Developing an Energy-Efficient Electrostatic-Actuated Micro-Accelerometer for Low-Frequency Sensing Applications

Abstract

Micro-accelerometers are in high demand across many due to their compact size, low energy consumption, and excellent precision. Since gravity causes a large movement when the device is positioned vertically, measuring low gravitational acceleration is challenging. This study examines the intrinsic relationship between applied voltage levels and displacement in micro-accelerometers. The study introduces a novel design that integrates hybrid flexures, comprising both linear and angular configurations, with an out-of-plane overlap varying (OPOV) electrostatic actuation mechanism. This design aims to measure the micro-accelerometer’s movement and low frequency response. The proposed device with silicon material is designed and simulated using the IntelliSuite^® software, considering its small dimensions and 25 µm thickness. The norm value of 28.0916 μN from gravity’s reaction forces on the body, a resonant frequency of 179.668 Hz at the first desired mode, and a maximum stress of 24.7 MPa were obtained through the electro-mechanical analysis. A comparison of the proposed design was conducted with other configurations, measuring a frequency of 179.668 Hz at a minimum downward displacement of 7.69916 µm under the influence of gravity without electrostatic mechanisms. Following this, an electrostatic actuation mechanism was introduced to minimize displacement by applying different voltage levels, including 1 V, 1.5 V, and 3 V. At 3 V, a significant improvement in displacement reduction was observed compared to the other applied voltages. Additionally, dynamic and sensitivity analyses were carried out to validate the performance of the proposed design further.

1. Introduction

In recent decades, there has been substantial growth in micro-device development, marked by rapid advancements in fabricating miniaturized structures and their integration with microelectronic components [1,2,3,4]. Micro-devices include energy harvesters, accelerometers, actuators, etc. [5,6,7,8]. Micro-accelerometers, characterized by their compact size, lightweight design, affordability, and energy efficiency, have garnered noteworthy commercial success over the past few years [9,10]. Piezoresistive, electrostatic or capacitive, piezoelectric, thermal, optical, resonant, and magnetic accelerometers are among the different types of micro-accelerometers. Compared to other accelerometers, capacitive accelerometers have low noise, and are less sensitive to variations in temperature [11,12,13,14,15].

Microelectromechanical systems (MEMS)-based electrostatic mechanisms leverage electrostatic forces for actuation, sensing, and controlling mechanical movements at the microscale, making them essential in various real-world industrial applications. They operate through electrostatic actuation, where forces generated between charged plates allow precise movement and sensing elements that detect changes in physical properties by measuring variations in capacitance [16,17]. These mechanisms are crucial in automotive systems for accelerometers, in consumer electronics for microphones, in healthcare for drug delivery, and in industrial automation for flow sensors, due to their high precision, low power consumption, and miniaturization [18,19].

The frequency of micro-accelerometers can be reduced by optimizing the mass and spring stiffness [20,21,22]. However, lowering the frequency by increasing the moving mass of the device is not an effective approach for micro-accelerometers Additionally, existing micro-accelerometers designed by different authors depend on linear flexure and in-plane gap-closing mechanisms.

Previous studies [9,23,24,25,26] have demonstrated comb-drive capacitive accelerometers operating at relatively high resonant frequencies (ranging from 1.43 kHz to 12.79 kHz), typically employing in-plane gap-closing mechanisms and linear flexures. In contrast, low-frequency designs, such as the 15.2 Hz resonator developed in [27], require significantly larger device dimensions, thicker substrates, and heavier proof masses. Other approaches, like the one in [28], combine gap-closing mechanisms with linear flexures in compact packages to enable low-level ground motion detection. These studies highlight the trade-off between device miniaturization and operating frequency, which motivates the need for alternative strategies such as the one proposed in this work.

Several studies have explored capacitive accelerometer designs and performance enhancements. For example, a MEMS based accelerometer design was proposed that significantly reduces parasitic capacitance and improves sensitivity [29], while others have addressed critical factors such as bias stability for navigation applications through mass and structural optimization [30]. In addition, nanoscale effects like rippling deformation in carbon nanotube-based actuators have been shown to significantly influence dynamic behavior and pull-in characteristics [31].

