects (hotspots) in electronic and optoelectronic devices [12], and huge thermal tunability in the nanoelectromechanical systems (NEMS) [13–15]. Consequently, investigation of thermal conduction in 2D materials is crucial for ensuring the performance of 2D semiconductor devices and achieving optimal thermal management of these devices.

In contrast to 2D layered materials, which are stacked through van der Waals interactions, 2D non-layered materials are unique in that they are formed by chemical bonds in all three dimensions. This is expected to give rise to intriguing properties in thermal conduction, thermal stability and phonon dissipation. Further, as the thickness decreases to nanoscale, 2D non-layered materials undergo bond breakage, crystal rearrangement and structural deformation [16], resulting in excellent tunability in their band structures, electrical conductivity and ferromagnetism [17–20]. Moreover, the abundance of surface dangling bonds facilitates unique surface activity on these materials, rendering them highly promising for sensing applications and potentially useful in heterogeneous integration [21–24], all of which are affected by and can be further combined with their unique thermal properties to enable new device designs. Therefore, understanding the thermal conduction process in 2D non-layered materials is essential for the full exploitation of the aforementioned outstanding properties and for enabling new applications.

To date, however, the research on thermal conduction in 2D non-layered materials is largely absent, and the utilization of their thermal capabilities remains to be explored. The challenge in experimental techniques is a key hindering factor. Due to the minuscule sample sizes, especially the atomic-scale thinness, conventional thermal conductivity measurement techniques, such as laser flash and 3ω methods, are not suitable for measuring in-plane thermal conductivity in these nanoscale samples [25,26]. While some alternatives, such as thermal bridge, Raman spectroscopy and scanning thermal microscopy (SThM), have been developed for measuring thermal parameters in layered 2D materials [8,27–31], such methods can only determine one unknown thermal parameter at a time, often requiring pre-knowledge of another thermal conduction coefficient, such as one derived from theory. Therefore, the recent emergence of 2D non-layered materials has faced greater challenges with regard to studying their thermal properties, largely due to the simultaneous absence of any knowledge about their thermal conductivity and their interfacial thermal conductance with heat source/substrate. This impedes the distinction between their effects in thermal measurements, further hindering the decoupling and quantification of the different thermal conduction coefficients. In addition, the responsivity (output-to-input ratio, i.e. gain) and sensitivity (smallest measurable signal) of many existing thermal-transport techniques in nanoscale samples have also hampered the accurate extraction of thermal parameters.

In this work, we study thermal conduction of β-In2S3 (a typical non-layered 2D material) using a resonant NEMS platform with a variable laser heat source. We leverage two degrees of freedom (DOF) in the 2D NEMS platform, laser position and laser power, to simultaneously determine both the thermal conductivity κ of β-In2S3 as 3.7 W m−1 K−1 and the interfacial thermal conductance GB between β-In2S3 and SiO2 as 6.4 MW m−2 K−1. For this specific type of non-layered 2D material, such a NEMS-based 2-DOF approach is estimated to be 1 million times more responsive and >2000 times more sensitive than the Raman-spectroscopy-based method. Furthermore, we demonstrate that the unusual thermal conductivity translates to an outstanding power-to-frequency responsivity of the β-In2S3 resonator, reaching −447 ppm/μW at 532 nm, the best among drumhead NEMS-based bolometers. Our findings provide insights into the thermal properties of 2D β-In2S3 and offer opportunities for exploring potential thermal applications for 2D non-layered materials.

RESULTS AND DISCUSSION

We use a custom-built 2D NEMS platform to explore the thermal response of 2D devices using resonance frequency shifts. As depicted in Fig. 1a, a 532 nm power-tunable laser, with a spot size of ∼1.4 μm (Methods), serves two functions at the same time, as a detection laser for measuring resonance motion [32–34] (through laser interferometry [35–37], see Section S1), and as a source of thermal flux (through optothermal effect, see Sections S2 and S3). All devices are measured under vacuum (∼1 × 10−5 Torr), and a displacement stage with a 0.3 μm resolution is employed to precisely control the device position. The devices we use are β-In2S3 (a prototypical non-layered 2D semiconductor) drumhead resonators. Figure 1b and c show the crystal structure and optical image of a representative device (Device #1, ∼147 nm thick and 10 μm in diameter). It is important to note that both the thermal conductivity κ of 2D β-In2S3 and the interfacial thermal conductance GB between 2D β-In2S3 and SiO2 have not yet been reported, which prevents the application of established measurement techniques.

