# A MEMS Electromagnetic Vibration Energy Harvester with Monolithically Integrated NdFeB Micromagnets

Ilona Lecerf, José Elías Angulo-Cervera, Frederico Orlandini-Keller, Pierre Moritz, Fabrice Mathieu, David Bourrier, Samuel Charlot, Liviu Nicu, Thierry Leïchlé, Thibaut Devillers, et al.

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Ilona Lecerf, José Elías Angulo-Cervera, Frederico Orlandini-Keller, Pierre Moritz, Fabrice Mathieu, et al. A MEMS Electromagnetic Vibration Energy Harvester with Monolithically Integrated NdFeB Micromagnets. Advanced Materials Technologies, 2025, 10 (10), pp.2401817. 10.1002/admt.202401817. hal-05293836

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# A MEMS Electromagnetic Vibration Energy Harvester with Monolithically Integrated NdFeB Micromagnets

Ilona Lecerf, José Elías Angulo-Cervera, Frederico Orlandini-Keller, Pierre Moritz, Fabrice Mathieu, David Bourrier, Samuel Charlot, Liviu Nicu, Thierry Leïchlé,* Thibaut Devillers, Richard Haettel, Nora M. Dempsey,* Thomas Blon,* and Lise-Marie Lacroix*

The monolithic integration of high-performance magnets into microfabricated devices remains a technological challenge despite the great interest for telecommunications, automotive, biomedical or space applications. Here the integration of 50 µm thick sputtered arrays of NdFeB micromagnets into a functional micro-electro mechanical system (MEMS) in-plane electromagnetic vibration energy harvester is reported. A combination of analytical modeling and numerical simulations guided the design of the magnet arrays along with ad-hoc planar coils, to produce a high transduction factor. The resulting energy harvesters deliver a voltage of 2.5 mV, a power of 6 nW under an acceleration of 0.8 g and a normalized power density of $3 \times 10^{-4} \text{ kg s m}^{-3}$ ($20 \text{ mW m}^{-3}$) for a device volume of roughly 300 mm$^3$, which is comparable to state-of-the-art MEMS electromagnetic vibration harvesters. This study serves as a show-case for the possibility of integrating high-performance micromagnets into functional devices using microfabrication processes.

## 1. Introduction

Portable and flexible electronics are widespread in countless devices encountered in our daily lives, thanks to the tremendous efforts of the semiconductor industry to keep on integrating smaller and more efficient transistors. Surprisingly, micromachined devices requiring magnetic actuation, such as actuators,[1] relays,[2] sensors,[3] and isolators,[4] did not benefit from the same

development. Their compactness and portability are often restrained by the use of external macroscopic permanent magnets (PM) to produce the large magnetic stray fields required for the application, due to the lack of mature technologies for integrating high-performance micromagnets.[5,6]

A major technological challenge therefore consists in developing and integrating micromagnets with high coercivity ($H_c$) and remanent induction ($B_r$), and sufficient thickness to yield appropriate stray field values and thus address the massive demand for portable magnetic devices. Integrated MEMS (IoT sensors, actuators...) share multi-step technological processes mastered by semiconductor manufacturers such as ion

implantation, annealing, metallization, and reactive-ion etching. To be fully implementable, the micromagnet integration should take place without altering the complex architecture of the device.

The monolithic integration onto Si-based devices of downsized PM, prepared through classical metallurgical processes (sintering, melt spinning...), is not feasible. Therefore, alternative approaches have been developed. Electrodeposition, a commonly used microfabrication process, allows depositing fairly

I. Lecerf, P. Moritz, T. Blon, L.-M. Lacroix
UMR 5215 INSA
CNRS
UPS
Université de Toulouse
Laboratoire de Physique et Chimie des Nano-Objets
135 avenue de Rangueil, Toulouse 31077, France
E-mail: tblon@insa-toulouse.fr; lmlacroi@insa-toulouse.fr

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/admt.202401817

© 2025 The Author(s). Advanced Materials Technologies published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

DOI: 10.1002/admt.202401817

I. Lecerf, J. E. Angulo-Cervera, P. Moritz, F. Mathieu, D. Bourrier, S. Charlot, L. Nicu, T. Leïchlé
Laboratoire d'analyse et d'architecture des systèmes
LAAS-CNRS
7 avenue du Colonel Roche, Toulouse 31077, France
E-mail: tleichle@laas.fr