In [32], the authors presented a MEMS-based electrostatic gripper utilizing inchworm motors and integrated sensing, capable of generating up to 15 mN of force with a 1 mm displacement range, demonstrating precise actuation suitable for microscale manipulation tasks. Complementing such advancements in MEMS actuation, the work in [33] introduced ZnO nanowire resonators with enhanced room-temperature sensitivity through feedback control, enabling single-molecule detection with a resolution of 0.076 zg and a low error margin of 3.9%. These studies collectively underscore key innovations in MEMS actuators and small-scale sensing, both of which are critical for advancing high-resolution, high-sensitivity micro-accelerometer systems.

Designing micro-accelerometers to operate efficiently at low gravitational accelerations (g) poses a significant challenge. Many current capacitive accelerometers employ linear or folded beam flexures, often exhibiting substantial deflection at low frequencies. Moreover, the gap-closing mechanisms in these devices can cause potential collisions between fixed and moving fingers. Therefore, this research presents an innovative method for designing a capacitive accelerometer without increasing the proof mass of the device. The main research contributions of this study include:

• A novel design has been presented to achieve low frequency with minimal deflection, accomplished without increasing the device’s proof mass. Hybrid flexures, combining both linear and angular configurations, were utilized instead of relying solely on linear flexures. This approach effectively minimizes deflection in vertically positioned devices;
• The design has incorporated an out-of-plane overlap varying (OPOV) mechanism to prevent potential collisions between driving and sensing fingers, especially when the devices are mounted vertically;
• The study investigated the effect of different voltage levels on minimizing device deflection. A comparison of the proposed device with other flexure configurations was also provided. Various types of analyses, including electromechanical analysis, dynamic analysis, and sensitivity analysis, were performed for different cases.

The structure of this paper is as follows: Section 2 describes the materials and methodology, Section 3 reports and interprets the results, and Section 4 summarizes the conclusions along with directions for future work.

2. Materials and Methods

An accelerometer functions as a sensor specifically designed to measure acceleration. In this research, the proposed accelerometer design utilizes a non-linear mass–spring–damper system to detect displacement or deformation resulting from acceleration. The simulation experiments utilize a finite element method (FEM) approach and have been conducted using the thermo-electromechanical (TEM) module within the IntelliSuite^® software (version 8.8).

2.1. Proposed System

The proposed device is designed as a mass–spring–damper system, incorporating electrostatic comb drives as actuation mechanisms, as shown in the 2D schematic diagram in Figure 1. It consists of a central proof mass (m), with arrows at the center indicating the direction of motion. The flexure configuration is hybrid, combining both linear and angular flexures. The system includes fixed and movable comb drives functioning as electrostatic actuators by applying an external voltage through a voltage source. The entire structure is supported and constrained by anchors, which serve as mechanical ground and establish fixed reference points for the device’s movement.

For a design incorporating comb drive fingers, the $m$ can be calculated using (1)–(2), which considers mass length ($l_m)$, mass width ($w_m)$, and device thickness ($t_d)$, along with the material density ($\rho )$.

$$m=\rho \left(l_m·w_m·t_d\right)$$

(1)

$$m\approx \rho t_d(l_{cm}·w_{cm}+{N_{combs}·l}_{m\_ac}·w_{m\_ac}+4·(l_{lf}·w_{lf}+l_{af}·w_{af}\left)\right)$$

(2)

where:

$l_{cm}$: length of central movable mass;

$w_{cm}$: width of central movable mass;

$N_{combs}$: Total Number of movable actuator combs;

$l_{m\_ac}$: length of movable actuator comb.

$w_{m\_ac}$: width of movable actuator comb;

$l_{lf}$: length of linear flexure;

$w_{lf}$: width of linear flexure;

$l_{af}$: length of angular flexure;

$w_{af}$: width of angular flexure.

The natural frequency in hertz (Hz) is given by (2).

$$f={\displaystyle \frac{1}{2\pi }}\sqrt{{\displaystyle \frac{k_{eff}}{m}}}$$

(3)

where, $k_{eff}$ is the effective stiffness of hybrid flexure.

