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Guo Chen, [Zilong Zhang](https://orcid.org/0000-0002-9759-9253), Keyun Gu, [Liwen Sang](https://orcid.org/0000-0003-0946-1025), [Satoshi Koizumi](https://orcid.org/0000-0003-4961-5658), Masaya Toda, Haitao Ye, [Yasuo Koide](https://orcid.org/0000-0001-8321-9822), Zhaohui Huang, [Meiyong Liao](https://orcid.org/0000-0003-1361-4266)

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[Higher-order resonance of single-crystal diamond cantilever sensors toward high f‧Q products](https://mdr.nims.go.jp/datasets/c3fa257f-703e-43c8-9956-4f576b53c020)

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Higher-order resonance of single-crystal diamond cantilever sensors toward high f‧Q productsApplied Physics Express     LETTER • OPEN ACCESSHigher-order resonance of single-crystal diamondcantilever sensors toward high f‧Q productsTo cite this article: Guo Chen et al 2024 Appl. Phys. Express 17 021001 View the article online for updates and enhancements.You may also likeGeneral parallel cosmologyDébora Aguiar Gomes, Jose BeltránJiménez and Tomi S. Koivisto-Exciton-carrier coupling in a metal halideperovskite nanocrystal assembly probedby two-dimensional coherent spectroscopyEsteban Rojas-Gatjens, David Tiede,Katherine A Koch et al.-Late-time cosmology with phantom dark-energy in f(Q) gravityAndreas Lymperis-This content was downloaded from IP address 144.213.253.16 on 03/02/2024 at 03:42https://doi.org/10.35848/1882-0786/ad2027/article/10.1088/1475-7516/2023/12/010/article/10.1088/2515-7639/ad229a/article/10.1088/2515-7639/ad229a/article/10.1088/2515-7639/ad229a/article/10.1088/1475-7516/2022/11/018/article/10.1088/1475-7516/2022/11/018/article/10.1088/1475-7516/2022/11/018/article/10.1088/1475-7516/2022/11/018/article/10.1088/1475-7516/2022/11/018https://pagead2.googlesyndication.com/pcs/click?xai=AKAOjstSsWfM8qFc0e_bkZ_-79u_0n6x-Db_hbisIl9QCYr4sSzZCkZK9CA8wLpfyX0M4CtcDpJcS3_UUlmlv1zowJ4XeMs3t8M1RV5tTDWUj2Rwy6SzPtlvXUc9OaKJE60RWqp3PHsLx_UQ43I29rPgUZfrrceBwG91aIqCLwb_FgCLqDUeiSpmSeaBKMF4-efpbRKoVg8bbYqRq903luWqtHp3Kq6fB2t6Dpi-LmkQYYjj5pkNxroMJfbordvXs2VNGkppmDDZo0nODkyXwDyPXvmde4sP5xOBBjSdiNpNjOaxRNDbYFRrVUO8IdCjNKUYFSKNtAo0N0oo&sig=Cg0ArKJSzGCrCM30koDp&fbs_aeid=%5Bgw_fbsaeid%5D&adurl=https://ecs.confex.com/ecs/prime2024/cfp.cgi%3Futm_source%3DIOP%26utm_medium%3Dbanner%26utm_campaign%3Dprime_abstract_submissionHigher-order resonance of single-crystal diamond cantilever sensors toward highf‧Q productsGuo Chen1,2, Zilong Zhang1, Keyun Gu1, Liwen Sang1, Satoshi Koizumi1, Masaya Toda3, Haitao Ye4, Yasuo Koide1,Zhaohui Huang2*, and Meiyong Liao1*1National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan2School of Materials Science and Technology, China University of Geosciences, Beijing 100083, People’s Republic of China3Graduate School of Engineering, Tohoku University, Sendai, Miyagi 980-8579, Japan4School of Engineering, University of Leicester, Leicester, LE1 7RH, United Kingdom*E-mail: huang118@cugb.edu.cn; meiyong.liao@nims.go.jpReceived December 26, 2023; revised January 15, 2024; accepted January 18, 2024; published online February 2, 2024MEMS resonant sensing devices require both HF ( f ) and low dissipation or high quality factor (Q) to ensure high sensitivity and high speed. In thisstudy, we investigate the resonance properties and energy loss in the first three resonance modes, resulting in a significant increase in f‧Q productat higher orders. The third order resonance exhibits an approximately 15-fold increase in f‧Q product, while the Q factor remains nearly constant.Consequently, we achieved an ultrahigh f‧Q product exceeding 1012 Hz by higher-order resonances in single-crystal diamond cantilevers.