Electrical actuation of single-crystal diamond MEMS resonators at high temperatures

Abstract

Achieving efficient low-voltage actuation of microelectromechanical system (MEMS) resonators in high-temperature environments poses a difficult topic due to the thermal interference and the risk of high-temperature failure. In this work, the single-crystal diamond (SCD) resonators fabricated through the ion implantation-assisted lift-off (IAL) technique exhibit a SCD-on-SCD cantilever structure. We propose an electrical actuation system based on the electrostatic effect specifically designed for SCD MEMS resonators with a low radio-frequency amplitude of ∼ 100 mV. The SCD resonators demonstrate stable and efficient actuation across a wide temperature range, from room temperature to 500 °C. Importantly, the actuation voltage exhibits little impact on the resonance frequency and the Q factor of the resonator. The SCD resonator showcases exceptional thermal stability in resonance frequency, with a low temperature coefficient of frequency (TCF) below −12 ppm/°C up to 500 °C. The developed actuation scheme holds tremendous potential as a robust platform for realizing SCD MEMS devices, particularly in applications requiring high integration at high temperatures.

Graphic Abstract

An electrical actuation system harnessing the electrostatic effect is showcased for SCD MEMS resonators. In this setup, the electrode on the resonator is grounded, while the electrode on the SCD substrate, connected to an RF signal, is utilized to actuate the motion of the resonator. Notably, the SCD resonators exhibit reliable and efficient actuation across a wide temperature range, from room temperature to 500 °C.

Keywords:

• Single-crystal diamond
• MEMS
• actuation
• high temperature

1. Introduction

Microelectromechanical system (MEMS) resonators have various applications in high-temperature fields due to their small size, low power consumption, and ability to withstand harsh environments, such as sensors, actuators, oscillators, and accelerometers [1–3]. Single-crystal diamond (SCD) is a promising material for MEMS by virtue of its superior electronic properties, outstanding mechanical properties, the highest thermal conductivity, and chemical inertness [4–10]. SCD MEMS resonators exhibit significant potential across diverse applications, such as atomic force microscopies [11–13], nitrogen-vacancy (NV) center magnetic sensors [14, 15], magnetostriction-based magnetic sensors [6, 16, 17], and radio-frequency switch [18], especially for employing in high temperatures. The actuation and signal readout are pivotal in achieving optimal performance for MEMS resonators operating in high-temperature environments. Currently, a variety of readout techniques have been devised for MEMS resonators, encompassing optical, piezoresistive, piezoelectric, and capacitive methods [19]. Amongst these readout systems, the optical and piezoresistive methods have been employed for SCD MEMS resonators under high temperatures [16, 20, 21].

Alternatively, several approaches are commonly utilized to actuate a resonator beam, which involve electromagnetic, electrothermal, piezoelectric and electrostatic techniques [22]. The electromagnetic approach offers the advantages of straightforward implementation and efficient actuation. However, its reliance on a substantial external magnetic field and an electric current poses difficulty for the integration with other electronic components and microsystems [19]. In the electrothermal approach, it offers the benefit of achieving significant displacement and excellent integration. However, it has the weakness of samples heating, sensitivity to ambient temperature, and high energy consumption. The piezoelectric approach offers the benefit of integrating actuation and readout functionalities, while achieving appropriate displacements by tailoring the applying voltages [23]. However, it is susceptible to issues commonly associated with microfabrication processes, sensitivity to ambient temperature, and external interference from self-resonance signals. The electrostatic method is easy to integrate with electronics and microsystems [24–26]. It suffers from the compromise between force and displacement amplitude and the occurrence of pull-in effect. The functions of actuation and readout can be achieved through the piezoelectric effect and electrostatic actuation. At room temperature, these mentioned actuation techniques can be employed to diamond MEMS resonators. In high temperature conditions, a crucial factor is the thermal stability of the actuation system. The electrothermal effect and electrostatic effect in the actuation process are basically able to achieve effective high-temperature actuation for SCD MEMS resonators [27, 28]. The utilization of the electrothermal effect in the actuation process leads to the generation of external Joule heat, thereby hampering the device performance at elevated temperatures. The electrostatic system was initially used to achieve high-temperature actuation of SCD MEMS resonator without dedicated design [16, 20, 21]. In high-temperature conditions, the effectiveness and reliability of the electrostatic actuation of SCD MEMS resonators is an issue. In order to integrate SCD MEMS resonators into diverse applications that involve high temperatures, a more comprehensive understanding of electrostatic actuation with well-designed structure for SCD MEMS resonators is required.