Electrostatic force ($F_e)$ is directly proportional to the square of the applied voltage ($V$) and to the rate of change of capacitance ($C)$ with respect to displacement ($y$), as defined in (4).

$$F_e={\displaystyle \frac{1}{2}}{\displaystyle \frac{\partial C}{\partial y}}{V}^2$$

(4)

The gravitational force ($F_g)$ and the spring force ${(F}_s)$ are defined in (5) and (6), respectively.

$$F_g=mg$$

(5)

$$F_s=k_{eff}·y$$

(6)

The net force ${(F}_{net})$ is defined in (7).

$$F_{net}=F_s-F_g-F_e$$

(7)

At equilibrium, $F_{net}=0$. In the context of gravitational acceleration, the initial displacement of a moving body, in the absence of applied voltage or $F_e=0$, can be calculated using (8). This equation accounts for the gravitational influence on the body’s motion, used to determine its initial displacement ($y)$ based on the given acceleration due to gravity.

$$y={\displaystyle \frac{mg+F_e}{k_{eff}}}$$

(8)

The magnitude of a 3D force vector with components along the x-, y-, and z-axes can be determined by (9). It gives the total resultant force acting on an object by combining these directional forces to maintain stability and structural integrity. Reaction forces, in this context, counter external forces.

$$‖F‖=\sqrt{F_x^2+F_y^2+F_z^2}$$

(9)

Stress (σ) can be defined by (10).

σ = ε E

(10)

where:

E: Young’s modulus in Pascal (Pa); and ε = strain.

2.2. Electrostatic-Actuated Mechanism

In this study, an OPOV electrostatic-actuated mechanism employing capacitive comb drives is utilized to counteract displacements induced by gravitational acceleration (1 g = 9.8 m/s²) when the device is vertically positioned. This configuration comprises fixed and moving combs separated by a dielectric medium. At the equilibrium position (zero volts), no capacitance variation is observed. The capacitance achieves its maximum and minimum values when the overlap distance between the fixed and moving plates is at its maximum and minimum, respectively, as shown in Figure 2.

Sensing and driving fingers are considered as fixed and moveable fingers, respectively. Initially, the OPOV mechanism acts as an electrostatic actuating mechanism by applying different levels of input voltages to minimize the displacement of the vertically mounted proof mass of the device. After the desired displacement is reached, the input voltage supply is cut off, and the OPOV mechanism functions as a capacitive sensor, detecting changes in capacitance as the device oscillates up down under the influence of gravitational acceleration. Capacitance, $C_0\left(y\right)$ at equilibrium position, and $C_{1a}\left(y\right)$ and $C_{1b}\left(y\right)$ at a certain direction of displacement ($y),$ is indicated in (11–13). When the device moves vertically downward, the capacitance $C_{1a}\left(y\right)$ will be maximum due to the maximum overlap between fixed and movable fingers. Conversely, capacitance $C_{1a}\left(y\right)$ will be minimum when the device moves upward due to minimum overlap. The overall capacitance will result from all maximum and minimum capacitance values at each value of $y$. $C_{1b}\left(y\right)$ will be a small capacitance value that will be increased and decreased slightly when the device moves upward and downward, respectively. Equivalent capacitance $C_t\left(y\right)$ can be calculated by (14).

At equilibrium: x = 0.

$$C_0(y)={\displaystyle \frac{{\epsilon }_0{N}_{combs}{t}_d}{d_{gap}}}\left(d_{overlap}\right)$$

(11)

Downward direction:

$$C_{1a}(y)={\displaystyle \frac{{\epsilon }_0{N}_{combs}{t}_d}{d_{gap}}}\left(d_{overlap\_1}-y\right)$$

(12)

Upward direction:

$$C_{1b}(y)={\displaystyle \frac{{\epsilon }_0{N}_{combs}{t}_d}{d_{gap}}}\left(d_{overlap\_2}+y\right)$$

(13)

$$C_t\left(y\right)=C_{1a}\left(y\right)+C_{1b}\left(y\right)$$

(14)

2.3. Design and Simulation Process

IntelliSuite^® (Version 8.8), an industry-standard MEMS software, was used for the design and simulation in this study. Figure 3 illustrates the sequential flow from design conception to simulation outcomes using different software modules. These modules guide the entire process, encompassing the design stage to simulation experiments. The interconnected nature of these modules facilitates a seamless transition from conceptualization to analysis, enhancing the efficiency of the overall design and simulation workflow.

2.4. Material and Properties

This research utilizes silicon material for the proposed device simulations due to its cost-effectiveness, mechanical strength, and compatibility with Silicon-On-Insulator Multi-User MEMS Processes (SOIMUMPs). In the context of SOIMUMPs, key considerations for temperature sensitivity include silicon’s thermal expansion, temperature-dependent Young’s modulus, and changes in resistivity. Silicon exhibits lower thermal expansion and higher thermal conductivity, which contribute to its thermal stability. The material properties of silicon are presented in

Table 1. Properties of material.