© 2024 The Author(s). Published on behalf of The Japan Society of Applied Physics by IOP Publishing LtdMEMS, emerging as pivotal technologies, play anincreasingly vital role in a wide range of applica-tions, from classic use like sensing, actuation, andswitches in environmental monitoring, smart phones, IoTnodes, robotic servants, and autonomous vehicles to precisequantum sensors.1–4) Resonance frequency ( f ) and quality(Q) factor are two fundamental parameters determining theperformance of the MEMS sensors, such as response speed,detectivity, stability, and signal-to-noise ratio.5–7) Whensensing is based on the frequency shift, Q factor is ofparamount importance.8,9) However, increasing the resonancefrequency always leads to the degradation of the Q factor forthe fundamental resonance mode due to increased dissipationin the system.10,11) Therefore, the product of f‧Q presents as afigure of merit for MEMS resonators. High f‧Q product isgenerally desirable to achieve high sensitivity, fast responsespeed, and enhanced resilience to mechanical noisesources.11) Higher-order resonance modes have been shownpromising to enhance the performance of the sensors, i.e.scanning speed and image contrast of atomic force micro-scope (AFM) and mass sensitivity of a cantilever.12–14)Nevertheless, the Q factor of higher-order resonance modesis left uncontrolled.12)Diamond has been considered the best candidate for high-performance and high-reliability MEMS sensors in termsof its exceptional mechanical, thermal, and chemicalproperties.15–18) Despite the theoretical f‧Q of diamond inAkhieser regime is lower than Si, the practical Q factor over1 million at room temperature was achieved, much higher thanthat of Si.19,20) By using diamond cantilevers, the durability ofthe AFM probe and the reliability of magnetic or mass sensorsunder extreme conditions can be much improved.8,13,21,22)In this study, we investigated the higher-order resonance ofsingle-crystal diamond (SCD) cantilevers and the f‧Q atdifferent resonance modes. Remarkably, with little changeof the Q factors at the higher-order resonance, the f‧Q productof the SCD increased by over 15 times, for the third orderresonance relative to the first order resonance. This workprovides a promising application scene for SCD MEMScantilevers, such as AFM probes, magnetic and mass sensors.The SCD cantilevers were fabricated using a smart-cutmethod from a SCD epilayer grown on an ion implanted SCDsubstrate, as reported previously, as shown in Fig. 1(a). 20,23)Before the fabrication of the cantilevers, a microwave plasmaCVD technique was used to grow the high-quality diamondepilayer on the ion-implanted high-pressure high-temperaturetype-Ib SCD (100) substrate. The ion implantation was used tocreate a graphitized carbon layer, that would then be etched tofacilitate the release of the cantilevers. During the wet-etchingprocess, the graphite layer was removed without affecting theSCD epilayer.24,25) Figure 1(b) shows the SCD-on-SCDstructure of the fabricated diamond resonators. The SCDcantilevers had varying lengths (L) ranging from 30 to 160μm, a thickness (t) of approximately 880 nm and a width (w)of 10 μm, as illustrated in Fig. 1(c). A 3D profile image of theMEMS cantilever distinctly depicts the upward bending, dueto the existence of residual stress, as shown in Fig. 1(d). Theresonance properties of the SCD cantilevers were measured ina vacuum (10−4 Torr) with a laser Doppler vibrometer. TheSCD cantilevers were actuated by a piezoelectric ceramic or anRF probe.We show the initial three resonance modes of a 140 μmlength cantilever in Fig. 2(a). Evidently, lower-order modesexhibit larger amplitudes than higher-order modes subject tothe same measurement conditions. The resonance amplitude ofthe first mode is 40 times greater than that of the third mode,demonstrating the increased challenge in exciting higher-ordermodes. The inset shows the corresponding mode shapes of thethree orders. We investigated the resonance properties withinthe first three orders modes of SCD cantilevers. In Figs. 2(b)–2(d), we present a representative set of resonance spectra froma 140 μm length cantilever. These spectra span various ordersof vibration modes, ranging from the 1st order to the 3rd order.To compare the resonance amplitudes within these higher-order modes, all measurements were performed under thesame RF magnitude.Content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of