# Fileset [perspective-20241226.pdf](https://mdr.nims.go.jp/filesets/16803d39-2726-46b6-a71c-82d89908ab02/download) ## Creator [Zilong Zhang](https://orcid.org/0000-0002-9759-9253), Keyun Gu, [Masaya Toda](https://orcid.org/0000-0003-3849-6948), [Meiyong Liao](https://orcid.org/0000-0003-1361-4266) ## Rights This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Zilong Zhang, Keyun Gu, Masaya Toda, Meiyong Liao; A perspective on diamond MEMS magnetic sensors. Appl. Phys. Lett. 10 March 2025; 126 (10): 100501 and may be found at https://doi.org/10.1063/5.0255014.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/) ## Other metadata [A perspective on diamond MEMS magnetic sensors](https://mdr.nims.go.jp/datasets/c1e8d5b7-2ae0-4bb6-9d3b-0ca9d939481f) ## Fulltext 1 A perspective on Diamond MEMS magnetic sensors 1 2 Zilong Zhang1, 2, Keyun Gu1, Masaya Toda2, and Meiyong Liao1＊ 3 1 Research Center for Electronic and Optical Materials, National Institute for Materials Science 4 (NIMS), Tsukuba, Ibaraki, Japan 5 2 Graduate School of Engineering, Tohoku University, Sendai, Miyagi 9808579, Japan 6 7 Correspondence should be addressed to Meiyong Liao* (Email: meiyong.liao@nims.go.jp) 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 mailto:meiyong.liao@nims.go.jp2 ABSTRACT 23 Microelectromechanical system (MEMS) has unlocked a wide range of applications 24 in electronics, mobility, medical and energy from sensors and actuators to switches. 25 Diamond, in particular, stands out for its exceptional mechanical robustness and 26 electronic performance in extreme conditions, offering sensitivity and reliability super to 27 other semiconductor materials for MEMS sensors. In this perspective, we review the 28 principles of MEMS magnetic sensors, diamond for MEMS, thermal stability of diamond 29 MEMS resonators, and diamond MEMS magnetic sensors, particularly for the 30 applications under high temperatures. We present the interface engineering of diamond 31 MEMS magnetic sensors to improve the thermal stability. Finally, we discuss the potential 32 solutions, outline future research directions, and discuss the prospects for continued 33 progress of diamond MEMS. 34 35 36 3 I. INTRODUCTION 37 Magnetic sensors have become increasingly vital in modern applications, including 38 automotive sensors, navigation systems, non-contact sensing, biomedical devices, and 39 nondestructive testing etc.1-3. Currently, the most common types of magnetic sensors 40 include superconducting quantum interference devices (SQUID), fluxgate sensors, Hall 41 sensors, giant magnetoresistance (GMR) sensors, and micro-electromechanical systems 42 (MEMS) magnetic sensors, etc.1-5 Although these magnetic sensors have been widely 43 applied in either industry, daily life, aerospace and scientific research, the development 44 of alternative magnetic sensors are still in demand to overcome the limitations of each 45 kind of sensors, i.e. the low-temperature requirement of SQUID devices a, low sensitivity 46 of Hall sensors, high-power consumption of fluxgate sensors, and poor thermal stability 47 of GMR sensors.2,6 In contrast, MEMS magnetic sensors offer several advantages, 48 including microscale size, batch manufacturing, low-power consumption, high sensitivity 49 and resolution, and smart system integration with CMOS technology.2 Silicon based 50 MEMS has experienced explosive growth due to the maturity in micromachining and 51 CMOS process. Next-generation MEMS devices are expected to be more precise, highly 52 reliable and entering from the classic sensors to quantum field. 53 Diamond with an ultra-wide bandgap energy, exceptional electronic, mechanical, and 54 thermal properties, has been extensively investigated as the next-generation 55 semiconductors not only for conventional electronics superior to the other 56 semiconductors, but also for high-performance and high-reliability MEMS devices. The 57 high quality (Q) factor over 1 million at room temperature and the thermal stability up to 58 500oC based on single-crystal diamond (SCD) MEMS cantilevers were demonstrated.7,8 59 This Perspective aims to furnish a brief overview of the latest research and discuss 60 4 challenges and opportunities of SCD MEMS magnetic sensors for extreme conditions. 61 We provide a brief introduction of the principles of MEMS resonant-type magnetic 62 sensors and show the merits of diamond for MEMS applications. We then present the 63 diamond MEMS magnetic sensors operable up to 500oC. We explore the interface 64 engineering to improve either the sensitivity and reliability of the diamond MEMS 65 magnetic sensors. We summarize the recent advance in this field and discuss the future 66 roadmap of diamond MEMS magnetic sensors. Section II introduces intrinsic material 67 properties, highlighting various SCD MEMS fabrication techniques of diamond MEMS. 68 Section III provides a device concept and recent advance of SCD MEMS in high-69 temperature magnetic sensing. Section IV outlines the challenges and opportunities ahead. 