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## Creator

[Zilong Zhang](https://orcid.org/0000-0002-9759-9253), Wen Zhao, Guo Chen, Masaya Toda, [Satoshi Koizumi](https://orcid.org/0000-0003-4961-5658), [Yasuo Koide](https://orcid.org/0000-0001-8321-9822), [Meiyong Liao](https://orcid.org/0000-0003-1361-4266)

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This is the peer reviewed version of the following article: On-chip Diamond MEMS Magnetic Sensing through Multifunctionalized Magnetostrictive Thin Film, which has been published in final form at https://doi.org/10.1002/adfm.202300805. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[On-chip Diamond MEMS Magnetic Sensing through Multifunctionalized Magnetostrictive Thin Film](https://mdr.nims.go.jp/datasets/f4a8a5a6-3540-4874-a7f0-2069170a14d2)

## Fulltext

1  On-chip diamond MEMS magnetic sensing through multifunctionalizing 1 magnetostrictive thin film  2 Zilong Zhang1, Wen Zhao2, Guo Chen1, Masaya Toda3, Satoshi Koizumi1, Yasuo Koide1, 3 Meiyong Liao1* 4 1 Research Center for Functional Materials, National Institute for Materials Science (NIMS), 1-5 1 Namiki, Tsukuba, Ibaraki 3050044, Japan 6 2 Physical Sciences and Engineering Division, King Abdullah University of Science and 7 Technology, Thuwal, Saudi Arabia 8 3 Graduate School of Engineering, Tohoku University, Sendai, Miyagi 9808579, Japan 9 Correspondence should be addressed to Meiyong Liao* (Email: meiyong.liao@nims.go.jp) 10  11 Abstract 12 Electrically integrable, high-sensitivity, and high-reliability magnetic sensors have not yet 13 been realized at high temperatures (500 °C). In this study, we demonstrate an integrated on-14 chip single-crystal diamond (SCD) micro-electromechanical system (MEMS) magnetic 15 transducer by coupling SCD with a large magnetostrictive FeGa film. The FeGa film is 16 multifunctionalized to actuate the resonator, self-sense the external magnetic field, and 17 electrically read the resonance signal. The on-chip SCD MEMS transducer shows a high-18 sensitivity of 3.2 Hz/mT from room temperature to 500 °C and a low noise level of 9.45 19 nT/Hz1/2 up to 300 °C. The minimum fluctuation of the resonance frequency is 1.9 × 10-6 at 20 room temperature and 2.3 × 10-6 at 300 °C. An SCD MEMS resonator array with parallel 21 electric readout is subsequently achieved, thus providing a basis for the development of 22 magnetic image sensors. The present study facilitates the development of highly integrated on-23 chip MEMS resonator transducers with high performance and high thermal stability. 24  25 Keywords: Single-crystal diamond, MEMS, on-chip actuation and sensing, magnetic sensor  26  27  28  29   2  1. Introduction  30 Real-time health care of human beings for Internet of Things, precise biomedical diagnosis, 31 and infrastructure maintenance, particularly under extreme conditions, increases the immediate 32 demand for developing integrated magnetic sensing technology with high sensitivity, high 33 reliability, low power consumption, and minimized size.[1-8] The current magnetic sensors 34 primarily include superconducting quantum interference device (SQUID) sensors, Hall sensors, 35 fluxgate sensors, magneto-resistive (MR) sensors, nitrogen-vacancy (NV) sensors, and micro-36 electromechanical system (MEMS) sensors.[2, 9-14] The SQUID sensors with the highest 37 magnetic resolution of fT level require high cost and liquid nitrogen/helium as a refrigerant, 38 which render them less advantageous compared with other magnetic sensors.[15] For Hall 39 sensors, their low sensitivity and resolution limit their performance and applications.[14] 40 Fluxgate sensors require complex processes to fabricate their magnetic cores and coils, which 41 feature large masses and high power consumption.[16] The restricted magnetic field magnitude 42 appearance of MR sensors suppresses their application regimes.[17] Another promising magnetic 43 sensor is based on the NV center in diamond, which in principle shows high sensitivity and 44 nanoscale resolution. However, the controllability of the NV center and the electrical readout 45 of NV signals are challenging.[18-20] MEMS technology exhibits the merits of batch fabrication, 46 controllability in dimensions down to the nanoscale, low power consumption, low cost, high 47 sensitivity, and high integration.[21] 48 In addition, for harsh application fields such as mineral/oil exploration, space exploration, 49 high-temperature magnetic valves, and engine and transmission speed control in cars, magnetic 50 sensors with high thermal-stability performance are in high demand.