Figure 1. Resonance measurement setup and resonance response with varying laser position/laser power. (a) Schematic of the custom-built resonant NEMS measurement system [39,40]. PD: photodetector, BS: beam splitter. (b) Illustration of a unit cell in the β-In2S3 lattice, with larger and smaller spheres symbolizing In and S atoms, respectively. (c) An optical image of a representative β-In2S3 resonator with a diameter of 10 μm and a thickness of ∼147 nm. Scale bar: 10 μm. (d–e) Measured resonance response (blue spheres) with (d) various laser positions (along the radius) and (e) various laser powers. The dashed curves (red) represent the fitting results. (f) Frequency mapping of Device #1. The mapping region spans 11.5 μm × 11.5 μm, and the dashed outline delineates the suspended area (see Section S9 for details).

To address this challenge, we exploit two DOFs enabled by the 2D NEMS platform in order to simultaneously extract the values of κ and GB. Specifically, we vary both laser position and laser power when measuring the fundamental mode resonance frequency f0 for the devices, and the measurement results for Device #1 are shown in Fig. 1d−f. We make two observations from the data: first, the device frequency increases as the laser spot moves from device center towards the edge; second, the frequency increases as the laser power decreases. The high responsivity of resonance frequency to both the DOFs suggests that f0 is an effective indicator for exploring thermal properties. Furthermore, we conduct a mapping of resonance frequency f0 while maintaining a fixed laser power (448 μW), with results shown in Fig. 1f. We find that the f0 map is azimuthally symmetric, with a minimum f0 at the center. This observation confirms that the in-plane thermal property of 2D β-In2S3 crystal is isotropic (otherwise the mapping result would not exhibit a circularly symmetric pattern [38]), thus we can use just one set of κ and GB values to describe the system.

In order to quantify the relationship between thermal conduction and resonance frequency, we first analyze the optothermal process (Fig. 2a). As shown in Fig. 2b, once the laser is incident onto the device (scene 1), heat conduction initially occurs (scene 2) within the 2D material (primarily governed by its in-plane thermal conductivity), and then between the 2D material and the substrate, with the interfacial thermal conductance becoming important (scene 3). Within nanoseconds, thermal equilibrium is established (scene 4), resulting in a stable temperature distribution with an average temperature increase ΔTavg.

Figure 2. Mechanism of laser-heating-induced frequency tuning. (a) Illustration of a fully clamped 2D-material-based resonator vibrating in fundamental mode. Laser heating (green vertical beam) generates a temperature gradient across the membrane (depicted by the yellow-red colour). (b) Modeling of the in-device thermal conduction process. Upon laser illumination (scene 1), heat initially conducts across the in-plane direction of the drumhead, dominated by the thermal conductivity κ (scene 2). Subsequently, heat conducts across the supported region and establishes a thermal pathway to the underlying substrate (SiO2) through the interfacial thermal conductance GB (scene 3). The device reaches a thermally steady state in a matter of nanoseconds (scene 4). (c–d) Theoretical analyses of the frequency tuning process while (c) sweeping the laser power and (d) sweeping the laser position. The color scale of the temperature distribution maps is consistent with that in (b). (e) 3D plot by amalgamating both mechanisms. When sweeping the laser position, as depicted in (d), the resonance frequency shifts as the laser moves from the center [β1] to the edge [β2] along the blue dashed line. A similar trajectory, as illustrated in (c), is presented with the red spheres ([α1] and [α2]) and the red dashed line.

For a drumhead resonator with a thickness of t and an area of A, the optothermal surface tension γth (in N/m, also averaged over the entire device) induced by ΔTavg is [38,41]:

(1) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{eqnarray*} {{\gamma }_{{\mathrm{th}}}} = \frac{t}{A}\int\!\!\!\!\int_A {\frac{2}{3}}\sigma {\mathrm{d}}x{\mathrm{d}}y = - \frac{{2t{{E}_{\mathrm{Y}}}\alpha \Delta {{T}_{{\mathrm{avg}}}}}}{{3\left( {1 - v} \right)}}, \end{eqnarray*}\end{document}

where σ is the thermally induced stress per unit length (in N/m), α is the thermal expansion coefficient of the 2D material, and EY and v are the Young's modulus and Poisson's ratio of the material, respectively. We use α = 10 ppm/K and EY = 60 GPa for a 2D β-In2S3 crystal, both derived from our measurements (see Sections S4 and S5). The minus sign indicates that a larger ΔTavg leads to a more negative γth (less total tension).

