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Sensors and Materials, Vol. 36, No. 8 (2024) 3395–3405
MYU Tokyo
S & M 3739

Temperature Dependence of Electrostatic Frequency Tunabilityof Ultrathin Si Nanoresonators
Wei Yu, Amit Banerjee,* Jun Hirotani, and Toshiyuki Tsuchiya
Department of Micro Engineering, Graduate School of Engineering, Kyoto University,
Kyoto Daigaku-Katsura C3, Nishikyo-ku, Kyoto 615-8540, Japan(Received April 30, 2024; accepted July 8, 2024)

Keywords: NEMS resonators, resonance frequency, electrostatic tuning, temperature coefficient of
frequency

Nanoresonators are crucial elements of various nano-electromechanical systems for thedevelopment of ultrasensitive sensing, efficient signal processing, biological detection, and soforth. Implementing methods that facilitate the wide tuning of the resonance frequency isbeneficial for many of these applications. Ultrathin Si nanoresonators (width ~10 nm, length~100 µm) can exhibit a wide electrostatic tunability of resonance frequency, which can be used
for the easy electrostatic compensation of the thermal drift in resonance frequency among manyother potential applications. How this tunability is impacted by temperature variation is apertinent issue in many potential applications of tunable Si nanoresonators but currently remains
unknown. In this study, we experimentally investigate the temperature dependence of theelectrostatic tuning of a Si nanoresonator of ~80 nm width and ~200 µm length across atemperature range of 100–300 K. The results show significant decreases in electrostatic tuning
range, efficiency, and resonance frequency tendency with decreasing temperature. We provide
an approximate thermo-electromechanical model to describe this behavior and discuss how adual tuning strategy by gate voltage and temperature can potentially bring further opportunities
in terms of on-the-spot adjustment of the nanoresonator’s frequency as demanded in specificapplications.

1.

Introduction

Nanomechanical resonators have emerged as crucial elements in various nanoelectromechanical system (NEMS) applications, serving as the essential components for thedevelopment of ultrasensitive mass,(1) force,(2) and electric charge detection systems,(3) ultrafast
and efficient communication methods,(4) next-generation computing devices,(5) and so forth. The
efficient and often unprecedented performance of nanoresonators in many of these applicationsis attributed to their small mass and rich dynamic behavior.(6) Therefore, the degree to which thecore dynamic characteristics of these nanoresonators, such as their resonance frequency ( f0), canbe tuned plays a vital role in enhancing their functionality, ensuring stability, bringing operation*Corresponding author: e-mail: banerjee.amit.3v@kyoto-u.ac.jp

https://doi.org/10.18494/SAM5096

ISSN 0914-4935 © MYU K.K.
https://myukk.org/

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Sensors and Materials, Vol. 36, No. 8 (2024)