F. Orlandini-Keller, T. Devillers, R. Haettel, N. M. Dempsey
Université Grenoble Alpes
CNRS
Institut Néel
Grenoble 38042, France
E-mail: nora.dempsey@neel.cnrs.fr

T. Leïchlé
School of Electrical and Computer Engineering
Georgia Tech-CNRS International Research Laboratory
Atlantic Drive, Atlanta, GA 30332, USA

L.-M. Lacroix
Institut Universitaire de France (IUF)
1 rue Descartes, Paris 75231 CEDEX 05, France
thick magnetic layers (up to 200 µm). Despite important efforts, the electrodeposition of rare-earth-based materials remains challenging under mild conditions.[7] Studies are thus limited to materials exhibiting either moderate hard magnetic properties, such as CoNiMnP,[8] or requiring high-temperature annealing to stabilize the magnetically-hard L1₀ phase found in Pt-based alloys.[9,10] Patterning of magnetic polymers by inkjet,[11] imprinting or through molds[12] allowed preparing integrated magnets without any thickness limitation. However, to preserve the mechanical properties of the host matrix, the magnetic content barely exceeds a few wt.%, leading to limited remanent induction. To prepare polymer-free magnets, we reported the directed assembly of nanoparticles driven by a magnetophoresis process.[13,14] Alternatively, doctor-blade-based techniques were used to dry-press micrometric NdFeB particles into pre-etched cavities,[15,16] This approach was recently optimized using atomic layer deposition (ALD) to favor the agglomeration of NdFeB microparticles, allowing wafer-level fabrication of micromagnets with variable lateral dimensions and thicknesses up to 550 µm.[17] The maximum remanent induction achievable with this approach (0.59T) is however intrinsically limited by the isotropic nature of the nanocrystalline NdFeB microparticles used, and the inevitable presence of voids, which limits the maximum filling factors of ≈80%. Sputtering techniques allow the depositing of fully dense films while avoiding the manipulation of micro/nanoparticles within cleanroom facilities. High-rate (> 18 µm h⁻¹) triode sputtering[18] has been shown to be suitable for the deposition of thick films of NdFeB on Si substrates. Films deposited at room-temperature and subsequently annealed to crystallize the hard magnetic Nd₂Fe₁₄B phase are isotropic, while out-of-plane texture can be induced in films deposited at elevated temperatures. In the latter case, 1-step (directly crystallized in the as-deposited state) or 2-step (crystallized during post-deposition annealing) processing may be used. High-rate triode sputtering combined with pre-patterning of topographic features into the substrate, recently allowed the deposition of fully dense, out-of-plane textured 50 µm thick NdFeB films (M₀T/M₇.₅T = 0.85, giving µ₀Mₜ ≈ 1.2 T, µ₀Hₐ = 2.2 T) on Si substrates.[19] The integration of these NdFeB micro-magnets will be a major step forward for MEMS devices requiring a high permanent magnetic field.

The present work aims at demonstrating the wide applicability of sputtered micromagnets through their integration into a MEMS process flow. As a case study, the fabrication of an electromagnetic (EM) vibration energy harvester (EVEH) is reported (Figure 1). Environmental mechanical vibrations, characterized by low-frequency excitations, may be considered as renewable energy sources providing an efficient energy conversion using piezoelectric, triboelectric, electrostatic, or EM-based transducers.[5,6] At the macroscale, electromagnetic transduction which is induced by the damping of a resonant magnetic mass in front of a coil, provides the best performance and longevity among the different transduction mechanisms.[6] However, the problem of magnet integration prevented the efficient use of this EM-based technology at the micro-scale.[5] An optimized design for a microscale in-plane EM energy harvester has been proposed by Han et al. consisting of an electroplated CoNiMnP magnet array placed on a Cu mass that vibrates laterally above a copper coil (a variant of such a device, developed within the present study,

is schematized in Figure 1).[8] Using finite element simulations, Paul et al.[20] and our team[21] have previously reported guidelines for the dimensioning of the magnet arrays and the facing 2D micro-coil, to efficiently convert the energy, considering 50 µm thick NdFeB magnets.