To simplify the analysis, we follow the convention of assuming that EY remains mostly constant with temperature [42,43]. Taking into account the influence of the thermal stress γth, the resonance frequency (see Section S6) becomes [44–46]:

(2) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{eqnarray*} {{f}_0}\!=\! \left(\frac{{kd}}{{4\pi }}\right)\sqrt {\frac{{{\mathrm{16}}D}}{{{{\rho }_{2D}}{{d}^{\mathrm{4}}}}}\left[\left(\frac{{kd}}{{\mathrm{2}}}\right)^{\mathrm{2}}\! +\!\frac{{\left( {{{\gamma }_0} + {{\gamma }_{{\mathrm{th}}}}} \right){{d}^{\mathrm{2}}}}}{{{\mathrm{4}}D}}\right]}, \end{eqnarray*}\end{document}

where k is a modal parameter determined numerically [47,48], and γ0 is the initial surface tension (assumed to be uniform across the device) without thermal stress (in N/m). The flexural rigidity D is given by D = EYt3/[12(1–ν2)], and ρ2D denotes the areal mass density (for β-In2S3, ρ3D = ρ2D/t = 4.613 g/cm3) [49]. Since γth is negative for positive ΔTavg, laser heating always leads to decreased f0.

From the above analysis (see Section S6 for detailed calculations), we can explain the experimental observations (Fig. 1d−f): when the laser power is decreased, it reduces ΔTavg and thus increases total tension γ0 + γth, causing f0 to increase (Fig. 2c). Similarly, when the laser spot moves toward the device edge, the heat dissipation into the substrate becomes easier, which reduces ΔTavg and increases γ0 + γth, also leading to a higher f0 (Fig. 2d). To better illustrate such an optothermal response in f0, we construct a 3D plot (Fig. 2e) to visualize the entire 2-DOF parameter space, using the above equations. Each set of measurements (varying laser position or power) corresponds to a vertical slice on this curved surface, as indicated by the curved lines of different orientations on this curved surface.

In order to extract the thermal conductivity κ of β-In2S3 and the interfacial thermal conductance GB between β-In2S3 and SiO2, we examine how this curved surface evolves in response to κ and GB. To quantify the contribution from individual parameters, we focus on those vertical slices (along both directions) of such 3D stack to decouple the effects from the two experimental DOFs, laser position and power (curves in Fig. 3). This will also allow direct comparison to the experimental results.

Figure 3. Exploring the effects of κ, GB and γ0 on position and power response curves. (a−c) Theoretical frequency responses to laser position for various (a) thermal conductivities κ, (b) interfacial thermal conductance GB, and (c) initial in-plane stress γ0. (d−f) Theoretical frequency responses to laser power for various (d) thermal conductivities κ, (e) interfacial thermal conductance GB, and (f) initial in-plane stress γ0. Parameters of Device #1 are used in simulations.

We first direct our attention to the ‘position’ curves (Fig. 3a−c). We observe that κ plays a unique role in this case: it can affect the curvature and steepness of the curve, whereas GB and γ0 mostly just translate the curve. This suggests that by fitting measurements to the calculated ‘position’ curve, we can precisely extract the value of κ even with just rough ranges for GB and γ0. Next, by examining the ‘power’ curves (Fig. 3d−f), we note that they are almost linear (negligible curvature), with their slopes tuned by κ and GB, but not γ0. Consequently, upon determining the value of κ, we can further extract GB based on the slope of the ‘power’ curve, independent of device initial tension γ0. Therefore, with such 2-DOF measurements and analysis, one can simultaneously extract both of the unknown thermal parameters (see Section S7 for detailed discussion). This also offers the advantage that even if one of the parameters such as the thermal contact resistance is affected by clamping conditions, the other thermal parameter such as thermal conductivity can still be independently and reliably extracted.