flexibility and versatility, and so forth.(6) Achieving practicable means to attain significant
resonance frequency tunability at the application stage of nanoresonators promises potential
benefits for numerous practical applications, such as improving the nanoresonator-based sensor’s
responsivity,(7) developing filters with adjustable bandwidths,(8) mode matching in inertial
sensors,(9) enhancing the efficiency of mechanical energy-harvesting devices,(10) impedance
matching in nanoelectronic circuits,(11) and developing precise NEMS timing devices.(12) A
common strategy for tuning the resonance frequency of nanoresonators is by employing various
physical mechanisms, such as mechanical stress,(13,14) electrostatic force,(15) and thermal andelectrothermal effects to manipulate the axial strain on nanoresonators.(16,17) A common themein these tuning mechanisms is attributed to the fact that nanoresonators’ natural frequencies arestrongly affected by the axial strain, unlike their micrometer-scale counterparts where thenatural frequency is predominantly governed by elastic stiffness determined by the material andgeometry. Thus, in post-fabricated devices, mechanisms capable of manipulating the axial strain
on nanoresonators provide easy access to resonance frequency tuning. For instance, Ning et al.
demonstrated the tuning of resonance frequency of their carbon nanotube nanoresonators using
a piezoelectric substrate to exert an axial strain.(13) The resonance frequency can be tuned 20
times in this way. Similarly, Truax et al. reported a mechanical strain modification strategy thatinvolves using a MEMS electrothermal actuator to apply in-plane tension to a carbon nanotube
resonator, which resulted in an increase in resonance frequency from 10 to 60 MHz.(14)
Additionally, the application of electrostatic force has been shown to effectively tune theresonance frequency of graphene NEMS resonators by up to 58%, which is performed byvarying the DC gate voltage Vg between the resonator and a nearby gate electrode.(15) In otherstudies, the resonance frequencies of MoS2 and graphene resonators have also been shown to be
tunable by varying the thermal pulse(16) or temperature.(17)The ultrawide tunability of resonance frequency is predominantly achieved in atomically thinmaterial-based resonators, which are notably sensitive to strain variations owing to their extreme
aspect ratio that leads to a negligible elastic stiffness. The resonance frequency tuning ranges(TR) exceeding 100% have been reported using purely electrostatic forces at room temperature ingraphene,(18) black phosphorus,(19) and MoS2 resonators.(20) In a recent work, we havedemonstrated that a comparable room-temperature electrostatic frequency tunability is alsoachievable in monolithically fabricated ultrathin Si nanoresonators.(21) To demonstrate this, wedeveloped a top-down fabrication method to create 20–300-nm-wide and 100–300-µm-long Si
nanoresonators. In one of our Si nanoresonators with a width of ~40 nm and a length of ~200 µm(height ~7.5 µm), we achieved a tuning range of ~70% of initial frequency at the average tuning
efficiency Te of ~7% V−1.(21) These ultrathin Si nanoresonator devices are fabricated from astandard, commercially purchased silicon-on-insulator (SOI) wafer using a standardized
cleanroom Si microfabrication process [Fig. 1(A)]. The developed fabrication processsimultaneously fabricates all device components, namely, the nanoresonators and in-plane,parallel side gates for the electrostatic actuation and capacitive detection of the nanoresonators’
motion [Fig. 1(B)]. Achieving such a high tunability in nanoresonators fabricated using
conventional SOI materials and by established microfabrication processes can lead to the rapid
development of a scalable fabrication process for tunable nanoresonators. In addition, since ourSensors and Materials, Vol. 36, No. 8 (2024)

3397

Vac

Electrode (Cr/Au/Cr)
Cr
Device layer (Si)
SiO2

Device layer

SOI substrate

Nanoresonator

SOI wafer

Ic(c) DRIE

Vc

TIA
Controlled heater

Vg

(B)

(d) Sacrificial
layer etching(a) Metal electrodepatterning(b) Nanobeam
patterning
(A)

Si

Cr

Au

SiO2

Vac

Actuation

Detection

Vg(C)

200 μmFig. 1. (Color online) Fabrication, geometry, and characterization setup of the developed ultrathin siliconnanoresonator. (A) Fabrication of developed ultrathin Si NEMS resonator devices. (B) Schematic illustration of thedevice structure and actuation/read-out circuits. (C) SEM image of a device.

nanoresonators and their substrates are both made from the same material (Si), our ultrathin
nanoresonators show a relatively smaller temperature coefficient of frequency (TCF),(21)promising a lesser drift in resonance frequency due to temperature fluctuation. This canpotentially lead to a higher frequency stability and an efficient drift compensation byelectrostatic tuning. However, in such ultrathin nanoresonator devices, the electrostatic tuning
efficiency itself is expected to be significantly affected by temperature variation, as reported invarious atomically thin resonators, where the resonance frequency tunability typically decreases
when temperature decreases.(17) A quantitative experimental investigation of the temperaturedependence of this electrostatic tunability of resonance frequency of Si nanoresonators canprovide (a) means to control the electrostatic tuning efficiency by substrate temperature control
and (b) insight into the efficacy and limitations of the electrostatic compensation of thermalfluctuation-induced frequency drift. In this work, we report a detailed experimental investigationon the temperature dependence of the electrostatic resonance frequency tuning behavior ofultrathin Si nanoresonators with a width of ~80 nm, a length of ~200 µm, and a height of 7.5 µm

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Sensors and Materials, Vol. 36, No. 8 (2024)

between room temperature (~300 K) and 100 K. We observed that the frequency tuning range,
efficiency, and tuning trend (upward versus downward shift in frequency with an increase ingate voltage) strongly depend on the substrate temperature. The tuning range for an identical Vg(10–20 V) range was observed to steadily decline as the nanoresonator temperature was reduced.
Moreover, the tuning trend was also observed to vary with temperature, viz., with increasing Vg,
a strictly upward frequency tuning was observed at room temperature, while a non-monotonic
trend emerged as the temperature was reduced. We explain these behaviors using an approximate
thermo-electromechanical model of the Si nanoresonator device. We believe that the results ofthis study will contribute to the development of scalable, tunable, and stable Si nanoresonatorsfor various applications.

