# Fileset

[041124_1_5.0250902-min.pdf](https://mdr.nims.go.jp/filesets/3a04033d-0b29-4cff-a3aa-33d290dea357/download)

## Creator

[Wen Zhao](https://orcid.org/0000-0001-8159-8195), [Guo Chen](https://orcid.org/0009-0004-9263-5616), [Keyun Gu](https://orcid.org/0000-0002-7505-7744), Masaya Toda, [Yasuo Koide](https://orcid.org/0000-0001-8321-9822), [Meiyong Liao](https://orcid.org/0000-0003-1361-4266)

## Rights

[Creative Commons BY-NC Attribution-NonCommercial 4.0 International](https://creativecommons.org/licenses/by-nc/4.0/)

## Other metadata

[High-order resonance enhancing the mass sensitivity of diamond cantilevers](https://mdr.nims.go.jp/datasets/2b05237c-da9f-42f5-8d9e-ab3840628abb)

## Fulltext

High-order resonance enhancing the mass sensitivity of diamond cantileversViewOnlineExportCitationRESEARCH ARTICLE |  APRIL 22 2025High-order resonance enhancing the mass sensitivity ofdiamond cantileversSpecial Collection: Ultrawide Bandgap SemiconductorsWen Zhao  ; Guo Chen  ; Keyun Gu  ; Masaya Toda; Yasuo Koide  ; Meiyong Liao  APL Mater. 13, 041124 (2025)https://doi.org/10.1063/5.0250902Articles You May Be Interested InTransverse vibration of a cantilever beam under base excitation using fractional rheological modelAIP Conf. Proc. (October 2018)Effect of the ligament of double cantilever beam specimens on the cantilever deflectionAIP Conf. Proc. (December 2017)Design and simulation of micro cantilevers for sensing applicationAIP Conf. Proc. (May 2023)  23 April 2025 00:35:54https://pubs.aip.org/aip/apm/article/13/4/041124/3344902/High-order-resonance-enhancing-the-masshttps://pubs.aip.org/aip/apm/article/13/4/041124/3344902/High-order-resonance-enhancing-the-mass?pdfCoverIconEvent=citehttps://pubs.aip.org/apm/collection/516311/Ultrawide-Bandgap-Semiconductorsjavascript:;https://orcid.org/0000-0001-8159-8195javascript:;https://orcid.org/0009-0004-9263-5616javascript:;https://orcid.org/0000-0002-7505-7744javascript:;javascript:;https://orcid.org/0000-0001-8321-9822javascript:;https://orcid.org/0000-0003-1361-4266https://crossmark.crossref.org/dialog/?doi=10.1063/5.0250902&domain=pdf&date_stamp=2025-04-22https://doi.org/10.1063/5.0250902https://pubs.aip.org/aip/acp/article/2029/1/020034/818194/Transverse-vibration-of-a-cantilever-beam-underhttps://pubs.aip.org/aip/acp/article/1909/1/020032/833568/Effect-of-the-ligament-of-double-cantilever-beamhttps://pubs.aip.org/aip/acp/article/2715/1/020002/2890535/Design-and-simulation-of-micro-cantilevers-forhttps://e-11492.adzerk.net/r?e=eyJ2IjoiMS4xMiIsImF2IjozMzYxNTcyLCJhdCI6MTA0NTAsImJ0IjowLCJjbSI6NDE2NzY3NzcxLCJjaCI6NjExNDcsImNrIjp7fSwiY3IiOjQ3NjAwOTc4MywiZGkiOiIyYmM4NzIzNTNjNzI0YzQ0OTdjZjY2NGIxYzIxZjRiYiIsImRqIjowLCJpaSI6Ijg5ODI5ODU3MDdkYTRiYTQ5NTMxN2VjNDQxNzFiYTI0IiwiZG0iOjMsImZjIjo2NTA4NjMwMzksImZsIjo2MTkxODEwMjEsImlwIjoiMjAuODEuMzQuMTc3IiwibnciOjExNDkyLCJwYyI6MCwib3AiOjAsIm1wIjowLCJlYyI6MCwiZ20iOjAsImVwIjpudWxsLCJwciI6MjQwMDM3LCJydCI6MSwicnMiOjUwMCwic2EiOiI5NyIsInNiIjoiaS0wMWFkNjlmZjhmZjgxNDZmYyIsInNwIjozNjU2Njk2LCJzdCI6MTI4ODE2NiwidWsiOiJ1ZTEtMmMxNGI3OTI4N2ZjNDQ2YTkyZjliMTYyZjE5MzExYWUiLCJ6biI6MzA3MzcwLCJ0cyI6MTc0NTM2ODU1NDE1MCwiZ2MiOnRydWUsImdDIjp0cnVlLCJncyI6Im5vbmUiLCJ0eiI6IlVUQyIsInVyIjoiaHR0cHM6Ly9wdWJsaXNoaW5nLmFpcC5vcmcvcHVibGljYXRpb25zL2pvdXJuYWxzL3NwZWNpYWwtdG9waWNzL2FwbC1tYXRlcmlhbHMvP3V0bV9zb3VyY2U9cGRmLWRvd25sb2FkcyZ1dG1fbWVkaXVtPWJhbm5lciZ1dG1fY2FtcGFpZ249SEFfQVBNX1NUK09wZW4rZm9yK1N1YnNfUERGXzIwMjQifQ&s=bFju59N1irmtKyX_nV6743hclFUAPL Materials ARTICLE pubs.aip.org/aip/apmHigh-order resonance enhancing the masssensitivity of diamond cantileversCite as: APL Mater. 13, 041124 (2025); doi: 10.1063/5.0250902Submitted: 28 November 2024 • Accepted: 8 April 2025 •Published Online: 22 April 2025Wen Zhao,1 Guo Chen,1 Keyun Gu,1 Masaya Toda,2 Yasuo Koide,1 and Meiyong Liao1,a)AFFILIATIONS1 Research Center for Electronic and Optical Materials, National Institute for Materials Science, Namiki 1-1, Tsukuba,Ibaraki 305-0044, Japan2Graduate School of Engineering, Tohoku University, Sendai, Miyagi 9808579, JapanNote: This paper is part of the Special Topic on Ultrawide Bandgap Semiconductors.a)Author to whom correspondence should be addressed: meiyong.liao@nims.go.jpABSTRACTDiamond has been demonstrated as an exceptional semiconductor for microelectromechanical system (MEMS) sensors, offering high sen-sitivity and reliability due to its ultra-wide bandgap energy, superior mechanical properties, and high thermal conductivity. For