Properties	Value	Properties	Value
Poisson ratio	0.226	Specific heat	0.71 J/g/C
Relative permittivity	1	Coefficient of thermal expansion	2.9 $\times$ ${10}^{-6}$ °C−1
Resistivity	1 ohm·cm	Thermal conductivity	1.5 W/cm/°C
Young’s modulus (E)	160 GPa	Density	2.3 g/cm3
Permittivity of free space	8.854 × 10−12 F·m

.

3. Results and Discussions

This section presents the results and discussions.

3.1. Micro-Accelerometer Design

The proposed micro-accelerometer device was designed using the Intellimask module.

Table 2. Dimensions of the proposed device.

Dimension	Symbol	Value
Length of proof mass	$l_m$	2 mm
Width of proof mass	$w_m$	2 mm
Length of linear flexure	$l_{lf}$	0.98 mm
Width of linear flexure	$w_{lf}$	2 µm
Length of angular flexure	$l_{af}$	160 µm
Width of angular flexure	$w_{af}$	4 µm
Length of actuator’s comb	$l_{ac}$	160 µm
Width of actuator’s comb	$w_{ac}$	2 µm
Overlap distance between fixed and moving comb	$d_{overlap}$	40 µm
Gap between fixed and moving comb	$d_{gap}$	2 µm
Total number of combs	$N_{combs}$	250
Device thickness	$t_d$	25 µm

outlines the dimensions of the micro-accelerometer, detailing the sizes of its various components.

Table 3. Analytical findings based on device dimensions and material properties.

Analytical Findings	Symbol	Value
Damping coefficient	$b$	3.95 × 10−5 Ns/m
Damping ratio	$\zeta$	0.0244
Initial displacement at gravity	$y_0$	7.70 $\mathsf{\mu }\mathrm{m}$
Stiffness of flexure	$k$	0.88968 N/m
Mass of movable device	$m$	6.98124 × 10−7 kg

provides analytical findings related to the proposed device, including results from simulations and theoretical calculations that enhance the understanding of the device’s performance and behavior. Figure 4 presents a 2D representation of the actual design.

3.2. TEM Simulations

Two scenarios have been presented for analyzing the design: one without the electrostatic mechanism and the other incorporating it.

3.2.1. Case I: Design Without Electrostatic-Actuated Mechanism

TEM simulations were conducted under various conditions, including scenarios with no electrostatic actuation (zero applied voltage) while the device was subjected to 1 g acceleration. Figure 5 shows the displacements of the device along each y-axis.

When positioned vertically, the device exhibits its maximum negative displacement along the y-axis, measuring 7.69916 µm, reflecting downward motion caused by gravitational acceleration. Conversely, the displacements along the x-axis and z-axis are smaller, measured at 0.02379 µm and 0.153855 nm, respectively. These displacement measurements provide valuable insights into the device’s behavior under complex circumstances.

As the movable part of the device deviates from its equilibrium position due to gravitational acceleration, it initiates reaction forces that act in the opposite direction of the motion. The maximum norm, which represents the overall magnitude of all reaction forces ($F_x,F_{y}and{F}_z)$, is measured at 28.0916 μN as indicated in Figure 6. This data is essential for evaluating the mechanical response of the device under the influence of gravity, supporting the assessment of its stability and structural integrity.

Stress analysis was performed to ensure that the device operates under safe conditions, as shown in Figure 7. The simulation results indicate that the maximum stress is around 24.7 MPa, which is significantly less than the yield strength for strain values ranging from 5 to 10. This is a positive indicator, suggesting that the material will not undergo plastic deformation under this level of stress.

To compare with other flexure configurations, the proposed design, shown in Figure 5, is designated as design A. This design features symmetric flexure configurations without an electrostatic actuation mechanism. In contrast, design B employs a mirror-symmetric approach, with the bottom flexure inverted compared to design A. Design C consists of all-linear flexures with a width size of 2 µm. Finally, design D incorporates angular-symmetric flexures, where the largest flexures are shifted by 3 degrees.

A comparative study was conducted on all design configurations, subjecting them to gravitational acceleration. The obtained frequencies for design A, B, C, and D were 179.668 Hz, 203.376 Hz, 94.4886 Hz, and 1986.990 Hz, respectively, as shown in

Table 4. Comparison between different design configurations.