In this work, we demonstrated the electrostatic actuation by designing metal electrodes on the SCD substrate and the SCD resonator to enable high-temperature actuation of the SCD MEMS resonators. The actuation principle of the electrostatic system was demonstrated. The impacts of the actuation voltage on the resonance frequency and vibration amplitudes were investigated in detail. Through this actuation method, the thermal-stability of SCD MEMS resonators was examined, revealing a low temperature ­coefficient of frequency (TCF) below −12 ppm/°C up to 500 °C. This work provides an actuation scheme for SCD MEMS resonators designed for high-temperature environments, ensuring both high reliability and high performance.

2. Experimental

We implemented a smart-cut fabrication approach for SCD MEMS resonators by the utilization of the ion implantation-assisted lift-off (IAL) technique [6, 29–31]. The method facilitated the precise control of dimensions for the SCD MEMS resonators, ranging from the nanoscale to the microscale. The fabrication process commenced with a high-pressure, high-temperature (HPHT) type-Ib SCD substrate, as shown in Figure 1a. The carbon ions were selectively implanted into the HPHT SCD substrate. Subsequently, the as-implanted SCD substrate was undergone the cleaning process in a boiling acid solution of HNO₃/H₂SO₄ before the homoepitaxial diamond growth. The growth of diamond epilayer was achieved by using the MPCVD apparatus. Throughout the MPCVD growth, the CH₄/H₂ flow ratio was maintained as 0.1%, with a hydrogen flow rate of 500 sccm. The growth temperature ranged from 850 to 950 °C. The thickness of the epitaxial layer is about 0.4 μm. The root mean square (RMS) of surface roughness is 0.13 nm (Fig. S1, Supporting information). Post to the growth, the diamond epilayer underwent annealing at 1100 °C for 3 h in an ultrahigh vacuum chamber (base pressure 10⁻⁷Pa) to minimize ion-impinged defects within the diamond. During the growth and annealing process, the damaged layer induced by the ion implantation was transformed into graphite-like carbon (GLC). The buried GLC layer served as a sacrificial layer for the creation of free-standing SCD resonator structure. After a boiling process in a HNO₃/H₂SO₄ acid solution, a photolithography procedure was employed to pattern the homoepitaxial layer to realize cantilever shapes. A metallic layer of aluminum film with 200 nm thickness was deposited on the patterned diamond epilayer as a mask for the dry etching, which was completed by the reactive ion etching (RIE) with oxygen gas. The lengths of the cantilevers were controlled by the dimension of the metal mask. Post to the etching treatment, the metallization was removed through photolithography. The SCD MEMS resonators was then released in the boiling acid solution (HNO₃/H₂SO₄). This manufacturing process produces a MEMS resonator with a SCD-on-SCD structure. A 10 nm-thick Au film was deposited onto the SCD substrate and the SCD resonators using an e-beam evaporator system, serving as the electrodes. Subsequently, a laser photolithography process was employed to define the actuation structure on the SCD resonator.

Figure 1. (a) Fabrication process of SCD MEMS resonators through the ion implantation-assisted lift-off (IAL) method. (b) Laser optical image of SCD MEMS resonators with different lengths, ranging from 50 to 160 μm. (c) Optical image of a 140 μm-length SCD cantilever with the electrical actuation configuration.