70 By reviewing the current state of the field and highlighting potential research directions, 71 this paper seeks to provide valuable insights and inspire future work in this growing area. 72 73 II. MEMS RESONANT MAGNETIC SENSORS 74 MEMS resonant magnetic sensors are designed to detect magnetic fields by 75 leveraging changes in resonance frequency. These sensors exploit the interaction between 76 magnetic fields and mechanical structures, which causes change in the resonance of the 77 sensor's mechanical components. In general, the sensor consists of a resonant structure, 78 such as a cantilever beam, a double-clamped beam, or a membrane, etc, which is 79 subjected to magnetic forces when exposed to a magnetic field. These forces cause 80 mechanical deformation or vibration in the structure, altering its resonance frequency. 81 The magnetic field is then quantified by measuring these resonance frequency shifts. The 82 principles underlying MEMS resonant magnetic sensing can be mainly categorized into 83 the following types: (1) Lorentz force principle,9-14 (2) ΔE effect, which is based on the 84 5 magnetostrictive effect,5,15-20 (3) magnetoelectric effect,21-23 (4) torque effect,24,25 and (5) 85 magnetic gradient effect.26 The Lorentz force principle need a conductive component on 86 the MEMS structure, in which the electric current flows. The interaction between the 87 current and the field generates a Lorentz force on the conductor. In MEMS devices, this 88 force induces mechanical displacement, altering the system's resonant frequency. By 89 accurately measuring these frequency shifts, the sensor can determine the strength of the 90 magnetic field.9-14 The ΔE effect, a manifestation of the magnetostrictive effect, underpins 91 the operation of many high-performance MEMS resonance magnetic sensors. For 92 materials with magnetostrictive properties, such as FeGa, the Young's modulus changes 93 when subjected to an external magnetic field. This variation in stiffness directly 94 influences the resonant frequency of the MEMS device, where the frequency shift is 95 proportional to the intensity of the magnetic field.5,15-20 This sensing mechanism is 96 particularly advantageous in applications requiring dynamic field detection. The 97 magnetoelectric (ME) effect, involves the interaction between magnetic fields and electric 98 polarization in multiferroic or composite materials. In MEMS resonance sensors, this 99 effect is achieved by creating strain in the piezoelectric material generated in the 100 magnetrostrictive material. This strain generates an electric field which can be enhanced 101 at the MEMS sensor’s resonant frequency.21-23 This coupling provides a highly sensitive 102 method for converting magnetic field variations into measurable electrical signals, 103 making it ideal for compact, energy-efficient sensing applications. The torque effect in 104 MEMS magnetic sensors occurs when a magnetic element or dipole within the sensor 105 interacts with an external magnetic field. The external field exerts a torque on the 106 magnetic dipole, resulting in mechanical rotation or bending of the MEMS structure. In 107 cantilever-based sensors, this torque produces a twisting force that shifts the resonator’s 108 6 resonant frequency. By measuring the changes in resonance caused by the torque, the 109 sensor can detect the magnetic field’s magnitude and direction.24,25 This principle is 110 particularly valuable in applications requiring precise directional sensing of magnetic 111 fields. The magnetic gradient effect is employed in MEMS sensors to detect spatial 112 variations in magnetic fields. When the magnetic field is non-uniform, different parts of 113 the sensor experience varying magnetic forces, creating a mechanical response. This 114 differential force distribution induces changes in the resonant behavior of the MEMS 115 structure. By analyzing these changes, the sensor can measure the magnetic field gradient, 116 which is the rate of change of the magnetic field over a given distance. 26 This principle 117 is often used in magnetic gradiometers for applications requiring high spatial resolution, 118 such as detecting localized magnetic sources or performing fine-scale magnetic mapping. 119 Especially, the ΔE effect, has aroused great attention to develop MEMS resonant 120 magnetic sensors with exceptional sensitivity to low frequencies and low magnetic fields 121 and high integration.17,27-30. The MEMS magnetic sensors based on the ΔE effect is the 122 preferred solution for certain specific applications under extreme conditions.8,31,32 By 123 optimizing device structure and selecting appropriate ferromagnetic materials, the 124 performance such as the sensitivity, resolution, response time and reliability of the MEMS 125 magnetic sensors based ΔE effect can be tuned. 126 III. DIAMOND MEMS 127 A. Overview of diamond MEMS 128 Micro- and nano-electromechanical systems (MEMS/NEMS) represent an advanced 129 interdisciplinary field that integrates electrical and mechanical components. Due to their 130 compact size, high sensitivity, low power consumption, and compatibility with modern 131 electronics, these devices are highly promising for applications in automation, industry, 132 7 edge computing, augmented and virtual reality, biomedicine, telecommunications, and 133 quantum mechanics.33,34 A high product of frequency and quality (Q) factor are desirable 134 in many cases for achieving high sensitivity, high resolution, and high speed.35,36 However, 135 the inherent limitations of silicon, including its narrow bandgap, prone to oxidation, and 136 mechanical brittleness, especially at the nanoscale, have limited the performance, such as 137 sensitivity, precision, and reliability of current MEMS devices. 