Micro-Electromagnetic Vibration Energy Harvesters: Analysis and Comparative Assessment ^†

Abstract

The development of Micro-electro-magnetic Vibration Energy Harvesters (MEMVEHs) plays a crucial role in advancing self-powered nanophotonic, nanoelectronic, and nanosensor systems. As energy autonomy becomes critical for miniaturized devices, MEMVEHs offer a sustainable power source for low-power nanodevices operating in wireless sensor networks, wearable electronics, and biomedical implants. This study provides a comparative assessment of MEMVEH technologies and evaluates their integration potential within next-generation nanoscale systems, enabling enhanced performance, longevity, and energy efficiency of emerging nanotechnologies. Electromagnetic vibration energy harvesters (EMEHs) based on microelectromechanical system (MEMS) technology are promising solutions for powering small-scale, autonomous electronic devices. In this study, two electromagnetic vibration energy harvesters based on microelectromechanical (MEMS) technology are presented. Two models with distinct vibration structures were designed and fabricated. A permanent magnet is connected to a silicon vibration structure (resonator) and a tiny wire-wound coil as part of the energy harvester. The coil has a total volume of roughly 0.8 cm³. Two energy harvesters with various resonators are tested and compared. Model A’s maximum load voltage is 163 mV, whereas Model B’s is 208 mV. A maximum load power of 59.52 μW was produced by Model A at 347 Hz across a 405 Ω load. At 311.4 Hz, Model B produced a maximum load power of 149.13 μW while accelerating by 0.4 g. Model B features a larger working bandwidth and a higher output voltage than Model A. Model B performs better than Model A in comparable experimental settings. Simple study revealed that Model B’s electromagnetic energy harvesting produced superior outcomes. Additionally, it indicates that a nonlinear spring may be able to raise the output voltage and widen the frequency bandwidth.

1. Introduction

Energy harvesters, also known as micro power generators, have grown in importance in recent years as a means of enabling tiny sensors and actuators to be self-powered and avoid the need for frequent power replacement. The availability of sources including outside light, human motion, mechanical vibration, thermal energy, etc., has drawn a lot of attention to the topic of environmental energy harvesting. It has been demonstrated that mechanical vibrations are a viable environmental energy source with a wide range of uses [1,2,3,4,5].

Thus, vibration energy harvesters have gained popularity in the field of self-sustaining electricity. Electrostatic, piezoelectric, and electromagnetic methods are typically used to convert kinetic energy into electrical energy. Due to its low internal impedance, electromagnetic energy conversion offers the advantage of generating a high output current without the need for an external voltage source [6,7,8,9]. Since a stronger induction electromotive force may be produced at higher frequencies, several of the earliest devices that were documented operated at frequencies of several kHz [10,11,12,13,14,15]. As an example, Santosh Kulkarni et al. [4] designed a micro-scale energy harvester consisting of four magnets connected to a moving coil mounted on a cantilever beam [16,17,18,19,20]. This compact device, with a total volume of 106 mm³, is capable of producing 148 nW of power when subjected to an excitation of 3.9 ms⁻² at 8.08 kHz. However, most ambient vibration sources are classified as “low-level” vibrations, typically characterized by low frequencies (<500 Hz), minimal displacements (a few micrometers), and low accelerations (<2 g) [12]. Numerous research teams have continued to focus on the vibration energy harvester’s nonlinear properties in an effort to enhance its performance in recent years [21].

The comprehensive review [22], presents translational electromagnetic vibration energy harvesters (TEMEHs) as reliable and low-frequency power solutions for wireless sensor nodes, valued for their durability and structural simplicity. It identifies the main challenge as achieving high power density and discusses strategies such as nonlinear dynamics, multi-degree-of-freedom (multi-DOF) systems, and frequency tuning to expand bandwidth and improve efficiency. The paper categorizes TEMEHs into mechanical, MEMS-based, and magnetic suspension systems, outlining their respective trade-offs in miniaturization and adaptability. To standardize performance evaluation, it introduces metrics like Normalized Power Density (NPD) and Figure of Merit for Vibration (FoMv). Overall, the review underscores recent innovations and comparative benchmarks that guide the design of more efficient and miniaturized vibration energy harvesters [23].