[22, 23] Recently, the main 51 high-temperature magnetic sensors, including MR sensors, fluxgate sensors, and Hall sensors, 52 are affected by material and physical limitations under extreme conditions, which result in low 53 sensitivity, weak thermal stability, and restrained operating temperatures.[24-26] MEMS 54 resonators coupled with soft magnetic materials provide a new paradigm for fabricating various 55   3  magnetic transducers.[27, 28] Furthermore, a MEMS resonator array with high integration can be 56 developed, which yields efficient and precise special mapping of magnetic fields.[29] To develop 57 MEMS magnetic sensor arrays, all electrical actuation and sensing are necessary for integration 58 with electronics. 59 Single-crystal diamond (SCD) is a promising material for high-performance and high-60 reliability MEMS devices owing to its outstanding physical, chemical, mechanical, and 61 electrical properties.[30-42] SCD MEMS resonators combined with galfenol (FeGa), a material 62 with a large magnetostrictive coefficient of 375 ppm and an ultrahigh Curie temperature of 63 675 °C, provide an ideal scheme for high-sensitivity and thermal-stability magnetic transducers 64 via the delta-E (ΔE) effect.[43, 44] To achieve highly integrated high-sensitivity SCD MEMS 65 transducers, all-electrical on-chip actuation and sensing are required.[45] The piezoelectric effect 66 and electrostatic or dielectric actuation with capacitive sensing were developed to fulfill the 67 functions of actuation and readout.[46-49] The piezoelectric method offers an efficient route with 68 high electromechanical coupling efficiency, but the energy dissipation induced by the 69 multilayer degrades the sensitivity. The dielectric actuation overcomes the energy dissipation 70 problem, and an off-chip bulky optical readout was achieved.[50] For highly integrated MEMS 71 magnetic sensors, a scheme with multiple functions including actuation, sensing, and signal 72 readout is desired. In this study, we propose and demonstrate an on-chip SCD MEMS magnetic 73 sensor by multifunctionalizing a magneto-strictive FeGa film for harmonic actuation, magnetic 74 sensing, and resonance signal readout. To enhance adhesion at the interface between FeGa and 75 the SCD, a Ti thin film was added to form a FeGa/Ti/SCD magnetic transducer. The magnetic 76 transducer fulfilled magnetic transducing performance with high-temperature operation up to 77 500 °C, a sensitivity of 3.2 Hz/mT from room temperature to 500 °C, and a low noise level of 78 9.45 nT/Hz1/2 at 300 °C. The fluctuation of the resonance frequency was 1.9 × 10-6 at room 79 temperature and 2.3 × 10-6 at 300 °C. Furthermore, a prototype magnetic transducer array based 80 on on-chip FeGa/Ti/SCD MEMS magnetic transducers was developed. This study provides a 81   4  promising strategy for developing highly integrated MEMS magnetic transducers with high 82 performance and reliability, which are superior to the present magnetic transducers. 83 2. Results and Discussion 84 SCD cantilevers with an SCD-on-SCD structure provide a robust platform for fabricating 85 MEMS magnetic transducers. The fabrication process of the SCD cantilever-based magnetic 86 transducer is shown in Figure S1 (Supporting Information). First, bare SCD cantilevers were 87 fabricated via the smart-cut technique, which primarily includes carbon ion implantation, 88 diamond growth, photolithography treatment, metal mask deposition, reactive ion etching, and 89 structure release. The bare SCD cantilevers fabricated via this technique exhibit high reliability 90 and high Q factors. The details of this approach for batch production are available in our 91 previous publication.[51, 52] Subsequently, a 2-nm-thick Ti film followed by a 90-nm-thick FeGa 92 film was deposited on the bare SCD cantilevers using a magnetron sputtering system, followed 93 by a 1-nm-thick Ti film and a 7-nm-thick Au film using an e-beam evaporator system. The 90 94 nm FeGa thin film is a trade-off for the quality  (Q) factor of the SCD resonator and the 95 optimization of the magnetic properties of the FeGa thin film. The thick FeGa film resulted in 96 a reduced Q factor, whereas the thin FeGa film degraded the magnetic properties. 97 2.1 Resonator elasticity vibration theory  98 The mechanical vibration characteristics of a rectangular uniform cantilever beam can be 99 described and analyzed based on the Euler–Bernoulli law (see the SI).[53] The resonance 100 frequency of the fundamental (first) mode is expressed as 101 𝑓 = 0.162𝑡𝑡ℎ𝐿2√𝐸𝜌,           (1) 102 where E and ρ are the Young’s modulus and mass density of the beam, respectively; and L and 103 tth denote beam length and thickness, respectively. The resonance frequency is determined by 104 the dimensions and material properties of the cantilever.  