MEMSresonator-type sensors that rely on frequency shift detection, such as mass sensors, the overall performance, including the sensitivity, speed,resolution, and noise level, is collectively determined by the stability of the resonance frequency. To improve the sensing performance, geom-etry optimization and nonlinear operation methods have been used, but these methods lead to increased fabrication complexity or increasedenergy dissipation. In this work, we propose the utilization of high-order resonance modes to enhance the resonance frequency stability ofsingle-crystal diamond (SCD) MEMS resonators, achieving a significant improvement in mass resolution to as low as 0.15 atto-grams at roomtemperature. This approach offers a streamlined and competitive strategy for advancing the sensing capabilities of MEMS sensors.© 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial 4.0International (CC BY-NC) license (https://creativecommons.org/licenses/by-nc/4.0/). https://doi.org/10.1063/5.0250902I. INTRODUCTIONMicroelectromechanical system (MEMS) resonantmicrobeams, due to their small size, low power consumption,and high sensitivity, have garnered significant attention for high-resolution sensing applications,1–6 including biological detection,7–9environmental monitoring,10,11 and physical characterization.12,13The sensing performance of these advanced sensors is predom-inantly determined by their frequency stability when the externalquantities are detected by the resonance frequency shift. In manycases, the sensing mechanism relies on detecting a mass changeinduced by the target, which manifests as a resonance shift inamplitude-frequency response.14,15 In such a case, the resolution ofthe resonant-type MEMS sensor is governed by the relation Δm/m= 2Δf/f0, where Δm represents the mass resolution, m is the effectivemass of the resonator, Δf denotes the frequency shift, and f0 is theresonance frequency of the resonator. This equation highlights twoprimary approaches to enhance mass resolution: reducing Δf/f0 ordecreasing the effective mass m of the resonator.Achieving high frequency stability favors a high quality (Q) fac-tor,16 which can be enhanced through stain dilution techniques.17Another approach to improving mass resolution is miniaturizingthe resonator to reduce its overall mass. However, extreme sizereduction to nanoscale increases fabrication complexity and oftenleads to Q-factor degradation,18–21 thereby compromising frequencystability and sensing performance. Another alternative and widelyapplicable strategy is to increase the resonance frequency f0 withoutaltering the resonator’s mass. Operating at higher-order resonancemodes, their shorter vibration period enables rapid response, effec-tively mitigating fluctuation-induced limitations. In addition, theirincreased stiffness makes the microsystem less sensitive to exter-nal environmental factors such as temperature fluctuations, furtherimproving stability and reliability. In addition, when combined witha diamond MEMS resonator, the exceptional mechanical and ther-mal properties of diamond further enhance resonance frequencystability and mass sensitivity.22–25 For example, diamond resonatorspossess a unique feature of low thermal coefficient of frequency(TCF), less than −10 ppm/K, which is better than −30 ppm/K ofAPL Mater. 13, 041124 (2025); doi: 10.1063/5.0250902 13, 041124-1© Author(s) 2025 23 April 2025 00:35:54https://pubs.aip.org/aip/apmhttps://doi.org/10.1063/5.0250902https://pubs.aip.org/action/showCitFormats?type=show&doi=10.1063/5.0250902https://crossmark.crossref.org/dialog/?doi=10.1063/5.0250902&domain=pdf&date_stamp=2025-April-22https://doi.org/10.1063/5.0250902https://orcid.org/0000-0001-8159-8195https://orcid.org/0009-0004-9263-5616https://orcid.org/0000-0002-7505-7744https://orcid.org/0000-0001-8321-9822https://orcid.org/0000-0003-1361-4266mailto:meiyong.liao@nims.go.jphttps://doi.org/10.1063/5.0250902APL Materials ARTICLE pubs.aip.org/aip/apmsilicon,26 making diamond MEMS resonators less sensitive tothermal fluctuation.In this work, we propose the utilization of higher-order res-onance mode to enhance the frequency stability of single-crystaldiamond (SCD) MEMS resonators. We focus on the first three res-onant vibration modes, with frequency fluctuations tracked andanalyzed at each mode by using Allan deviation, a standard met-ric for quantifying in precision measurements. Our findings reveala