We now compare the measurement results (spheres in Fig. 4a and b) to the calculated results (lines). First, by fitting data to the ‘position’ curve (Fig. 4a) we are able to directly extract the in-plane thermal conductivity of β-In2S3, κ = 5.2 W m−1 K−1, with a fitting that results in an R2 = 0.9946 (see Section S8 for details and estimation of uncertainties). Next, by performing data analysis using the ‘power’ curve, we obtain the interfacial thermal conductance between β-In2S3 and SiO2 as GB = −6 MW m−2 K−1 with an R2 = 0.9981. This clearly demonstrates the effectiveness of our 2-DOF method using such a NEMS platform. The extracted thermal transport properties, which do not exhibit clear dependence on thickness for samples up to a few hundred nanometers, are consistent with expectations from molecular dynamic (MD) studies and other experimental investigations in the literature [8,50,51,52]. We further apply this method to multiple 2D β-In2S3 resonators of different sizes (see Section S9 and Table S2 for detailed device information), and we find that the extracted thermal conductivity values are reasonably close to each other with a κavg = 3.7 W m−1 K−1, and an interfacial thermal conductance GB,avg = 6.4 MW m−2 K−1 (Fig. 4c and d).

Figure 4. Extraction of thermal conductivity κ and thermal conductance GB. (a, b) Measured (green spheres) and simulated (blue lines) frequency response of Device #1 vs. laser position and laser power. The best-fit simulation yields a k value of 5.2 W m−1 K−1 and a GB value of 6 MW m−2 K−1. (c, d) Summary for κ and GB values extracted from all devices (see Table S2 for a complete list).

It is worth noting that the unusual thermal conductivity of 2D β-In2S3, significantly lower than that of layered 2D materials [27–29,53,54], makes such NEMS devices much more prone to optothermal frequency shifts. This can translate to high power-to-frequency responsivity in NEMS optical sensors. Here we show the data from device #5 (Fig. 5) functioning as a bolometer, which exhibits a significant response from 6.78 MHz to 7.19 MHz over a laser power variation of just 0.133 mW. This constitutes a record-high responsivity of –447 ppm/μW at room temperature, the best reported to date among all drumhead NEMS-based light power meters [15,55–58] (see Section S10 and S11). This demonstrates the great promise of 2D non-layered devices in enabling high-performance light sensors.

Figure 5. Demonstration of a high-performance bolometer. (a) Evolution of normalized resonance response with increasing laser power. The blue solid lines represent the fitting results using the simple harmonic oscillator model, while the measured data are shown in light gray lines. (b) The resonance frequency decreases with increasing laser power, suggesting excellent bolometric performance with a power-to-frequency responsivity of –447 ppm/μW. The green spheres are the frequencies derived from (a), and the purple dashed line shows the linear fit.

The above results, in turn, further highlight some of the key advantages of our approach, i.e. superb responsivity and sensitivity, which in principle can be applied to different types of 2D crystals. Critical to any measurement technique is the detection efficiency (responsivity) and limit (sensitivity). Here we compare our technique with the Raman spectroscopy method previously reported for studying thermal properties in 2D layered materials (see Section S12 for details). We measure the maximum power-to-frequency responsivity of the method, which relies on detecting Raman peak shift upon heating, to be 0.0047 ppm/μW. This demonstrates that our NEMS approach is 1 million times more responsive for a given change in laser power. Furthermore, we estimate the measurement sensitivity (minimum resolvable laser power change, see Section S13 for details) of the two methods, and find that our approach is >2000 times more sensitive than the spectroscopy method (0.11 μW vs. 242 μW). This again demonstrates the excellent responsivity and sensitivity of the NEMS technique, which allows efficient and reliable (see Section S14 for details) extraction of the unknown thermal properties in emerging nanomaterials.

In summary, we experimentally determine the thermal properties in 2D non-layered material, β-In2S3. We demonstrate an effective NEMS-based method, which leverages two DOFs in the measurement (laser position and laser power) to simultaneously determine multiple unknown thermal parameters, and is 1 million times more responsive and >2000 times more sensitive than Raman spectroscopy. Based on this method, we extract the thermal conductivity of 2D β-In2S3 crystal as κavg = 3.7 W m−1 K−1, and the interfacial thermal conductance between β-In2S3 and SiO2 as GB,avg = 6.4 MW m−2 K−1. Interestingly and importantly, the low thermal conductivity of 2D β-In2S3 translates to an excellent power-to-frequency responsivity of –447 ppm/μW, far surpassing the performance of all other drumhead NEMS-based bolometers. In addition, our findings could inspire further exploration on thermal properties of both layered and non-layered 2D materials, which could lead to an improved understanding of the underlying physics, such as the roles of electrons and phonons in the thermal transport of atomically thin crystals. Our work can offer important guidelines for studying thermal properties in nanoscale samples using the NEMS platform, and provide valuable insights into the design and development of 2D non-layered sensing and signal processing devices [59].