The 3D profiles of SCD resonators were examined by using 3D laser optical microscopy (VK-9710). The mechanical resonance characteristics of the SCD resonators were measured through using the Laser Doppler Vibrometry (LV 1710) system in conjunction with an optical readout system. These measurements were conducted within a vacuum chamber, maintaining a pressure below 10⁻³Pa. The electrode on the SCD resonator is grounded, while the electrode on the SCD substrate, connected to an RF signal, is utilized to actuate the motion of the resonator. Optical signals resulting from harmonic vibrations of the SCD resonators were detected using a lock-in amplifier system. Additionally, in order to ensure the stability of the structure and performance of the metal electrode, the maximum working temperature of this device was 500 °C. A heater beneath the SCD resonators was employed to control temperatures, ranging from 25 to 500 °C. The thermal-stability performance of a SCD resonator, denoted by the temperature coefficient of resonance frequency (TCF), signifies the proportional change in resonance frequency in response to temperature variations. In the case of a compact MEMS resonator, the TCF represents the proportional change in resonance frequency relative to temperature variations, expressed as [32–34], (1) $$\mathit{\text{TCF}}=\frac{\mathit{\text{df}}}{f_0\mathit{\text{dT}}}$$(1) f₀ is the resonance frequency at room temperature.

3. Results and discussion

Through the smart-cut method, the SCD resonators demonstrate impressive dimensional controllablity and reproucibility, as illustrated in Figure 1b. Figure 1c presents an optical image of a 140 μm-length SCD cantilever with the electrical actuation configuration. The Au eldctordes deposited on the SCD substrate and the SCD resonator, respectively, are utilized to actuate the movemetn of the SCD resonators from 25 to 500 °C. Figure 2a displays the schematic image of the SCD resonaotor actuated by the electrostatic force and readed out by the optical system. The electrode on the SCD resonator is connected to the ground, while the electrode on the SCD substrate, connected to an RF signal with an amplitude of V and a frequency of ω, is employed to induce the motion of the resonator. For a specific actuation voltage, V, a charge q is induced on a cantilever, represented by q = CV, where C is the capacitance between the Au electrode on the substrate surface and the resonator. The electrostatic force induces the bending in the resonator. In this work, V is defined as V = V'cos(ωτ). The total energy stored in the capacitor is denoted as E_eng = 1/2C(z)V² [35]. Wherein z is the distance between the Au electrode on the substrate and the resonator. The total electrostatic force on the resonator, which is given as [35], (2) $$F=\frac{\partial E_{\mathit{\text{eng}}}}{\partial z}=\frac{1}{2}\frac{\mathit{\text{dC}}}{\mathit{\text{dz}}}{(V\prime \mathrm{\text{cos}}\omega \tau )}^2$$(2)

Figure 2. (a) Schematic diagram of measurement setup of resonance vibration of SCD MEMS resonator. The electrode on the SCD resonator is grounded and the electrode on the SCD substrate connected to an RF signal is utilized to actuate the movement of resonator. (b) Distribution of the potential around the suspended SCD resonator stimulated by the finite element analysis. The applied voltage on the electrode is set as 1 V. (c) Dependence of electric field on the distance between the top surface of the resonator and the center of the electrode.

The periodic electric force generated by V'cos(ωτ), induces vibrational motion in the resonator. The maximum displacement of the cantilever occurs when the driving frequency matches its resonance frequency. We stimulated the distributions of potential and electric field surrounding the SCD resonator by using finite element analysis, as illustrated in Figure 2b. The Au electrodes are subjected to an applied voltage of 1 V. It is revealed that the electric field is concentrated around the resonator, which can achieve the efficient actuation (Figure 2b). Through this stimulation of the SCD resonator with various widths, it is noted that the efficient actuation relies on maintaining a small distance between the Au electrodes and the SCD resonator (Figure 2c).