thiswork must maintain attribution to the author(s) and the title of the work, journal citation and DOI.021001-1© 2024 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdApplied Physics Express 17, 021001 (2024) LETTERhttps://doi.org/10.35848/1882-0786/ad2027https://crossmark.crossref.org/dialog/?doi=10.35848/1882-0786/ad2027&domain=pdf&date_stamp=2024-02-02https://orcid.org/0000-0003-1361-4266https://orcid.org/0000-0003-1361-4266mailto:huang118@cugb.edu.cnmailto:meiyong.liao@nims.go.jphttps://creativecommons.org/licenses/by/4.0/https://doi.org/10.35848/1882-0786/ad2027In Fig. 3, we present the dependence of the resonancefrequency on the cantilever length for the first three modes.According to the Euler–Bernoulli theory, the resonancefrequency of cantilevers can typically be expressed asFig. 1. (a) Fabrication process of the SCD MEMS cantilevers. (b) Thestructure of a SCD MEMS cantilever. (c) The optical microscope image ofthe SCD MEMS cantilevers. (d) The 3D geometrical profile image depictingthe SCD cantilevers.(a) (c)(b) (d)Fig. 2. Resonance frequency spectra of a SCD cantilever, under (a) the first three orders, and individually at the (b) 1st, (c) 2nd, (d) 3rd order mode.(a)(b)Fig. 3. (a) Dependence of the resonance frequency on the cantilever lengthat the first three modes. (b) The linear fit of the measured resonancefrequency with 1/L2 for the first three modes.021001-2© 2024 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 17, 021001 (2024) G. Chen et al.wplp r r= = = ( )ftLEktLE2 2 12, 1nn nn22 2where n refers to the vibration mode number. λ takes valuesof 1.875, 4.694, 7.855, (2n−1) π/2 ∙∙∙ (n = 1, 2, 3, n > 3 ∙∙∙).k1 = 0.162, k2 = 1.012, and k3 = 2.835. ω, E, L, t, and ρrepresent the angular resonance frequency, Young’s mod-ulus, cantilever length, thickness, and mass density,respectively.26,27) For the SCD cantilever in this study,E = 1100 GPa and ρ = 3.5 g cm−3, respectively. As revealedin Fig. 3, the variation of the resonance frequency versuslength exhibits remarkable consistency between experimentaland theoretical results for all the three modes.Higher-order modes are pursued in AFM imaging, whichare more sensitive to the position of the probe, an additionalmass, and application of force.28) In the meantime, the Qfactor determines the image resolution and resonanceamplitude. Therefore, optimizing the f·Q product is ofcritical importance that directly influences the measurementband width and vibration amplitude.29) We obtained the Qfactors by using the band width method through aLorentzian fitting of the frequency spectra. We show therelationship between the cantilever length and both Q factorand f‧Q product, respectively, as presented in Fig. 4(a).Significantly, the f‧Q product for higher-order vibrationsremarkably exceeds that of the fundamental mode.Furthermore, the f‧Q product exhibits a decrease with anincrease in cantilever length due to the reduction inresonance frequency. A comparative assessment of the Qfactor and f‧Q product in the first three modes is depicted inFig. 4(b). It becomes apparent that the f‧Q for the SCDcantilevers experiences a substantial increase with higher-order resonances. Specifically, the third order mode exhibitsa f‧Q value of approximately ∼1010 Hz, marking a nearlyfifteen-fold enhancement compared to the first order mode.However, due to the ion-implantation induced defects in thediamond cantilever, the Q factor is similar for differentresonance orders. This highlights that the f·Q value isgreatly enhanced through the utilization of higher-orderresonance modes.We investigated the dissipation mechanisms of the higher-order resonance modes. Since the measurements were con-ducted in high vacuum environment, the air damping isneglected. The overall Q factor is determined by thefollowing diverse dissipation mechanisms= + + +- - - - - ( )Q Q Q Q Q , 21clamp1TED1MD1surface1where clamp, TED, MD, and surface signify the Q factorsattributed to the energy loss mechanisms of clamping losses,thermoelastic damping, mechanical defects, and surface loss,respectively.30,31) Higher-order resonances are shown tosuffer less from clamping loss compared to the fundamentalmode.31) This is possibly because higher-order resonancesstore a larger amount of mechanical energy at nodes that aresituated farther away from the clamping points.32)Thermoelastic loss does not dominate due to QTED exceeding107 at room temperature.33) The crystal quality of diamondaffects the Q factor of the diamond cantilevers.25,34) In ourcase, we disclosed that the diamond cantilever has single-crystal nature by high-resolution transmission electron micro-scope. 