METHODS

Sample preparation

We synthesize β-In2S3 nanoflakes using a controlled heating system equipped with a 21-mm-diameter quartz tube under ambient pressure. The indium trifluoride (InF3) and sulfur (S) powders, serving as precursors, are placed in the center of the heating furnace and out of the central hot zone, respectively. A fluorophlogopite mica [KMg3AlSi3O10F2] substrate with a size of 10 mm × 10 mm is placed at the center of the heating furnace above the InF3 powder. Before heating, the whole system is purged with 200 sccm Ar for 10 minutes. Then the furnace is heated to 750ºC at a rate of 40ºC/min with Ar flow of 40 sccm, and maintained for 5 minutes for the growth of β-In2S3. The temperature of the sulfur is maintained at 180–200ºC through the growth stage. After growth, the heating belt for the sulfur is shut down immediately and the furnace is cooled to room temperature.

Device fabrication

We employ a water-assisted lift-off and dry transfer technique to fabricate β-In2S3 NEMS resonators. Instead of cleaving bulk crystals, we start with synthetic β-In2S3 nanoflakes [60] and transfer them onto a polydimethylsiloxane (PDMS) stamp using water-assisted lift-off. We then select uniform large-sized β-In2S3 flakes and transfer each flake to a pre-patterned circular microtrench on a SiO2/Si substrate. In this process, we adjust the alignment of the flakes to ensure their contact with the pre-fabricated metal electrodes, enabling electrical excitation of the devices.

Raman measurements

The β-In2S3 sample is measured using a continuous wave laser at 532 nm with an incident power of 10–30 mW, and a 50× objective with a numerical aperture of 0.5. For Raman measurements (see Section S12), we use an integration time of 600 s with a standard 2400 lines/mm grating.

Estimating laser spot size

To determine the laser spot diameter, we employ a calibrated charge-coupled device (CCD) camera positioned in front of the objective lens to capture the original laser spot, yielding a 1/e2 diameter of Doriginal = 2124 μm. Considering a wavelength (λ) of 532 nm, a 50× objective lens focal length (f) of 4 mm, and a propagation M2 value of 1.1, we further calculate the 1/e2 diameter of the projected laser spot as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $d = 4{{M}^2}\lambda f/\pi {{D}_{\rm {original}}} = 1.4$\end{document}  \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\mathrm{\mu m}}$\end{document}.

Supplementary Material

nwae248_Supplemental_File

FUNDING

This work is supported by the National Key R&D Program of China (2022YFB3203600), the National Natural Science Foundation of China (T2325007, 62450003, 62250073, U21A20459, 62004026, 61774029), the Sichuan Science and Technology Program (2021JDTD0028), the China Postdoctoral Science Foundation (GZB20230107, GZB20240109), the Natural Science Foundation of Sichuan Province (2024NSFSC1430 and 2024NSFSC1408), and the Science and Technology Innovation Program of Hunan Province (“HuXiang Young Talents”, 2021RC3021).

AUTHOR CONTRIBUTIONS

Luming Wang and Jiankai Zhu conceived the concept, performed the data analysis and wrote the initial manuscript; Song Wu and Zejuan Zhang performed most of the measurements; Luwei Zou was responsible for synthesizing 2D β-In2S3; Bo Xu, Jiaqi Wu, Junzhi Zhu and Fei Xiao participated in data analysis and experimental measurements; Zenghui Wang, Juan Xia, Yu Zhou and Jiankai Zhu oversaw the entire project, and revised the manuscript. All authors participated in manuscript discussion.