Based on the electrical actuation structure, the resonance performances of SCD resonators were measured in detail under varying temperatures. The harmonic vibration characteristics of a rectangular MEMS resonator were described using the Euler-Bernoulli beam theory [5, 29, 36]. The resonance frequency is expressed as, (3) $$f=k\frac{t}{L^2}\sqrt{\frac{E}{\rho }}$$(3) wherein k represents the coefficient of 0.162 corresponding to the first vibration mode of the resonator. t and L denote the thickness and width of the resonator, respectively. E and ρ are the Young’s modulus and mass density of the resonator, respectively. In the case of a resonator comprising multiple layers, the Young’s modulus and mass density are characterized as the effective Young’s modulus and effective mass density, respectively. Figure 3a depicts the resonance frequency spectrum of a SCD MEMS resonator varied with the actuation voltages at room temperature. The vibration amplitude of the SCD MEMS resonator shows a linear increase with increasing actuation voltage, as illustrated in the inset of Figure 3a. Notably, the impact of actuation voltage on the resonance frequency of the resonator is minimal, as observed in Figure 3b. The length-dependent resonance frequency of the SCD MEMS resonator is presented in Figure 3c, d, aligning with the relationship between f and 1/L² expressed by Eq. (3)(3) $$f=k\frac{t}{L^2}\sqrt{\frac{E}{\rho }}$$(3) . The consistence between experimental and fitting data underscores the high reproducibility of the SCD MEMS resonators.

Figure 3. (a) Resonance spectrum of a SCD MEMS resonator (L = 140 μm) vs the actuation voltage at room temperature. (b) Resonance frequency and (c) peak amplitude as a function of the actuation voltage. (c) Dependences of resonance frequencies on (d) length, L and (c) L⁻² of SCD cantilevers.

Based on the actuation method, the resonance performances of the SCD MEMS resonator at high temperatures were examined. The temperature dependence of the resonance frequency spectrum with the normalized amplitude of a 140 μm-length SCD MEMS resonator is indicated in Figure 4a under the actuation voltage of 1 V. The resonance frequency undergoes a shift towards lower frequency as the Young’s modulus of SCD decreases with an increase in temperature. Generally, the temperature has an adverse effect on the Young’s modulus of materials [37–39]. A model was proposed to elucidate this phenomenon through an expression [39], (4) $$E=E_{T0}-\mathit{\text{AT}}\mathrm{\text{exp}}(-\frac{T_0}{T})$$(4) where E_T0 represents the Young’s modulus of the material at temperature T₀, and A is a constant. The rising temperature contributes to a reduction in the Young’s modulus of SCD, leading to a decrease in resonance frequency, as illustrated in Figure 4a. At elevated temperatures, as shown in Figure 4b, the amplitude of the resonance spectrum exhibits a linear increase with the actuation voltage, indicating the effective actuation of the SCD MEMS resonator. The temperature exhibits week impact on the peak amplitude of resonance spectrum due to the variations in the measurement laser positions on the cantilever under various temperatures. Notably, the actuation voltage of 100 mV can efficiently actuate the vibration of SCD MEMS resonator, contributing to realizing the low power consumption for the SCD resonator-based applications. Alternatively, at a specific temperature, the actuation voltage enhances the amplitude of the resonance spectrum due to the heightened electrostatic force associated with the actuation voltage. At different temperatures, the resonance frequency of the SCD MEMS resonator exhibits weak change with the actuation voltage (Figure 4c). It is attributed to the actuation voltage has an impact on the vibration amplitude of a SCD cantilever not the dimension and material properties, as show in Eq. (2)(2) $$F=\frac{\partial E_{\mathit{\text{eng}}}}{\partial z}=\frac{1}{2}\frac{\mathit{\text{dC}}}{\mathit{\text{dz}}}{(V\prime \mathrm{\text{cos}}\omega \tau )}^2$$(2) . The resonance frequency of the SCD MEMS resonator exhibits a dependence on the assessed temperature when subjected to different actuation voltages, as depicted in the inset of Figure 4d. The disclosed findings reveal that the resonance frequency decreases with rising temperature, attributed to the reduction in Young’s modulus (Eq. 4(4) $$E=E_{T0}-\mathit{\text{AT}}\mathrm{\text{exp}}(-\frac{T_0}{T})$$(4) ). Conversely, the influence of the actuation voltage on the decreasing trend of resonance frequency with temperature is relatively weak. Referring to Eq. (1)(1) $$\mathit{\text{TCF}}=\frac{\mathit{\text{df}}}{f_0\mathit{\text{dT}}}$$(1) , the variations of the TCF of the SCD MEMS resonator with the evaluated temperature by applying various actuation voltages are indicated in Figure 4d. The results demonstrate that the TCF consistently remains below −12 ppm/°C across different actuation voltages up to 500 °C, underscoring the remarkable thermal stability of the SCD MEMS resonators. The absolute value of TCF of the SCD is significantly lower than that of Si with an absolute value of 35 ppm/K [40, 41]. This actuation approach is in favor of realizing the efficient actuation for the SCD MEMS resonators when applied in high temperature regimes without scarifying performances. The Q factors of SCD cantilevers are obtained by the Lorentz-fitting of the measured resonance spectra. In Figure 4e, the relationships between the Q factors and actuation voltages are presented at various temperatures. Notably, it is observed that the actuation voltage exerts little influence on the Q factor across different temperatures. Alternatively, Figure 4f illustrates the changes in Q factors with varying temperatures under different actuation voltages. The Q factor initially decreases and then increases with the temperature rising. Firstly, the thermoelastic dissipation (TED) loss increases with the temperature, resulting in the reduction in Q factor. The increase in Q factor with temperature rising is attributed to the excitation of deep defects at evaluated temperature, which leads to the decrease in mechanical defect dissipation [42]. Importantly, the applied actuation voltage does not alter the observed variation tendency of the Q factor with the temperature.