The Review [24] highlights electromagnetic harvesters as durable, low-frequency power sources suitable for wireless sensor nodes and microdevices. It identifies achieving high power density as the main challenge and discusses strategies such as nonlinear dynamics, multi-DOF structures, and frequency tuning to improve efficiency and bandwidth. The paper also classifies devices by suspension type (mechanical, MEMS-based, and magnetic) and introduces standardized metrics like Normalized Power Density (NPD) for fair performance comparison. Overall, it provides a comprehensive overview of recent advances and design approaches for efficient, miniaturized vibration energy harvesters [24]. This study presents the design and simulation of MEMS-based electrostatic actuators, focusing on their structural behavior and energy conversion efficiency. Using modeling and analysis, the authors highlight how design parameters influence displacement, capacitance, and force generation. The work demonstrates the potential of electrostatic devices for micro-scale applications, while also noting challenges such as pull-in instability and fabrication complexity [25].

The study investigates the use of aluminum nitride (AlN) for MEMS piezoelectric devices by combining dynamic testing, static profilometry, and advanced reduced-order modeling to achieve precise characterization of electromechanical properties. Their synergistic approach enables precise characterization of AlN’s electromechanical properties, improving accuracy in predicting device behavior. The study underscores AlN’s suitability for high-performance MEMS harvesters and sensors, while also providing a robust methodology for material evaluation [26]. Lecerf et al. report a MEMS electromagnetic vibration energy harvester with monolithically integrated NdFeB micromagnets, overcoming limitations of external magnet assembly. The integration process achieves compactness and compatibility with MEMS fabrication, while maintaining strong magnetic performance. Experimental results confirm efficient power generation at micro-scale, making the design highly promising for self-powered IoT and sensor applications [27].

The review by [28] analyzes sound and vibration energy harvesting techniques for railway applications, comparing linear and nonlinear approaches. It highlights that nonlinear designs can overcome bandwidth limitations of linear systems, making them more suitable for variable railway vibrations. The study concludes that integrating hybrid and nonlinear harvesters offers the greatest potential for powering wireless monitoring systems in rail infrastructure [28]. The study [29] compares linear and nonlinear strategies for harvesting energy from mechanical vibrations. The authors show that while linear harvesters perform well under steady narrowband excitations, nonlinear systems are more effective for broadband and variable-frequency vibrations. The main finding is that nonlinear approaches significantly enhance energy capture efficiency in real-world, unpredictable vibration environments [29]. The work by M. Rosso explores both intentional and inherent nonlinearities in piezoelectric energy harvesting systems. It shows how nonlinear effects can be leveraged to broaden operational bandwidth, enhance energy capture, and improve adaptability to variable vibration sources. The study highlights design strategies for exploiting nonlinear dynamics to overcome the limitations of linear piezoelectric harvesters [30]. The study integrates signal-processing techniques with mechanical modeling to enhance the detection and diagnosis of faults in dynamic environments such as ship hulls and offshore platforms. By combining time–frequency analysis, machine learning algorithms, and experimental validation, the authors aim to improve the accuracy and reliability of monitoring systems under complex loading and environmental conditions. This research contributes to the ongoing development of intelligent condition-based maintenance frameworks in maritime engineering [30].

In light of these developments, the present work contributes to the field by designing and experimentally evaluating two MEMS-based electromagnetic vibration energy harvesters that employ distinct vibrating spring geometries. Unlike previous studies that primarily focus on high-frequency devices, nonlinear dynamics, or integrated micromagnets, our approach directly compares the influence of different planar spring structures on output power and efficiency under identical low-frequency operating conditions. The novelty of this work lies in demonstrating that specific nonlinear spring geometries can significantly enhance harvested voltage and power without increasing device size or fabrication complexity. This contribution provides new design insights for improving the performance of compact electromagnetic harvesters, particularly for low-frequency, low-level vibration environments relevant to wireless sensor and IoT applications. The design and construction of two electromagnetic vibration energy harvesters with distinct vibrating structures and operating frequencies of roughly 300 Hz are the main topics of this research. The output voltage and power of the electromagnetic vibration energy harvester varied significantly due to the various geometries of the vibrating structure. Using MEMS technology, two planar springs with distinct beam structures were created. Two prototypes were put together using a wire-wound coil and a separate vibrating spring. We evaluated two vibration energy harvesters, and the comparative analysis of the test results reveals that, under identical experimental conditions, the electromagnetic harvester equipped with the nonlinear vibrating spring B produced higher output voltage and power.

