High-Strength Amorphous Silicon Carbide for Nanomechanics

For decades, mechanical resonators with high sensitivity have been realized using thin-film materials under high tensile loads. Although there have been remarkable strides in achieving low-dissipation mechanical sensors by utilizing high tensile stress, the performance of even the best strategy is limited by the tensile fracture strength of the resonator materials. In this study, a wafer-scale amorphous thin film is uncovered, which has the highest ultimate tensile strength ever measured for a nanostructured amorphous material. This silicon carbide (SiC) material exhibits an ultimate tensile strength of over 10 GPa, reaching the regime reserved for strong crystalline materials and approaching levels experimentally shown in graphene nanoribbons. Amorphous SiC strings with high aspect ratios are fabricated, with mechanical modes exceeding quality factors 10^8 at room temperature, the highest value achieved among SiC resonators. These performances are demonstrated faithfully after characterizing the mechanical properties of the thin film using the resonance behaviors of free-standing resonators. This robust thin-film material has significant potential for applications in nanomechanical sensors, solar cells, biological applications, space exploration and other areas requiring strength and stability in dynamic environments. The findings of this study open up new possibilities for the use of amorphous thin-film materials in high-performance applications.

Advances in nanotechnology have revolutionized a broad spectrum of fields, with the development of tensileloaded, thin-film mechanical devices playing a pivotal role in state-of-the-art force, acceleration, and displacement sensing [1][2][3][4][5][6][7].Two approaches are used to boost the sensitivity of nanomechanical resonators under tensile loads.One approach fabricates the resonators using different thin-film materials in pursuit of films with low mechanical loss tangents resulting in higher intrinsic mechanical quality factors.In room temperature environments, high-tensile amorphous silicon nitride (a-Si 3 N 4 ) nanomechanical resonators have marked some of the best performing devices in ultra-sensitive mechanical detectors [8][9][10][11][12][13].Despite the fact that crystalline thin film materials (e.g.crystalline silicon (c-Si) [14], crystalline silicon carbide (c-SiC) [15,16]) and graphene are expected to have higher theoretical limits, their projected performance relies on having perfect crystal structures with no defects (e.g.edge defects).Additionally it is difficult to practically attain crystalline thin-films [14,15] which can be easily deposited, have good film isotropy [17] and few lattice imperfections [14,15].By nanostructuring edges into free-standing crystalline devices, one introduces a form of defect by exposing the edge of the crystal where fracture can initiate under high-tensile loads [18][19][20].
The other approach to attain state-of-the-art sensors is by innovating designs of the nanomechanical resonators' geometries to have high stresses at crucial regions of the resonator when it vibrates.Ultimately the design space of these resonators is constrained by the thin film materials' tensile fracture limits or ultimate tensile strength (UTS).The UTS of a thin-film is fundamentally lower after being nanostructured into a suspended geometry with edges, since the introduced crystalline defects such as dislocations can facilitate the propagation of cracks [21,22].For example, the UTS of a-Si 3 N 4 thin film has been shown to be 6.8 GPa [23].To date, only crystalline and 2D materials have experimentally demonstrated UTS surpassing 10 GPa after being top-down nanofabricated [19,[24][25][26].Among 2D crystalline materials, graphene harbors one of the highest theoretical UTS [26,27], but practically reaching the limit is also challenging due to lattice imperfections [28], atomically irregular edges [19], or sparser grain boundaries [29] resulting from nanostructuring processes, which lead to a reduced fracture limit when it is tensile-loaded.In this regard, amorphous thin films with high UTS offer more design freedom for free-standing nanostructures, due to their lack of both crystalline defects and sensitivity to notches [30][31][32][33].Apart from allowing the enhancement of the Q factor of nanomechanical resonators, higher material UTS can enable the devices to perform better in diverse and harsh environments.
In this work, we demonstrate wafer-scale amorphous films that harbor an ultimate tensile strength over 10 GPa after nanostructuring, a regime that is conventionally reserved for ultra-strong crystalline and 2D materials.Using delicate nanofabrication techniques, we produce several different nanomechanical resonators that can accurately determine the mechanical properties of SiC thin films such as density, Young's modulus, Poisson ratio, and ultimate tensile strength.Notably, our highest measured tensile strength (>10 GPa) is comparable to the values shown for c-SiC [24] and approaching the experimental values obtained for double-clamped graphene nano-ribbon [19].We achieve mechanical quality factor up to 2 × 10 8 with a-SiC mechanical resonators, and measure loss-tangents on par with other materials used in high-precision sensors.Beyond sensing, these strong films open up new possibilities in high-performance nanotechnology, including thin solar cell technologies [53], mechanical sensing [70], biological technologies [71] and even lightsail space exploration [72].