substantial improvement in the evaluated mass resolution of theSCD MEMS resonator-based sensors, from 0.66 atto-gram (ag) forthe first resonance mode to an impressive 0.15 ag for the thirdresonance mode.II. EXPERIMENTSWe conducted the smart-cut technique to fabricate the SCDMEMS cantilever resonators.27 The detailed fabrication process isdemonstrated in Fig. 1(a), encompassing diamond growth, lithog-raphy, metal mask deposition, etching, and releasing. High-qualitydiamond epilayers were grown using microwave plasma chemicalvapor deposition (CVD) on ion-implanted high-pressure, high-temperature (HPHT) type-lb SCD substrates.28,29 Ion implantationcreated a graphitized carbon layer, which was subsequently etchedto facilitate the release of the cantilevers. Finally, the graphitelayer was selectively removed without affecting the SCD epilayer.Once fully released, the diamond microcantilever resonator arraywas successfully fabricated. The dimensions of the fabricated can-tilevers are a width of 6 μm and a length ranging from 180FIG. 1. (a) Fabrication procedure of the MEMS diamond cantilever resonatorbased on the smart-cut method. (b) Optical image of the fabricated SCD cantileverarray.to 40 μm, as shown in Fig. 1(b). It is noted that ion implan-tation can degrade device performance by introducing defectsrelated energy dissipation. The device performance can be optimizedby completely removing the damaged layer or by increasing theepilayer thickness.30,31A laser Doppler vibrometer (LDV) was used to measure theout-of-plane displacement and velocity.32,33 The SCD cantilevers areactuated by a radio frequency (RF) signal from the lock-in ampli-fier, equipped with a phase locked loop (PLL), which is also used toinvestigate the frequency stability by tracking the frequency fluctua-tion over the time regime. The noise analysis is based on the theoryof Allan deviation.16,34 To efficiently reduce the air damping andenhance the Q factor, all the measurements were conducted in a veryhigh vacuum chamber with a pressure less than the value of 10−4 Paat room temperature. It is worth mentioning that all the displace-ment measurements are taken by positioning the laser spot at the tipof the microbeam (maximum displacement point) to achieve a highsignal-to-noise ratio (SNR).28III. RESULTS AND DISCUSSIONTo examine the length effect on the resonance frequency ofthe SCD cantilever beams, we measured the first three modes ofthe cantilever beams by sweeping the excitation frequency aroundtheir corresponding resonance. Figure 2 illustrates the resonancefrequency values of the first three modes of the SCD cantileversas a dependence of the cantilever lengths (L) ranging from 40to 180 μm. As shown in Fig. 3(a), the resonance frequenciesdecrease as the length increases due to the reduced effective stiff-ness for all three modes. Resonance frequencies exhibit a linearrelationship with 1/L2, consistent with Euler–Bernoulli theory. Theconsistency between experiments and theory confirms the repro-ducibility of the current fabrication method for SCD MEMS struc-ture fabrication and also reveals the availability of the obtainedexperimental data.We focus on one typical SCD cantilever to investigate theresonance performance with a length L = 170 μm and a widthw = 6 μm in Secs. IV A and IV B. First, to fully understand theresonance frequency of the micro-diamond cantilever beam, wefirst conduct the excitation frequency sweep around the first threemodes under various actuation RF AC amplitudes, as shown inFigs. 3(a)–3(c), respectively. The resonance frequency and Q factorof the out-of-plane vibration motion are f1 = 174.894 kHz and Q1∼ 14 015 for the first resonance mode, f2 = 1087.301 kHz and Q2 ∼ 11243 for the second resonance mode, and f3 = 3018.439 kHz and Q3∼ 8300 for the third resonance mode.The increased AC amplitude enhances the resonance vibra-tion amplitude. For all modes, the actuation AC amplitude linearlyincreases the resonance vibration amplitudes, as illustrated in Fig. 4.The Q factors here for each mode are calculated based on the fullwidth at half maximum (FWHM) and are also plotted in Fig. 4. Theincreased AC voltage has little effect on the Q factors due to theoperation in the linear domain. Note that the calculated Q factorsare obtained by Lorentz fitting of each frequency response, and eachvalue is marked in corresponding plots. In addition, the Q-factordecreases with the increased mode number due to the high energydissipation induced by the damping ratio of higher order modes.Higher-order modes (HOMs) exhibit increasingly complex modeAPL Mater. 