138 Wide-bandgap semiconductors like SiC, GaN, AlN, and diamond are considered 139 promising for MEMS applications. Among these semiconductors, diamond stands out as 140 an ideal choice due to its exceptional electrical properties, mechanical strength, and 141 chemical resistance in harsh environments.37 Fig. 1 summarizes the superlative properties 142 of diamond materials, such as high Young’s modulus, compressive strength, the highest 143 mechanical hardness and low coefficient of friction, compared with other semiconductors. 144 The superior tribological properties of diamond ensure that its wear lifetime is 10,000 145 times greater than that of silicon, enhancing the reliability of MEMS devices. Additionally, 146 diamond has low inherent losses, such as those from thermoelastic damping, leading to 147 MEMS devices with higher Q factors.38 Fig. 2 compares and summarizes the resonance 148 frequencies and Q factors, and the fQ product of the representative MEMS resonators 149 based on various semiconductors. It is disclosed that the as-fabricated diamond MEMS 150 resonators can achieve higher Q factors than those of other semiconductors (Fig. 2(a)). 151 In addition, for a certain resonance frequency, the product fQ of diamond is higher than 152 other materials (Fig. 2(b)). Diamond’s chemical inertness means that its surface remains 153 free of natural solid oxides, minimizing the surface loss in MEMS devices. Its wide 154 bandgap and high resistance to radiation further ensure stable performance in harsh 155 conditions. Consequently, diamond stands out as an ideal material for MEMS 156 8 applications.39,40 157 158 FIG. 1. Comparison of mechanical material properties of various semiconductors.41-47 159 160 161 FIG. 2. Comparisons of (a) resonance frequencies, f and Q factors and (b) the product of 162 f and Q, fQ of representative MEMS resonators made from various 163 semiconductors.7,34,36,48-66 164 165 Polycrystalline diamonds, including microcrystalline, nanocrystalline, and 166 9 ultrananocrystalline varieties have been explored for MEMS and exciting proto-type 167 MEMS devices were reported.42,53 These materials have numerous grain boundaries and 168 impurities, leading to increased internal losses and limiting the resonance performance.67 169 Compared to these above-mentioned diamonds, SCD can make full use of the ultimate 170 properties of diamond material in every aspect for MEMS applications with high 171 performance and high reliability, especially under extreme conditions. SCD MEMS can 172 be employed in classic sensing, actuator and switch applications68 as well as photonic 173 devices.69,70 We briefly summarize the development of SCD MEMS technology in Fig. 3. 174 175 FIG. 3. Development timeline of SCD MEMS technology.7,8,32,37,48,71-73,81,82,87,88 176 177 Note that Fig. 3 does not includes the technology like embedding diamond nanowire as a 178 tip on a silicon cantilever. Based on the smart-cut method for SCD plate,71 SCD 179 membrane87 was created and the first device concept of SCD MEMS with movable 180 10 cantilever beams in a electromechanical switch configuration was reported in 2010.72 The 181 smart-cut process enables mass production of SCD MEMS/NEMS structures with high 182 controllability and reproducibility and thus the development of SCD MEMS magnetic 183 sensors capable of working at high temperatures.8,31,32,37,73 The reported applications of 184 SCD MEMS are summarized in Fig. 4, such as capacitive pressure sensors,74 atomic force 185 microscopy,75-77 actuators,78 and NV center magnetic imaging sensors.79,80 Particularly, 186 the SCD MEMS was used for high-temperature magnetic sensors,8,32,37 switch,72 187 temperature sensor,81 and thermogravimetric sensor.82 In addition, the SCD MEMS 188 photonics applications, such as waveguides, photonic crystals, and optical micro-nano 189 resonators,83,84 have significantly advanced the field of cavity optomechanics.85,86 190 191 192 FIG. 4. Developed SCD MEMS/NEMS devices for general conditions and extreme 193 11 conditions. Reprinted with permission from Fu et al., Sci. Rep. 9 (1), 1 (2019). Copyright 194 2019 Springer Nature Limited,74 Tao et al., Nano Lett. 15 (12), 7893 (2015). Copyright 195 2015 American Chemical Society,77 Liao et al., Adv. Sci. 11 (13), 2306013 (2024). 196 Copyright 2024 Wiley-VCH GmbH,78 Appel et al., Rev. Sci. Instrum. 87 (6), 063703 197 (2016). Copyright 2016 AIP Publishing LLC,80 Zhang et al., Adv. Funct. Mater. 33 (27), 198 2300805 (2023). Copyright 2023 Wiley-VCH GmbH,8 Liao et al., Adv. Mater. 22 (47), 199 5393 (2010). Copyright 2010 Wiley-VCH GmbH.72 Liao et al., Adv. Mater. Technol. 