2. Energy Harvester Design and Simulation

The modal analysis confirmed that both resonators primarily oscillate in the out-of-plane direction, with first mode frequencies of 299.16 Hz for Resonator A and 279.52 Hz for Resonator B. After applying the SU-8 coating, these frequencies increased to 327 Hz and 338 Hz, respectively, clearly demonstrating the reinforcing effect of the polymer layer on the structural stiffness. Static displacement simulations were conducted in both linear (small displacement) and nonlinear (large displacement) modes. The results revealed negligible nonlinearity in Resonator A, whereas Resonator B exhibited significant nonlinear deflection, indicating greater sensitivity to applied loads. The comparison between simulated and experimental resonance frequencies showed close agreement, validating the reliability and accuracy of the COMSOL models 5.5. Furthermore, the analysis emphasized that geometry and spring stiffness are critical parameters influencing both resonance frequency and output power, with Resonator B’s design proving superior in terms of performance.

The simulations were performed using COMSOL Multiphysics 5.5, where the material properties were carefully defined to ensure accuracy and reproducibility. The silicon substrate was modeled with a Young’s modulus of 170 GPa, Poisson’s ratio of 0.28, and density of 2330 kg/m³, while the SU-8 polymer layer was assigned a Young’s modulus of 2.0 GPa, Poisson’s ratio of 0.22, and density of 1200 kg/m³. For the NdFeB permanent magnet, a density of 7500 kg/m³ was used to capture its inertial and electromagnetic effects. The boundary conditions included a fixed constraint at the anchor points of the resonant springs, with harmonic excitation applied at the base to simulate real vibration inputs. Both modal analysis and static deflection studies were performed under an acceleration range of 0.4–0.5 g, across a frequency range of 200–400 Hz, in order to evaluate the dynamic response and displacement behavior of the structures.

The material properties used in the design and simulation of the proposed device were carefully defined to ensure accuracy and reproducibility. The permanent magnet (NdFeB35) was modeled with a remanent magnetization of approximately 1.2 T, along with its coercivity and a density of 7500 kg/m³. The silicon substrate was characterized by a Young’s modulus of 170 GPa, a Poisson’s ratio of 0.28, and a density of 2330 kg/m³, while the thin-film layers of silicon dioxide (SiO₂) and silicon nitride (Si₃N₄) were specified with their respective thicknesses and elastic properties. For the SU-8 photoresist layer, the parameters included a Young’s modulus of 2.0 GPa, a Poisson’s ratio of 0.22, and a density of 1200 kg/m³. Finally, the copper coil was modeled using its electrical resistivity and precise wire dimensions, which are critical to evaluating the device’s electromagnetic response.

The dynamic model of resonant electromagnetic energy harvester can be considered as a second-order spring-mass-damping system. The differential equation of motion is expressed as follows:

$$m\ddot{z}\left(t\right)+d_t\dot{z}\left(t\right)+kz\left(t\right)=m\ddot{y}\left(t\right)$$

(1)

In Equation (1), m, k and dt are the mass, spring stiffness and total damping of the system, respectively. The total damping dt that is composed of the electromechanical produced (de) and the parasitic part (dm). z(t) is the relative displacement between the mass and housing. y(t) = Yosinωt is the amplitude of harmonic excitation. The steady state solution of Equation (1) can be expressed:

$$z\left(t\right)={\displaystyle \frac{{\omega }_r^2{Y}_0}{\sqrt{{\left(1-{\omega }_r^2\right)}^2+{\left(2{\zeta }_t{\omega }_r\right)}^2}}}\mathrm{s}\mathrm{i}\mathrm{n}(\omega t-\phi )$$