2.

Device Fabrication and Characterization

The Si nanoresonator device fabricated for this study is composed of a straight, doubleclamped Si nanostructure with a rectangular cross section, an electrostatic actuation electrode,and a capacitive detection electrode [Fig. 1(B)]. As schematically depicted in Fig. 1(A), thefabrication of our silicon nanomechanical resonators started from a SOI wafer with a 7.5-µmthick n-type single-crystal (100) silicon device layer (dopant: As, ~3 × 1019 cm−3; resistivity~0.002 Ω.cm). The sacrificial layer was made of a ~2-µm-thick SiO2 film and the handle layer
was made of a 508 ± 5-µm-thick Si film. Following wafer cleaning and the removal of the nativeoxide from the top of the device layer, the actuation and detection electrodes were patterned by
UV lithography (Union PEM-800, double-sided aligner), Cr/Au/Cr metal thin-film (thicknessesof 10/70/50 nm, respectively) deposition, and a lift-off process. Subsequently, electron beamlithography (ELS-F130HM, Elionix) was employed to pattern the ultrathin nanoscale resonatorstructure, and a Cr film (50 nm) pattern of the nanoresonator was achieved after the lift-off
process. The device layer Si was then etched by deep reactive-ion etching (Bosch process,Samco, RIE-800iPB-KU), and the nanoresonator structure was suspended by vapor hydrofluoric(HF) acid etching (Sumitomo Precision Products, MLT-SLE-Ox), which selectively removes theunderlying sacrificial SiO2 layer. This vapor phase chemical etching process can prevent thestiction of the suspended nanoresonator with nearby structures such as the gate electrodes andthe handle layer. Further details of the fabrication steps, recipes, and so forth are provided
elsewhere.(21) By this fabrication process, nanoresonators with lengths (L) between 100 and 300µm, widths (t) from 20 to 300 nm, heights of ~7.5 µm (determined by the device layer thickness),and gap distances (g0) between the nanoresonator and the actuation and the detection electrodefrom 1 to 3 µm were successfully fabricated, as we reported in our previous study on their roomtemperature electrostatic tunability.(21) An SEM image of a Si nanoresonator device is shown in
Fig. 1(C).
For the dynamic characterization of our Si nanoresonators, DC bias voltage (Vg) was applied(Agilent, E3647A) to one of the nanoresonators՚ anchors via the metal thin film on top of it. The
DC and AC (Vac) voltages applied between the beam and the electrostatic actuator periodicallyactuated the nanoresonators at the AC voltage’s angular frequency. This oscillation induces
capacitance fluctuations between the beam and the detection electrode, generating a periodic

Sensors and Materials, Vol. 36, No. 8 (2024)

3399

current signal (Ic) for electrical read-out. This signal was amplified and converted to a voltage
output (Vc) through a transimpedance amplifier (TIA) and analyzed using a lock-in amplifier(Zurich Instruments MFLI 500 kHz/5 MHz). When the frequency of the applied drive voltage
approached the resonator’s resonance frequency of its fundamental flexural mode vibration, theamplitude of vibration of the beam and, consequently, the read-out signal of the device reachedtheir maximum values; thus, the resonance response can be detected by frequency sweep aroundthis frequency. All measurements were conducted within a high-vacuum environment(~1.1 × 10 –4 Pa) in a vacuum probe station equipped with a substrate temperature control facility,
which was achieved by cooling the sample stage via liquid nitrogen and varying the stage
temperature with a stage heater that automatically stabilizes the temperature at a set point.

3.

Results and Discussion

3.1

Temperature effect on electrostatic tuning

A nanoresonator device of 80 nm width and 200 μm length was chosen for the investigationof the electrostatic resonance frequency tuning behavior at various temperatures within thevacuum chamber. The substrate temperature in the vacuum chamber was reduced from room
temperature (~300 K) to 100 K at intervals of 50 K. At each temperature, the nanoresonator’sfrequency responses were measured in its linear response regime with a constant AC drive
voltage of 1 mV, while Vg was varied from 10 to 20 V. Figure 2(a) shows the detected frequency
response at 300 and 200 K. At both temperatures, an increase in resonance frequency wasobserved with increasing Vg, indicating an upward electrostatic frequency tunability. This
upward resonance frequency tuning with increasing Vg is attributed to a static deflection of the

200 K

300 K

(a)

(b)

Fig. 2. (Color online) (a) Experimental results of resonance response detected from a device with length of 200 μm
and width of 80 nm as gate voltage (Vg) varies from 10 to 20 V at substrate temperatures of 300 and 200 K. (b)Measured resonance frequency tuning range (TR) (bar chart), alongside tuning efficiency (Te) (dot-line chart), where
Te is calculated as TR divided by the applied voltage range. The upward and downward tuning conditions are
separately presented.