II. FABRICATION OF AMORPHOUS SIC RESONATORS
In pursuit of thin film materials for nanomechanical resonators with low mechanical dissipation, high film quality and high tensile stress are desirable.The Low Pressure Chemical Vapor Deposition (LPCVD) technique is preferred for these requirements, since its low pressure and high temperature deposition environment ensures lower defect density and higher thermal stress.The non-stoichiometric LPCVD a-SiC films used in this paper are deposited with different gas flow ratios (GFR) between SiH 2 Cl 2 and 5% C 2 H 2 in H 2 (GFR=2,3,4), various deposition pressures (170 and 600 mTorr), and on both silicon and fused silica substrates (Table I).This variation of deposition parameters allows us to systematically characterize the mechanical properties of LPCVD a-SiC thin films.All a-SiC thin films were deposited for the same period of time (3 hours 47 minutes) at a temperature of 760 • C in order to better determine the effect of various deposition environments while maintaining the films in the amorphous form [73].With the fabrication process demonstrated in the Supporting Information (H), nanomechanical resonators made of a-SiC can be suspended over the substrates with high yield using dry etching processes due to their extremely high chemical selectivity.
Better chemical stability and inertness of the sensing components can significantly improve the sensors' reliability, particularly for their operation under chemically harsh environments.Meanwhile, thin film materials' chemical inertness allows them to be deposited on various substrates, patterned, and then suspended as nanomechanical resonators by removing the substrate underneath (i.e.undercutting).A high selectivity between the thin film and the substrate allows for higher yield and accuracy in fabricating suspended nanostructures .Similar to their crystalline counterpart, LPCVD a-SiC thin films have been reported to have very high chemical inertness to various wet etchants [43].Likewise, we found that a-SiC also has high chemical inertness to the widely used dry etchants, such as SF 6 isotropic plasma etching for silicon substrate, and vapor hydrofluoric acid etching for silicon oxide substrate, as illustrated in Figure 1(a).The excellent chemical stability implies high selectivity between a-SiC and various commonly used substrates during undercutting, as shown in Figure 1(b).Dry etchants are preferred for suspending high-aspect-ratio nanomechanical structures, since they help to avoid stiction during liquid etchant evaporation and thus improve the yield rate of working devices.To take advantage of the superior chemical inertness, we fabricated nanomechanical resonators with continuous films down to 5nm, as shown in SEM pictures in Supporting Information (F).
structures with different maximum tensile stresses to accurately determine the ultimate tensile strength (UTS) of a-SiC films.As a result, we demonstrate that a-SiC films have UTS up to 10-12 GPa, which are the highest among amorphous materials after patterning and are approaching the UTS of strong materials like c-SiC [24] and graphene nano-ribbons [19], both of which are known for their high UTS.The comparison of UTS between LPCVD a-SiC and other materials commonly used for nanomechanics is shown in Figure 1(c).

III. MECHANICAL PROPERTY CHARACTERIZATION WITH RESONANCE METHOD
In order to design desired nanomechanical resonators with a specific thin film material, it is necessary to accurately characterize the material's mechanical parameters, such as film stress, Young's modulus, Poisson ratio and density.Various methods are developed to measure these parameters, including static methods, like nanoindentation [78,79] and dynamic methods like resonance response [80][81][82][83].Many studies aiming to design highperformance nanomechanical resonators have relied on mechanical parameter values obtained from literature without considering potential variations of thin film properties due to different deposition environments, such as commonly used materials like a-Si 3 N 4 [10,12], c-Si [14], and c-SiC [15,16].While these adaptations are usually reasonable and align well with experimental results, characterizing the exact parameters of the materials used would be beneficial when exploring the optimal performance of nanomechanical resonators [80,84].In this section, we present a simple and universal method to systematically characterize the important mechanical parameters of LPCVD a-SiC thin films.
The characterization flow of the method begins with measuring the thickness of the a-SiC thin film (t) after LPCVD deposition using a spectroscopic ellipsometer, which is an optical technique to confirm the thin film thickness and investigate its dielectric properties simultaneously.We then identify the film stress (σ) using the wafer bending method.After dicing the wafer into small chips, we pattern the a-SiC thin film and suspend it in the form of membranes, cantilevers, and strings with different lengths (L).The suspended nanomechanical resonators are measured with a laser Doppler vibrometer (LDV) in the vacuum environment down to 10 −7 mbar.The measured resonant frequencies of the fundamental modes of the membranes (f mem ), cantilevers (f can ), and strings (f str ) can be fitted with their corresponding analytical expressions, which reveal the Young's modulus (E), Poisson ratio (ν), and density (ρ) of the a-SiC thin film, respectively.During the fitting process, finite element method (FEM) simulation is used to describe the patterned resonators more precisely by taking into account the holes on the membranes and the overhangs from under-cutting adjacent to the cantilevers and strings.More detailed information about the measurements, analytical fitting, and simulations are shown in Supporting Information (A) and (B).