(2)

where ω_r represents the ratio of input frequency to natural resonant frequency ω_r = ω/ω_n. ζ_t is the total damping ration (ζ_t = dt/(2mωn)). For the case in Figure 1, the magnetic field varies with the vibration of the permanent magnet. The induced electromotive force is given by

$$e.m.f==-{\displaystyle \frac{d\phi }{dz}}\times {\displaystyle \frac{dz}{dt}}=k·{\displaystyle \frac{dz}{dt}}$$

(3)

dφ/dz is the gradient of the magnetic flux linkage along with the direction of relative motion between the magnet and the coil. k is the electromagnetic coupling factor which equals −dφ/dz. It represents the change in couple flux per unit displacement [30].

The damping coefficient induced form electromagnetic transduction is as follows:

$$d_e={\displaystyle \frac{1}{R_L+R_c}}\times {\left({\displaystyle \frac{dphi}{dz}}\right)}^2$$

(4)

The maximum power that can be extracted from the vibration is

$$P\left(t\right)={\displaystyle \frac{d}{dt}}{\int }_0^z{d}_e{z}_{dot}dz=\left({\displaystyle \frac{1}{2}}\right)d_e{z}_{dot}^2={\displaystyle \frac{\left(d_e{Y}_0^2{\omega }_0^4{\omega }^2\ast co{s}^{2\left(\omega t-\phi \right)}\right)}{2\left({\left(1-{\omega }_r^2\right)}^2+{\left(2{\zeta }_r{\omega }_r\right)}^2\right)}}$$

(5)

For operation at resonance (ω_r = 1), the generated electrical power can be reduced to

$$P={\displaystyle \frac{\left(m^2{d}_e{Y}_0^2{\omega }^4\right)}{\left(2{\left(d_e+d_m\right)}^2\right)}}$$

(6)

Equations (5) and (6) indicate that the maximization of the electromagnetic damping (d_e) is an important goal for the design of an electromagnetic energy harvester to extract the maximum power in the form of electrical energy. According to Equation (4), the electromagnetic damping is determined by the flux linkage gradient and the coil resistance.

Two MEMS-based resonator structures were created in order to implement energy harvesting through environmental vibration. A and B, respectively, were the names of the two resonators discussed in this study. Shapes A and B share a central platform and four folded beams. Figure 1 depicts their intricate shapes.

Different structures of resonators A and B with center plate diameters of 7 × 7 mm² are depicted in Figure 1a,b. In order to reduce the mechanical resonance frequency and increase the vibratory amplitude, folded beams were used. The resonator chip measures 11 × 11 mm² in total. The fixed magnet’s center spring platform, encircled by folding beams. The folded beams’ varying diameters and shapes are the primary distinction between A and B. For resonator A, U-shaped beams were used, and for resonator B, S-shaped beams.

Table 1. Principal resonant spring parameters.

Parameters	Model A	Model B
Small Beam Length (µm)	500	500
Small Beam Width (µm)	200	200
Long Beam (µm)	6000	3000/6000
Long Beam Width (µm)	300	250
Thickness (µm)	200	200
Young’s modulus of the spring	120 Gpa	120 Gpa
Poisson’s ration of the spring	0.31	0.31
Density of the spring	3.14 g/cm3	3.14 g/cm3
Magnet size	5 × 5 × 4.84 mm3	5 × 5 × 4.84 mm3
Young’s modulus of the magnet	170 Gpa	170 Gpa
Density of the magnet	7.66 g/cm3	7.66 g/cm3

displays the characteristics for the folded beams of two resonators. The resonant frequencies and associated vibration modes of resonators were simulated using the COMSOL program.

The resonant frequency range (300–350 Hz) was carefully selected to align with typical environmental vibrations encountered in wireless sensor applications. The dimensions of the resonant springs and proof mass were optimized through simulations to allow sufficient displacement while ensuring that the stress levels remained within the safe limits of silicon. In addition, the overall footprint was determined by wafer processing constraints and the requirement to maintain a compact device volume of approximately 0.9 cm³, making the design well-suited for MEMS integration. This iterative design process allowed us to achieve an effective balance between compactness, structural robustness, and efficient energy harvesting performance.