Design	Flexure Configuration	$\mathit{d}\left(\mathsf{\mu }\mathbf{m}\right)$	Desired Mode	$\mathit{f}\left(\mathbf{H}\mathbf{z}\right)$
A	Hybrid-symmetric	−7.69916	First	179.668
B	Hybrid-mirror symmetric	−6.00764	First	203.376
C	All linear	−27.8324	First	94.4886
D	All angular	−0.06395	Third	1986.990

. The design-C exhibits the lowest frequency compared to the other configurations, but its corresponding displacement is too large. For design D, the displacement is small, but the frequency associated with its desired mode is very high, making these two configurations less reliable. Designs A and B have similar displacements; however, there is a significant variation in their frequencies. Design A is considered the most favorable for this study due to its lower frequency compared to designs B and D, and its smaller displacement compared to design C.

Discretizing the model’s geometry into small, finite-sized elements is the standard approach for meshing in FEM simulations. A mesh study was performed on Design A to observe changes in frequency at different mesh sizes, as shown in

Table 5. Comparison between natural frequencies at different mesh sizes.

S. No	Max. Mesh Size (µm)	Frequency (Hz)	Percentage Change in Frequency
1	100	220.33	N/A
2	50	210	−4.92%
3	25	179.668	−14.44%
4	15	179.235	−0.24%
5	5	178.543	−0.386%

. At a 25 µm mesh size, a frequency of 179.668 Hz was obtained, which is lower than the frequencies at 50 µm and 100 µm mesh sizes, indicating convergence. Further reduction in element size significantly increases computational cost, simulation run time and can introduce numerical instability without noticeable improvement in accuracy. Importantly, the frequency at this mesh resolution closely matches the analytically calculated frequency, supporting the adequacy of the chosen mesh size.

The natural frequency is directly proportional to the square root of flexure stiffness. The proposed Design A configuration demonstrates a resonant frequency of 179.668 Hz at a stiffness of 0.88968 N/m. Figure 8 shows the changes in resonant frequency behavior at various flexure stiffness levels, a parabolic growth pattern emerges between different flexure stiffnesses and resonant frequency values. Therefore, for the same device weight, different small frequency values can be obtained by varying the flexure configuration.

3.2.2. Case II: Design with Electrostatic-Actuated Mechanism

In this case, the OPOV electrostatic-actuated mechanism design has been utilized for simulation purposes. To mitigate the displacement of vertically mounted devices caused by gravitational acceleration, specific voltage levels are used. In this study, we have chosen three voltage levels: 1 V, 1.5 V, and 3 V, applied to the electrostatic mechanisms and analysis are shown in Figure 9, Figure 10 and Figure 11. These voltages result in displacement reductions of approximately –5.42414 μm, −3.05423 μm, and −1.37246 × ${10}^{-5}$ μm, respectively, as shown in Figure 12.

Increasing applied voltages correspond to more significant reductions in displacement, showcasing the adjustable capability of the electrostatic-actuated mechanism to counteract gravitational effects on the device. Figure 12 shows a box plot of the displacement variation across different applied voltages. As shown, at 3 V, the device moves upward from the bottom position of −7.69916 μm (at 0 V) to a mean position of −1.37246 × 10⁻⁵ μm. In comparison, at 1 V and 1.5 V, the respective displacements are −5.42414 μm and −3.05423 μm.

Applying voltages to the electrostatic actuators resulted in changes in capacitance as well as a decrease in displacement.

Table 6. Comparison between different levels of electrostatic actuation.

Voltage (V)	Capacitance (pF)	$\mathit{y}\left(\mathsf{\mu }\mathbf{m}\right)$	$\mathbf{Percentage}\mathbf{Improvement}\mathbf{in}\mathit{y}$
0	N/A	−7.69916	0%
1	1.26	−5.42414	29.55%
1.5	1.19	−3.05423	60.33%
3	1.11	−1.37246 × 10−5	99.96%

compares different voltage levels applied to proposed design A to determine the percentage improvement in displacement $y$, using −7.69916 μm as the baseline value at 0V. Percentage improvement in displacement $y$ is determined by (15).

$$\%Improvementiny={\displaystyle \frac{(y_{new}-y_{base})}{y_{base}}}\times 100\%$$

(15)

As the voltage increases, the capacitance decreases, and the displacement is progressively reduced. For example, at 1 V, the displacement decreases to −5.42414 μm, which represents a 29.55% improvement compared to the baseline. With further increases in voltage to 1.5 V and 3 V, the displacement reduces to −3.05423 μm (a 60.33% improvement) and −1.37246 × 10⁻⁵ μm (a 99.96% improvement), respectively.