105 2.2 Self-sensing and actuation of cantilever resonance  106   5  In this study, Au/FeGa/Ti was deposited on the SCD substrate as the gate (G) electrode 107 for on-chip actuation and on the SCD cantilevers as source–drain (S–D) electrodes to sense the 108 magnetic fields and electrically readout the resonance signal. Figure 1a shows the actuation 109 and readout circuits of the on-chip SCD resonator. The ultimate optical feature of a 160-μm-110 long SCD cantilever magnetic transducer is shown in Figure 1b. A radio-frequency (RF) signal 111 with an amplitude of Vac g and a frequency of ω was applied to the G electrode. Another RF signal 112 with an amplitude of Vac sd  and a frequency of ω+Δω was connected to the S–D electrodes to read 113 out the vibration signal. For a certain gate voltage Vg, a charge q was induced on the cantilever, 114 which is expressed as q = CgVg, where Cg is the capacitance between the G electrode and 115 cantilever. The electrostatic force results in the bending of the cantilever. In this study, Vg = V116 ac g cos(ωτ). The total energy stored in the capacitor is Een g =1/2Cg(z)Vg2,[54] where z is the distance 117 between the G electrode and cantilever. The total electrostatic force on the cantilever is 118 expressed as[54] 119 𝐹𝑒𝑙 =𝜕𝐸𝑒𝑛𝑔𝜕𝑧=12𝑑𝐶𝑔𝑑𝑧(𝑉𝑔𝑎𝑐𝑐𝑜𝑠 𝜔𝜏)2        (2) 120 Vac g cos(ωτ) results in a periodic electric force that causes the cantilever to vibrate. The 121 displacement of the cantilever is the largest when the driving frequency is at its resonance 122 frequency. 123 The signal readout resulting from the cantilever motion is based on the piezoresistive effect 124 of the S–D electrode on the cantilever. To characterize the output signal, a modulation 125 frequency Δω of 5 kHz was set. The output signal generated at the S electrode is a mixture of 126 signals from the G and D electrodes, which is expressed as[55, 56]  127 𝑉𝑜𝑢𝑡 =∆𝑅0𝑅+𝑅0𝑉𝑠𝑑𝑎𝑐[𝑐𝑜𝑠(∆𝜔𝜏 − 𝜑) + 𝑐𝑜𝑠((2𝜔 + ∆𝑤) 𝜏 + 𝜑)],     (3) 128 where R is the circuit resistance; R0 is the resistance of the electrode deposited on the cantilever, 129 which is approximately 100 Ω; Vac sd  is the voltage applied to the S–D electrodes; and ΔR0 130 represents the resistance change of the metal electrode on the cantilever owing to its vibration 131   6  motion. The bias signal mixes with the vibration motion of the metal electrode and generates 132 signals at frequencies Δω and 2ω+Δω. A low-pass filter was utilized to filter the frequency of 133 2ω+Δω. The remaining signals were fed into a lock-in amplifier for the readout. The output 134 signal at a frequency of Δω is expressed as 135 𝑉𝑜𝑢𝑡 =∆𝑅0𝑅+𝑅0𝑉𝑠𝑑𝑎𝑐 𝑐𝑜𝑠(∆𝜔𝜏 − 𝜑)        (4) 136 The amplitude of the output voltage reached its maximum value when the cantilever vibrated 137 at its resonance frequency. Thus, the SCD cantilever with the actuation and sensing structure 138 can realize the actuation and detection of mechanical motion. This actuation and sensing 139 scheme provides a strategy to design MEMS devices with an electrical interface for integration 140 with electronics.  141 2.3 Magnetic sensing principle based on ΔE effect 142 For a magnetostrictive material, the Young’s modulus changes during the magnetization 143 process, which is known as the ΔE effect.[57, 58] The ΔE effect is expressed as  144 ∆𝐸 = 𝐸0 − 𝐸𝐻,          (5) 145 where E0 and EH are Young’s moduli of the material without and with the application of a 146 magnetic field, respectively. The ΔE effect of the ferromagnetic thin film deposited on the SCD 147 cantilever is regarded as the magnetic sensing principle. Figure 1c schematically shows the 148 fundamental sensing principle of the magnetic transducer based on the SCD cantilever structure. 149 By applying an external magnetic field, the SCD cantilever is subjected to bending stress 150 induced by the FeGa film. The shape of the FeGa film varies depending on the ΔE effect, which 151 results in a change in its Young’s modulus. Consequently, the effective Young’s modulus of 152 the SCD-based cantilever with multiple layers changes. Subsequently, the resonance frequency 153 of the SCD-based cantilever shifts owing to the ΔE effect. The magnetic sensitivity of the SCD-154 based cantilever transducer is characterized as the resonance frequency response to the 155 magnetic field. 156   7  2.4 Fundamental mechanical resonance 157  158 Figure 1. Measurement setup and resonance performances of the SCD-based resonators. A) 159 Schematic diagram of the measurement setup for the SCD-based cantilever magnetic transducer 160 with the on-chip self-sensing and actuation configuration. LPF: low frequency filter. B) Optical 161 images of a 160-μm-long SCD-based cantilever magnetic transducer. C) Magnetic sensing 162 principle of a cantilever resonator with resonance frequency shift. D) Schematic image of the 163 measurement setup with an optical readout system. E) Simulation of the electric field 164 distribution of a SCD-based resonator with on-chip actuation. S–D electrodes are grounded and 165 Vac g  = 1 V. F) Typical resonance frequency spectra of a 160-μm-long SCD-based cantilever. 