Conflict of interest statement. None declared.
==== Refs
REFERENCES

1. Kim  K, Choi  J, Kim  T  et al.  A role for graphene in silicon-based semiconductor devices. Nature  2011; 479 : 338–44.10.1038/nature10680 22094694
2. Fendrich  J, Feng  M.  Nearly noise-free transistor operated in the 2–18 GHz range. Appl Phys Lett  1998; 72 : 368–70.10.1063/1.120739
3. Fortunato  E, Barquinha  P, Martins  R.  Oxide semiconductor thin-film transistors: a review of recent advances. Adv Mater  2012; 24 : 2945–86.10.1002/adma.201103228 22573414
4. Qiu  H, Yu  Z, Zhao  T  et al.  Two-dimensional materials for future information technology: status and prospects. Sci China Inf Sci  2024; 67 : 160400.10.1007/s11432-024-4033-8
5. Wang  Z, Xu  B, Pei  S  et al.  Recent progress in 2D van der Waals heterostructures: fabrication, properties, and applications. Sci China Inf Sci  2022; 65 : 211401.10.1007/s11432-021-3432-6
6. Balandin  A.  Thermal properties of graphene and nanostructured carbon materials. Nat Mater  2011; 10 : 569–81.10.1038/nmat3064 21778997
7. Fugallo  G, Cepellotti  A, Paulatto  L  et al.  Thermal conductivity of graphene and graphite: collective excitations and mean free paths. Nano Lett  2014; 14 : 6109–14.10.1021/nl502059f 25343716
8. Xu  X, Pereira  L, Wang  Y  et al.  Length-dependent thermal conductivity in suspended single-layer graphene. Nat Commun  2014; 5 : 3689.10.1038/ncomms4689 24736666
9. Pop  E.  Energy dissipation and transport in nanoscale devices. Nano Res  2010; 3 : 147–69.10.1007/s12274-010-1019-z
10. Ahmed  F, Kim  YD, Choi  MS  et al.  High electric field carrier transport and power dissipation in multilayer black phosphorus field effect transistor with dielectric engineering. Adv Funct Mater  2017; 27 : 160402.10.1002/adfm.201604025
11. Chen  G.  Non-Fourier phonon heat conduction at the microscale and nanoscale. Nat Rev Phys  2021; 3 : 555–69.10.1038/s42254-021-00334-1
12. Cahill  DG, Braun  PV, Chen  G  et al.  Nanoscale thermal transport. II. 2003–2012. Appl Phys Rev  2014; 1 : 011305.10.1063/1.4832615
13. Ye  F, Lee  J, Feng  PX-L. Electrothermally tunable graphene resonators operating at very high temperature up to 1200 K. Nano Lett  2018; 18 : 1678–85.10.1021/acs.nanolett.7b04685 29385804
14. Morell  N, Tepsic  S, Reserbat-Plantey  A  et al.  Optomechanical measurement of thermal transport in two-dimensional MoSe2 lattices. Nano Lett  2019; 19 : 3143–50.10.1021/acs.nanolett.9b00560 30939027
15. Wang  Z, Yang  R, Philip  X-L, Feng  PX-L. Thermal hysteresis controlled reconfigurable MoS2 nanomechanical resonators. Nanoscale  2024; 43 : D1NR03286K.10.1039/D1NR03286K
16. Sun  Y, Sun  Z, Gao  S  et al.  Fabrication of flexible and freestanding zinc chalcogenide single layers. Nat Commun  2012; 3 : 1057.10.1038/ncomms2066 22968703
17. Zhou  N, Yang  R, Zhai  T. Two-dimensional non-layered materials. Mater Today Nano  2019; 8 : 100051.10.1016/j.mtnano.2019.100051
18. Sun  Y, Gao  S, Xie  Y.  Atomically-thick two-dimensional crystals: electronic structure regulation and energy device construction. Chem Soc Rev  2014; 43 : 530–46.10.1039/C3CS60231A 24122032
19. Wang  Y, Zhang  Z, Mao  Y  et al.  Two-dimensional nonlayered materials for electrocatalysis. Energy Environ Sci  2020; 13 : 3993–4016.10.1039/D0EE01714K
20. Wang  F, Wang  Z, Shifa  TA  et al.  Two-dimensional non-layered materials: synthesis, properties and applications. Adv Funct Mater  2017; 27 : 21.
21. Tan  J, Zhang  Z, Zeng  S  et al.  Dual-metal precursors for the universal growth of non-layered 2D transition metal chalcogenides with ordered cation vacancies. Sci Bull  2022; 67 : 1649–58.10.1016/j.scib.2022.06.022