The vibration energy harvesting system is primarily composed of two elements: a resonant spring that acts as the elastic structure and a permanent magnet fabricated from neodymium–iron–boron (NdFeB35), which serves as the inertial mass. Together, these components form the vibration-picking mechanism responsible for converting mechanical oscillations into electrical energy. To evaluate the dynamic characteristics of the system, modal simulations were performed for two different resonator designs, referred to as Resonator A and Resonator B. The results of these simulations indicated that in both designs, the dominant mode shape corresponds to oscillations occurring mainly in a direction perpendicular to the plane of the spring, confirming the effective out-of-plane motion of the structures. The first natural frequency of the vibration-picking system was found to be 299.16 Hz for Resonator A and 279.52 Hz for Resonator B.

Additionally, COMSOL Multiphysics was used to compute the static deflections of the resonant springs under different loading conditions. Both “Small Displacement Static” (linear) and “Large Displacement Static” (nonlinear) simulation modes were applied to capture the linear and nonlinear responses, respectively. The relationship between the applied load and the central deflection of the resonant springs is presented in Figure 2. As shown in Figure 2a, the difference between linear and nonlinear responses in Resonator A is minimal, indicating that nonlinear effects in Resonator A are negligible. In contrast, Resonator B exhibits significant nonlinear behavior, as its central deflection is markedly higher than that of Resonator A under the same loading conditions. This suggests that the geometry of Resonator B introduces stronger nonlinearities, which could influence its energy harvesting performance.

Resonator B exhibits more pronounced nonlinear behavior, as evidenced by the larger deviation between its linear and nonlinear deflection curves under the same loading conditions. Although the absolute deflection magnitude is comparable to that of Resonator A, the nonlinear response of Resonator B diverges more significantly from its linear prediction, indicating stronger geometric nonlinearity in its spring structure. The different behaviors of Springs A and B can be explained by their geometry and stiffness. Spring A, being stiffer, exhibits smaller deflections under applied loads and shows only minimal nonlinear response. In contrast, Spring B, with lower stiffness, facilitates larger deflections, which introduces noticeable nonlinear behavior. This explains why the nonlinear displacement curve of Spring B deviates more significantly from the linear prediction compared to Spring A. The larger deflection of Spring B also enhances the electromagnetic coupling between the magnet and the coil, leading to the higher output voltage and power observed experimentally.

Figure 2 presents the simulated load–deflection behavior of Resonators A and B obtained using COMSOL Multiphysics. Both “Small Displacement” (linear) and “Large Displacement” (nonlinear) analyses were performed to evaluate the structural response under varying loads. Resonator A exhibits minimal difference between its linear and nonlinear deflection curves, indicating nearly linear stiffness behavior. In contrast, Resonator B shows a more noticeable deviation between the two curves, confirming the presence of geometric nonlinearity due to its more compliant S-shaped spring structure. The load was applied at the central proof mass, and the boundary conditions were fixed at the anchor points to replicate experimental constraints. These results demonstrate that Resonator B’s geometry induces stronger nonlinear effects, which influence its vibration and energy harvesting performance.

The observed improvement in vibration energy harvesting performance of Model B can be primarily attributed to the geometric nonlinearity introduced by its longer and more compliant S-shaped beam structure. Both prototypes share identical materials, magnet dimensions, coil parameters, and overall device volume, ensuring that the principal structural variation lies in the spring geometry. Static deflection simulations clearly demonstrated that Resonator B exhibits significant nonlinear displacement under the same loading conditions, whereas Resonator A behaves linearly. This nonlinear stiffness facilitates larger vibration amplitudes at resonance, leading to an enhanced change in magnetic flux linkage (−dφ/dz) between the magnet and coil, as described by Equation (3). Consequently, the induced electromotive force and harvested power increase proportionally. The broader operational bandwidth observed in Model B is also consistent with typical nonlinear resonance behavior, where the resonance curve flattens and extends over a wider frequency range. Therefore, the higher voltage and power output of Model B are direct outcomes of the nonlinear deflection behavior of its resonant spring. While small differences due to damping or fabrication tolerances may exist, their influence is comparatively minor. Future work will include parametric modeling and controlled fabrication to isolate these effects and quantitatively confirm the degree of nonlinear contribution.