166 Inset shows the motion amplitude with linear dependence on the gate voltage. G) Resonance 167 frequencies and H) Q factors of SCD-based cantilevers dependence on length L without and 168 with deposition of FeGa/Ti film. 169  170 To investigate the harmonic oscillation characteristics of SCD-based cantilevers, the S–D 171 electrodes were grounded and the G electrode was connected to an RF signal source. A laser 172 Doppler vibrometer was utilized to analyze the harmonic signal of the SCD-based oscillator, as 173 shown in Figure 1d.[51, 52] The electric field distribution of the SCD-based oscillator was 174   8  simulated using the COMSOL software as the S–D electrodes were grounded and Vac g  = 1 V, 175 which reflected the electric field confined around the SCD cantilever (Figure 1e and Figure 176 S2, Supporting Information) The gate voltage did not significantly affect the resonance 177 frequency (Figure 1f) and linearly enhanced the amplitude of the resonance spectrum (the inset 178 of Figure 1f). The dependence of the resonance frequency on the length of the oscillator with 179 and without the deposition of FeGa/Ti films is depicted in Figure 1g. The dependences of the 180 resonance frequency of the SCD-based oscillator with and without FeGa/Ti films on the length 181 agreed well with Equation 1. The Q factors of the SCD oscillators decrease after the deposition 182 of the FeGa/Ti films (Figure 1h and Equation S6, Supporting Information) but remained as 183 high as approximately 4000. 184  185 Figure 2. Resonance performances of the SCD-based cantilever transducer with on-chip 186 actuation and sensing scheme. A) Resonance frequency spectra of a 160-μm-long SCD-based 187 cantilever transducer measured by the electrical readout system at various Vac sd  and Vac g =3 V 188 @25 °C. The resonance frequency shifts downward as Vac sd  increases. B) Dependences of Q 189 factors on Vac sd  at Vac g =3 V @25 °C. C) Resonance frequency spectra of a 160-μm-long SCD-190 based cantilever transducer measured by the electrical readout system at various Vac g  and Vac sd  = 191 8 V @25 °C. D) Variations in Q factors with Vac g  at Vac sd  = 8 V. E) Resonance frequency spectra 192 of a 160-μm-long SCD-based cantilever transducer measured via the electrical readout system 193   9  from 25 °C to 500 °C at Vac sd  = 3 V and Vac g  = 7 V. F) Resonance frequencies and Q factors as a 194 function of temperature. 195  196 The measurement setup for the on-chip sensing and actuation of the SCD cantilevers 197 through an electrical system has been previously described (Figure 1a). The resonance 198 frequency spectra of a 160-μm-long SCD-based oscillator were customized by changing Vac sd  to 199 Vac g  = 3 V at 25 °C, as shown in Figure 2a. The resonance frequency spectrum shifted downward 200 as Vac sd  increased, whereas the resonance frequency amplitude increased with Vac sd . The reduction 201 in resonance frequency, which is known as the “softening” of the SCD-based oscillator, may 202 be attributed to two reasons:1) the existence of an electric field force gradient and 2) Joule 203 heating from the S–D electrodes. When an external electric field Vac sd  is applied, the resonance 204 frequency of the cantilever oscillator can be expressed as f≈f0+α(Vac sd )2/(mf0),[59] where α is the 205 coefficient related to the SCD polarizability and electric field gradient, f0 is the resonance 206 frequency of the oscillator without an electric field force, and m is the oscillator mass. The 207 resonance frequency exhibits a square relationship with Vac sd , as shown in Figure S3 208 (Supporting Information). Furthermore, the inset of Figure S3 (Supporting Information) 209 shows that the ratio of the resonance frequency variation (Δf = f - f0) to f0 increases linearly with 210 (Vac sd )2. Meanwhile, the local temperature of the SCD cantilever increases with Vac sd , which 211 decreases the effective Young’s modulus and thus induce a downward shift of the resonance 212 frequency. The function of the resonance frequency shift with the temperature coefficient of 213 Young’s modulus is expressed as[60] 214 ∆𝑓𝑓≈12∆𝐸𝐸≈12𝛼𝐸𝑑𝑇𝑑𝑊𝑊 ∝ (𝑉𝑠𝑑𝑎𝑐)2,        (6) 215 wherein αE = dE/(EdT); and W is the input electrical energy, which is proportional to (Vac sd )2. 216 Thus, Δf/f exhibits a linear relationship with (Vac sd )2. The exact reason for the downward shift of 217 the resonance frequency of the cantilever oscillator is yet to be confirmed. The plot of the Q 218 factor vs. Vac sd  is presented in Figure 2b, which shows that the Q factor decreases as Vac sd  increases. 