Using the above measurements, we can characterize the important mechanical parameters of LPCVD a-SiC thin films, then design and fabricate nanomechanical resonators with desired performance.Note that this straightforward and non-contact method can be universally applied to characterize the mechanical properties of other tensile thin film materials that can be fabricated into resonators with various geometries, i.e. cantilevers, strings, and membranes.This allows for quality control of thin films deposited in different batches or under varied deposition environments.As a result, nanomechanical resonators manufactured for various applications can be characterized in an efficient and economical manner, resulting in higher reliability for both industrial and academic applications.With all the relevant mechanical parameters accurately measured, we can fabricate a series of suspended devices specifically designed for character- izing the ultimate tensile strengths of a-SiC thin films in the following section.

IV. ULTIMATE TENSILE STRENGTH OF AMORPHOUS SIC
Ultimate tensile strength (UTS), or sometimes coinciding with yield strength for brittle materials such as a-SiC [35], describes the maximum tensile stress a material can endure before breaking while being stretched.Materials with higher UTS not only allows them to operate more reliably as mechanical sensors or coating in harsh environments, but also enlarges the design space for nanomechanical resonators.High UTS has been shown for nanowires fabricated with various materials, whose small cross-section areas minimize the appearance of defects [85,86], and for nanomechanical membranes without nano-patterning to avoid the presence of rough sidewalls [87].However, both scenarios above do not allow for further shape modification, reducing interest in their potential for various applications.While the crystalline form of materials usually tend to be mechanically stronger than their amorphous forms due to long-range order, examples such as glassy metal [88] and synthesized AM-III carbon [89] demonstrate extraordinary mechanical properties comparable to their celebrated crystalline counterparts in terms of fracture toughness and yield strength, or hardness and compressive strength, respectively.This correspondence remains between c-SiC and a-SiC.While c-SiC has shown a UTS as high as 12-18 GPa via micro-pillars so far [24], a-SiC nanowires have been measured to have a UTS up to 8.8 GPa via a tensile test with its two ends fixed by silver epoxy [35], which is higher than the ones shown for LPCVD a-Si 3 N 4 (6.8GPa [23]) and Si (7.6 GPa [70]).
With the aim of characterizing the design space of nanomechanical resonators using LPCVD a-SiC thin film, we characterized its UTS by geometrically tapering the suspended a-SiC thin film in order to concentrate the tensile stress up to the fracture point.Unlike other tensile test methods [90], the presented method allows to determine the UTS of the tensile nanostructured film accurately, while avoiding the ambiguity caused by external loads, glues, and limitations of nano-fabrication, e.g.limited accuracy of nano-patterning and stiction during wet undercut.With the mechanical parameters characterized in Section III, a-SiC hourglass-shaped devices consisting of a short and narrow tether surrounded by long and wide pads on both sides which are designed and suspended to measure the UTS of LPCVD a-SiC thin films.The devices have a total length of 1500um, with pads on both sides that have a width of 15 um, and the middle tethers that have varying lengths and a width of 500 nm, as shown in Figure 3(a).After being suspended with dry etchants, the tensile stress on the hourglass-shaped device will redistribute and result in an increase of stress on the middle tether due to the pulling of the pads caused by residual stresses arising from the fabrication.The redistributed stress profile in Figure 3  finite element method (FEM).The devices are designed to have varying tether lengths from short to long, which are then arranged adjacently as shown in Figure 3(b).
To establish a force equilibrium between the tether and the pads on each device, the ratio between the tensile stresses on the tether and the pads is inversely proportional to the ratio between their widths, combined with a small proportion of the lengths between the two, which enhances the strain (percentage of elongation) on the tether, the tensile stress on the tether in our hourglass-shaped devices can be significantly amplified during stress relaxation after suspending.As shown with FEM simulation in Figure 3(c), devices with shorter tether lengths contain higher maximum concentrated tensile stresses on the tethers.This method allows the determination of the UTS of the nanostruc-tured a-SiC thin films by counting the number of surviving devices after suspension.As shown in Figure 3(b), a series of hourglass-shaped devices are fabricated with a-SiCR2.The 18 devices have tether lengths ranging from 30 to 115 um, corresponding to stresses from 12.53 to 5.97 GPa, respectively.The adjacent devices have tether lengths that differ for 5 um, the shorter the tethers are, the larger difference in concentrated stress the devices contain, e.g. the concentrated stress difference between devices with 115 um and 110 um tether lengths is 0.18 GPa, while one between devices with 35 um and 30 um is 0.72 GPa.In the case of each a-SiC thin film, the survival rate of each tensile interval shown in Figure 3(d) is determined, by employing 36 to 72 devices for testing.
The survival of the suspending hour-glass-shaped device with the tether length below 50 um, corresponds to a UTS above 10 GPa for a-SiCR2.Similarly, we can identify the UTS for all a-SiC thin films used in this study to be higher than 10 GPa, as shown in the histograms of ratios of survival devices in Figure 3(d).