13, 041124 (2025); doi: 10.1063/5.0250902 13, 041124-2© Author(s) 2025 23 April 2025 00:35:54https://pubs.aip.org/aip/apmAPL Materials ARTICLE pubs.aip.org/aip/apmFIG. 2. (a) Dependence of the resonance frequency on the cantilever length at the first three modes. (b) Linear fitting of the measured resonance frequency with 1/L2 on thefirst three modes.FIG. 3. First three mode responses: (a) first mode, (b) second mode, and (c) third mode.FIG. 4. Resonance frequency spectra and Q-factor of the first three modes under different AC voltages for the SCD cantilever with a length of 170 μm: (a) first mode, (b)second mode, and (c) third mode. The marked point as the star has a similar signal-to-noise ratio (SNR) in each mode and is used to compare the frequency stability inSec. III.APL Mater. 13, 041124 (2025); doi: 10.1063/5.0250902 13, 041124-3© Author(s) 2025 23 April 2025 00:35:54https://pubs.aip.org/aip/apmAPL Materials ARTICLE pubs.aip.org/aip/apmTABLE I. Values of a quality factor with actuated modes of MEMS cantilever beamswith various lengths.Q1 Q2 Q3Cantilever length (L) (μm) (first mode) (second mode) (third mode)180 13 965 10 402 5088170 14 696 11 409 8261160 15 047 10 330NA150 13 345 10 867140 14 992 11 574130 14 911 9966120 14 098 8346110 14 385 8701100 12 012 773990 12 143 838880 12 764NA70 12 75760 10 776shapes, generating multiple nodal regions along the beam length fordifferent vibration modes. First, these nodal regions lead to highlylocalized strain distributions, amplifying internal friction losses andconsequently reducing the Q-factor. Second, the intricate vibrationprofiles of HOMs could induce stronger anchor interactions andenhance thermoelastic damping due to the rapid cyclic compressionand expansion of the resonator. As a result, the Q-factor decreasesas the mode order increases.To further examine the length-dependent Q-factor, we brieflyillustrate the Q-factor values of the cantilever beams with lengthsranging from 60 to 180 μm in Table I. The results indicate thatthe Q factors show little independence on the beam lengths forL > 100 μm. The clamping loss becomes dominant for the caseswith L less than 60 μm, consistent with our previous study.35 It isnoted that the Q-factor determines the minimum detectable fre-quency shift, which directly affects the short-term stability of theresonator.16,36 A higher Q-factor can reduce noise and improvesfrequency stability, thereby lowering the Allan deviation at shortintegration times.IV. FREQUENCY STABILITYWe utilize Allan deviation to analyze the frequency stability,which is mathematically quantified as16,34σ(τ) =¿ÁÁÁÀ 12(N − 1)N−1∑i=1( fi+1 − fif0)2, (1)where N is the number of samples of the resonance frequencyf1. . .fN, each with averaged integration time τ within a total of Nintervals. f0 is the reference resonance frequency. Measurementshere for Allan analysis are made in the closed-loop configurationby tracking the frequency fluctuation within 5 min in the lock-inamplifier. The sampling rate is set to be 1799 Sa/s for all frequencyfluctuation measurements.A. Fundamental mode (first mode)We first investigate the frequency stability of the first resonancemode using the phase locked loop (PLL) circuit at different band-widths (BWs) of 1, 50, 100, and 400 Hz, as shown in Figs. 5(a)–5(d).The frequency stability under different actuation AC amplitudes wascharacterized. The signal-to-noise ratio (SNR) is controlled throughvariation in the applied voltages, which increases with the vibra-tional amplitude. An order of magnitude reduction of σ(τ) is clearlyobserved for lower BW = 1 Hz compared with that of BW = 100 Hz.Due to the large sampling rates (1799 Sa/s), we can also detect theinvolved noise from the measurement system. The results indicatethat the noise is mainly dominated by detection and thermome-chanical noise together, especially in the case with a lower BW. Theclosed-loop response time relies on the bandwidth value in the phaselocked loop (PLL) system instead of the intrinsic response time ofthe target resonator in our case. Apparently, the reduced bandwidthcan significantly enhance the minimal detection. In the case of BW= 1 Hz, the minimal detection can reach σ(τ) ∼2.6 × 10−8, for thefirst mode. When enlarging the bandwidth of the PLL, the pointof