22. Wu  Y, Zheng  J, Li  Q  et al.  Synthesis of superconducting two-dimensional non-layered PdTe by interfacial reactions. Nat Synth  2022; 1 : 908.10.1038/s44160-022-00149-7
23. Lu  J, Zheng  Z, Gao  W  et al.  Epitaxial growth of large-scale In2S3 nanoflakes and the construction of a high performance In2S3/Si photodetector. J Mater Chem C  2022; 7 : 12104–13.10.1039/C9TC03795K
24. Gong  C, Chu  J, Yin  C  et al.  Self-confined growth of ultrathin 2D nonlayered wide-bandgap semiconductor CuBr flakes. Adv Mater  2019; 31 : 1903580.10.1002/adma.201903580
25. Fu  Y, Hansson  J, Liu  Y  et al.  Graphene related materials for thermal management. 2D Mater  2020; 7 : 012001.10.1088/2053-1583/ab48d9
26. Balandin  AA, Ghosh  S, Bao  W  et al.  Superior thermal conductivity of single-layer graphene. Nano Lett  2008; 8 : 902–7.10.1021/nl0731872 18284217
27. Cai  W, Moore  AL, Zhu  Y  et al.  Thermal transport in suspended and supported monolayer graphene grown by chemical vapor deposition. Nano Lett  2010; 10 : 1645.10.1021/nl9041966 20405895
28. Yan  R, Simpson  JR, Bertolazzi  S  et al.  Thermal conductivity of monolayer molybdenum disulfide obtained from temperature-dependent Raman spectroscopy. ACS Nano  2014; 8 : 986–93.10.1021/nn405826k 24377295
29. Luo  Z, Maassen  J, Deng  Y  et al.  Anisotropic in-plane thermal conductivity observed in few-layer black phosphorus. Nat Commun  2015; 6 : 8572.10.1038/ncomms9572 26472191
30. Pumarol  ME, Rosamond  MC, Tovee  P  et al.  Direct nanoscale imaging of ballistic and diffusive thermal transport in graphene nanostructures. Nano Lett  2012; 12 : 2906–11.10.1021/nl3004946 22524441
31. Buckley  D, Kudrynskyi  ZR, Balakrishnan  N  et al.  Anomalous low thermal conductivity of atomically thin InSe probed by scanning thermal microscopy. Adv Funct Mater  2021; 31 : 2008967.10.1002/adfm.202008967
32. Xu  B, Zhu  J, Xiao  F  et al.  Identifying, resolving, and quantifying anisotropy in ReS2 nanomechanical resonators. small  2023; 19 : 2300631.10.1002/smll.202300631
33. Zhu  J, Wang  L, Wu  J  et al.  Achieving 1.2 fm/Hz1/2 displacement sensitivity with laser interferometry in two-dimensional nanomechanical resonators: pathways towards quantum-noise-limited measurement at room temperature. Chin Phys Lett  2023; 40 : 038102.10.1088/0256-307X/40/3/038102
34. Wang  Z, Feng  PX-L.  Interferometric motion detection in atomic layer 2D nanostructures: visualizing signal transduction efficiency and optimization pathways. Sci Rep  2016; 6 : 28923.10.1038/srep28923 27464908
35. Zhu  J, Zhang  P, Yang  R  et al.  Analyzing electrostatic modulation of signal transduction efficiency in MoS2 nanoelectromechanical resonators with interferometric readout. Sci China Inf Sci  2022; 65 : 122409.10.1007/s11432-021-3297-x
36. Anders  H.  Thin Films in Optics. London: Focal Press, 1967.
37. Blake  P, Hill  EW, Castro Neto  AH  et al.  Making graphene visible. Appl Phys Lett  2007; 91 : 063124.10.1063/1.2768624
38. Islam  A, van den Akker  A, Feng  PX-L. Anisotropic thermal conductivity of suspended black phosphorus probed by opto-thermomechanical resonance spectromicroscopy. Nano Lett  2018; 18 : 7683–91.10.1021/acs.nanolett.8b03333 30372081
39. Xu  B, Zhu  J, Xiao  F  et al.  Electrically tunable MXene nanomechanical resonators vibrating at very high frequencies. ACS Nano  2022; 16 : 20229–37.10.1021/acsnano.2c05742 36508311
40. Xu  B, Zhang  P, Zhu  J  et al.  Nanomechanical resonators: toward atomic scale. ACS Nano  2022; 16 : 15545–85.10.1021/acsnano.2c01673 36054880
41. Murakami  Y.  Theory of Elasticity and Stress Concentration. New York: John Wiley & Sons, 2016.
