# High-Strength Amorphous Silicon Carbide for Nanomechanics

Minxing Xu  Department of Precision and Microsystems Engineering, Delft
University of Technology, Delft 2628 CD, The Netherlands  Kavli Institute of
Nanoscience, Department of Quantum Nanoscience, Delft University of
Technology, Delft 2628 CD, The Netherlands  Dongil Shin  Department of
Precision and Microsystems Engineering, Delft University of Technology, Delft
2628 CD, The Netherlands  Department of Materials Science and Engineering,
Delft University of Technology, Delft 2628 CD, The Netherlands  Paolo M.
Sberna  Else Kooi Laboratory, Faculty of Electrical Engineering, Mathematics
and Computer Science , Delft University of Technology, Delft 2628 CD, The
Netherlands  Roald van der Kolk  Kavli Nanolab, Department of Quantum
Nanoscience, Delft University of Technology, Delft 2628 CD, The Netherlands
Andrea Cupertino  Department of Precision and Microsystems Engineering, Delft
University of Technology, Delft 2628 CD, The Netherlands  Miguel A. Bessa
<EMAIL_ADDRESS>School of Engineering, Brown University, Providence, RI
02912, USA  Richard A. Norte<EMAIL_ADDRESS>Department of Precision and
Microsystems Engineering, Delft University of Technology, Delft 2628 CD, The
Netherlands  Kavli Institute of Nanoscience, Department of Quantum
Nanoscience, Delft University of Technology, Delft 2628 CD, The Netherlands

###### Abstract

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.

††preprint: APS/123-QED

##  I Introduction

Advances in nanotechnology have revolutionized a broad spectrum of fields,
with the development of tensile-loaded, 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-Si3N4) 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 [15, 14] which can be easily deposited, have good film isotropy
[17] and few lattice imperfections [15, 14]. 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-Si3N4
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 [24, 25, 26, 19]. Among 2D crystalline materials,
graphene harbors one of the highest theoretical UTS [27, 26], 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.

Among the materials processing the highest ultimate tensile strengths [24, 34,
35], silicon carbide (SiC) is attracting rising interest and demand both in
industry and in academia in recent years due to its exceptional mechanical,
chemical, electrical and optical properties [36, 37, 38, 39, 40, 41, 42]. SiC
exists in three forms: single crystalline, poly-crystalline, and amorphous,
all of which can be fabricated into thin films for various applications [36].
Among them, amorphous SiC (a-SiC) thin film offers distinct advantages over
their crystalline counterparts [43, 44, 45, 46, 47, 48, 19, 25], including
lower deposition temperature, compatibility with various substrates, isotropic
physical properties, and the ability to deposit on large wafer scales. The
widespread applications of a-SiC range from protective coatings to avoid
mechanical wear [49] and chemical corrosion [50, 51], low-loss deposited
dielectrics [52], device and functional layers for solar cells [53, 54, 55],
MEMS sensors [56, 57, 58, 44] and electron transparent windows [43], low-loss
optical resonators [59] and integrated photonics [60, 61], bio-molecular [62]
and medical [63] applications, as well as gratings with nano-pillars [64, 65],
to name a few. The versatility of a-SiC makes it a promising material for the
high-yield production of integrated mechanical, electronic and photonic
devices on a chip, paving the way for applications in sensing [6, 66],
transduction [67], and quantum technology [68, 69].

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 $2\times 10^{8}$ 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 SiH2Cl2 and 5% C2H2 in H2 (GFR=2,3,4),
various deposition pressures (170 and 600 mTorr), and on both silicon and
fused silica substrates (Table 1). 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.