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Sensors and Materials, Vol. 36, No. 8 (2024)

nanoresonator due to the applied electrostatic force, which increases the axial strain of thenanoresonator.(21) The significant role of the axial strain on the resonance frequency wasappreciable even at the lowest Vg (10 V) since the measured frequency ( f0) was ~17.3 times(under the 300 K condition) and 19.1 times (under the 200 K condition) higher than what would
be expected from an equivalent tension-free Euler–Bernoulli beam.(22) In the plot of Fig. 2(a),notably, at 200 K, a higher f0 at Vg of 10 V and a lower f0 at 20 V were recorded compared withthe observation made at 300 K, indicating an increased initial resonance frequency ( f0 at Vg = 10
V) and a narrower electrostatic tuning range and a lower tuning efficiency. To quantify suchmeasurements, we define thve tuning range for both upward tuning and downward tuningt r e n d s , w h e r e t h e u p w a r d t u n i n g r a n g e TR-upward i s g i v e n b y
TR-upward = fumax - f 0min / f 0min × 100%, where f 0min and fumax are the minimum and upwardtuned maximum resonance frequencies, respectively, measured within a Vg range of 10–20 V.
S i m i l a r l y, t h e d o w n w a r d t u n i n g r a n g e TR-downward i s d e f i n e d a s
TR-downward = f dmax - f 0min / f dmax × 100 %, where f dmax is the maximum resonance frequency
during downward tuning. We also define the local tuning efficiency Te for both tuning trends,
which is the ratio of the tuning range, either upward ( TR-upward ) or downward ( TR-upward ), to thevoltages required for the respective tuning.
In Fig. 2(a), the measured TR achieved diminished from 20.5% at 300 K to 7.5% at 200 K. The
bar plot in Fig. 2(b) shows the measured resonance frequency tuning range, and the circle-dashline plot shows the corresponding tuning efficiency Te as Vg was varied between 10 and 20 V
across different substrate temperatures. Note that the frequency tuning trend can be nonmonotonic, viz., the minimum frequency is observed at an intermediate value of Vg [Fig. 3(a)].(21)In such a scenario, with increasing Vg, one part of the tuning data will show a downward
frequency tuning trend, while the other part will show an upward frequency tuning trend. In theplot of Fig. 2(b), the downward trends are indicated by red bars in the plot, while the upward
frequency trends are indicated by blue bars. A consistent decrease in TR was observed with the
reduction in temperature below 300 K. The downward tuning trend was observed at temperaturesof 150 and 100 K. The upward Te decreased from 300 to 200 K and remained at relatively low
values in the range from 200 to 100 K. The downward Te showed a certain increase when thetemperature changed from 150 to 100 K.
The results of the electrostatic tuning of resonance frequency conducted at various
temperatures are shown in the plot of Fig. 3(a). Beside the reduction in TR as mentioned above, anon-monotonic trend in tuning emerged at a lower temperature. The downward trend in
frequency tuning signifies a dominant role of the electrostatic softening effect(23) over the
deflection-induced stretching of the nanoresonator, leading to an overall downward tuning of theresonance frequency. The competition between these two mechanisms can be understood using
an approximate electromechanical model of the nanoresonator,(21) which can approximately
predict the resonance frequency.

(

)

(

(

)

)

f 0 Vg ,T =

1
2π



2Eε ( T )   o2ζ 0 2  
3o12ζ 202
Et 2

+
J
V
+
Vg4 


 J 2

g
1
4
2
3
4
2
2
  4ρ g Et ε ( T )ρ L   ρ tg 0
0
 6ρL
 


(1)

3401

375000380

360000360

345000330000

Theory Experiment
100
150
200
250
300

315000300000

10

12

14

16

18

f0 (Vg=10 V) (kHz)Frequency (Hz)Sensors and Materials, Vol. 36, No. 8 (2024)

Experimentfitting

340
320
300
280

20

100

150

Vg (V)

200

250

300

T (K)

(a)

(b)

Fig. 3. (Color online) (a) Estimated resonance frequency tuned by gate voltage during the device’s temperature
decrease from 300 to 100 K based on the approximate tuning model expressed in Eq. (1) with the experimentallymeasured results. (b) Experimental frequency data at Vg = 10 V fitted with the theoretically expected frequency value
assuming a thermal expansion coefficient difference (Δath) of ~1.3 × 10 −6 K−1 between the nanoresonator and thesubstrate.