transition between detection noise and thermomechanical noisechanges to the lower value of integration time τ, that is, becausehigher BW allows more high-frequency detection noise, raising theinitial Allan deviation at short integration times. In addition, thethermomechanical noise starts to dominate over the detection noiseduring the evolution of Allan deviation. For example, in the case ofBW = 400 Hz in Fig. 5(d), the system noise from the starting point isburied in Allan deviation, while the thermomechanical noise dom-inates overall. For the time constant of the PLL (lower BW) lowerthan the resonator response time, the detection noise limit is smaller.The filter from the PLL, in addition to the filtering by the intrin-sic response of the resonator and the demodulator filter, reduces theσ(τ) of the system.37To further clarify the BW effect, we specifically investigateseveral cases with different BWs for a high SNR measured atAC = 1.0 V, as shown in Fig. 6(a). The increased bandwidth shortensthe transition time from detection noise to thermomechanical noise.In addition, the obtained experimental results further confirm thatthe minimum detection value is not influenced by the bandwidth.This is attributed to the phase-locked loop (PLL) bandwidth beingconfigured to accommodate frequency signals within the designatedsignal bandwidth, ensuring accurate frequency tracking withoutcompromising sensitivity. We plot the minimal detection value offrequency relativity at BW = 100 Hz by varying the applied AC volt-age, as shown in Fig. 6(b). When increasing the AC volts rangingfrom 0.2 to 1.0 V, the minimal detection can be highly improveddue to a larger SNR value in amplitude–frequency response. In addi-tion, it is noticeable that applying an excessively large AC voltageto drive a microdevice can induce pull-in instability, a nonlinearphenomenon that causes the microresonator to come into contactwith the substrate. As a result, the minimal detection value (fun-damental limits) saturates and becomes largely independent of theapplied voltage.APL Mater. 13, 041124 (2025); doi: 10.1063/5.0250902 13, 041124-4© Author(s) 2025 23 April 2025 00:35:54https://pubs.aip.org/aip/apmAPL Materials ARTICLE pubs.aip.org/aip/apmFIG. 5. AC voltage effects of varying noise on Allan deviation, for the first mode, at (a) BW = 1 Hz, (b) BW = 50 Hz, (c) BW = 100 Hz, and (d) BW = 400 Hz. The thermalnoise limit (green dashed line, Nth) and detection noise limits (red dashed line, Nd), calculated based on Ref. 16, are marked in (a). It is worth mentioning that the detectionnoise limits from the testing instruments can be captured when increasing the sampling rate to at least 104 Sa/s.FIG. 6. (a) BW effects of varying noise on Allan deviation at AC = 0.4 V for the first mode; (b) AC effects on the minimal detection at the first mode.APL Mater. 13, 041124 (2025); doi: 10.1063/5.0250902 13, 041124-5© Author(s) 2025 23 April 2025 00:35:54https://pubs.aip.org/aip/apmAPL Materials ARTICLE pubs.aip.org/aip/apmFIG. 7. First resonance mode fluctuationover the time domain. (a) AC effects atBW = 100 Hz and (b) BW effects at AC= 1.0 V.To better illustrate how the AC and BW affect the frequencystability in the time domain, we plot the first resonance mode fluc-tuation over the time with varying AC voltages and bandwidths inFig. 7. Notably, the resonance mode fluctuation remains stable overthe investigated period (5 min). Increasing AC voltage within thelinear frequency response domain reduces frequency fluctuations,improving the frequency stability due to the higher SNR, whichmakes the resonance less susceptible to noise-induced variations. Inaddition, a smaller BW acts as a filter, effectively attenuates varioustypes of involved noise, and contributes to a more stable frequencyresponse.B. Higher order modes (second and third modes)Higher-order modes normally exhibit higher resonance fre-quencies, a wide dynamic range, high sensitivity, and fast responsetime. In this section, we mainly investigate the frequency stabil-ity of the second mode and the third mode due to the upper-frequency limit of our LDV measurement system based on the Allandeviation.Figures 8(a)–8(d) illustrate the impact of different bandwidths(1, 50, 100, and 400 Hz) on Allan deviation for the second reso-nance mode under various applied AC amplitudes. The obtainedresults indicate that both detection (facility) noise and thermo-mechanical noise dominate