Figure 1: (a) Schematic of dry under-cut processes with cryogenic SF6 plasma
isotropic etching (top) and vapor hydrofluoric acid etching (bottom), to
suspend a-SiC nanomechanical resonators (green) on silicon (orange) and fuse
silica (blue) substrates, respectively. (b) Etch rates of cryogenic SF6 plasma
isotropic etching (log scale) and vapor hydrofluoric acid etching (linear
scale), on four commonly used Si-based materials: Si, SiO2, a-Si3N4, and
a-SiC. (c) Ultimate tensile strength comparison between LPCVD a-SiC,
crystalline (blue), and amorphous (red) materials. Reference: SiO2 [74], steel
[75], Kevlar [76], InGaP [17], a-Si3N4 [9, 23], c-Si [70, 77], a-SiC [35],
6H-SiC (crystalline) [24], 3C-SiC (crystalline) [24], graphene [19, 25]. The
solid and transparent colors of bars represent the lower and upper limits of
the materials’ ultimate tensile strengths, respectively.

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 SF6 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).

Moreover, the undercut method based on dry etchants introduces little
perturbation to the suspended nano-structure, making it possible to perform
tensile testing on chips. In Section IV, we fabricate suspended nano-
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 nano-indentation [78, 79] and dynamic methods like resonance
response [80, 81, 82, 83]. Many studies aiming to design high-performance
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-Si3N4 [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 [84, 80].
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 ($\sigma$) 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 ($\nu$), and density ($\rho$) 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).

Figure 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).

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 characterizing the ultimate tensile strengths of
a-SiC thin films in the following section.

Recipe |  GFR |  P (mTorr) |  Substrate |  $t$ (nm) |  $\sigma$ (MPa) |  $\rho$ (kg/m3) |  $E$ (GPa) |  $\nu$ |  $Q_{0}$ |  UTS (GPa)
---|---|---|---|---|---|---|---|---|---|---
a-SiCR2 |  2 |  600 |  Silicon |  71 |  760 |  2830 |  223 |  0.203 |  5175 |  12.04
a-SiCR2FS |  2 |  600 |  Fuse Silica |  71∗ |  1596 |  2830∗ |  223∗ |  0.203∗ |  4554 |  12.04∗
a-SiC170 |  2 |  170 |  Silicon |  86 |  636 |  2966 |  220 |  0.218 |  4485 |  10.27
a-SiCR3 |  3 |  600 |  Silicon |  81 |  960 |  2962 |  210 |  0.199 |  4692 |  11.12
a-SiCR4 |  4 |  600 |  Silicon |  137 |  670 |  3087 |  200 |  0.162 |  1035 |  $<$3.5
Table 1: LPCVD a-SiC deposition parameters and the corresponding mechanical
properties. From left to right columns, recipe name, gas flow ratio (GFR),
deposition pressure P, thickness $t$, deposition stress $\sigma$, density
$\rho$, Young’s modulus $E$, Poisson ratio $\nu$, intrinsic quality factor
$Q_{0}$ (per 100nm), and ultimate tensile strength (UTS), are shown.
∗ Parameters of a-SiCR2FS are adapted from a-SiCR2 due to its transparent
substrate

##  IV Ultimate Tensile Strength of amorphous SiC

Figure 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 under-cutting, 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 12.04/10.27/11.12 GPa, respectively.

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-Si3N4 (6.8 GPa [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 re-distributed
stress profile in Figure 3(a) is obtained via 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 nanostructured 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-Si3N4 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 11.82/11.66/11.13 GPa,
respectively, matching well with the experimentally extracted data from the
survived devices 12.04/10.27/11.12 GPa shown in Table 1. 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 $Q=D_{Q}\cdot Q_{0}$ 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 [92, 10]. Since the upper bound for $D_{Q}$
of a nanomechanical string vibrating at a certain frequency $\omega$ is given
by $D_{Q}\leq 12E\epsilon^{2}_{UTS}/(\rho t^{2}\omega^{2})$, where
$\epsilon_{UTS}$ 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 $\epsilon_{UTS}$, 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 $\omega$.

##  V Intrinsic Quality Factor and High Q Mechanical Resonators

Figure 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 Ldef. (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 $Q_{0}$ 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 $Q_{0}$ 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 $Q_{exp}=1.98\times 10^{8}$ is measured.