The histograms also show that, with relatively higher deposition pressure and lower gas flow ratios, a maximum UTS up to 12 GPa can be achieved with a-SiCR2, which is almost twice that of the UTS shown for nanostructured LPCVD a-Si 3 N 4 films.The measured UTS of a-SiCR4 is below 3.5 GPa, which is not attractive for further characterization.In the future, with a larger number of fabricated devices and a denser range of tether lengths, one can determine the UTS of the LPCVD a-SiC thin films more precisely.In practice, the nanopatterning with electron beam lithography can readily achieve an accuracy of 10 nm, which allows for the method's accuracy to be as low as 1.2 MPa on a-SiCR2, i.e. an error of less than 0.2% when measuring the UTS.Higher UTS is found for recipes deposited with lower gas flow ratios (a-SiCR2/3/4), which might due to a higher carbon composition in the thin film [73], and C-C chemical bonds are stronger than Si-C and Si-Si bonds [91].For a-SiC films deposited with different pressure, a-SiCR2 (600 mTorr) is found to have a higher UTS, while a-SiC170 (170 mTorr) exhibits better yield under lower concentrated stresses as shown by the survival rates.According to the relationship between strength and Young's modulus E of SiC shown in [35], UTS (or fracture strength) is 5.3% of E, therefore the theoretically predicted UTS for a-SiCR2/a-SiC170/a-SiCR3, are 11.82/11.66/11.13GPa, respectively, matching well with the experimentally extracted data from the survived devices 12.04/10.27/11.12GPa shown in Table I.The small offset for the values of a-SiC170 may be due to its rougher surface as shown in Supporting Information (G).
With strain engineering techniques, one can amplify the mechanical quality factor Q = D Q • Q 0 of a nanomechanical resonator by boosting their dissipation dilution factor D Q , where Q 0 is the intrinsic quality factor of the thin film material [10,92].Since the upper bound for D Q of a nanomechanical string vibrating at a certain frequency ω is given by , where U T S denotes the UTS of the thin film material [93], thin film materials with higher UTS and lower thickness are advantageous to obtain a higher D Q .Among all a-SiC thin films shown in this work, a-SiCR2 is the most promising one to maximize the Q factor, thanks to its high Q 0 and UTS.The superior chemical resistivity of a-SiC enables the fabrication of thin films into suspending resonators with a thickness as low as 5 nm (shown in Supporting Information (F)).This combined with its elevated ultimate tensile strength U T S , which measures above 10 GPa in thicker films, makes a-SiC string resonators highly promising in achieving a supreme upper bound for D Q at a certain frequency ω.

V. INTRINSIC QUALITY FACTOR AND HIGH Q MECHANICAL RESONATORS
In this section we characterize the intrinsic quality factor Q 0 of LPCVD a-SiC, then design and fabricate high-Q nanomechanical resonators with it.High mechanical quality (Q) factor nanomechanical resonators are desirable for various applications, ranging from precise force/acceleration sensing [1,6], microwave-to-optical conversion [67], to quantum optomechanics [66,94].Following the method introduced by LIGO [95], the field of strain engineering is advancing rapidly, boosting the Q factor of nanomechanical resonators by several orders of magnitude.A variety of strategies have been proposed aiming to improve the Q factors of tensile-loaded nanomechanical resonators.These include patterning 2D geometries appropriately [9,[11][12][13][96][97][98], modifying mass distribution [2,99] and mode of interest (e.g., from fundamental to higher order or from flexural to torsional modes [2]), in-situ annealing for surface cleaning [100], as well as cooling down to cryogenic temperatures [14,101].The methods mentioned above can benefit from utilizing the LPCVD a-SiC thin film we characterized in this work, due to its high deposition film tensile stress, superior chemical resistivity, and impressive ultimate tensile strength.
The intrinsic quality factors Q 0 of a-SiC thin films are identified by experimentally measuring the Q factors of phononic crystal (PnC) nanostrings [10], whose many spurious loss mechanisms are eliminated, and dissipation dilution factor D Q is well defined, leading to an expected intrinsic Q factor Q 0 = Q/D Q .For thin nanomechanical resonators, Q 0 can be assumed to depend linearly on the film thickness, since it is predominantly determined by surface loss rather than bulk loss [92].We fabricate a series of uniformly corrugated high-aspect-ratio (PnC) nanostrings with a length of 4 mm, varying unitcell lengths L uc and defect lengths L def in the middle (Figure 4(a)), leading to PnC nanostrings with unitcell numbers from 20 to 44.The widths of the wide and narrow parts of the nanostrings are 3 um and 1 um respectively.The vibration amplitude of the nanostrings as a function of frequency is acquired (Figure 4(b)) with a custom balanced homodyne detection interferometer at the vacuum environment of 4 × 10 −9 mbar (see Supporting Information (I)).Using the ringdown method, the Q factors of defect modes for each PnC nanostring are measured.For example, the ones of 10 unit-cells PnC nanostrings fabricated wtih a-SiCR2 and a-SiCR2FS are plotted in Figure 4(d).Using FEM simulation, the dilution factor D Q of each PnC nanostring geometry can be numerically calculated.Together with the Q factors of the corresponding nanostring measured experimentally, the intrinsic Q factor Q 0 of the different a-SiC thin films are determined.For example, the Q 0 of a-SiCR2 and a-SiCR2FS are shown in Figure 4(c) and (e) respectively.The Q 0 of the other a-SiC films are shown in Table I, and the corresponding measurement data can be found in Supporting Information (D).In order to compare the Q 0 of a-SiC thin films with different thicknesses, we present them with the unit Q 0 per 100 nm, as Q 0 of a thin film is shown to be a function of thickness [84].Deposited with the same recipe, a-SiCR2 (5175/100 nm) and a-SiCR2FS (4554/100 nm) have similar Q 0 .The similar performance on the transparent substrate allows for integrating high-Q nanomechanical sensors into free-space optical systems in a practical manner.By reasonably assuming the films have similar mechanical properties on different substrates, a-SiCR2FS is measured to have a deposition stress of 1596 MPa, a factor of two higher than a-SiCR2 due to a larger thermal expansion coefficients difference between the a-SiC thin film and fused silica substrate.Worth noting is that the Q 0 of a-SiCR2 is the highest among all LPCVD a-SiC investigated, indicating that a lower gas flow ratio (GFR=2), i.e., more carbon content [73], and a moderate deposition pressure (600 mTorr) is beneficial to have better film quality.