We report here the fabrication and integration of electromagnetic energy harvesters based on two different micromagnet array designs composed of 300 and 500 µm wide micromagnets. After a brief introduction to the spring-mass model used and the importance of the electromechanical coupling, the fabrication of energy harvesters by transferring optimized magnetic resonators onto a substrate hosting an ad hoc planar inductor is detailed. The fabricated devices comprising 300 and 500 µm wide micromagnets output 4 and 6 nW, respectively, through a load resistance of 100–300 Ω for a mass displacement of 70 µm, corresponding to a 0.8 g acceleration.

## 2. Mass-Spring Harmonic Oscillator Model of the Electromagnetic Energy Harvester

An electromagnetic energy harvester consists of a mass with a permanent magnet moving above a fixed coil where an electromotive force is generated due to induction (Figure 1a; Video S1, Supporting Information). The magnet can be set in motion by environmental vibrations such as those generated by the movement of a washing machine, a car engine or even walking.[22]

The system studied, shown schematically in Figure 1b, consists of a mass *m* connected to a frame through a spring of stiffness constant *k*. When the frame is set in motion by ambient vibration, modeled as an external sinusoidal force (*F* = *F*₀ sin (*ω* *t*)), a relative movement of the mass is induced. This movement is affected by an overall damping coefficient *d* composed of mechanical (*d*<sub>m</sub>) and electrical (*d*<sub>e</sub>) contributions (*d* = *d*<sub>m</sub> + *d*<sub>e</sub>) and characterized by the damping factor:

$$ \zeta = d/2m\omega_0 = 1/2Q \quad (1) $$

with $\omega_0 = \sqrt{k/m}$ the undamped resonant angular frequency and Q the quality factor.

The differential equation resulting from Newton's second law allows calculating the mass movement equation in this driven harmonic oscillator and the resulting steady-state solution of the displacement relative to the frame: *x* (*t*) = *X*₀ cos (*ω* *t* + *φ*). As further detailed by Stephen,[23] the oscillation amplitude *X*₀ is maximized at the resonant frequency $\omega_r$. For a weakly damped system ($\zeta \ll 1$), $\omega_r \sim \omega_0$ and the maximum power one can extract from the ambient vibration is given by:

$$ P^{\omega=\omega_0} = m\omega_0^3 X_0^2 \zeta \quad (2) $$

Interestingly, the power not only scales with the oscillation amplitude $X_0$ but also with the damping factor $\zeta$, which thus should not be strictly null. Replacing the mass by a moving magnet allows inducing an electromotive force (emf) in the facing coil (Figure 1b), according to Faraday's law:

$$ e(t) = -\frac{d\varphi}{dt} = -\frac{d\varphi}{dx} \cdot \frac{dx}{dt} = -K \cdot \dot{x}(t) = KX_0\omega \sin(\omega t + \varphi) \quad (3) $$
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Schematic view of a) the electromagnetic energy harvester constituted of a magnet array (squares) vibrating, thanks to folded beams (blue) above a fixed coil (brown). b) The corresponding spring-mass model is characterized by the damping factor *d* and c) the resulting electric model with *R*<sub>C</sub> the resistance and *L*<sub>C</sub> the inductance of the coil.</figcaption></figure>

with φ the magnetic flux through the surface enclosed by the coil's loops. The time variation of the magnetic flux can be rewritten as the speed of motion *x* (t) times the magnetic flux gradient *dφ/dx*, which is referred to as the transduction factor *K*.[24] When connected to a load resistor *R*<sub>L</sub>, the resulting electronic circuit can be schematized as shown in Figure 1c. The impedance matching is expected for a specific *R*<sub>L</sub> which depends on the coil properties, namely its resistance *R*<sub>C</sub> and inductance *L*<sub>C</sub>,[23]

$$R_L = R_C + K^2/d_m \qquad (4)$$

The maximum power transferred to the load resistor is given by:

$$P_{\text{load}}^{\text{MAX}} = \frac{K^2 m^2 \omega_0^4 X_0^2 \zeta^2}{2 d_m (d_m R_c + K^2)} \qquad (5)$$

which can be rewritten as a function of the maximum mechanical power retrieved:

$$P_{\text{load}}^{\text{MAX}} = \frac{P_{\omega=\omega_0}}{2} \left( \frac{R_L - R_C}{R_L + R_C} \right) = \frac{P_{\omega=\omega_0}}{2} \left( \frac{d_c}{d_m} \right) \qquad (6)$$
Thus, the best energy conversion efficiency for electromagnetic transduction is intrinsically limited to 50% for $R_c$ as small as possible and strongly depends on the transduction factor K and the oscillation amplitude $X_0$.