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 [6, 1],
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, 13, 12, 96, 97, 98],
modifying mass distribution [99, 2] 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 [101, 14]. 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 unit-cell lengths $L_{uc}$ and defect lengths $L_{def}$ in the
middle (Figure 4(a)), leading to PnC nanostrings with 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. 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 $4\times
10^{-9}$ 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 1, 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
simulation-based 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 $Q_{sim}=2.11\pm 0.17\times
10^{8}$ 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 $4\times 10^{-9}$ mbar. As a result, an high Q
factor mechanical mode with $Q=(1.98\pm 0.03)\times 10^{8}$ 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 $Q\times f=1.791\times 10^{14}$, which is
significantly higher than the quantum limit $Q\times f=2\pi
k_{B}T/\hbar=6.24\times 10^{12}$. This paves the way towards engineering
quantum states in room temperature environments [94, 9]. This high quality
factor of the nanomechanical resonator with an effective mass
$m_{eff}=1.27\times 10^{-13}$ kg corresponds to a force sensitivity of
$\sqrt{S_{F}}=\sqrt{4k_{B}Tm_{eff}\cdot 2\pi f/Q}=$ 7.7 aN/Hz1/2 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-Si3N4 [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
$\sqrt{S_{F}}=$ 7.7 aN/Hz1/2. 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.

###### Acknowledgements.

We wish to acknowledge Peter G. Steeneken, Gerard Verbiest, and Martin Lee for
their helpful suggestions on the manuscript and their support of our project.
We want to thank Satadal Dutta, Ali Sarafraz, Matthijs de Jong for the helpful
discussions. M.X. and R.N. also thank the staffs of both the Kavli Nanolab
Delft and the Else Kooi Lab, in particular from C. de Boer, for supporting our
fabrication efforts. This publication is part of the project, Probing the
physics of exotic superconductors with microchip Casimir experiments
(740.018.020) of the research programme NWO Start-up which is partly financed
by the Dutch Research Council (NWO).This work has received funding from the
EMPIR programme co-financed by the Participating States and from the European
Union’s Horizon 2020 research and innovation programme (No. 17FUN05
PhotoQuant). R.N. would like to acknowledge support from the Limitless Space
Institute’s I2 Grant.

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## 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 $\sigma$ can be determined
from wafer bending method by Stoney’s equation

$\sigma=\frac{E_{sub}D_{sub}^{2}}{6(1-\nu_{sub})t}(\frac{1}{R_{1}}-\frac{1}{R_{2}}),$
(1)

where $E_{sub}$, $\nu_{sub}$ 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 $\nu$ and density $\rho$
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]

$f_{mem}\approx\frac{1}{\sqrt{2}L_{eff}}\sqrt{\frac{\sigma}{\rho_{eff}}},$ (2)

where $L_{eff}=L+L_{oh}$ is the effective length includes the overhang size
$L_{oh}$ generated during undercut, $\rho_{eff}=A_{corr}\times\rho$ 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 $\rho$ of the thin film since
$\sigma$ 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

$f_{str,n}=\frac{n^{2}\pi}{2L^{2}}\sqrt{\frac{Et^{2}}{12\rho}}\sqrt{1+\frac{12\sigma_{\text{1D}}L^{2}}{n^{2}\pi^{2}Et^{2}}}$
(3)

where $L$ is the length of the string, and needed to be modified into
$L_{\text{eff}}$ due to the overhang from undercutting, $n$ is the eigenmode
number, $\rho$ is the material density,
$\sigma_{\text{1D}}=\sigma\times(1-\nu)$ is the tensile stress on the string,
$\sigma$ is the film stress and $\nu$ 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 $12\sigma_{\text{1D}}L^{2}\gg
n^{2}\pi^{2}Et^{2}$, and the formula of the fundamental mode is reduced to the
form one can use to fit the measurement data

$f_{str}\approx\frac{1}{2L_{eff}}\sqrt{\frac{\sigma\cdot(1-\nu)}{\rho}},$ (4)

from which the Poisson ratio $\nu$ 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

$f_{can}\approx\frac{1.8751^{2}}{2\pi L_{eff}^{2}}\sqrt{\frac{E\cdot
t^{2}}{12\rho}},$ (5)

from which the Young’s modulus $E$ of a-SiC can be determined.