3. Fabrication

Figure 3 depicts the schematic resonant morphologies of two distinct resonators that were directly constructed using Si substrate. The microstructure of the resonators (resonant planar spring) was fabricated using standard micromachining. The selection of materials streamlined the fabrication process and reduced production costs. Figure 3 depicts the resonant springs’ fabrication scheme.

The fabrication of the suspension microstructure was performed using a standard silicon micromachining process, as illustrated in Figure 3.

(a). Starting Substrate (Figure 3a)

A 4-inch, <100>-oriented silicon wafer with a thickness of 500 μm was used as the starting substrate for the device fabrication. This served as the base for constructing the resonant suspension structures.

(b). Thermal Oxidation and Dielectric Deposition (Figure 3b)

A wet thermal oxidation process was first performed to grow a silicon dioxide (SiO₂) layer of approximately 0.3 μm on both sides of the wafer. Subsequently, a thin layer (~0.20 μm) of silicon nitride (Si₃N₄) was deposited on top of the oxide layers using low-pressure chemical vapor deposition (LPCVD). The combined SiO₂/Si₃N₄ bilayers acted as masking and insulating layers during subsequent etching steps.

(c). Backside Patterning (Figure 3c)

Standard photolithography was employed to pattern the backside Si₃N₄/SiO₂ layers. The exposed dielectric regions were etched away using reactive ion etching (RIE), creating windows that defined the etching areas for the subsequent silicon bulk micromachining step.

(d). Backside Wet Etching (Figure 3d)

Potassium hydroxide (KOH) anisotropic etching was used to etch the exposed silicon regions through the patterned backside openings. The etching was performed at 80 °C in a 33% KOH solution for approximately 3.5 h, producing an etch depth of about 300 μm. This step created cavities and partially released the suspended regions of the resonator structure.

(e). Frontside SU-8 Coating (Figure 3e)

To define the cantilever and resonator geometry, an 80 μm thick SU-8 photoresist layer was spin-coated on the front side of the wafer. SU-8 was selected for its high mechanical stability and compatibility with MEMS fabrication.

(f). Frontside Photolithography (Figure 3f)

The SU-8 layer was patterned using photolithography to define the precise geometry of the suspension beams and resonator structures. This step ensured accurate control over device dimensions and stiffness.

(g). Final Release by ICP Etching (Figure 3g)

Inductively coupled plasma (ICP) dry etching was then applied to release the suspension microstructure by removing the remaining sacrificial layers and unwanted material. This step produced the final freestanding resonator beams.

COMSOL simulations verified that the presence of the SU-8 coating reduced static beam deformation and slightly increased the resonant frequency (less than 5%). Given these minor effects, the SU-8 layer was retained to improve the robustness of the suspension spring without compromising device performance.

4. Results

The experimental evaluation of the prototypes was performed using a dedicated vibration testing setup designed to accurately measure voltage and power output. The setup consisted of an electromagnetic shaker, a function/signal generator, an accelerometer, a data acquisition computer, and a digital oscilloscope. The micro-electromagnetic energy harvester was securely mounted in a Perspex frame, which was then fixed onto the vibration table of the shaker. The Perspex frame was intentionally chosen as a non-magnetic holder to minimize interference from the magnetic fields generated by the shaker, thereby ensuring accurate measurements.

During testing, the function generator supplied a sinusoidal excitation signal to the shaker, producing controlled vibrations at varying frequencies and accelerations. These vibrations induced periodic motion in the harvester’s resonant structure, causing relative displacement between the NdFeB permanent magnet and the microscale wound coil, which in turn generated an induced voltage through electromagnetic induction. The accelerometer, attached to the setup, monitored the input acceleration to ensure precise control and calibration of vibration levels. The induced voltage across the load resistance was continuously recorded using the oscilloscope, while the computer facilitated storage and further analysis of the data. The output response was carefully examined around the resonance frequencies of the two prototypes. The measured voltage at resonance for Prototype A and Prototype B under identical testing conditions is presented in Figure 4, clearly showing the difference in performance between the two designs.