The time-domain acceleration at various actuation voltage levels, showcasing oscillations as shown in Figure 13. The acceleration is measured in Gal, where 1 Gal is equivalent to 0.01 m/s². The figure demonstrates that at an actuation voltage of 3 V, the system exhibits oscillations with minimal acceleration values, resulting in lower acceleration levels compared to other applied voltage cases. This behavior is critical for applications requiring the measurement of low gravitational accelerations (low g). The device’s ability to capture and record small acceleration levels, as indicated by the response at 3V, underscores its sensitivity and suitability for precision measurements in scenarios where low-g forces are of importance. This characteristic makes the accelerometer highly suitable for applications that demand both high sensitivity and accuracy in detecting subtle changes in acceleration.

A dynamic analysis of the system at a DC bias voltage of 3 V was performed through the calculation of the transfer function, Q-factor, and Bode plots to characterize its frequency response as shown in Figure 14. The magnitude plot starts near 0 dB at low frequencies, indicating minimal attenuation. As the frequency increases, the magnitude rises sharply and reaches a pronounced peak of approximately 30 dB around 179 Hz, corresponding to the resonant frequency. Beyond this peak, the magnitude decreases steadily, falling below −30 dB at higher frequencies. The phase plot begins near 0 degrees at low frequencies and remains relatively constant until close to the resonant frequency. At around 179 Hz, the phase drops sharply to approximately −175 degrees, reflecting the system’s resonant behavior. After this drop, the phase stabilizes again and remains nearly constant for frequencies well beyond 1000 Hz. These features are consistent with the expected response of a damped mass–spring system with electrostatic softening.

At different applied voltage levels, varying displacements are observed, which lead to the determination of forces acting on the moving device, such as electrostatic force, gravitational force, spring force, and the resultant net force. If, after a small displacement, the net force restores the system toward equilibrium, the system is considered stable. At 3V, the system approaches the equilibrium state and steady state condition, as the net forces at the corresponding displacement are close to the net forces at the equilibrium.

Figure 15 shows sensitivity analysis performed using different applied voltages and spring constants. The observed peak sensitivity within the 2.5–3 V and 0–0.88 N/m region corresponds to a dynamic range where the electrostatic and mechanical restoring forces are favorably balanced, producing a strong system response optimal for sensing applications. The variations in sensitivity throughout the rest of the parameter space arise from the system’s inherent nonlinearities and illustrate how sensitivity decreases outside this optimal operating window.

4. Conclusions

Micro-accelerometers are widely utilized across various sectors, including industrial monitoring, automotive systems, structural health monitoring, space missions, and seismic monitoring. However, designing low-frequency micro-accelerometers, particularly for vertically mounted devices, presents several challenges. These difficulties arise from the substantial deflection induced by gravitational forces, resulting in a significant increase in displacements. To overcome this challenge, a novel design is proposed, integrating both linear and angular flexures, along with an electrostatic-actuated mechanism. By applying varying voltage levels, such as 1 V, 1.5 V, and 3 V, through the actuation mechanism, the movable part’s deflection is reduced, effectively maintaining the mass close to its mean position with minimal displacements. The reaction forces exerted on the body due to gravity yield a norm value of 28.0916 μN. Remarkably, a significant performance improvement in minimizing displacement is observed at 3 V among different voltage levels. At this voltage level, the system achieves a steady-state condition and approaches near-equilibrium. Sensitivity analysis conducted with varying applied voltages and spring constants indicated a maximum acceleration of 0.30–0.31 Gal. The modeled device is cost-effective and compact, with dimensions of 2 mm × 2 mm and a thickness of 25 μm, utilizing silicon material properties. The proposed device achieves a low frequency of 179.668 Hz compared to another geometric configuration

Silicon material was chosen for this study due to its proven mechanical properties, thermal stability, and compatibility with standard SOIMUMPs, making it ideal for MEMS applications. While alternative materials may offer specific advantages, the reliability and manufacturability of silicon justify its exclusive use in this investigation. Future research work will explore other materials for specialized applications. Additionally, experimental validation in conjunction with simulations performed using IntelliSuite software is recommended. Real-world testing can provide critical insights into the practical performance of the proposed design post-fabrication, allowing for a comprehensive assessment of its effectiveness and reliability under actual operating conditions. This combined approach can enhance understanding of the device’s behavior and facilitate further optimization of the design for practical applications.