# 3. Results

## 3.1. Design and Fabrication

Electromagnetic energy harvesters with integrated NdFeB micromagnet arrays have been designed using finite element simulations so as to exhibit an optimized transduction factor $K$[21] along with a fairly low resonance frequency ($f = \omega/2\pi \approx 1000$ Hz), typical of vehicle engines and consumer products such as washing machines and vacuum cleaners.[25] Mechanical simulations have shown that coupling a 4 × 6 mm² silicon vibrating plate to the external frame, through four folded beams, allows achieving a fundamental mode at $f_0 = 1029$ Hz, consisting of a pure in-plane vibration (along $\vec{e}_x$) (see Figure S1, Supporting Information). Varying the geometry of the folded beams affects the vibration modes, using three folds of lateral dimensions 175 × 5850 µm² allows a pure planar vibration (see Figure S2, Supporting Information). The geometry of the 4 × 6 mm² magnet array has been optimized numerically so as to exhibit the largest transduction factor $K = \frac{d\varphi}{dx}$ with the constraint of a micromagnet thickness of 50 µm, and assuming remanent magnetization values of 1.2 T (i.e., out-of-plane textured NdFeB micromagnets). The effects of the micromagnets' geometry (width L and spacing $\Delta x$), as well as the number and position of coil turns, have been studied (Figure S3, Supporting Information).[21] The trade-off between high magnetic flux gradients, obtained for smaller micromagnets, and a high number of coil turns above each column of magnets (Figure S3c,d; Video S2, Supporting Information), maximized for larger micromagnets, leads to two optimized magnet array/coil configurations (Figure S4, Supporting Information) consisting of:

* 10 columns of micromagnets of width $L = 300$ µm, spaced by $\Delta x = 100$ µm, facing an asymmetric coil of 10 × 6 turns,

* 7 columns of micromagnets with $L = 500$ µm and $\Delta x = 50$ µm, facing an asymmetric coil of 7 × 16 turns.

These configurations should yield a transduction factor $K = 18$ and 23 mWb m⁻¹, respectively.

Guided by these results, a process was developed to separately fabricate the MEMS resonator (Figure 2a,c) and the electroplated coil (Figure 2b,d; Figure S5, Supporting Information), and to assemble them using a flip-chip method (Figure 2e). Considering mechanical robustness and durability, all elements were designed considering 525 µm-thick Si substrates. Key process steps, further described in the Experimental section, include i) dry etching of the silicon mass to create 50 µm deep topographical features to define the in-plane dimensions of individual micromagnets (with in-plane dimensions 300 × 300 µm² and 500 × 500 µm²), ii) deposition of a 50 µm thick NdFeB layer by triode sputtering through a shadow mask to localize the magnetic deposit (Figure S6, Supporting Information), iii) deep etching of the Si wafer to fabricate the MEMS resonator, i.e., to release the vibrating mass (Figure S7, Supporting Information), and iv) bonding of the vibrating mass

onto a silicon substrate with integrated coils, using a polymer adhesive.

## 3.2. Characterization

Cu coils with turns exhibiting a width and interspacing of 10 µm were prepared by electrodeposition (Figure 2d). Low-frequency electrical measurements ($f < 100$ kHz) revealed that the coil's impedance is purely resistive: $Z_{eq} = R_c$. Depending on the Cu coil thickness (6 or 26 µm) and the total number of turns (60 and 112 for $L = 300$ and 500 µm, resp.), resistances varying between 130 and 1130 Ω were measured.