over the overall responses, similarto the first mode resonance. In particular, the detection noisedominates for a lower bandwidth [Fig. 8(a)], while thermochem-ical noise dominates at a higher bandwidth [Fig. 8(d)]. With thetransition between detection noise and thermomechanical noisedown to the lower time regime, larger bandwidths can mitigatethe effect of detection noise. By closer observation, the minimaldetection value is highly enhanced by the increased AC voltagedue to the large dynamic response; at a bandwidth of 1 Hz, theminimal detection value reaches σ(τ) = 1.21 × 10−8 for the sec-ond mode, slightly lower than that of the first resonance mode[σ(τ) = 2.62 × 10−8].In Figs. 9(a)–9(c), we illustrate the bandwidth effects on the fre-quency stability at the various applied AC voltages. It is evident thatthe increased BW shortens the transition time between detectionnoise and thermomechanical noise. For higher BW, the detectionnoise eventually disappears, similar to that of the first resonanceAPL Mater. 13, 041124 (2025); doi: 10.1063/5.0250902 13, 041124-6© Author(s) 2025 23 April 2025 00:35:54https://pubs.aip.org/aip/apmAPL Materials ARTICLE pubs.aip.org/aip/apmFIG. 8. AC voltage effects of varyingnoise on Allan deviation, for the secondmode, at (a) BW = 1 Hz, (b) BW = 50 Hz,(c) BW = 100 Hz, and (d) BW = 400 Hz.FIG. 9. Bandwidth effects of varyingnoise on Allan deviation, for the secondmode, at (a) AC = 2.0 V, (b) AC = 4.0 V,and (c) AC = 6.0 V; (d) applied AC effectson the minimal detection at the first modewhen BW = 100 Hz.APL Mater. 13, 041124 (2025); doi: 10.1063/5.0250902 13, 041124-7© Author(s) 2025 23 April 2025 00:35:54https://pubs.aip.org/aip/apmAPL Materials ARTICLE pubs.aip.org/aip/apmFIG. 10. Actuation RF AC voltage effects of varying noise on Allan deviation, for the third mode, at (a) BW = 1 Hz, (b) BW = 50 Hz, (c) BW = 100 Hz, (d) BW = 400 Hz, (e)BW = 500 Hz, and (f) BW = 1000 Hz.APL Mater. 13, 041124 (2025); doi: 10.1063/5.0250902 13, 041124-8© Author(s) 2025 23 April 2025 00:35:54https://pubs.aip.org/aip/apmAPL Materials ARTICLE pubs.aip.org/aip/apmmode. A closer analysis in Fig. 9(d) shows that the minimal detec-tion value continues to decrease with increasing AC voltage, furtherenhancing the sensor’s performance.Similarly, we analyze the frequency stability of the third modewith a resonance frequency of f3 = 3018.439 kHz, as shown in Figs. 10and 11. Similar to the previous modes, increasing the AC voltageleads to a reduction in the magnitude of σ(τ), with detection noiseremaining at a low level. As the bandwidth in the PLL is broadened,detection noise gradually disappears, and thermomechanical noisebecomes dominant. However, compared to the results of the firstmode, higher-order mode resonance significantly reduces noise con-straints because the increased resonance frequency results in a largerrelative frequency shift (Δf/f0) compared to the fundamental mode,resulting in a marked improvement in minimal force detection andmass resolution.Based on the formula for mass sensing, Δ f = ( f0/2m0) × Δm,38the mass resolution significantly improves to 1.5 × 10−19 g (0.15 ag)for the third resonance mode from 6.6× 10−19 g (0.66 ag) for the firstresonance mode by utilizing higher order modes for mass sensing.To further elucidate the advantage of higher-order modes, wecompare amplitude–frequency response of the first three modesunder the same signal-to-noise ratio conditions in the lineardomain, as shown in Figs. 12(a)–12(c). The comparison highlightsthe enhanced stability provided by higher-order modes actuation.As a result, the diamond resonator’s mass detection capability isenhanced from 0.66 ag for the first resonance mode to 0.15 atto-gram (ag) for the third resonance mode, surpassing that of theprevious report (1.4 ag),39 as listed in Table II. Therefore, it is a clearassessment of how higher-order modes outperform fundamentalmodes in terms of sensing performance and frequency stability.FIG. 11. BW effects on Allan deviation, for the third mode, at (a) AC = 2.0 V and (b) AC = 10.0 V; (c) applied AC effects on the minimal detection at the first modewhen BW = 100 Hz.APL Mater. 13, 041124 (2025); doi: 10.1063/5.0250902 13, 041124-9© Author(s) 2025 23 April 2025 00:35:54https://pubs.aip.org/aip/apmAPL Materials ARTICLE pubs.aip.org/aip/apmFIG. 