Figure 4. (a) Resonance spectrum shifts of a SCD MEMS resonator (L = 140 μm) as a function of the measurement temperature at the actuation voltage of 1 V. (b) Peak amplitudes of resonance spectra vs the actuation voltages at various temperatures. (c) Dependences of resonance frequencies on the actuation voltages at various temperatures. (d) Variations in the temperature coefficient of resonance frequency (TCF) with the temperatures under different actuation voltages. The inset is the correlation between resonance frequencies and the actuation voltages at various temperatures. (e) Q factors vs the actuation voltages at various temperatures. (f) Q factors as a function of the temperatures at various actuation voltages.

4. Conclusions

In summary, we developed a one-side clamped SCD MEMS resonator that utilizes the electrostatic force for actuation, demonstrating operational capability across a wide temperature range from room temperature to elevated temperatures. We achieved the efficient actuation of SCD resonators with the fundamental out-of-plane vibrations, with the resonance frequencies ranging from a few kHz to nearly 500 kHz. Higher amplitude actuation was expected to be measured by the displacement of optical readout scheme. Notably, a low actuation voltage of 100 mV proved sufficient for the efficient operation of the SCD MEMS resonator even at 500 °C. Remarkably, the actuation voltage demonstrated minimal impact on the resonance frequency and the Q factor of the resonator, particularly under high-temperature conditions. The SCD MEMS resonator exhibited exceptional thermal stability in resonance frequency, showcasing a low TCF below −12 ppm/°C up to 500 °C. The advanced actuation scheme shows significant potential as a resilient platform for implementing SCD MEMS/NEMS devices, especially in scenarios demanding extensive electrical integration under elevated temperatures.

Authors’ Contributions

Zilong Zhang: Methodology, investigation, writing-original draft and editing, writing-review and editing. Keyun Gu: writing-editing. Guo Chen: writing-editing. Masataka Imura: writing-editing. Meiyong Liao: Conceptualization, methodology, supervision, writing-original draft review and editing, writing-review and editing.

Disclosure statement

The authors declare that they have no competing interests.

Additional information

Funding

This work was supported by JSPS KAKENHI (Nos. 20H02212, 22K18957, 15H03999), a Grant-in-Aid for JSPS Research Fellows (No. 22KF0382), and Bilateral joint research between JSPS/CAS, Advanced Research Infrastructure for Materials and Nanotechnology in Japan (ARIM) of MEXT (JPMX­P1223NM5297) sponsored by the Ministry of Education, Culture, Sports, and Technology (MEXT) of Japan.