4 200 (2), 1800325 (2019). Copyright 2019 Wiley-VCH GmbH,81 Voiculescu et al., Sens. 201 Actuators A: Phys. 271, 356 (2018). Copyright 2018 Elsevier B.V.82 202 203 204 B. Fabrication of SCD MEMS 205 Due to its exceptional mechanical hardness and chemical stability, the 206 microfabrication process for SCD cannot directly mirror the methods used for silicon and 207 other wide bandgap semiconductors. The significant advancements in the growth and 208 micromachining techniques of SCD have led to the development of specialized 209 microfabrication approaches for SCD-based MEMS devices. These methods, include: (1) 210 the smart-cut process utilizing ion-implantation-assisted lift-off (IAL) technology,87,89,90 211 (2) diamond thinning via anisotropic plasma etching (APE),88,91 and (3) diamond-on-212 insulator (DOI) technology, which involves bonding an SCD plate to an insulating 213 substrate and thinning the plate to the designed level.48,92. The methods described above 214 were thoroughly discussed in previous works.37,40 Parikh et al. were the first to propose 215 the Ion-Assisted Lift-Off (IAL) technique for fabricating freestanding diamond plates.71 216 This process involves directly manufacturing devices on a thick SCD substrate. A key 217 step in IAL is ion implantation, which creates an ion-damaged layer beneath the surface 218 of the diamond, serving as a sacrificial layer during the subsequent etching process. Once 219 this layer is selectively removed, the desired device structure is released. Based on the 220 12 microfabrication techniques for freestanding diamond plates, the IAL process has been 221 further developed to create various SCD MEMS structures, which is also named smart-222 cut method.37,72,74,87,89 This technique is particularly advantageous for producing SCD 223 MEMS devices with an SCD-on-SCD configuration, offering precise control over 224 dimensions from the nanoscale to the microscale and ensuring high reproducibility. The 225 APE process begun with standard photolithography and etching on SCD material to 226 define the design pattern, followed by anisotropic etching to release the device structure.91 227 In contrast, the DOI technique involves bonding diamond to a foreign substrate and 228 thinning it to the desired thickness through mechanical polishing and RIE/ICP etching. 229 The device structure is then released by removing the oxide layer.48,92,93 This method is 230 advantageous for achieving high Q factors for diamond MEMS if the initial SCD plate 231 has high crystal quality. Up to now, most of the SCD MEMS devices have been reported 232 by the smart-cut method. 233 234 IV. SCD MEMS MAGNETIC SENSORS 235 The key components used in SCD MEMS devices are the mechanically vibrational 236 resonators, which can detect various physical, chemical, and biological quantities through 237 nano- and micro-scale displacements. In our previous research, we demonstrated that the 238 Q factors of SCD cantilever resonators surpassed 10⁶, which is one to two orders of 239 magnitude higher than those of resonators made from silicon and other 240 semiconductors.7,94 SCD offers exceptional thermal stability due to its ultra-low thermal 241 expansion and strong chemical resistance, making it an excellent platform for minimizing 242 13 interfacial diffusion. Given the excellent high-temperature properties of diamond, 243 combining SCD MEMS with magnetostrictive thin films offers an effective approach to 244 creating magnetic sensors that can operate from room temperature to high temperatures. 245 Galfenol (FeGa), with its exceptionally high magnetostriction coefficient and a Curie 246 temperature of around 950 K, presents as an ideal choice for high-temperature magnetic 247 sensors.5,95-97. The combination of SCD and FeGa offers exceptional material properties, 248 making their integration in MEMS devices a promising choice for creating high-249 performance and reliable magnetic sensors. Building on this concept, we developed 250 MEMS magnetic sensors using FeGa thin films and SCD resonators. These sensors 251 demonstrated both high sensitivity and reliability across a broad temperature range, from 252 room temperature to extreme conditions. 253 254 A. Magnetrostrictive FeGa/SCD MEMS for magnetic sensors 255 The SCD MEMS resonators were fabricated using the smart-cut method, as detailed 256 in our previous works.31,32,37,98,99 The SCD MEMS magnetic sensors were constructed by 257 integrating these resonators with a magnetostrictive FeGa thin film using RF magnetron 258 sputtering. The resulting FeGa properties on SCD substate showed desirable soft 259 magnetic properties, such as a low coercivity (Hc) of 26.2 Oe, a low saturation 260 magnetization field (Hs) of 450 Oe, and a high remanence ratio (Mr/Ms) of 0.9.100 To 261 fabricate diamond based magnetic sensors with diverse structures, the interlayers of 262 titanium (10 nm), tungsten carbide (20 nm), and a combination of titanium (5 nm) and 263 tungsten carbide (10 nm) were deposited on the SCD substrates using RF magnetron 264 14 sputtering before the FeGa film growth. In SCD-based magnetic sensors, the Ti interlayer 265 serves two primary functions: first, it reduced the possible reaction of between FeGa layer 266 and the SCD, and