To exploit the sensing potential of LPCVD a-SiC, we designed and optimized a tapered PnC nanostring with a length of 6mm and a thickness of 71 nm using a a-SiCR2 thin film.Bayesian optimization [12] was used to find designs with high Q-factor -more details can be found in Supporting Information (E).This simulationbased optimization is largely possible due to the accurate characterization of the material properties of the a-SiC thin films in previous sections.As shown in Figure 4(f ), the optimized PnC nanostring consists of fixed 24 unit cells with different widths and lengths, leading to a stress concentration of up to 1.2 GPa towards its center part.Within the phononic bandgap generated by the optimized tapered PnC nanostring, a soft clamped defect mode with a simulated Q factor Q sim = 2.11 ± 0.17 × 10 8 appears at the frequency of f sim = 921 kHz, as shown at the bottom of Figure 4(f ).The optimized tapered PnC nanostring was fabricated based on the design at the top of Figure 4(f ), and it was measured at an interferometer under ultra-high vacuum of 4 × 10 −9 mbar.As a result, an high Q factor mechanical mode with Q = (1.98 ± 0.03) × 10 8 was measured experimentally at a frequency of f = 896 kHz at room temperature, shown by its ringdown curve plotted in Figure 4(g).This result demonstrates, for the first time, a mechanical quality factor exceeding 10 8 for silicon carbide nanomechanical resonators, as predicted by simulation.This also suggests that future design strategies to enhance resonator performance can be carried out using the LPCVD a-SiC thin films.
In addition, the quality factor-frequency product of the optimized LPCVD a-SiC tapered PnC nanostring is Q × f = 1.791 × 10 14 , which is significantly higher than the quantum limit Q × f = 2πk B T / = 6.24 × 10 12 .This paves the way towards engineering quantum states in room temperature environments [9,94].This high quality factor of the nanomechanical resonator with an effective mass m ef f = 1.27 × 10 −13 kg corresponds to a force sensitivity of √ S F = 4k B T m ef f • 2πf /Q = 7.7 aN/Hz 1/2 at room temperature, which is comparable to a typical atomic force microscope cantilever operating at liquid helium temperature.With the high quality factor shown above, LPCVD a-SiC is shown to be the third material that can reach Q > 10 8 at room temperature using strain engineering, after conventional a-Si 3 N 4 [10] and strained silicon [14].Moreover, the superior chemical and mechanical properties of LPCVD a-SiC allow for the fabrication of thinner and stronger resonators, enabling it to be more compatible with the dissipation dilution method.With advantages such as a relatively simple and low-cost fabrication process, compatibility with various substrates, including transparent ones, and its potential to perform better and more stably in harsh environments as high-Q nanomechanical resonators, LPCVD a-SiC is a promising material for fabricating commercial mechanical sensors.

VI. CONCLUSION AND OUTLOOK
In summary, our study has uncovered an amorphous silicon carbide thin film with a ultimate tensile strength above 10 GPa, the highest value ever measured for a nanostructured amorphous material and approaching the experimental values shown by graphene nano-ribbons [19].Their robustness to chemicals allow us to fabricate nanostructures with very high fidelity even when their geometries make them delicate high-aspect-ratio structures.This ability to produce structures with high fidelity also allow us to measure the film's mechanical properties with high precision.We deposit amorphous silicon carbide in varying deposition conditions and substrates to understand new approaches towards increasing ultimate yield strength.Then using the a-SiC with the highest UTS, we designed and fabricated a variety of well-understood nanostructures such as cantilever, membranes and doubly-clamped strings to measure the thin films mechanical properties such as density, Young's modulus, Poisson ratio, and mechanical loss tangents.For the latter we employ nanostrings patterned with phononic bandstructures which conventionally have some of the lowest mechanical dissipations in literature, and this allows us to measure very low mechanical dissipation.The a-SiC nanostrings support soft-clamped mechanical modes with quality factors exceeding 10 8 at room temperature; a new regime for SiC devices and on par with the state-of-the-art SiN resonators.This corresponds to a high force sensitivity of √ S F = 7.7 aN/Hz 1/2 .We demonstrate a robust characterization process based on the simple fabrication and optical techniques which does not rely on complex tension loading setups.