Hysteresis loops measured on arrays of 300 and 500 µm Nd-FeB micromagnets are shown in Figure S8 (Supporting Information). The arrays are characterized by coercivity values of ≈2.6 T, and are magnetically isotropic, as they were deposited at room-temperature, and then crystallized during a post-deposition annealing step. The absolute value of remanent magnetization is estimated to be 0.6 T, based on measurements made on comparable films deposited on non-patterned Si, for which the volume of material can be accurately measured. Maps of the out-of-plane component of the magnetic stray field measured at nominal distances of between 5 and 255 µm from the surface of the arrays are shown in Figure S9 (Supporting Information), together with simulations of the expected field patterns. Individual micromagnets are clearly resolved at measurement distances of 5 and 55 µm, which underlines the importance of minimizing the gap between the micromagnet arrays and the coils. The lower values of measured peak-to-peak field intensities compared to the simulated ones are attributed to the fact that isolated micro-magnets were considered in the simulations (i.e., NdFeB deposited on the side-walls of the Si pillars and between them are neglected). It should be noted that hysteresis and stray field measurements were carried out on arrays that were taken from dismantled energy harvesters, following their electrical characterization (see below). In this way, we were sure to characterize the magnetic properties of arrays that served in working devices, thus validating the successful integration of high-performance sputtered NdFeB micro-magnets.

Both parts (the coil and the vibrating plate supporting the micromagnet array) were stuck together with a 100 µm thick adhesive tape (Figure 2e), and the resulting energy harvester was glued onto a PCB electrically connected to the chip (Figure 3a). Considering the thickness of the micromagnets (50 µm) and that of the different coils, the coil-magnet distances are taken to be 24 or 44 µm. The energy harvester was then characterized by mounting the PCB onto a mini-shaker with adjustable vibration amplitude (Figure 3b, inset). Displacement of the shaker and of the MEMS resonator (Figure 3b) were both measured using a confocal microscope (Figure S10 and Video S3, Supporting Information). Considering five measured energy harvesters with various widths ($L$) and coil-magnet distances, the mean resonant frequency and quality factor are 1225 Hz and 527, with standard deviation of 39 and 123, respectively.

Electrically, the energy harvester is a voltage source of electromagnetic force $e$ and internal impedance $Z_{eq}$, connected in series to a variable load resistor $R_L$ through which the voltage $V_{out}$ is measured (Figure 1c). Using a high load resistance ($R_L = 1$ MΩ)
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Optical images of a) the MEMS resonator including the NdFeB micromagnet array and b) the asymmetric planar coil. Red dashed squares: enlarged views in c,d). Scanning Electron Microscopy (SEM) images of (c) an array of 300 µm-wide micro-magnets and (d) the electroplated Cu coil with 10 µm wide turns, revealing the grouping of six turns to face a micromagnet column. e) Schematic view of the final assembly of both parts using adhesive tape to fix the gap between the coil and the micromagnets.</figcaption></figure>

resulted in an open circuit-like configuration, from which the electromotive force was directly measured as $V_{out}(t) = e(t)$. Representative measurements obtained from the energy harvesters with integrated arrays of micromagnets of width $L = 300$ and 500 µm submitted to an external sinusoidal force are shown in **Figure 4**. For limited displacement of the moving plate ($X_0 = 30$ and $70$ µm) the output voltages were found to be fairly sinusoidal, as one could expect from the model. Distortions observed for large displacement ($X_0 = 150$ µm) were reproduced numerically with good agreement, as further described hereafter (Figure 4c,f). For both sizes of micromagnets, the root mean square (RMS) amplitude $E$ of $e(t)$ was found to increase with the displacement $X_0$.

To further characterize this behavior, measurements were made adapting the shaker excitation so as to probe displacement amplitude varying from a few microns to $150$ µm, on a set of five energy harvesters. The results, reported in **Figure 5a**, show a linear behavior, as expected from the model (Equation 3), even for the largest displacement. The fabrication

process of the energy harvesters is fairly robust, since all the tested devices exhibit similar properties, as evidenced by overlapping of the curves. Measuring the slope of these curves allows us to directly measure the transduction factor $K$ of the devices. Values of $K_{exp} = 3.5$ and $6.5$ mWb m$^{-1}$ were found for arrays of micromagnets of $L = 300$ and $500$ µm, respectively. Not surprisingly, these values are lower than that expected from our initial simulations ($18$ and $23$ mWb m$^{-1}$), for which we considered textured isolated micromagnets with a remanence of $1.20$ T.[21]

To account for the 4-fold reduction in transduction factor and the distortions observed for large displacements, additional simulations have been realized, considering the real characteristics of our devices which are:

1) A magnetic remanence of 0.68 T, owing to the isotropic nature of the deposited NdFeB film,
<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /><figcaption>Figure 3. a) Optical image of the final device fixed on a PCB and b) the evolution of the amplitude of vibration X₀ as a function of excitation frequency measured between 1170 and 1300 Hz, evidencing the 1st resonance peak.</figcaption></figure>

2) The deposition of NdFeB not only on top of the etched Si pillars, but in the spaces between them also (Figure 2c; Figure S7g, Supporting Information),

3) a coil-magnet distance d = 24 or 44 µm,

4) A potential misalignment during the bonding of the two chips, resulting in the coil's turns not being well centered above the columns of micromagnets.

Using the same methodology that we established in ref.,[21] the simulated electromotive forces are plotted and compared with measurements in Figure 4. A fairly good agreement is observed when comparing the normalized electromotive force ($V_{out}/V_{out,max}$, right hand side axis). The distortions from the sinusoidal behavior were satisfactorily reproduced and resulted from both the large amplitude of oscillation $X_0$, which eventually results in some of the micromagnets moving outside of the coil's turns thus inducing a negative magnetic flux gradient (see Figure S3d, Supporting Information); and/or a slight misalignment induced during the flip-chip process. By adjusting the simulations to fit the experimental data, misalignments of less than 10 µm were determined for the various devices, demonstrating an impressive control over the fabrication process.

Considering the real characteristics, a fairly good agreement was found for the transduction factor $K_{sim}$ (7.0 and 9.0 mWb m⁻¹ for L = 300 and L = 500 µm, respectively) which are now only two times larger than $K_{exp}$. The remaining differences are tentatively attributed to the idealized shape of the lower level of deposited magnetic material considered in the simulations (i.e., distortions in the shape of the buried magnets, due to shadowing, are neglected).

Reducing the value of $R_L$ leads to a simple series resistor circuit. The evolution of $V_{out}$ as a function of the load resistor was nicely fitted by a simple voltage divider, considering solely the resistive contribution $Z_{eq} = R_C$. Figure 5b also highlights the progressive transition from a closed-circuit to an open-circuit configuration as $R_L$ increases, the latter being reached for several tens of kΩ. While the induced current was in the µA range for $R_L$ = 1 kΩ, it became negligible in the open-circuit configuration (nA for $R_L$ = 1 mΩ). Electrical damping in energy harvesters being due to the magnetic countereffect associated with the current induced in the coil, it should be observed for low $R_L$ values but not for larger ones. In our case, the motion of the vibrating plate in both electrical configurations is similar (Figure S11, Supporting Information), the electrical damping was thus negligible compared to the mechanical damping, i.e., $d_e \ll d_m$ and $d \approx d_m$. Considering the experimental Q factor ($Q$ = 500), the resonance frequency ($f_0$ = 1225 Hz) and the vibrating mass ($m$ = 42 mg), a mechanical damping $d_m$ = 0.65 × 10⁻³ kg s⁻¹ was deduced from Equation (1). Though of significant interest for modeling energy harvesters, the experimental determination of mechanical damping is, to our knowledge, never addressed in the literature.

The electrical power transferred into the load:

$$P = V_{out}^{2}/R_{L} \qquad (7)$$

is plotted as a function of $R_L$ in Figure 5c for two typical devices corresponding to magnet arrays with lateral sizes L = 300 and 500 µm. In both cases, the maximum power transfer was found when $R_L$ is strictly equal to $R_C$, while Equation (4) stated that $R_L = R_C + K^2/d_m$. Considering the experimental values of $R_C$, K and $d_m$, one can indeed deduce that $R_C \gg K^2/d_m$ and thus that $R_L = R_C$.

The maximum power transfer for an acceleration of 0.8 g was $P$ = 4.0 and 5.9 nW for L = 300 and 500 µm, respectively. Considering Equation (5), $P_{theo}^{MAX}$ can be determined considering the experimental values of $f$, $X_0$, $Q$, $R_C$, K and $d_m$, leading to a $P_{theo}^{MAX}$ = 2.7 and 5.3 nW. The order of magnitude is in good agreement, showing the robustness of the analytical model.