Figure S1: Mechanical properties characterizations. After identifying the film
stress and thickness with wafer bending and ellipsometry methods, the density
$\rho$ / Young’s modulus $E$ / Poisson ratio $\nu$ 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 [12, 10], validating the generality
of the method.

## Supporting Information (B). Validation of the resonance method with COMSOL

Figure 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 ($L_{eff}$) 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 $\nu$ 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 $\nu$, validating the accuracy on
identifying both mechanical properties with this method based on measuring the
resonant frequencies of cantilevers and strings.

## Supporting Information (C): Theory of dissipation dilution, and dilution
factors of 1d PnC nanostings

In this work, the intrinsic quality factor $Q_{int}$ is determined by
measuring the mechanical quality factors $Q_{D}$ of PnC nanostrings [93]

$Q_{D}=D\cdot Q_{int},$ (6)

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

$D_{n}=\frac{1}{2\lambda+\pi^{2}n^{2}\lambda^{2}},$ (7)

where $n$ is the mode number of the resonator and $\lambda$ is defined as

$\lambda=\frac{h}{L}\sqrt{\frac{E}{12\sigma}}.$ (8)

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 $4\times 10^{-9}$
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. $Q_{0}=(1/Q_{vol}+1/Q_{surf}\cdot t)^{-1}$, 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. $Q_{surf}^{SiC}=x\cdot Q_{surf}^{SiN}$, where $x$ is the
ratio between the two surface loss and $Q_{surf}^{SiN}=6900\cdot t/100[nm]$ is
the surface loss of a-SiN.

Figure S3: 1d phononic crystal (PnC) nanostrings for checking the intrinsic
quality factors (Q factor) of a-SiC films. (a) geometry of a 20 unit-cell (uc)
PnC nanostring. (b) Mode shapes and frequency spectrums of 20/32/44 uc PnC
nanostrings. (c) Resonant frequencies of the defect/localized modes of PnC
nanostrings with 20-44 uc nanostrings, the measured data (hollow dot) are
fitted linearly (solid line). (d) and (e): Dilution factor $D_{n}$ as a
function of PnC nanostrings with different numbers of unit cells, in linear
and log scales respectively. (f) Q factors fitted with different bulk
intrinsic quality factor, the small deviation between the adjacent lines
indicates thicker thin film resonators and more accurate measurement data are
required to get proper values for this value.

## Supporting Information (D): More data on ringdown measurement of 1d PnC
nanostrings, and intrinsic Q factor characterization of a-SiC thin films

Figure 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 Table 1.

## Supporting Information (E): Machine learning technique for designing high-Q
resonator

Figure S5: (a) Parameters for optimization. (b) The optimized designs up to a
certain optimization cycle are marked with red dots, these 4 designs’
geometries and localized mode shapes. (c) Optimized Q factors results from
intermediate steps, here we assume the intrinsic Q factor of a-SiCR2 to be
5175/100nm. Together with its Q factor the other properties of the designed
resonator can be obtained, here its resonant frequency, frequency (f) times
quality factor (Q) product, and the maximum tensile stress on the nanostring
are shown in (d), (e) and (f), respectively.

Bayesian optimization for ultra-high Q a-SiC nanostring made with a-SiCR2. The
nanostring has a total length of 6 mm and the number of unit cells is fixed to
24. In the Bayesian optimization algorithm, the Q factor of the nanomechanical
resonators is being optimized. 9 design parameters are setup for the
optimization. The iteration steps are in total 500. Among the parameters, v1
is the defect width, constrained between 1 to 3 um; v2 is the defect length,
constrained between 50 to 500 um; v3 is unitcell width ratio, constrained
between 1:1.5 to 1:3; v4 is unitcell length ratio, constrained between 1:3 to
3:1; v5 to v9 are the widths of the unitcells’ thin parts, the width
parameters defining the tapering shape, constrained between 1 to 3 um. Lengths
of the unitcells was determined considering bandgap frequency matching
condition, once the set of each unitcell’s width is defined [10]. One can find
that the 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.