second, it enhanced the interface adhesion, enabling efficient force 267 transfer from the deformed FeGa film to the SCD cantilevers. The tungsten carbide (WC) 268 interlayer helped align the FeGa film in the (200) crystal orientation, which has a higher 269 magnetostrictive coefficient. Various multilayer structures of FeGa/SCD, FeGa/Ti/SCD, 270 FeGa/WC/SCD, and FeGa/Ti/WC/SCD were fabricated for MEMS magnetic sensors 271 which can work from room temperature (RT) to 773 K. 272 273 B. Magnetic sensing principle 274 The bending behavior of SCD beams can be solved exactly using the eigenmode 275 approach. This analysis is based on the Euler–Bernoulli beam theory. Assuming the beam 276 is made of a linear elastic material and experiences small deflections, u(x, t), the motion 277 of the beam follows the Euler–Bernoulli equation.101,102 278 𝐸𝐼𝜕4𝑢(𝑥,𝜏)𝜕𝑥4+ 𝜌𝐴𝜕2𝑢(𝑥,𝜏)𝜕𝜏2= 0 (1) 279 The variable x represents position, while τ denotes time. The terms E and ρ correspond to 280 the Young's modulus and the mass density of the beam, respectively. Similarly, A refers 281 to the cross-sectional area of the beam, and I represents its moment of inertia. The solution 282 to this differential equation consists of a combination of normal modes. These modes can 283 be expressed as separate terms: one depending on position and the other on time, achieved 284 through the method of separation of variables, 285 𝑢(𝑥, 𝑡) = ∑ 𝑢𝑛(𝑥)cos⁡(𝜔𝑡)∞𝑖=1 (2) 286 15 For a SCD MEMS resonator where the thickness and width are significantly smaller than 287 the length, the vibrational behavior is primarily determined by flexural motion. The 288 resonance frequency of the SCD MEMS resonator can be expressed as, 289 𝑓𝑛 == 𝑘𝑡𝐿2√𝐸𝜌 (3) 290 where t and L are thickness and length of the SCD resonator, respectively. k is a parameter 291 depending on the vibration mode and the resonator structure. For the first mode, k is equal 292 to 0.162. 293 Fig. 5 presents the fundamental device structure and operating principle of a 294 magnetic sensor that combines an SCD cantilever with a large magnetostrictive FeGa film. 295 When an external magnetic field is applied to the cantilever, the stress state and Young’s 296 modulus of the bilayer system change, leading to a shift in the resonance frequency. The 297 magnetic sensing mechanism of this SCD magnetic sensor relies on the ΔE effect, which 298 refers to changes in the Young’s modulus under magnetic fields.15,103 This effect arises 299 from the deformation or dimension changes in the soft magnetic material due to the 300 applied magnetic field. A higher magnetostrictive constant in the soft magnetic material 301 amplifies the ΔE effect. Upon applying an external magnetic field without changing other 302 quantalities, the resonance frequency shift of the SCD-based magnetic sensor can be 303 expressed as, 304 ∆𝑓𝑇 = |𝑓𝑇𝐻 − 𝑓𝑇0| = 0.162𝑡𝐿2√𝜌|√𝐸𝑇𝐻 −√𝐸𝑇0| (3) 305 where EH, and E0 are the Young’s modulus with and without applying the magnetic field, 306 respectively. fTH and fT0 represent the resonance frequencies of the magnetic sensor with 307 and without applying the magnetic field at a certain temperature. The magnetic sensitivity 308 16 of the FeGa/SCD MEMS sensor is characterized by the frequency sensitivity, Df/DH, 309 where DH is the variation of the magnetic field. 310 311 FIG. 5. Schematic diagram of sensing principle of a SCD resonant magnetic sensor that 312 employs a FeGa/SCD cantilever resonator with a heterogeneous structure. When a 313 magnetic field is applied, the magnetostrictive effect alters the Young's modulus and stress 314 condition of the cantilever. These changes in stress affect the resonance frequency of the 315 sensor, with compressive stress causing a decrease in resonance frequency and tensile 316 stress causing an increase. The cantilever's vibrations are measured using optical readout 317 in conjunction with a lock-in amplifier. Scale bar: 20 μm. Reprinted with permission from 318 Zhang et al., Carbon, 152, 788-795 (2019). Copyright 2021 Elsevier B.V.37 319 320 V. SCD MEMS for HIGH TEMPERATURE MAGNETIC SENSING 321 A. Thermal-stability of SCD MEMS 322 The temperature coefficient of resonance frequency (TCF), defined as TCF = 323 (∂f/f0∂T), was utilized to assess the thermal stability of SCD cantilevers. f0 represents the 324 fundamental resonance frequency at 300 K. According to this equation, the resonance 325 frequency is strongly influenced by the Young’s modulus of the cantilever. Additionally, 326 temperature has an inverse effect on the Young’s modulus of the material.104-106 327 𝐸 = 𝐸𝑇0 − 𝐴𝑇𝑒𝑥𝑝(−𝑇0𝑇) (4) 328 ET0 represents the Young’s modulus of the material at temperature of T0. A is a constant. 329 17 The resonance frequency of the cantilever decreases as temperature increased, due to the 330 reduction in Young’s modulus (Figs. 6(a) and (b)). Fig. 6(c) illustrates that the TCF of 331 the bare SCD cantilever was below -3.2 ppm/K over a temperature range from 300 K to 332 773 K. This TCF is notably lower than that of Si, which is about -35 ppm/K.107,108 It 333 reveals that the SCD cantilever can offer a promising platform for MEMS devices capable 334 of stably working under high temperatures. Furthermore, the Q factors of the SCD 335 cantilevers remained above 3000 at 773 K (Fig. 6(d)). The Q factor exhibited a negative 336 temperature dependence. As temperature increased, the energy dissipation also increased. 