The discovery of this amorphous SiC material represents an advancement in the field of high-strength material science which is conventionally dominated by crystalline and 2D materials.However, our findings demonstrate that amorphous materials have the potential to surpass crystalline materials in certain applications due to their inherently isotropic mechanical properties, which allow for more design freedom and ease of fabrication.The high ultimate tensile strength of this amorphous material is particularly attractive for mechanical sensors, as it enables greater flexibility in strain engineering.This discovery opens up new possibilities for the use of amorphous materials in a variety of high-performance applications.

SUPPORTING INFORMATION (A): MECHANICAL PROPERTIES CHARACTERIZATION OF LPCVD A-SIC THIN FILMS USING RESONANCE METHOD
The characterization flow of the method start with measuring the a-SiC thin film thickness t after the LPCVD a-SiC deposition using the Spectroscopic Ellipsometer (Woollam M-2000F).Then we identify the film stress by measuring the radius curvature R 1 of the silicon wafer before the deposition with the stress meter (Flexus, Toho), and measuring again the curvature R 2 after the deposition with the a-SiC on the backside of the wafer removed with CHF3/Ar plasma anisotropic etching.The film stress σ can be determined from wafer bending method by Stoney's equation where E sub , ν sub and D sub is the real component of Young's modulus, Poisson ratio and thickness of the substrate (silicon wafer in our case), respectively, and t is the thickness of the a-SiC thin film.Apart from film stress, Young's modulus E, Poisson ratio ν and density ρ of a-SiC are most relevant among all material properties to designing a-SiC resonator with targeted resonant frequency and stress distribution, which can be measured by patterning and then suspending the thin film as squared membrane, cantilevers and strings of different lengths L. After suspended, the nanomechanical resonators are measured with Laser Doppler Vibrometer (LDV, Polytec PSV-400), while they are placed in a vacuum chamber pumped down to 10 −7 mbar vacuum environment.After measuring the resonant frequencies of the squared membranes with lengths L varying from 200 to 2000 um, we fit the measured data with the analytical formula for fundamental mode [105] where L ef f = L + L oh is the effective length includes the overhang size L oh generated during undercut, ρ ef f = A corr × ρ is the effective density of the thin film, and A corr is the correction factor due to the arrays of holes on top for fast undercut, which in our case A corr = 0.804 calculated from COMSOL (corresponds to the holes with diameter 1.5 um are placed 3 um apart between adjacent centers, see Figure S1).We can therefore determine the density ρ of the thin film since σ and L are known beforehand.The resonant frequencies of strings [104] with lengths from 200 to 6000 um is measured with LDV.The eigenfrequency of string resonators can be analytically formulated as where L is the length of the string, and needed to be modified into L eff due to the overhang from undercutting, n is the eigenmode number, ρ is the material density, σ 1D = σ × (1 − ν) is the tensile stress on the string, σ is the film stress and ν is the Poisson ratio, E is the Young's modulus and t is the thickness of the film.In our case, a-SiC thin films have high tensile stress, which leads to 12σ 1D L 2 n 2 π 2 Et 2 , and the formula of the fundamental mode is reduced to the form one can use to fit the measurement data from which the Poisson ratio ν of a-SiC can be determined.Also the resonant frequency of cantilevers [117] with lengths from 7 to 80 um are also measured, and can be fitted to the analytical formula in the following form from which the Young's modulus E of a-SiC can be determined.The ratios of error between the two methods are less than 1.5% for determining E and less than 1.6% for determining ν, validating the accuracy on identifying both mechanical properties with this method based on measuring the resonant frequencies of cantilevers and strings.