## Supporting Information (F): Thin a-SiC resonator

Both the force sensitivity and force responsivity of nanomechanical sensors
are limited by the minimum thickness achievable for the continuous films. For
thin film sensors with high intrinsic tensile stress , higher aspect-ratio
(length/thickness) can increase the feasibility of higher Q factor, thus
higher force sensitivity due to lower noise level; While for the ones with low
film stress, thinner films lead to lower stiffness, therefore larger
deflection under given forces, or higher force responsivity. Unlike 2D
materials such as graphene, which use the bottom-up approach to construct
ultra-thin suspended resonators (e.g. growing the thin film layer by layer
atomically), engineerable thin films such as a-SiN and s-Si usually use the
top-down approach to get ultra-thin resonators. As respectively shown in [102]
and [14], in order to fabricate high-aspect-ratio (HAR) resonators with
thicknesses down to 12nm SiN and 15nm (sSi) thin films, encapsulating layers
are required to hold up as well as to protect the thin SiN and sSi structures,
which complicate the fabrication processes and may even introduce
contamination. Compared to the above materials commonly used for
nanomechanics, a-SiC thin films can be fabricated into thinner resonators
thanks to its superior chemical inertness. As shown previously, even with
LPCVD, which is considered to deposit continuous and conformal films, cannot
avoid pinholes on the films while depositing the first nanometers. In order to
find out the minimum thickness achievale for a-SiC thin film, the ion beam
etcher (SCIA Ion Mill 150) is used to thin down the thicker and more uniform
GFR2 films down to the desire thickness. The ion beam etcher, compared to
other techniques, such as reactive plasma etching, is preferred to get ultra-
thin films down to sub-nanometer accuracy, with a physical sputtering process
applicable to a wide range of materials called ion beam milling, which avoid
surface contamination and local charge accumulation that might hinder to
obtain the desired conformal thin film accurately. The GFE2 films with initial
thickness 71nm are thinned down with a beam voltage of 120V (kinetic energy
120eV per ion) and an incident angle of 4 degrees sheering, resulting in an
etch rate of 7 nm/h. By suspending resonators with polished film thicknesses
from 3 to 6 nm on silicon substrate, we found that minimum continuous smooth
LPCVD a-SiC GFR2 film achievable is between 4.1 and 4.9 nm. Worth to note that
buckling patterns are observed on the trampoline resonator, due to the facts
that: 1. the thinner and larger the resonator is, the smaller stress gradients
in both in-plane and out-of-plane directions are required in order to keep the
resonator flat [14, 23]; 2. the first several nanometers of the a-SiC film is
with less tensile or even compressive stress due to defects at the material
interface at the start of the deposition, which are also shown in [102, 15].

The surface topography of the a-SiCR2 thin film polished down to 3nm, is
measured with AFM shown in SI. G(d), which is only half the RMS compared to
the one prior to being polished.

Figure S6: LPCVD a-SiC trampoline resonator fabricated with a-SiCR2 thin films
of length 250 um and thickness 4.9 nm, polished with the ion beam etcher (SCIA
Ion Mill 150). The trampoline resonator remains suspended after undercut. No
pinholes are observed on the thin film. The aspect ratio of this trampoline
resonator is comparable to the best ones a-Si3N4 resonators have achieved.
Figure 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.

## Supporting Information (G): Surface topography of a-SiC thin films with
Atomic force microscopy

Among all recipes, a-SiCR2 and a-SiCR3 have the lowest roughness. Yet one can
still find large bright spots on a-SiCR3 films with the dark field image from
the optical microscope, indicating that it is not as flat in a larger
landscape. After polishing with the ion beam miller, a-SiCR2 with 3 nm is
scanned, with only half the roughness compared to the one prior to polishing.
Interesting to note that, with lower deposition pressure, a-SiC170 is rougher
than a-SiCR2, which matches well with its lower intrinsic Q factor and lower
fracture strength. The topography of a-SiCR4 is very rough, can be due to the
re-crystallization of Si components in the thin film.

Figure S8: Surface topography of LPCVD a-SiC thin films scanned with atomic
force microscope (AFM). From left to right, the first row shows topography of
(a) a-SiCR2, (b) a-SiCR2FS, (c) a-SiC170; the second row shows topograph of
(d) a-SiCR2 being polished down to a thickness of 3 nm using the ion beam
miller, (e) a-SiCR3, and (f) a-SiCR4. Figure S9: Zoom-out Surface topography
of a-a-SiCR3 thin film scanned with atomic force microscope (AFM).