337 338 FIG. 6. (a) Resonance frequency shifts of a bare SCD cantilever with changing 339 measurement temperature. (b) Temperature-dependent changes in resonance frequency 340 shifts of bare SCD cantilevers of different lengths. (c) Temperature coefficients of the 341 resonance frequencies for SCD cantilevers. (d) Temperature-dependent variations in the 342 Q factors of SCD cantilevers. Reprinted with permission from Zhang et al., Mater. Res. 343 Lett., 8(5), 180-186 (2020) Copyright 2020 Informa UK Limited.31 344 345 18 B. High-temperature SCD MEMS magnetic sensing 346 The integration of a magneto-strictive FeGa thin film with a SCD cantilever offers a 347 promising method for developing microscale magnetic sensors based on the ΔE effect 348 from room temperature to high temperatures.15-17,109. Fig. 7(a) schematically shows a 349 magnetic sensor composed of a 80 nm-thick FeGa film deposited on a SCD cantilever, 350 which is utilized to fabricate MEMS magnetic sensor at room temperature.37 The 351 frequency response of the FeGa/SCD sensor with a length of 160 μm to the magnetic field 352 is shown in Fig. 7(b). As the magnetic field increased, the resonance frequency of the 353 sensor decreased. The changes in resonance frequency of the FeGa/SCD sensor exhibited 354 a linear relationship with the applied magnetic field, regardless of the length of the 355 cantilevers (Fig. 7(c)). The magnetic field sensitivity was around 4.83 Hz/mT for the 356 FeGa/SCD sensor with a length of 60 μm. Additionally, the variations in magnetostrictive 357 force of the FeGa/SCD cantilevers subjected to different magnetic field strengths was 358 calculated to be around 10 fN (Fig. 7(d)).37 Presently, the magnetic sensors that rely on 359 resonance frequency shifts in response to magnetic fields are commonly based on the 360 Lorentz force and magnetostrictive force. Table 1 summarizes the magnetic sensitivities 361 of various MEMS magnetic sensors at room temperature, showing that the 362 magnetostrictive force MEMS sensors have higher sensitivity than those of Lorentz-type. 363 The sensitivity of the FeGa/SCD sensor was significantly improved by incorporating a Ti 364 thin film. 365 19 366 FIG. 7. (a) A schematic diagram of a magnetic sensor utilizing a FeGa/SCD sensor. (b) 367 The resonance frequency response of a 160 µm-length FeGa/SCD sensor as the applied 368 magnetic fields vary. (c) The relationship between the resonance frequency shifts and (d) 369 the detectable force of the FeGa/SCD sensors in response to magnetic fields. A negative 370 force indicates compressive stress. Reprinted with permission from Zhang et al., Carbon, 371 152, 788-795 (2019). Copyright 2019 Elsevier B.V.37 372 373 TABLE 1 An evaluation of the magnetic sensitivities of different MEMS magnetic 374 sensors at room temperature. 375 Magnetic sensor Material f (◊103) Q Sensitivity (Hz/mT) Ref. Lorentz force Si 38.074 15000 0.09 110 Lorentz force Si 175 ~600 60.00 10 Lorentz force SOI 49.3 100000 0.01 111 Lorentz force SOI 22.6 540 0.59 112 Magnetostrictive force FeGa/quartz 38.199 3318 35.00 5 Magnetostrictive force FeGa/PZT 12.450 1132 5.47 113 Magnetostrictive force FeGa/SCD 949.966 8201 4.83 37 20 Magnetostrictive force FeGa/Ti/SCD 147.916 3889 35.6 32 Silicon-on-insulator (SOI), lead zirconate titanate (PZT) 376 377 High-temperature magnetic sensors utilizing the FeGa/SCD MEMS resonators were 378 developed up to 573 K 31. The frequency shifts at elevated temperatures increased linearly 379 with the applied magnetic field. Notably, the FeGa/SCD cantilever maintained a stable 380 response to the magnetic field even at 573 K. The intrinsic magnetic noise (bn) of the 381 magnetic sensor, governed by thermomechanical noise, is represented by the following 382 expression,114 383 𝑏𝑛 =𝜇02(𝑑𝐻𝑑𝑓)√2𝜋𝑘𝐵𝑇𝑓0𝑄𝑉𝜎 (5) 384 The magnetic sensitivity is represented by m0(dH/df), while s denotes stress. To enhance 385 both the operating temperature and magnetic sensitivity, a Ti layer was introduced 386 between the FeGa and SCD, as the FeGa/Ti/SCD resonator structure.32. The change in 387 resonance frequency of a 100 μm-long FeGa/Ti/SCD cantilever when subjected to 388 magnetic fields at different temperatures during heating process is displayed in Fig. 8(a). 389 The frequency shifts showcased a linear dependence on magnetic field, reaching a 390 maximum sensitivity of 71.1 Hz/mT at temperatures up to 773 K (Fig. 8(b)). 