The fabricated copper spring and the assembled energy harvester are shown in Figure 5. The micro electromagnetic vibration energy harvester is composed of a spring magnet system and a wire-wound coil. The planar cooper spring is manufactured using laser precision cutting. A plexiglass-housing is used to support the spring-magnet and case devices.

Figure 6 shows simulated deflection results of the resonators obtained using COMSOL Multiphysics. The plots show that Prototype A reaches a peak deflection near 327 Hz, while Prototype B exhibits a higher peak deflection near 338 Hz with a broader bandwidth. Although direct experimental deflection measurements were not possible due to resource limitations, these simulation results were correlated with the measured frequency-response data, providing a reliable understanding of how each resonator deforms under applied vibration loads.

Figure 7 shows the simulated stress distribution analysis for the resonant beams of Prototype A and Prototype B. The results show that the maximum stresses remain well below the fracture strength of silicon (~7000 MPa), confirming that both devices are structurally reliable under the tested vibration conditions. Prototype B experiences slightly higher stress levels due to its greater deflection but still operates safely within material limits.

A detailed analysis of the voltage–frequency characteristics of both Prototype A and Prototype B was performed, clearly illustrating how resonance frequency directly influences device performance. The load power was calculated and compared for both prototypes, where Prototype B demonstrated nearly twice the harvested power of Prototype A under identical acceleration conditions, confirming its superior efficiency. Further, the results were discussed in relation to device geometry, damping ratio, and resonance frequency, establishing a strong link between the experimental findings and the finite element simulations performed in COMSOL. This correlation reinforces the reliability of the modeling approach. In addition, a new supporting figure of the fabricated device has been included, complementing the schematic diagrams and offering a clear structural visualization of the prototype harvesters.

The finite element analysis performed in COMSOL primarily focused on the structural mechanical behavior of the resonant springs, including modal frequency and static deflection. The simulated resonance frequencies of Resonators A and B (327 Hz and 338 Hz after SU-8 coating) showed close agreement with the experimentally measured values, confirming the reliability of the structural model. Although the electrical output was not directly simulated or validated through a coupled multiphysics model in this study, the experimental voltage–frequency response exhibited consistent trends with the simulated mechanical displacement curves, indicating a strong qualitative correlation between the two. Due to the limited availability of high-resolution displacement and flux-measurement equipment, a direct quantitative validation of the electromagnetic coupling was not performed. In future work, a fully integrated electromechanical model will be developed and experimentally calibrated using measured magnetic flux gradients, coil resistances, and induced damping coefficients to further refine the predictive accuracy of the simulation.

The proposed device demonstrates strong potential for practical applications due to its compact 0.9 cm³ volume and MEMS-compatible fabrication, enabling integration with microscale systems such as sensors and biomedical devices. The comparative analysis shows that geometric optimization nearly doubles the harvested power (182.78 μW vs. 91.56 μW). The incorporation of an SU-8 layer enhanced structural stability with minimal frequency shift (<5%), while Prototype B’s broader operational bandwidth ensures improved adaptability to variable real-world vibrations.

The device has certain limitations that will be addressed in ongoing work. Although SEM imaging could not be performed due to resource constraints, schematics and optical images are provided, with SEM planned in the next phase. Long-term voltage stability and temperature effects were not experimentally measured but are discussed based on prior studies. Finally, while the maximum power output (182.78 μW) is competitive at the microscale, it remains lower than some macro-scale harvesters, as our design is specifically optimized for compact size and low-acceleration environments.

In comparison with the recent literature, our prototypes demonstrate competitive performance among MEMS electromagnetic harvesters, offering broader bandwidth and fabrication simplicity through standard silicon micromachining. While piezoelectric devices often achieve higher power density, our electromagnetic approach provides greater durability and avoids depolarization issues, making it more reliable for long-term applications. Overall, the results confirm that our design achieves a strong balance between power output, robustness, and integration potential.

The prototype undergoes forced vibration when a sinusoidal signal from the waveform generator drives the vibrator, resulting in voltage induction in the coil. This induced voltage across the load resistance is measured using an oscilloscope. Figure 4 displays the voltage measurements at resonance for prototypes A and B. The input vibration acceleration in these studies is 0.5 g (g = 9.8 m/s²). Figure 8 shows the prototype energy harvesters’ voltage variation with frequency, and the load power may be computed.