219   10  A more accurate analysis should consider the thermal mismatch between diamond and FeGa, 220 which does not affect the magnetic sensitivity for a certain S–D voltage. 221 The resonance frequency spectra of the SCD-based resonator were characterized by 222 varying Vac g  at Vac sd  = 8 V and room temperature (Figure 2c). The resonance frequency shifted 223 downward as Vac g  increased, as shown in Figure S3 (Supporting Information). For a cantilever 224 beam, the resonance frequency is determined by the uniaxial compressive stress, σ of the 225 cantilever beam, which is expressed as[61] 226 𝑓 = 𝑓0(1 + 0.295𝜎𝐿2𝐸𝑡2)1/2         (7) 227 According to Equation 2, σ can be increased by adopting a higher value of Vac g . Thus, the 228 decrease in the resonance frequency with a higher Vac g  indicates that σ is a tension stress. This 229 is different from the case of the optical readout without applying an S–D voltage. The Q factor 230 shows a weak dependence on Vac g  (Figure 2d). The thermal stability of the resonance 231 performance of the SCD-based oscillator was examined as the temperature increased from 232 25 °C to 500 °C. The temperature dependence of the resonance frequency spectra of the SCD-233 based oscillator is shown in Figure 2e. Vac sd  and Vac g  were fixed at 3 and 7 V, respectively. The 234 temperature increase resulted in a decrease in the effective Young’s modulus of the multilayer 235 structure, which caused a downward shift in the resonance frequency (Figure 2f). Alternatively, 236 the temperature coefficient of the resonance frequency (TCF) was used to demonstrate the 237 thermal stability of the SCD-based oscillator (Figure S4, Supporting Information). The TCF 238 of SCD-based oscillators with various lengths can remain lower than 13 ppm/K, which is 239 superior to that of Si with a value of 35 ppm/K.[62] The Q factor of the SCD-based oscillator 240 decreased at high temperatures but remained as high as 1500 even at 500 °C. 241 2.5 Magnetic transducing at high temperatures 242   11   243 Figure 3. High-temperature magnetic transducing performance through on-chip actuation and 244 sensing. A) Resonance frequency shift of a 160-μm-long SCD-based cantilever transducer as a 245 function of the measurement temperature at a magnetic field of 2.82 mT, and at Vac sd  = 4 V and 246 Vac g  = 7 V from 25 °C to 500 °C. The peak amplitude of the etch spectrum is normalized. B) 247 Resonance frequency shifts of the magnetic transducer vs. the measurement temperature at 248 different magnetic fields. C) Q factor variations of the magnetic transducer vs. temperature 249 without and with applying a magnetic field of 2.82 mT. D) Magnetic noise spectra of the 250 magnetic transducer at 25 °C and 300 °C. 251  252 Based on the high thermal stability of SCD-based cantilevers with the on-chip actuation 253 and sensing structure, the magnetic transducing of the SCD-based magnetic transducers from 254 25 °C to 500 °C was realized through the ΔE effect. The dependence of the resonance frequency 255 shift on the magnetic field was utilized to indicate the magnetic sensitivity of the SCD-based 256 transducer. The magnetic sensitivity is defined as f = |fr0-frH|, where frH and fr0 represent the 257 resonance frequencies of the SCD-based transducer with and without the magnetic field, 258 respectively. Figure 3a shows the resonance frequency spectra shift of the 160-μm-long SCD-259   12  based magnetic transducer caused by applying a magnetic field of 2.82 mT with the temperature 260 increasing from 25 °C to 500 °C. The resonance frequency shifted as a function of the magnetic 261 fields tuned via temperature (Figure 3b). The resonance frequency shift increased with the 262 magnetic field. The SCD-based magnetic transducer with on-chip actuation and sensing 263 exhibited a stable magnetic sensitivity of 3.2 Hz/ mT at various temperatures. Therefore, the 264 on-chip SCD MEMS magnetic sensor with all-electrical actuation and sensing is robust at high 265 temperatures up to 500 °C. Another SCD-based transducer demonstrates similar magnetic 266 sensing performances (Figure S5, Supporting Information). To some extent, the Q factors of 267 the SCD-based magnetic transducer decreased as temperature increased (Figure 3c). However, 268 the overall magnetic sensing performance did not change significantly as the temperature 269 increased. In addition, the magnetic noise spectra resulting from the thermomechanical noise 270 of the SCD-based magnetic transducer were measured at 25 °C and 300 °C, as shown in Figure 271 3d. The magnetic noise levels of the SCD-based magnetic transducer reached a low level of 272 7.81 nT/Hz1/2 at 25 °C and 9.45 nT/Hz1/2 at 300 °C. For the MEMS magnetic transducer with 273 the oscillator structure, the intrinsic magnetic noise (bn) can be expressed as[63, 64] 274 𝑏𝑛 =12𝜇0𝑑𝐻𝑑𝑓√2𝜋𝑘𝐵𝑇𝑓𝑟0𝑄𝑉𝜎′bn,         (8) 275 which is utilized to predict the theoretical magnetic noise at the resonant frequency fr0. Here, 276 μ0(dH/df) is the magnetic sensitivity of the magnetic transducer, T the temperature, and V the 277 device volume. The stress, σ', is calculated from fr0, which is discussed in our previous 278 publication.