391 The magnetic noise levels of the FeGa/Ti/SCD resonator sensor at 300 K and 773 K 392 were examined through the relationship between the frequency shifts and the magnetic 393 fields. Figs. 8(c) and (d) present the magnetic noise spectra for the 100 μm-long 394 FeGa/Ti/SCD resonator, showing low magnetic noise levels of ~ 20 nT/√Hz at 300 K 395 21 and ~10 nT/√Hz at 773 K, respectively. Using Eq. (5), the intrinsic magnetic noise of 396 the FeGa/Ti/SCD magnetic sensor was estimated to be approximately 206.7 pT/√Hz at 397 300 K and 212.4 pT/√Hz at 773 K, respectively. The observed discrepancy between the 398 measured and estimated noise levels may be due to the noise characteristics of the 399 measurement apparatus. The improved thermal stability of the SCD MEMS magnetic 400 sensor is attributed to the enhanced adhesion between the FeGa and SCD facilitated by 401 the Ti layer. Additionally, Table 2 compares the magnetic sensing performance of the 402 FeGa/Ti/SCD sensor with other high-temperature magnetic sensors. The comparison 403 reveals that the SCD-based sensor offers lower noise, and higher thermal reliability 404 compared to its counterparts. 405 406 FIG. 8.1 (a) Resonance spectra of a FeGa/Ti/SCD sensor with changing the measurement 407 temperatures and the external magnetic fields. (b) Dependences of resonance frequency 408 shifts on magnetic fields during the heating process. (c) and (d) Magnetic noise spectra 409 22 of the FeGa/Ti/SCD sensor at temperatures of 300 K and 773 K, respectively 32. Reprinted 410 with permission from Zhang et al., ACS Appl. Mater. Interfaces, 12(20), 23155-23164 411 (2020). Copyright 2020, American Chemical Society. 412 413 TABLE 2 Comparison of high-temperature performances of various magnetic sensors 32. 414 Reprinted with permission from Copyright 2020, American Chemical Society 415 Magnetic sensor Materials Sensitivity Noise level Working temperature Ref. AMR Si-based -- ~2.6 nT/√Hz 498 K 115 Hall Si -- >82 nT/√Hz 673 K 116 Hall AlGaN∕GaN -- 35 μT/√Hz 873 K 117 Hall 4H-SiC 80 V/(A∙T) -- 770 K 118 Fluxgate Cu coil -- 0.79 nT/√Hz 523 K 119 MEMS FeGa/Ti/SCD 71.1 Hz/mT 10 nT/√Hz 773 K 32 416 C. On-chip SCD MEMS magnetic sensors 417 For highly integrated MEMS magnetic sensors, an electrical system that combines 418 actuation, sensing, and signal readout is desirable. An on-chip SCD MEMS magnetic 419 sensor designed for high-temperature applications was proposed and demonstrated, 420 utilizing a multifunctional magnetostrictive FeGa film for harmonic actuation, magnetic 421 sensing, and resonance signal readout.8 The Au/FeGa/Ti was deposited on the SCD 422 substrate as the gate (called G) electrode for the on-chip actuation and on the SCD 423 cantilevers as source-drain (called S-D) electrodes to sense the magnetic fields and 424 electrically readout the resonance signal (Fig. 9(a)). A preliminary SCD-based magnetic 425 transducer array comprising four cantilevers integrated on the same chip for magnetic 426 transducing with all-electrical actuation and sensing were fabricated (Fig. 9(b)). The 427 23 resonance frequency spectra shift of the 160 μm-long SCD-based magnetic sensor caused 428 by applying a magnetic field of 2.82 mT with the temperature increasing from RT to 773 429 K, as shown in Fig. 9(c). The SCD-based magnetic transducer via the on-chip actuation 430 and sensing had a stable magnetic sensitivity of 3.2 Hz/ mT at various temperatures. Due 431 to the independent resonance vibrations of each magnetic sensor, we successfully 432 achieved parallel signal readout from the four transducers. The resonance frequency 433 spectra of the transducer array displayed four distinct peaks with and without the presence 434 of a 0.28 mT magnetic field (Fig. 9(d)). This study opens the avenue for the integration 435 of SCD-based MEMS magnetic transducers with electronics. 436 437 FIG. 9. On-chip SCD MEMS magnetic transducer. a Schematic diagram of the 438 measurement setup for the SCD-based cantilever magnetic transducer with the on-chip 439 self-sensing and actuation configuration. LPF: low frequency filter. Vac g was applied to 440 the G electrode. And Vac sd was connected to the S–D electrodes. b Optical image of an 441 SCD-based magnetic transducer array. c Resonance frequency shift of a 160 μm-long 442 SCD-based cantilever transducer as a function of the measurement temperature at a 443 magnetic field of 2.82 mT, and at Vac sd =4 V and Vac g =7 V from RT to 773K. The peak 444 amplitude of etch spectrum was normalized. d Resonance frequency shifts of the 445 magnetic transducer array under a 2.82 mT magnetic field at Vac sd = 10 V and Vac g = 10 V 446 @300K. Reprinted with permission from Zhang et al., Adv. Funct. Mater. 33 (27), 447 2300805 (2023). Copyright 2024 Wiley-VCH GmbH.8 448 24 449 VI. CURRENT CHALLENGES and PERSPECTIVES 450 For the development of the highly-reliable diamond-based MEMS magnetic sensors 451 at high temperatures, the following challenges need be considered. 1) Thermal Stability: 452 diamond MEMS magnetic sensors are renowned for their exceptional thermal stability. 453 However, ultrahigh temperatures (>773 K) can still pose challenges for the 454 heterostructures. Prolonged exposure to extreme temperatures can lead to degradation of 455 the interface between diamond and the functional magnetic thin films due to lattice and 456 thermal expansion coefficient discrepancy. The interface engineering between diamond 457 and the magnetic material requires further optimization. 2) Sensitivity limitation: high 458 temperatures introduce additional thermal noise, affecting the sensitivity and accuracy of 459 the diamond magnetic sensors. Balancing sensitivity with thermal noise mitigation is 460 crucial. 