Here, E is Young’s modulus, ρ is the density of the silicon, ε ( T ) is the axial tensile strain at Vg= 0 V and at a given temperature (T), 0 is the permittivity of free space, ζ ≈ 1 is a capacitancecorrection factor, and J i (i = 1, 2) and o j ( j = 1, 2) are dimensionless constants derived from theappropriate deflection-shape function. In this study, J1 = 5.3 , J 2 = 64.0 , o1 = 0.67 , ando2 = 0.53 are used on the basis of the parabolic function deflection shape.(21) The first term
under the square-root symbol in Eq. (1) represents the initial resonance frequency without theeffect of Vg, predominantly affected by ε ( T ) . The second term indicates the decrease in f0,
which is contributed by the electrostatic softening effect, and the final term indicates thestretching effect. The actual frequency tuning trend is determined by the competition between
these last two terms, while the initial frequency increases with ε ( T ) . The condition for the
upward tuning frequency is shown in Eq. (2), which indicates that in the case of an increase inaxial strain, a higher Vg is required to exhibit an upward frequency tuning trend.
Vg ≥2o2 g 0 Et
3o12ζ 0ε (T )(2)

The axial strain ε ( T ) in the nanoresonator is modeled by a difference in thermal expansion
coefficient (Δath) between the material of the nanoresonator (Si) and that of the substrate (SiO2/Si), which can be written as(24)ε ( T ) = ε 0 ( T0 ) + ∆ath ( T − T0 ) ,

(3)

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Sensors and Materials, Vol. 36, No. 8 (2024)

where ε 0 is the axial tensile strain at a reference temperature (T0). In Fig. 3(b), we plot
f 0 Vg = 10 V measured at different temperatures. We fit this trend using Eqs. (1) and (3) toextract the values of Δath ~1.3 × 10−6 K−1 and ε 0 (300 K) ~23 MPa. Note that the increase inf 0 Vg = 10 V with decreasing temperature suggests an increase in ε ( T ) in the resonator.
This explains the tuning trend variation [Fig. 3(a)], which goes from upward at higher
temperatures (T = 300, 250, and 200 K) to non-monotonic at lower temperatures (T = 150 and
100 K). Using the fitting parameters extracted from Fig. 3(b), we fit the resonance frequency
tuning data in Fig. 3(a).
3.2

(

)

(

)

Tunable temperature coefficients of frequency

The results shown in Figs. 2 and 3 reveal the temperature dependence of the electrostatic
tunability of resonance frequency in an ultrathin Si nanoresonator between 100 and 300 K,
where a strong relationship between temperature and tunability is observed. The results not only
indicate significant decreases in tuning ranges and tuning efficiencies but also show a more
complex behavior in terms of the frequency tuning trend, suggesting that the stage temperature
control can be a potential method to control the electrostatic tunability. Thus, a dual tuning
strategy of the nanoresonator by Vg and T can provide further opportunities in terms of on-thespot adjustment of the nanoresonator’s frequency as demanded in specific applications.
Another noteworthy observation from Fig. 3 is that the span of resonance frequencies acrossthe temperature range (100–300 K) shrinks with increasing Vg. The resonance frequency span
indicates the temperature-fluctuation-induced variability in the resonance frequency (thermal
drift) of the device during operation, which is a critical factor in the design and performance ofresonator devices used in telecommunications, navigation, and timekeeping.(25) A wider
frequency span suggests a higher sensitivity to temperature fluctuations, whereas a smaller span
indicates a higher temperature stability. Note that the higher temperature sensitivity of theresonance frequency of the device is not always undesirable; in applications such as resonatorbased temperature sensors, it can be advantageous. Compared with MEMS resonators, NEMS
resonators typically exhibit a higher sensitivity to temperature fluctuation because they are more
susceptible to strain change, making them well suited for temperature sensing but less desirable
in applications where frequency stability is important (such as in timing devices). The
temperature coefficient of frequency (TCF) defined as the relative resonance frequency shift per
degree Kelvin of temperature change is commonly used for evaluating such temperaturesensitivity. In recent reports, the TCFs of conventional NEMS resonators, such as the MoS2 andh-BN resonators, are around −3960(26) and −2850 ppm/K,(27) respectively. For grapheneresonators, TFC is much higher, which can reach around −8600 ppm/K.(18) In contrast,
conventional MEMS resonators exhibit typical TCFs in the range from −20 to −100 ppm/K.(28,29)
The measured device’s TCFs at different Vg values were estimated by calculating theresonance frequency shift per degree Kelvin as the temperature decreased from 300 to 250, 200,
150, and 100 K, as shown in Fig. 4. Initially, TCF exhibited negative values and increased withVg, and it subsequently exhibited positive values. The lowest observed absolute TCF wasapproximately 3.6 ppm/K at Vg of 17 V, comparable to those of conventional MEMS resonators,