[27] Based on the magnetic sensing performance of the 160-m-long on-chip 279 magnetic transducer, the intrinsic magnetic noises of the magnetic sensor were estimated as 280 0.632 nT/Hz1/2 at 25 °C, 0.825 nT/Hz1/2 at 300 °C, and 1.09 nT/Hz1/2 at 500 °C. Additionally, 281 the Allan deviation of the SCD-based magnetic transducer was investigated (Figure S6, 282 Supporting Information). The minimum fluctuation of the resonance frequency up to 300 °C 283 was 2.3 × 10-6. Based on the magnetic sensitivity, the minimum detectable magnetic fields for 284   13  the SCD-based magnetic transducer were calculated to be 2.0210-11 T (20.2 pT) and 3.47 10-285 11 T (34.7 pT) at 300 K and 773 K, respectively. Meanwhile, based on the stable magnetic 286 sensitivity, high Q factors result in low magnetic noise levels. To improve the magnetic 287 sensitivity of the SCD-MEMS magnetic transducer, smaller thickness of tens of nanometers in 288 SCD resonators is preferred. However, for high-speed response, high-frequency resonators with 289 shorter length (i.e. micrometer scale)  are desirable. A larger thickness of the FeGa film is 290 favorable as well, but a trade-off with the Q factor should be considered. The high-temperature 291 magnetic sensing performances of various representative high-temperature magnetic sensors 292 were compared with those of the present sensor in terms of magnetic sensitivity, magnetic noise, 293 and thermal stability, as summarized in Table 1. The on-chip magnetic sensor in this study 294 exhibits superior sensitivity, lower noise level, and higher thermal reliability compared with 295 other magnetic sensors.  296 Table 1. High-temperature sensing performance comparison of various high-temperature 297 magnetic sensors. 298 Magnetic sensor Materials Magnetic sensitivity Noise level Operating temperature Stable operating duration Ref. AMR Si-based -- ~2.6 nT/Hz1/2  498 K >2000 h [65] Hall Si -- >82 nT/Hz1/2 673 K -- [66] Hall AlGaN/ GaN -- 35 μT/√Hz1/2 873 K -- [67] Hall 4H-SiC 80 V/(A∙T) -- 770 K -- [68] Fluxgate Cu coil -- 0.79 nT/Hz1/2 523 K >100 h [26] MEMS FeGa/Ti/ SCD 3.2 Hz/mT 9.45 nT/Hz1/2 573 K >100 h This study  299   14   300 Figure 4. Magnetic transducing performances with changing Vac sd  and Vac g at room temperature. 301 A) Resonance frequency spectra of a 160 μm-long SCD-based magnetic transducer response to 302 a magnetic field of 2.82 mT by changing Vac sd  at Vac g  = 3 V. B) Tuning of resonance frequency 303 shift of the magnetic transducer via Vac sd  under a magnetic field of 2.82 mT at Vac g  = 3 V. C) 304 Dependence of Q factors of the magnetic transducer on Vac sd  without and with a magnetic field 305 of 2.82 mT. Vac g  is fixed at 3 V. D) Resonance frequency spectra of the magnetic transducer 306 response to a magnetic field of 2.82 mT by changing Vac g  at Vac sd  = 3 V. E) Resonance frequency 307 shifts of the magnetic transducer as a function of Vac g  under a magnetic field of 2.82 mT at Vac sd  308 = 3 V. F) Variation in Q factors of the magnetic transducer as Vac g  without and with a magnetic 309 field of 2.82 mT. Vac sd  is fixed at 3 V. 310  311 The effects of Vac sd  and Vac g  on the the magnetic sensing performance of the on-chip magnetic 312 transducer are investigated. Figure 4a shows the dependences of the resonance frequency 313 spectra shift of the SCD-based magnetic transducer on Vac sd  with or without applying a magnetic 314 field (H = 2.82 mT) at 25 °C and Vac g  =3 V. The solid and dashed lines represent the resonance 315 frequency spectra without and with the application of the magnetic field, respectively. Although 316 the resonance amplitude increased with Vac sd , the resonance frequency of the on-chip magnetic 317 transducer was barely affected by Vac sd  (Figure 4b) under a magnetic field. The Q factors of the 318 on-chip magnetic transducer without and with the magnetic field decreased as Vac sd  increased 319   15  (Figure 4c). The possible reasons have been discussed in the previous section. Thus, a suitable 320 Vac sd  should be selected with regard to two aspects: (1) a sufficient voltage to achieve a high 321 signal readout and (2) minimal impact on the Q factor. Figure 4d shows the effect of Vac