where the dilution factors D are calculated numerically, it depends on the various mechanical properties of the materials, as well as the geometry of the resonator.For a string-like resonator with thickness t and length L, the dilution factor has the factor where n is the mode number of the resonator and λ is defined as In order to further investigate its applicability to fabricate high-Q nanomechanical resonators, we need to identify the intrinsic quality factor Q 0 of a-SiC thin films, which is most accurately by experimentally measuring Q factor of geometrically strain-engineered resonators whose external loss mechanisms are eliminated and dissipation dilution factor D Q is well defined, leading to an expected intrinsic Q factor Q 0 = Q/D Q .To perform such experiments, we fabricate a series of uniformly corrugated high-aspect-ratio phononic crystal (PnC) nanostrings of length 4 mm, whose unit-cell lengths L uc together with defect lengths L def in the middle are varied (Figure 4(a)), leading to PnC nanostrings of unit-cell numbers from 20 to 44.The widths of the wide and narrow parts of the nanostrings are 3 um and 1 um respectively.With higher unit-cell number or shorter defect length, the PnC nanostring has a defect mode located in a phononic bandgap at higher frequency, the example of PnC nanostring with 20 unit cells is shown in Figure 4(b).The vibration amplitudes of the nanostrings as a function of frequency are acquired with a custom balanced homodyne detection interferometer under a vacuum level of 4 × 10 −9 mbar, with them the engineered phononic bandgaps of the PnC nanostrings are identify and the defect modes inside are confirmed.With the ringdown method, the defect mode Q factors of the PnC nanostrings are measured, see Figure 4(d).Using finite element method (FEM) simulation, the dilution factor D Q of each PnC nanostring geometry can be numerically calculated, together with the Q factors of the corresponding nanostring measured experimentally, the intrinsic Q factor Q 0 of a-SiC thin films are determined, as shown in Figure 4(e-f).We employ PnC nanostrings for intrinsic Q factor identification instead of other geometries such as membranes [84] or normal strings [17] as shown for other works, since their FEM simulated D Q are much less dependent on the meshing at the clamping edges, as well as the measured Q factors of the localized defect mode do not rely on how the resonators link to the substrate.The intrinsic loss Q 0 of a-SiC films can be attributed to the volume loss Q vol and the surface loss Q surf , i.e.Q 0 = (1/Q vol + 1/Q surf • t) −1 , for our thin film resonators the low surface-to-volume ratio allows us to set Q vol to be the same as the the one of LPCVD a-SiN, i.e. 28000 (see Figure S3(f ) for more detailed), and Q surf is proportional to the thickness t of the corresponding film, which we compare with the one of LPCVD a-SiN for clarification, i.e.Q SiC surf = x • Q SiN surf , where x is the ratio between the two surface loss and Q SiN surf = 6900 • t/100[nm] is the surface loss of a-SiN.1.
mode shapes are getting more and more confined from the clamping points to minimize the clamping loss.From the fifth optimized result (Iter 107) to the final optimized result (Iter 442), the geometry is changing from a uniformly corrugated design on the edge to a non-uniformly corrugated one, this interesting found might lead to interesting perspectives in designing the 1d PnC nanostring in the future.Interesting to note that the highest Q factor design doesn't coincide with the design with the highest tensile stress.).From top to bottom, the a-SiCR2 thin film is thinned down from 79 nm to 3/4.1/4.9/6.5 nm, respectively.The SEM images on the left are the zoom out image of the resonator, while the images on the right are the zoom in images of the top-right corner of the images on the left-hand side.One can observe that the down to 4.9 nm, the LPCVD a-SiC films are continuous and suspended membranes can be fabricated, the pinholes start to appear when the film thickness is polished down to 4.1 nm, and a rough surface is presented at the film thickness of 3 nm.The pinholes appearance on the first few nanometers put a limitation on the ultimate a-SiC resonator thickness one can work with.
FIG. 2. (a) Schematic of systematically characterizing mechanical properties of a tensile stress thin film material.(a-i): Measuring film thickness with ellipsometry.(a-ii): Measuring the film stress via wafer bending technique after film deposition.(a-iii) Extracting material density / (a-iv) Young's modulus / (a-v) Poisson ratio of a-SiC thin films by fitting resonant frequencies of square membranes / cantilevers / strings of different sizes, respectively.(a-vi): Designing a-SiC nano-mechanical resonators with desired performance.(b) Characterizing the mechanical properties of LPCVD a-SiC thin film (a-SiCR2) by numerically fitting the measured resonant frequencies of suspended resonators with different geometries and dimensions, including squared membranes (top), cantilevers (middle), strings (bottom).The resonant frequencies of the resonators mentioned above are measured with Laser Doppler Vibrometer (LDV, Polytec PSV-4).

FIG. 3 .
FIG. 3. Tensile test experiment to measure the ultimate tensile strength of a-SiC thin films (a) Simulated stress profile of a hourglass-shaped geometry of 50 um tether length made with a-SiCR2, the tensile stress is concentrated at the middle narrow tether up to 10 GPa, different maximum stress can be obtained with different tether lengths.(b) SEM image of a pad of a-SiCR2 hourglass-shaped structures with 18 different tether lengths, from 30 to 115 um.Below a certain tether length, the maximum stress surpass the ultimate tensile strength of the material, and the tethers break in the middle region after undercutting, indicating the ultimate tensile strength of a-SiC.A zoom-in view of the hourglass-shaped geometry with a 50 um tether length is shown on the left.(c) The stress profiles along the hourglass-shaped geometries with different tether lengths.(d) Survival ratios of hourglass-shaped geometries with maximum stress correspond to different stress interval (orange columns) for a-SiCR2 (top), a-SiC170 (middle) and a-SiCR3 (bottom).The maximum stresses shown for unbroken devices fabricated with a-SiCR2/a-SiC170/a-SiCR3 are 12.04/10.27/11.12GPa, respectively.

FIG. 4 .