Sensors and Materials, Vol. 36, No. 8 (2024)

3403

400
200

300 K to 250 K
300 K to 200 K
300 K to 150 K
300 K to 100 K

TCF (ppm/K)

0
-200
-400
-600
-800
-1000
-1200

10

11

12

13

14

15

16

17

18

19

20

Vg (V)
Fig. 4. (Color online) The measured TCFs calculated in different temperature variation ranges change with theincrease in Vg.

while the initial TCF with Vg = 10 V was around −1096 ppm/K, aligning with those of typical
NEMS resonators. Both the value and sign of TCF can be tuned by adjusting Vg, which indicatesthat the direction of frequency shift relative to the temperature variation can also be tuned. A
positive TCF implies that the frequency increases with temperature, whereas a negative TCF
suggests a decrease in frequency as temperature increases. These results demonstrate that the
proposed gate-voltage-controlled method effectively adjusts the resonators’ temperaturesensitivity, enabling the dual functions of temperature sensing and temperature stability within
the same device.
Note that although the proposed stage temperature control method while effective inlaboratory settings may pose significant challenges in practical applications, where attaining astable, cryogenic temperature may be difficult owing to cost or design limitations. The relatively
high TCF in our nanoresonators compared with conventional MEMS resonators can pose achallenge in applications requiring high frequency stability such as in timing applications.
Fortunately, the ultrawide electrostatic frequency tunability achievable at room temperature inour devices can potentially provide an efficient and easy frequency drift compensation for thenative stress (Eε 0(T0)) on the nanoresonators, i.e., stress not attributed to electrostatic force,
introduced during device fabrication and packaging is kept reasonably low. Thus, someconsideration regarding this point should be given during the design, fabrication, and packagingof the devices. Since, TCF and thus the frequency stability of the nanoresonator depend on thethermal expansion coefficient mismatch between the materials of the nanoresonator and that of
the substrate (SiO2/Si), a potential method to optimize the TCF will be to adjust the thickness ofthe sacrificial SiO2 layer within the limitations of the fabrication and detection processes, which
would require further experimental exploration in the future.

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Sensors and Materials, Vol. 36, No. 8 (2024)

Conclusions

In this study, we explored the resonance frequency tuning of an ultrathin Si NEMS resonatorof ~80 nm width and ~200 µm length, focusing on the interplay between the electrostatic andtemperature tuning of resonance frequency. We revealed that the electrostatic resonancefrequency tuning range consistently narrows as temperature decreases from 300 to 100 K,
suggesting that temperature control could serve as a potential method for controlling theelectrostatic tunability. This behavior is primarily attributed to the axial strain variation inducedby the differential thermal expansion of the materials of the nanoresonator and its substrate.
Furthermore, by manipulating the gate voltage, the temperature sensitivity of the device can be
precisely controlled. This capability enables the dual functionality of the resonators to act bothas highly sensitive temperature sensors and as devices exhibiting high temperature stability.
Currently, this study has concentrated on the process of cooling the developed ultrathin siliconnanoresonators. Future research will extend to exploring frequency tuning behavior during
heating, broadening our understanding of the frequency tuning of ultrathin siliconnanoresonators.

Acknowledgments
This work was supported by the Japan Society for the Promotion of Science (JSPS) Grants-inAid for Scientific Research (JSPS KAKENHI Grant Number JP21K14513), The Kyoto
University Research Fund for Young Scientists (Start-Up) FY 2020, and JST SPRING Grant
Number JPMJSP2110. Part of this work was supported by the “Advanced Research Infrastructure
for Materials and Nanotechnology in Japan (ARIM)” of the Ministry of Education, Culture,
Sports, Science and Technology (MEXT) (Grant Number JPMXP1222KT1420). We
acknowledge technical support from the Nanotechnology Hub in Kyoto University.

Conflict of Interest
The authors declare that they have no conflict of interest.

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