For the sake of comparison with state-of-the-art energy harvesters, the normalized power density has been calculated as: NPD = $P/Va^2$, with P the output power, V the energy harvester volume, and a the acceleration (estimated from $a = X_0\omega_n^2/Q$ = 0.8g). In our case, NPD was estimated to be 3 × 10⁻⁴ kg s m⁻³ (20 mW m⁻³) a value which is among the highest reported for fully-MEMS energy harvesters.[6] While there are efforts to develop ultra-low power consumption sensors, most monitoring microsensors now require power in the µW range. Thus, in the present form, the proposed energy harvester would not power much. However, thanks to the good agreement between the analytical model, the numerical simulations, and the experimental values, we have clear guidelines for improvements:
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Induced voltage ($V_{out}$) measured as a function of time for three different vibration amplitudes ($X_0$ = 30, 70, 150 µm) for energy harvesters with micromagnets of width $L$ = 300 µm a–c) and 500 µm d–f). All measurements were done in the open circuit-like configuration with $R_L$ = 1 MΩ, i.e., $V_{out}$ = *e*.</figcaption></figure>

1) Eliminating the lower level of deposited magnetic material, will triple the electromotive force *E*, as demonstrated numerically (Figure S12, Supporting Information).

2) The deposition of NdFeB at higher temperatures, to reach a remanent induction of 1.2 T, will increase the magnetic flux and the transduction factor four-fold.

3) Increasing the coil thickness will reduce the coil-micromagnet distance and reduce $R_C$. The delivered power being proportional to $E^2/R_C$, all these improvements would increase the delivered power by at least two orders of magnitude, i.e., ≈2 µW cm⁻³ for a single device.

**4. Conclusion**

Finite element simulations combined with analytical modeling were used to design MEMS electromagnetic energy harvesters based on an array of out-of-plane magnetized high-performance 50 µm thick NdFeB micromagnets vibrating in-plane above a Cu coil. Functional devices were then fabricated using high-rate triode sputtering coupled with standard microfabrication processes. The MEMS energy harvesters obtained exhibited a normalized power density of ≈3 × 10⁻⁴ kg s m⁻³ and delivered a power of up to 6 nW at 0.8 g. Given the small size of these energy harvesters, several devices could be integrated on the same chip in parallel and series, to increase power and deliv-

ered voltages so as to meet the requirements of today's sensors. Alternatively, thanks to the accuracy of our analytical modeling and finite element simulations, precise guidelines concerning both micromagnet and coil characteristics have been established to further improve the performance of such devices. More importantly, this study demonstrates that it is possible to integrate cleanroom-friendly thick fully dense sputtered NdFeB micromagnets into functioning devices, within a MEMS workflow. This, together with the proven capability to double the remanence of such micromagnets through deposition at elevated temperatures, opens the way for their exploitation in a myriad of micro devices with applications in fields as diverse as energy conversion, telecommunications, biotechnology, healthcare, and quantum computing.

**5. Experimental Section**

*Microfabrication:* The manufacturing process used to produce the MEMS energy harvester includes the production of the vibrating mass hosting the 4 × 6 mm² NdFeB micromagnet array (Figure S6 and S7, Supporting Information), the microfabrication of the coil (Figure S5, Supporting Information) and the assembly of these two parts using an adhesive to control the spacing between them (Figure 2e). First, DRIE (Alcatel AMS4200) is used to etch 50 µm deep patterns on a standard 100 mm Si substrate using AZ 40 XT photoresist as a masking layer, which serves to both define the in-plane dimensions of
<figure><img src="image_7.png" /><figcaption>**Figure 5.** a) Voltage amplitude (RMS) measured in open loop-like configuration using a load resistor $R_L = 1~mΩ$ as a function of the relative displacement $X_0$. Five devices were measured independently, 3 of them having arrays with $L = 500~µm$ (red triangles, black circles, and green diamonds) and 2 with $L = 300~µm$ (orange triangles and blue squares). Evolution as a function of the load resistance of b) the experimental electromotive force (RMS) and c) the power transferred to the load resistor for $X_0 = 70~µm$ ($a = 0.8$ g) using magnet arrays with $L = 300~µm$ (blue squares) and $L = 500~µm$ (black circles). Dashed lines: fits obtained considering a voltage divider circuit. Vertical dashed lines: experimentally determined values of the coil resistances $R_C$.</figcaption></figure>

individual micromagnets in the array and to reduce the stress within the magnetic layer. Following numerical simulation guidelines, two patterns were prepared consisting of square magnets with lateral sizes $L = 300~µm$, spaced by $Δx = 100~µm$, and $L = 500~µm$ spaced by $Δx = 50~µm$.