Prototype A’s load voltage was measured at 327 Hz frequency with a 405 Ω load resistance, as seen in Figure 8a. The maximum voltage value was 195 mV at 307 Hz resonant frequency and 0.5 g (g = 9.8 m/s²) acceleration. The highest possible power was 90.56 µW. The output power and voltage variation in prototype B as a function of frequency is displayed in Figure 8b. Prototype B exhibited a resonance frequency of 338 Hz. Under identical acceleration and load resistance conditions, it achieved a maximum load voltage of 440 mV and an output power of 182.78 µW.

Prototype A, with stiffer springs, shows higher resonance frequency but lower displacement, leading to reduced electromagnetic induction. By contrast, Prototype B, with more compliant springs, exhibits greater deflections and enhanced coupling between the magnet and coil, resulting in higher voltage output and wider bandwidth. Stress distribution analysis further confirms that these mechanical differences explain the superior performance of Prototype B while remaining within the safe stress limits of silicon.

The comparison

Table 2. Key finding from literature review and current work.

Device/Reference	Transduction and Structure	Resonant Frequency (Hz)	Drive Level	Max Load Voltage	Max Output Power	Volume/Footprint	Bandwidth (qual.)	Notes
This work—Prototype A	EM; folded-beam spring (U-shaped), NdFeB magnet + wire coil	327 (resonance used for power calc.); peak V at 307	0.5 g	195 mV	≈91.56 µW @ 405 Ω	~0.9 cm3 device; 11 × 11 mm chip	Narrower	Baseline design for comparison.
This work—Prototype B	EM; folded-beam spring (S-shaped), NdFeB magnet + wire coil	338	0.5 g	440 mV	≈182.78 µW @ 405 Ω	~0.9 cm3 device; 11 × 11 mm chip	Broader	~2× power vs. A; higher V and wider operational range under identical conditions.
Kulkarni et al. (2008) [12]	EM; moving coil on cantilever with 4 magnets (microscale)	8.08 kHz	3.9 m s−2	—	148 nW	106 mm3	Narrow (high-Q, high-f)	Illustrates earlier kHz-range EM MEMS with nW-level power at low acceleration. (Values as reported in your Introduction).

highlights several important findings. Prototype B delivers approximately 183 µW at 338 Hz and 0.5 g, which is significantly higher than the nanowatt-level output reported for early high-frequency (kHz) devices [30] and nearly double the output of Prototype A under identical conditions. In addition, Prototype B demonstrates a broader operational bandwidth while maintaining a compact, MEMS-compatible footprint of about 0.9 cm³, making it particularly well-suited for harvesting energy from low-frequency ambient vibrations, such as those found in wireless sensor applications. The results also emphasize the importance of spring geometry, with the side-by-side comparison showing how the shift from a U-shaped to an S-shaped resonator enhances voltage, power, and bandwidth without increasing device size. Furthermore, the incorporation of an SU-8 polymer layer is shown to modestly increase resonance frequency (<5%) while improving structural stability, representing a practical trade-off for more robust packaging.

5. Conclusions

This study presented the design, fabrication, and experimental evaluation of two MEMS-based electromagnetic vibration energy harvesters with a compact volume of 0.9 cm³. Finite element simulations guided the development of the prototypes, and experimental validation confirmed their performance. Under 0.5 g acceleration, Prototype A achieved a maximum output of 91.56 µW at 327 Hz, while Prototype B produced 182.78 µW at 338 Hz, demonstrating nearly double the power output, higher voltage, and a wider operational bandwidth. These findings confirm that device geometry and resonance frequency strongly affect harvester performance. While the results suggest that further optimization of vibratory structures could enhance efficiency and broaden the frequency range, such design modifications remain a promising avenue for future investigation. Future work will explore nonlinear spring designs to enhance bandwidth and energy capture, conduct SEM and temperature-dependent tests for material analysis, assess durability and voltage stability, and integrate the harvesters with low-power sensor nodes for practical self-powered applications.