12. BW effects of varying noise on normalized results of Allan deviation under different resonant modes (a) BW = 1 Hz, (b) BW = 1 Hz, and (c) BW = 400 Hz; (d) modenumber effects on the minimal detection value at BW = 1 Hz and BW = 100 Hz.TABLE II. Comparison values of the first three resonance modes.Mode-1 Mode-2 Mode-3f (Hz) 174 893.79 1 087 301.00 3 018 438.83Q 14 696 11 409 8261f ⋅Q (Hz) 2.57 × 109 1.24 × 1010 2.49 × 1010σmin 5.078 × 10−8 3.902 × 10−8 1.192 × 10−8Δm (g) 6.6 × 10−19 5.1 × 10−19 1.5 × 10−19V. CONCLUSIONSIn summary, we demonstrated a higher-order mode actu-ated SCD resonator and analyzed the frequency stability by track-ing the frequency fluctuation across the first three modes. Thehigh-order mode resonances exhibited an exceptional performancein mass sensing, with the minimal detectable mass improving from0.66 to 0.15 atto-gram (ag) utilizing the higher-order modes. Theseresults highlight that sensing capability improves with increas-ing mode order. Operating the diamond sensor at higher ordermodes, with its superior frequency stability and enhanced minimaldetection limits, offers a promising strategy for advanced sensingapplications.ACKNOWLEDGMENTSThis work was supported by JSPS KAKENHI (Grant Nos.24KF0085, 24H00287, and 22K18957) and ARIM (Grant Nos.JPMXP1223NM5297), sponsored by the Ministry of Education,Culture, Sports, and Technology (MEXT) of Japan.APL Mater. 13, 041124 (2025); doi: 10.1063/5.0250902 13, 041124-10© Author(s) 2025 23 April 2025 00:35:54https://pubs.aip.org/aip/apmAPL Materials ARTICLE pubs.aip.org/aip/apmAUTHOR DECLARATIONSConflict of InterestThe authors have no conflicts to disclose.Author ContributionsWen Zhao: Conceptualization (equal); Data curation (lead); For-mal analysis (equal); Investigation (lead); Methodology (equal);Resources (lead); Software (lead); Validation (equal); Visualization(equal); Writing – original draft (lead); Writing – review & edit-ing (lead). Guo Chen: Investigation (supporting); Writing – orig-inal draft (supporting); Writing – review & editing (supporting).KeyunGu: Investigation (supporting); Writing – original draft (sup-porting); Writing – review & editing (supporting). Masaya Toda:Investigation (supporting); Methodology (supporting); Writing –original draft (supporting); Writing – review & editing (support-ing). Yasuo Koide: Writing – original draft (supporting); Writing –review & editing (supporting). Meiyong Liao: Conceptualization(lead); Data curation (equal); Formal analysis (equal); Fundingacquisition (lead); Investigation (lead); Methodology (lead); Projectadministration (lead); Resources (lead); Software (lead); Supervision(lead); Validation (lead); Visualization (lead); Writing – originaldraft (lead); Writing – review & editing (lead).DATA AVAILABILITYThe data that support the findings of this study are availablefrom the corresponding author upon reasonable request.REFERENCES1N. V. Lavrik, M. J. Sepaniak, and P. G. Datskos, Rev. Sci. Instrum. 75(7),2229–2253 (2004).2J. Fritz, M. K. Baller, H. P. Lang, H. Rothuizen, P. Vettiger, E. Meyer, H. -JGuntherodt, C. Gerber, and J. K. Gimzewski, Science 288(5464), 316–318 (2000).3D. Lange, C. Hagleitner, A. Hierlemann, O. Brand, and H. Baltes, Anal. Chem.74(13), 3084–3095 (2002).4I. Voiculescu, M. E. Zaghloul, R. A. McGill, E. J. Houser, and G. K. Fedder, IEEESens. J. 5(4), 641–647 (2005).5C. Vančura, M. Rüegg, Y. Li, C. Hagleitner, and A. Hierlemann, Anal. Chem.77(9), 2690–2699 (2005).6L. Wang, W. Zhao, and M. Younis, Sens. Actuators, A 379, 115867 (2024).7P. S. Waggoner and H. G. Craighead, Lab Chip 7(10), 1238–1255 (2007).8N. Hossain, M. Z. A. Mahmud, A. Hossain, M. K. Rahman, M. S. Islam, R.Tasnim, and M. H. Mobarak, Results Eng. 22, 102115 (2024).9Y. Yoon, I. Chae, T. Thundat, and J. Lee, Adv. Mater. Technol. 4(3), 1800597(2019).10W. Zhao, N. Alcheikh, S. B. Mbarek, and M. I. Younis, J. Appl. Phys. 132(14),144502 (2022).11W. Zhao, N. Alcheikh, F. Khan, U. Yaqoob, and M. I. Younis, Sens. Actuators,A 344, 113688 (2022).12W. Zhao, S. Ahmed, H. Fariborzi, and M. I. Younis, J. Micromech. Microeng.31(12), 125010 (2021).13K. Park, N. Kim, D. T. Morisette, N. R. Aluru, and R. Bashir,J. Microelectromech. Syst. 21(3), 702–711 (2012).14S. K. Roy, V. T. K. Sauer, J. N. Westwood-Bachman, A. Venkatasubramanian,and W. K. Hiebert, Science 360(6394), eaar5220 (2018).15N. Hosseini, M. Neuenschwander, J. D. Adams, S. H. Andany, O. Peric, M. Win-hold, M. C. Giordano, V. S. Bhat, M. Penedo, D. Grundler, and G. E. Fantner, Nat.Electron. 