FIG. 4. Intrinsic quality factor characterization and high-Q factor a-SiC nanomechanical resonators optimized using Bayesian optimization.(a) The geometry of the defect mode, of a 20 unit-cell (UC) PnC nanostring with unit cell length Luc and defect length L def .(b) The measured frequency spectrum of a 20 UC PnC nanostring made with a-SiCR2.The yellow shaded area represents the engineered phononic band gap.(c) The intrinsic quality factor Q0 of a-SiCR2 is measured with 20 to 44 UC PnC nanostrings.(d) Ringdown measurements of 20 UC PnC nanostring made with a-SiCR2 (orange) and with a-SiCR2FS (blue).(e) Comparison of the intrinsic quality factors Q0 of a-SiCR2 (orange) and a-SiCR2FS (blue) with PnC nanostrings of 20 to 26 UC.The hollow rings and the solid line represent the measured Q factors and the numerical fittings respectively.(f) The stress distribution (top) and mode shape of the defect mode (bottom) of the 6 mm tapered a-SiCR2 PnC nanostring optimized by Bayesian optimization.The optimized tapered PnC nanostring has 24 unit cells and a maximum stress of 1.2 GPa concentrated on the middle.(g) Ringdown measurement of the optimized tapered PnC nanostring, high-Q factor up to Qexp = 1.98 × 10 8 is measured.
FIG. S1.Mechanical properties characterizations.After identifying the film stress and thickness with wafer bending and ellipsometry methods, the density ρ / Young's modulus E / Poisson ratio ν of a-SiC films deposited at different conditions are systematically measured with the resonant frequency of the a-SiC membranes (left column)/cantilevers (middle column)/strings (right column) made of the specific a-SiC film, as shown with images on the top.From top-to bottom of each row, resonant frequency data (hollow dots) and analytically fitting (solid line) for a-SiCR2/a-SiC170/a-SiCR3/a-SiCR4/a-Si3N4 thin films are shown respectively.The bottom row are measurement and fitting for the widely used material stoichiometric a-Si3N4 for reference purpose, whose fitted mechanical properties are close to the ones reported[10,12], validating the generality of the method.

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FIG. S2.Validation of using the resonant frequencies of membranes, strings and cantilevers to determine the density, Poisson ratio and Young's modulus of a thin film, respectively.The simulations are performed with finite element method (FEM) using COMSOL.In (a,b,c,-i and -ii), the geometrical shapes and mode shapes of their fundamental modes are illustrated.(a-iii) The influence on the effective density of the thin films due to the arrays of release holes, with hole radius 1.5 um and center separation 3.5 um.The sizes of the squared membranes are checked from 200 to 800 um, and the effective density values converge to 0.822 or close-by values in presence of the holes.(a-iv) For different a-SiC recipes, the density difference determined with FEM and the analytical formula is shown, which is less than 1% by using the ratio value 0.822.(b-iii) and (c-iii): Using the fundamental mode analytical formula of the string and cantilever (solid line), to fit their FEM simulated results (red dot).(b-iv) and (c-iv): Studying the effect of the overhangs on the sides of the cantilevers and strings generated during the undercut process, by fitting the FEM results given various undercut sizes, with the analytical formulas with effective lengths (L ef f ) of the geometries.The comparisons show that both for cantilevers and strings, the influence on the added effective lengths will saturate to some values smaller than the real overhang sizes, ensuring the stability of the method.(b-v) and (c-v): Comparing the Young's modulus E and Poisson ratio ν obtained with both the FEM simulations and analytical formulas, as a function of the undercut pad sizes.The ratios of error between the two methods are less than 1.5% for determining E and less than 1.6% for determining ν, validating the accuracy on identifying both mechanical properties with this method based on measuring the resonant frequencies of cantilevers and strings.
FIG. S4.More data on intrinsic quality factors of different LPCVD a-SiC thin films, from top to bottom rows: a-SiCR2, a-SiC170, a-SiCR3, a-SiCR2onFS, a-SiCR4.Plots on left, middle and right columns, show the ringdown data (left), fitting of intrinsic Q factors with measured Q factor before (middle) and after (right) divided by the dilution factors.The measured intrinsic Q factors are shown in Table1.
FIG. S7.LPCVD a-SiC squared membranes fabricated with a-SiCR2 thin films polished with the ion beam etcher (SCIA Ion Mill 150).From top to bottom, the a-SiCR2 thin film is thinned down from 79 nm to 3/4.1/4.9/6.5 nm, respectively.The SEM images on the left are the zoom out image of the resonator, while the images on the right are the zoom in images of the top-right corner of the images on the left-hand side.One can observe that the down to 4.9 nm, the LPCVD a-SiC films are continuous and suspended membranes can be fabricated, the pinholes start to appear when the film thickness is polished down to 4.1 nm, and a rough surface is presented at the film thickness of 3 nm.The pinholes appearance on the first few nanometers put a limitation on the ultimate a-SiC resonator thickness one can work with.
FIG. S9.Zoom-out Surface topography of a-a-SiCR3 thin film scanned with atomic force microscope (AFM).