g  on the 322 resonance frequency shift of the on-chip transducer with or without the application of a 323 magnetic field (H = 2.82 mT) at 25 °C and Vac sd  = 3 V. Similarly, the amplitude of the resonance 324 frequency with and without the application of the magnetic field increased with Vac g , as shown 325 in Figure 4e. Vac g  did not significantly affect the resonance frequency shift or Q factor when the 326 magnetic field was applied, as shown in Figures 4e and f. 327  328 Figure 5. Magnetic transducing of a transducer array. A) Measurement setup for an SCD-based 329 magnetic transducer array with the on-chip actuation and sensing configuration. The length and 330 width of each cantilever sensor were 120 and 10 µm, respectively. B) The magnetic flux density 331 in the xoy plane of a cylindrical magnet is simulated using the COMSOL software. The 332 magnetization of this magnet merely occurs in the y-axis direction, showing a magnetic 333 susceptibility of 1032000 A/m. The height and radius of the cylindrical magnet were 2 and 1 334   16  cm, respectively. C) Resonance frequency spectra shifts of the magnetic transducer array due 335 to the application of a 2.82 mT magnetic field at Vac sd  = 10 V and Vac g  = 10 V @25 °C. The 336 magnetic transducer array comprised four SCD-based magnetic sensors. 337  338 Finally, we demonstrate an SCD-based magnetic transducer array comprising four on-chip 339 magnetic transducers integrated on the same chip for magnetic transducing with all-electrical 340 actuation and sensing. Figure 5a shows an on-chip SCD-based magnetic transducer array. 341 COMSOL software was utilized to simulate the magnetic flux distribution of a two-dimensional 342 plane of a cylindrical magnet (Figure 5b). Owing to the independent resonance vibration of 343 each magnetic transducer, the parallel signal readout of the four magnetic transducers was 344 realized. The resonance frequency spectra of the magnetic transducer array exhibited four peaks 345 without and with the application of a magnetic field of 0.28 mT, respectively, as depicted in 346 Figure 5c. The resonance frequencies shifted downward in the magnetic transducer array 347 because of the ΔE effect. A view of the resonance frequency shift with the application of a 348 magnetic field is shown in Figure S7 (Supporting Information). Alternatively, applying a 349 magnetic field exhibited a weak effect on the Q factor of each magnetic sensor in the magnetic 350 transducer array (Figure S7, Supporting Information). The successful realization of the 351 magnetic sensing of the SCD-based magnetic transducer array is a first step toward the 352 development of robust magnetic image sensors with high sensitivity and spatial resolution. 353  354 3. Conclusion 355 In summary, we proposed and demonstrated an all-electrical on-chip diamond MEMS 356 magnetic sensor by integrating magnetostrictive FeGa with an SCD MEMS resonator. The 357 magnetostrictive FeGa film functioned as an actuation electrode, a sensing head for magnetic 358 fields, and an electrical readout unit. The SCD-based MEMS magnetic transducer exhibited 359 high-temperature operation up to 500 °C with a high-sensitivity of 3.2 Hz/mT and a low noise 360   17  level of 9.45 nT/Hz1/2 at 300 °C. The minimum fluctuation of the resonance frequency reached 361 1.9 × 10-6 at room temperature and 2.3 × 10-6 at 300 °C. The prototype SCD-based MEMS 362 magnetic transducer array was developed with the achievement of parallel signal readout. The 363 magnetic sensing performance can be further enhanced via nanoscale size design,[69] a high 364 quality factor,[70] and a large magneto-strictive thin film.[69, 71] The current study successfully 365 demonstrated the integration of SCD-based MEMS magnetic transducers with electronics, 366 which serves as a foundation toward the development of magnetic image sensors with high 367 sensitivity, reliability, and tunable spatial resolution.  368  369 4. Experimental section 370 4.1 Fabrication of on-chip SCD-based cantilever transducers 371 The fabrication of the SCD cantilevers was begun from the homoepitaxial layers grown 372 on the high-pressure high-temperature (HPHT) SCD substrates. Before the diamond growth, 373 the HPHT SCD substrates were orderly cleaned in boiling mixture acids (H2SO4+HNO3), 374 acetone, ethanol, and deionized water. Then, the cleaned HPHT SCD substrates were undergone 375 the implantation treatment of carbon ions at an energy of 180 keV and a dose of 1016 cm−2. The 376 diamond epilayers were grown on the HPHT SCD substrates via a microwave chemical vapor 377 deposition (MPCVD) facility with growth parameters of a methane concentration of 1 %, a 378 hydrogen flow of 500 sccm, a microwave power of 1000 W, a substrate temperature of 880°C 379 and a growth duration of 2 h. During the diamond growth, a 200 nm-thick graphite-like layer 380 resulted from the ion implantation was formed under the diamond surface, which was acted as 381 a sacrificial layer to produce the cantilever structure. The structure of the graphite-like layer 382 was characterized through a transmission electron microscopy (TEM) technique, as shown in 383 detail in our pervious works.