20) However, considering that the smart-cut method forthe SCD cantilever fabrication involves a high-energy ionimplantation, the ion-irradiated defects determine the ultimate(a) (c)(b) (d)Fig. 4. Dependence of Q and f‧Q on cantilever lengths (a), resonance orders (b), for diamond cantilever 1–3. (c) Resonance frequency spectrum, and (d) ring-down measurement of diamond cantilever 4 at the 2nd order.021001-3© 2024 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 17, 021001 (2024) G. Chen et al.Q factor. In this work, surface loss can be included in themechanical defects loss due to ion-implantation induceddefective layer at the bottom of the SCD cantilevers.20)Therefore, the relatively low Q factor can be attributed todefects induced by ion damage. By harnessing higher moderesonance, we are able to achieve the f‧Q product comparableto that of the SCD cantilevers fabricated using the transfertechnique, which boosts a Q factor exceeding 1 million.19)This enhancement of f‧Q was achieved without the need foradditional materials processing such as prolonged annealingor etching.20,35)Based on the discussion described above, we fabricated ahigher Q factor diamond resonator (cantilever 4), by removingthe defects within the cantilevers based on the atomic scaleetching.20) The resonance frequency of the 1st order mode is342.14 kHz and the 2nd order is 2.08MHz. In Fig. 4(c), theresonance frequency spectrum of cantilever 4 in the 2nd ordermode is presented. Since the resonance frequency of the 3rdorder mode is out of the limit (3MHz) of the setup, we solelypresent data for the 2nd order mode. To achieve greateraccuracy beyond the frequency resolution limit, we employedring-down measurements to obtain the Q factors. These Qfactors were then calculated by Q = πτf, where τ representsthe characteristic decay time of the resonator. The ring-downplots in Fig. 4(d) illustrate a decay time of 94.26 ms and anultrahigh Q factor over 6 × 105 in the 2nd order resonance.Remarkably, we achieved a high f‧Q product over 1012 Hz forthe 2nd order mode. This value is the highest in SCDcantilevers up to date.36)In conclusion, we investigated the higher-order reso-nances in SCD cantilevers. The resonance frequency ofdiamond cantilevers remained consistent in both experimentand theory under higher-order modes. Despite the low Qfactor dominated by the crystal defects within the cantilever,the f‧Q product was remarkably improved by over 15 timesrelated to the fundamental mode resonance. We achieved anunprecedented ultrahigh f‧Q product over 1012 Hz within ahigher-order resonance mode of a SCD cantilever.Acknowledgments This work was supported by JSPS KAKENHI (GrantNos. 20H02212, 22K18957, 15H03999), Bilateral joint research between JSPS/CAS, Advanced Research Infrastructure for Materials and Nanotechnology inJapan (ARIM) of MEXT (JPMXP1223NM5297), and European Union’s Horizon2020 Marie Skłodowska-Curie project (GA No 101027489). Guo Chen thankedto financial support from China Scholarship Council (No. 202006400023).ORCID iDs Meiyong Liao https://orcid.org/0000-0003-1361-42661) H. Sun, X. Shen, L. Sang, M. Imura, Y. Koide, J. You, T.-F. Li, S. Koizumi,and M. Liao, Appl. Phys. Express 14, 045501 (2021).2) Z. Zhang, G. Chen, K. Gu, S. Koizumi, and M. Liao, Funct. Diam. 3,2221280 (2023).3) R. Hajare, V. Reddy, and R. Srikanth, Mater. Today Proc. 49, 720 (2022).4) H. Sun, Z. Zhang, Y. Liu, G. Chen, T. Li, and M. Liao, Adv. QuantumTechnol. 6, 2300189 (2023).5) T. Yamada, Y. 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