7(7), 567–575 (2024).16P. Sadeghi, A. Demir, L. G. Villanueva, H. Kähler, and S. Schmid, Phys. Rev. B102(21), 214106 (2020).17S. A. Fedorov, N. J. Engelsen, A. H. Ghadimi, M. J. Bereyhi, R. Schilling, D. J.Wilson, and T. J. Kippenberg, Phys. Rev. B 99(5), 054107 (2019).18A. A. Basharin, V. Chuguevsky, N. Volsky, M. Kafesaki, and E. N. Economou,Phys. Rev. B 95(3), 035104 (2017).19L. Gu, W. Zhang, H. Lu, Y. Wu, and C. Fan, Microelectron. Eng. 271–272,111950 (2023).20N. S. Gireesh, T. Sundararajan, and S. S. Gautam, Gyroscopy Navig. 11(3),206–213 (2020).21D. D. Gerrard, C. H. Ahn, I. B. Flader, Y. Chen, E. J. Ng, Y. Yang, and T.W. Kenny, Presented at the 2016 IEEE 29th International Conference on MicroElectro Mechanical Systems (MEMS), 2016.22K. Gu, Z. Zhang, G. Chen, J. Huang, Y. Koide, S. Koizumi, W. Zhao, and M.Liao, Carbon 225, 119159 (2024).23Z. Zhang, G. Chen, K. Gu, S. Koizumi, and M. Liao, Fun. Diam. 3(1), 2221280(2023).24C. E. Nebel, Fun. Diam. 3(1), 2201592 (2023).25W. Zhao, S. Koizumi, and M. Liao, IEEE Electron Device Lett. 45, 2268 (2024).26L. Sang, H. Sun, X. Yang, T. Li, B. Shen, and M. Liao, Presented at the 2020 IEEEInternational Electron Devices Meeting (IEDM), 2020.27M. Liao, Fun. Diam. 1(1), 29–46 (2021).28Z. Zhang, W. Zhao, G. Chen, M. Toda, S. Koizumi, Y. Koide, and M. Liao, Adv.Funct. Mater. 33(27), 2300805 (2023).29M. Liao, Y. Koide, and L. Sang, in Novel Aspects of Diamond: From Growth toApplications, edited by N. Yang (Springer International Publishing, Cham, 2019),pp. 91–121.30M. Liao, M. Toda, L. Sang, T. Teraji, M. Imura, and Y. Koide, Jpn. J. Appl. Phys.56(2), 024101 (2017).31H. Wu, L. Sang, Y. Li, T. Teraji, T. Li, M. Imura, J. You, Y. Koide, M. Toda, andM. Liao, Phys. Rev. Mater. 2(9), 090601 (2018).32W. Zhao, R. T. Rocha, N. Alcheikh, and M. I Younis, Mech. Syst. Signal Process.196, 110347 (2023).33W. Zhao, F. Khan, N. Alcheikh, and M. I. Younis, IEEE Electron Device Lett.43(10), 1732–1735 (2022).34D. Antonio, D. H. Zanette, and D. López, Nat. Commun. 3(1), 806 (2012).35M. Liao, M. Toda, L. Sang, S. Hishita, S. Tanaka, and Y. Koide, Appl. Phys. Lett.105(25), 251904 (2014).36Y. Qiao, A. Elhady, M. Arabi, E. Abdel-Rahman, and W. Zhang, Microsyst.Nanoeng. 10(1), 90 (2024).37P. Neumann, I. Jakobi, F. Dolde, C. Burk, R. Reuter, G. Waldherr, J. Honert,T. Wolf, A. Brunner, J. H. Shim, D. Suter, H. Sumiya, J. Isoya, and J. Wrachtrup,Nano Lett. 13(6), 2738–2742 (2013).38T. A. Efimov, E. A. Rassolov, B. G. Andryukov, T. S. Zaporozhets, and R. V.Romashko, J. Phys.: Conf. Ser. 1439(1), 012006 (2020).39J. Verd, A. Uranga, G. Abadal, J. L. Teva, F. Torres, J. López, F. Pérez-Murano,J. Esteve, and N. Barniol, IEEE Electron Device Lett. 29(2), 146–148 (2008).APL Mater. 13, 041124 (2025); doi: 10.1063/5.0250902 13, 041124-11© Author(s) 2025 23 April 2025 00:35:54https://pubs.aip.org/aip/apmhttps://doi.org/10.1063/1.1763252https://doi.org/10.1126/science.288.5464.316https://doi.org/10.1021/ac011269jhttps://doi.org/10.1109/jsen.2005.851016https://doi.org/10.1109/jsen.2005.851016https://doi.org/10.1021/ac048378thttps://doi.org/10.1016/j.sna.2024.115867https://doi.org/10.1039/b707401hhttps://doi.org/10.1016/j.rineng.2024.102115https://doi.org/10.1002/admt.201800597https://doi.org/10.1063/5.0104007https://doi.org/10.1016/j.sna.2022.113688https://doi.org/10.1016/j.sna.2022.113688https://doi.org/10.1088/1361-6439/ac3219https://doi.org/10.1109/jmems.2012.2189359https://doi.org/10.1126/science.aar5220https://doi.org/10.1038/s41928-024-01195-zhttps://doi.org/10.1038/s41928-024-01195-zhttps://doi.org/10.1103/physrevb.102.214106https://doi.org/10.1103/physrevb.99.054107https://doi.org/10.1103/physrevb.95.035104https://doi.org/10.1016/j.mee.2023.111950https://doi.org/10.1134/s2075108720030074https://doi.org/10.1016/j.carbon.2024.119159https://doi.org/10.1080/26941112.2023.2221280https://doi.org/10.1080/26941112.2023.2201592https://doi.org/10.1109/led.2024.3485683https://doi.org/10.1080/26941112.2021.1877019https://doi.org/10.1002/adfm.202300805https://doi.org/10.1002/adfm.202300805https://doi.org/10.7567/jjap.56.024101https://doi.org/10.1103/physrevmaterials.2.090601https://doi.org/10.1016/j.ymssp.2023.110347https://doi.org/10.1109/led.2022.3196322https://doi.org/10.1038/ncomms1813https://doi.org/10.1063/1.4904990https://doi.org/10.1038/s41378-024-00718-0https://doi.org/10.1038/s41378-024-00718-0https://doi.org/10.1021/nl401216yhttps://doi.org/10.1088/1742-6596/1439/1/012006https://doi.org/10.1109/led.2007.914085