42. Sun  H, Liu  G, Li  Q  et al.  First-principles study of thermal expansion and thermomechanics of single-layer black and blue phosphorus. Phys Lett A  2016; 380 : 2098–104.10.1016/j.physleta.2016.04.021
43. Liu  G, Zhou  J.  First-principles study of thermal expansion and thermomechanics of group-V monolayers: blue phosphorene, arsenene, and antimonene. J Phys: Condens Matter  2019; 31 : 065302.30523811
44. Lee  J, Wang  Z, He  K  et al.  High frequency MoS2 nanomechanical resonators. ACS Nano  2013; 7 : 6086–91.10.1021/nn4018872 23738924
45. Zhu  J, Xu  B, Xiao  F  et al.  Frequency scaling, elastic transition, and broad-range frequency tuning in WSe2 nanomechanical resonators. Nano Lett  2022; 22 : 5107–13.10.1021/acs.nanolett.2c00494 35522819
46. Wang  Z, Feng  PX-L.  Design of black phosphorus 2D nanomechanical resonators by exploiting the intrinsic mechanical anisotropy. 2D Mater  2015; 2 : 021001.10.1088/2053-1583/2/2/021001
47. Suzuki  H, Yamaguchi  N, Izumi  H.  Theoretical and experimental studies on the resonance frequencies of a stretched circular plate: application to Japanese drum diaphragms. Acoust Sci & Tech  2009; 30 : 348–54.10.1250/ast.30.348
48. Wah  T.  Vibration of circular plates. J Acoust Soc Am  1962; 34 : 275–81.10.1121/1.1928110
49. King  G.  The space group of β-In2S3. Acta Cryst  1962; 15 : 512.10.1107/S0365110X62001280
50. Zhang  Z, Ouyang  Y, Cheng  Y  et al.  Size-dependent phononic thermal transport in low-dimensional nanomaterials. Phys Rep  2020; 860 : 1–26.10.1016/j.physrep.2020.03.001
51. Chen  J, Zhang  G, Li  B.  Substrate coupling suppresses size dependence of thermal conductivity in supported graphene. Nanoscale  2012; 5 : 532–6.10.1039/C2NR32949B 23223896
52. Zhong  W-R, Zhang  M-P, Ai  B-Q  et al.  Chirality and thickness-dependent thermal conductivity of few-layer graphene: a molecular dynamics study. Appl Phys Lett  2011; 98 : 113107.10.1063/1.3567415
53. Sang  Y, Guo  J, Chen  H  et al.  Measurement of thermal conductivity of suspended and supported single-layer WS2 using micro-photoluminescence spectroscopy. J Phys Chem C  2022; 126 : 6637–45.10.1021/acs.jpcc.2c00732
54. Easy  E, Gao  Y, Wang  Y  et al.  Experimental and computational investigation of layer-dependent thermal conductivities and interfacial thermal conductance of one- to three-layer WSe2. ACS Appl Mater Interfaces  2021; 13 : 13063–71.10.1021/acsami.0c21045 33720683
55. Islam  A, Lee  J, Feng  PX-L. Black phosphours NEMS resonant infrared (IR) detector. 33rd IEEE International Conference on Micro Electro Mechanical Systems (MEMS 2020), Vancouver BC, Canada, 18–22 January 2020.
56. Yang  R, Wang  Z, Feng  PX-L. All-electrical readout of atomically-thin MoS2 nanoelectromechanical resonators in the VHF band. 29th IEEE International Conference on Micro Electro Mechanical Systems (MEMS 2016), Shanghai, China, 24–28 January 2016.
57. Liu  S, Chen  Y, Lai  H  et al.  Room-temperature fiber tip nanoscale optomechanical bolometer. ACS Photonics  2022; 9 : 1586–93.10.1021/acsphotonics.1c01676
58. Blaikie  A, Miller  D, Alemán  BJ.  A fast and sensitive room-temperature graphene nanomechanical bolometer. Nat Commun  2019; 10 : 4726.10.1038/s41467-019-12562-2 31624243
59. Wang  L, Zhang  P, Liu  Z  et al.  On-chip mechanical computing: status, challenges, and opportunities. Chip  2023; 2 : 100038.10.1016/j.chip.2023.100038
60. Zhu  J, Wu  S, Wang  L  et al.  Broad-range, high-linearity, and fast-response pressure sensing enabled by nanomechanical resonators based on 2D non-layered material: β-In2S3. InfoMat  2024; 6 : e12553.10.1002/inf2.12553