3) Integration with electronics: integrating electronic components that can 461 withstand high temperatures remains a significant challenge. Conventional electronic 462 materials and electronics may fail under extreme thermal conditions, requiring the 463 development of high-temperature-compatible electronics and multi-technology solutions. 464 4) Calibration and measurement accuracy. High temperatures cause thermal drift in the 465 calibration of diamond-based sensors, impacting their measurement precision. Ensuring 466 accurate sensor performance demands advanced calibration methods and effective 467 temperature compensation algorithms. 468 For realizing high-sensitivity and high-reliability SCD magnetic sensors, the 469 25 following research topics can be conducted: 1) Advanced materials development: 470 research need focusing on optimizing the current or developing novel diamond 471 heterostructures with the magnetic materials that enhance thermal resistance and 472 minimize degradation. Such as the Tb-doped FeGa fim for improving the durability and 473 performance of diamond MEMS sensors at high temperatures. 2) Sensitivity improved 474 technologies. In order to realize high sensitivity of diamond-based magnetic sensors, 475 diamond resonators in nanoscale (the thickness < 100 nm) can be fabricated. The 476 enhancement of the Q factor is crucial for increasing the signal-to-noise ratio and 477 minimizing magnetic noise. Based on the high sensitivity for the nanoscale diamond 478 resonator, the dependence of the resonance frequency and Q factor on magnetic noise 479 level is evaluated in Fig. 10. A low magnetic noise level of 383.3 fT/Hz1/2 is expected to 480 achieve assuming the diamond cantilever thickness is reduced to 100 nm and the length 481 to 1 µm and the Q factor of one million still maintains. A refined method for improving 482 the Q factor in diamond resonators may be adopted, like the utilizing the established 483 dissipation dilution mechanism.33,34 3) Hetero-integration with other technologies. 484 Combining diamond MEMS sensors with other sensing technologies or data processing 485 systems is essential for practical applications. Multimodal sensing and data fusion 486 techniques may enhance the overall performance and reliability of these sensors. 4) 487 Calibration Techniques. Future work should involve the development of advanced 488 calibration methods and real-time temperature compensation algorithms for diamond 489 magnetic sensors under high temperatures. These approaches will help maintain accuracy 490 and precision under varying thermal conditions. By exploiting diamond sensors array, 491 MEMS magnetic imaging sensor can be also devleoped.8 492 26 493 FIG. 10. Perspective on the magnetic sensitivity of diamond MEMS magnetic sensors. 494 495 V. CONCLUSION 496 Diamond MEMS technology holds immense potential for revolutionizing magnetic 497 sensor applications in extreme environments. By leveraging the classical theory of the 498 magnetostrictive effect, diamond MEMS resonators combined with highly thermally 499 stable soft magnetic materials present a promising approach to develop sensors capable 500 of withstanding high temperatures. This perspective provides an overview of diamond 501 MEMS magnetic sensors designed for such conditions, covering fundamental material 502 properties, fabrication methods, and the progression of these structures into magnetic 503 sensors, from room temperature to high-temperature magnetic sensing applications. 504 Despite renewed interest in this field, spurred by advancements in diamond MEMS, 505 challenges remain. These include enhancing magnetic sensitivity, overcoming operational 506 27 temperature limitations, and developing suitable integration and calibration technologies 507 to meet real-application standards. With ongoing research, the creation of diamond 508 MEMS arrays and their integration with electronics in advanced systems shows potential 509 for groundbreaking advancements in magnetic field imaging at extreme temperatures and 510 beyond. 511 512 Author Declarations 513 Conflict of Interest 514 The authors have no conflicts to disclose. 515 Author Contributions 516 Zilong Zhang: Data curation (equal); Formal analysis (equal); Investigation (equal); 517 Methodology (equal); Validation (equal); Writing–original draft (equal); Writing–review 518 & editing (equal). 519 Keyun Gu: Writing –review & editing (equal). 520 Masaya Toda: Writing –review & editing (equal). 521 Meiyong Liao: Conceptualization (equal); Data curation (equal); Formal analysis (equal); 522 Funding acquisition; (equal); Methodology (equal); Project; Writing–original draft 523 (equal); Writing –review & editing (equal). 524 525 Acknowledgements 526 This was partially supported by a Grant-in-Aid of JSPS KAKENHI (Grant Number 527 24H00287, 22K18957, and 24K00828), Bilateral joint research between JSPS/CAS, and 528 Advanced Research Infrastructure for Materials and Nanotechnology in Japan (ARIM 529 JPMXP1223NM5297) of the Ministry of Education, Culture, Sports, and Technology 530 (MEXT) of Japan. 531 532 28 References 533 534 1 J. 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