A Ti (100 nm)/NdFeB (50 µm)/Ti (100 nm) trilayer was then deposited through a shadow mask onto the patterned Si substrate using high-rate triode sputtering.[18,19] The lower Ti layer serves as an adhesion layer, and prevents interdiffusion between the magnetic layer and the substrate during subsequent annealing, while the upper Ti layer prevents oxidation of the magnetic layer. Following the observation of mechanical issues with some micromagnets deposited at elevated temperatures, the substrate was not heated during the deposition of fully processed samples. After removal of the shadow mask, a 100 µm thick dry film photoresist (WBR 2100) was deposited using a nano-imprint tool (Nanonex). The dry film was then patterned by photolithography, to allow localized removal of the sputtered material in the regions where the underlying silicon substrate is to be etched to form the resonators. Following removal of the sputtered material by wet etching, the remaining photoresist was stripped. A new dry film photoresist was then deposited and patterned by photolithography to allow DRIE of the Si substrate using an Al-catalyzed AMS4200 plasma etch equipment to produce the MEMS resonators (mass and springs) and to separate the individual chips. Following stripping of the remaining photoresist, annealing was performed at 600 °C for 1 min in a Rapid Thermal Annealing (RTA) furnace, to crystallize the hard magnetic Nd₂Fe₁₄B phase. The thus produced micromagnets were magnetized out-of-plane, in a field of 7 T produced within an open-bore superconducting coil.

In parallel, the coil was produced by electroplating, using the following process. A 100 nm silicon substrate of thickness 525 µm was thermally oxidized to a depth of 200 nm and an AC450CT sputtering equipment (alliance concept) was used to deposit a 100 nm Ti adhesion layer followed by a 200 nm Cu seed layer. A layer of photoresist (AZ 40 XT) was spin-coated onto the seed bilayer and patterned by photolithography to define the geometry of the coil. Cu was then electroplated through the patterned photoresist using a Plating Set 4–6 inches from Yamamoto-MS. Following the removal of the latter, the Ti/Cu bi-layer was wet-etched in between the turns of the coil, to avoid electrical short circuits. Electroless deposition was then used to coat the coil with a 150 nm thick Au layer, to protect the Cu from oxidation. The thus prepared coils were annealed at 250 °C under $N_2$ for 20 min to reduce their resistivity, and the substrate was then cut into individual chips.

For a given energy harvester, the chip containing the vibrating mass hosting the micromagnet array and that hosting the coil were finally assembled using a flip-chip tool (FC150 from SET) and joined by two layers of adhesive (tesa 61 532), with a total thickness of 100 µm, manually cut and positioned. Finally, the energy harvesters were glued to a PCB, and the electrical contacts with the coil were realized by wire bonding.

**Characterization:** The magnetic properties of the micromagnet arrays were characterized at room-temperature using a Superconducting Quantum Interference Device Vibrating Sample Magnetometer (SQUID-VSM) between ±7 T and the stray fields produced by them were measured using a magneto-optical sensor based magnetic field mapper (Matesy, magview).

The energy harvesters were electrically characterized using a dedicated bench consisting of a 4810 mini-shaker from Brüel & Kjær (Figure 3b; Figure S9, Supporting Information). The shaker and the resulting vibrating plate displacement were both measured with a microscope using an IFS2407-3 confocal detector from micro-epsilon. The induced voltage in the coil was measured with an instrumentation system using a NI USB-6363 acquisition card.

## Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.
## Acknowledgements

This work was supported by the French National Research Agency (ANR) under the research project POMADE (ANR 19-CE09-0021-01) and by the French national technological network RENATECH. The authors would like to thank Pierre Le Berre of Institut Néel for assistance with magnetic measurements.

## Conflict of Interest

The authors declare no conflict of interest.

## Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

## Keywords

electromagnetic energy harvester, MEMS, micromachining, micromagnet array, monolithic integration, permanent magnets

Received: October 28, 2024

Revised: February 28, 2025

Published online: March 19, 2025

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