[72, 73] The existence of the graphite-like layer had little impact on 384   18  the crystal quality of the SCD epilayer, as disclosed by Raman spectroscopy mapping (Figure 385 S8, Supporting Information). The graphite-like layer was removed through wet or dry etching 386 to release the SCD cantilevers. Thus, the graphite-like layer has weak influence on the sensing 387 performance of the SCD-based magnetic transducers. However, the diamond at the bottom of 388 the cantilever was defective due to the ion implantation. To eliminate this damage, the SCD 389 samples were annealed at 1100°C for 3 h in an ultrahigh vacuum condition (~10-7 Pa). However, 390 we could not identify the damage induced by the ion-implantation through TEM and Raman. 391 By contrast, the Q factors of the SCD cantilevers were improved after annealing at 1100℃ 392 (Figure S9, Supporting Information). A laser photolithographic approach was utilized to 393 pattern the SCD samples and fabricate the SCD cantilevers.[32] 394 A further laser photolithography process was utilized to pattern the on-chip SCD 395 cantilevers with the actuation and sensing structure. A 2 nm-thick Ti film followed by a 90 nm-396 thick FeGa film was deposited on the SCD cantilevers by a magneto sputtering system. The 397 FeGa film was regarded as actuation electrode, magnetic transducing component, and electrical 398 readout unit. The growth conditions of the Ti and FeGa films were: a Ar flow of 10 sccm, a 399 working pressure of 1 Pa, a sputtering power of 100 W, and room temperature. Alternatively, a 400 1 nm-thick Ti film followed by a 7 nm-thick Au film was deposited on SCD cantilevers as the 401 source, drain, and gate electrodes by an e-beam evaporator system. The SCD cantilever 402 configuration with an actuation and sensing configuration was confirmed by an optical 403 microscope system. 404 4.2 Optical and electrical readout of the mechanical resonance  405 The mechanical resonance properties of the SCD cantilevers without and with the 406 deposition of films including FeGa/Ti films and Au electrodes were analyzed via an optical 407 readout system with the Laser Vibormetry.  The gate electrode connected to a RF signal was 408 used to actuate the SCD cantilevers. The optical signal reflected from the vibration of the SCD 409   19  cantilevers was read out by a lock-in amplifier. The magnetic transducing performance of the 410 SCD-based magnetic transducers with the actuation and sensing structure were measured by an 411 electrical readout system. The G electrode was connected to a radio-frequency (RF) signal with 412 an amplitude of Vac g  and a frequency of ω to actuate the cantilevers. Another RF signal with an 413 amplitude of Vac sd  and a frequency of ω+Δω was applied to the S-D electrode to capture the 414 vibrational signal. The displacement of the cantilevers led to the variation in the resistance of 415 the S-D electrode. A reference signal, Δω of 5 kHz was utilized to readout the electrical signal. 416 The magnetic fields were applied by the different magnets to accomplish the magnetic 417 transducing measurement. A heater below the magnetic transducer was utilized to control the 418 temperatures from room temperature to high temperatures. The measurements were performed 419 in a vacuum chamber with a pressure lower than 10-3 Pa. 420 Supporting Information 421 Supporting Information is available from the Wiley Online Library or from the author. 422 Acknowledgments 423 This work was supported by a Grant-in-Aid of JSPS KAKENHI (no. 20H02212, 22K18957, 424 15H03999), JSPS Research Fellowship (no. 22F21341), Bilateral joint research between JSPS 425 (JPJSBP120227203) and CAS, and Nanotechnology Platform projects sponsored by the 426 Ministry of Education, Culture, Sports, and Technology (MEXT) of Japan. 427  428 Conflict of Interest  429 The authors declare no conflict of interests.  430  431 Data Availability Statement 432 The data that support the findings of this study are available on request from the corresponding 433 author.   434   20  Received: ((will be filled in by the editorial staff)) 435 Revised: ((will be filled in by the editorial staff)) 436 Published online: ((will be filled in by the editorial staff)) 437 References 438 [1] M. 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