## Supporting Information (H): Fabrication process

Low pressure chemical vapor deposition (LPCVD) non-stoichiometric a-SiC films
were used in this paper, deposited with different gas flow ratios (GFR)
between SiH2Cl2 and 5% C2H2 in H2 (GFR=2,3,4), at various deposition pressures
(170/600 mTorr), and on both silicon and fused silica substrates (Table 1).
The variation in deposition parameters allows us to systematically
characterize the mechanical properties of LPCVD a-SiC. All a-SiC films were
deposited at a temperature 760C for the same period of time (3 hours 47
minutes) to avoid film property differences caused by thermal effects and to
ensure that the SiC films were composited of amorphous form instead of poly-
crystalline form [73, 118].

After LPCVD a-SiC deposition, the wafers are diced into smaller chips. The
chips are then exposed to electron beam lithograph to create desired patterns
on the e-beam resist coated on top. Subsequently, these patterns are
transferred into the a-SiC films using CHF3 anisotropic plasma etching. Next,
the patterned chips are cleaned with dimethylformamide and Piranha solution,
followed by the undercut of the silicon substrate or fused silica substrate
using cryogenic SF6 isotropic plasma etching or vapor hydrofluoric acid.
Finally, the designed a-SiC nanomechanical resonators are fabricated.

Figure S10: Fabrication process flow to fabricate a-SiC (green) nanomechanical
resonators on both silicon (orange) and fuse silica substrates (blue). (i)
Start with a die of the wafer. (ii) Spin coat ebeam resist AR-P 6200.13 at
spin speed 1500 rpm, then bake at 150 ∘C for 3 mins. (iii) Ebeam pattern of
the desired pattern, afterwards developing the pattern by sequently immersing
the die in Pentyl Acetate, MiBK:IPA=1:1, IPA solutions for 1 min. (iv)
Transfer the pattern into the a-SiC film with reactive ion etching (Sentech
Etchlab 200), with CHF3/Ar plasma at the power 60 watts. (v) Remove the ebeam
resist with hot Dimethylformamide solution in a supersonic bath, following by
Piranha and diluted hydrofluoric acid cleaning. (vi) Undercut the silicon
substrate to suspend a-SiC resonators with cryogenic (-120∘C) SF6 plasma
etching. (vii) Undercut the fuse silica substrate to suspend a-SiC resonators
with vapor hydrofluoric acid (at 35 to 60∘C).

## Supporting Information (I): Ringdown Measurement with Homodyne Detection

We use a balanced homodyne interferometer for performing ringdown experiments
on a-SiC nanoemchanical resonators. As shown in Figure S11, the a-SiC
nanomechanical resonator (green) on top on the substrate (brown) is placed in
an ultra-high vacuum (UHV) chamber under a pressure lower than $10^{-8}$ mbar.
This avoids mechanical losses due to gas damping. Ringdown measurements are
performed via a piezoelectric actuator which resonantly drives the corrugated
nanostrings. After reaching maximal amplitude, the drive is stopped to observe
the rate at which mechanical energy is dissipated from the nanostrings. The
vibration amplitude of the resonator is measured optically with a fiber
coupled infrared laser (1550 nm). The power of the laser is divided into two
parts, 90% of it is used for interference reference (local oscillator), while
the other 10% terminates with a lensed fiber shines on the resonator. The
reflected light from the resonator then compares its phase to the one from the
local oscillator using the balanced homodyne measurement setup, with which the
amplitude of the resonator is measured.

Figure S11: Schematic of the balanced homodyne interferometer used for
performing ringdown experiments. The nanomechanical resonator, placed in an
UHV chamber, is resonantly driven by a piezoelectric actuator, and its motion
is measured with the interferometer. Abbreviations: VOA, Variable Optical
Attenuator; FPC, Fiber Polarization Controller; $\varphi$: Phase shifter; PID:
Proportional–Integral–Derivative controller