# Biomechanical MEMS Electrostatic Energy Harvester for Pacemaker Application: a study of optimal interface circuit

Francisco Ambia, Nathalie Isac, Abdelmounaim Harouri, David Bouville, Elie Lefeuvre

► To cite this version:

Francisco Ambia, Nathalie Isac, Abdelmounaim Harouri, David Bouville, Elie Lefeuvre. Biomechanical MEMS Electrostatic Energy Harvester for Pacemaker Application: a study of optimal interface circuit. IEEE Transactions on Biomedical Engineering, 2024, 71 (4), pp.1127-1138. 10.1109/TBME.2023.3327957. [hal-04502887](https://hal.science/hal-04502887v1)

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# Biomechanical MEMS Electrostatic Energy
Harvester for Pacemaker Application: a study of
optimal interface circuit

Francisco Ambia, Nathalie Isac, Abdelmounaim Harouri, David Bouville and Elie Lefeuvre

***Abstract***—Leadless pacemaker is the most recent pacemaker concept which was developed to overcome the limitations of conventional pacemakers. This technology offers better comfort to the patients, lower risk of implantation and higher reliability. However, due to extreme miniaturization required for implantation inside the heart cavities, these devices suffer from limited battery lifetime. This work presents a solution to extend the battery lifetime by converting biomechanical heartbeats energy into electricity using an innovative electrostatic MEMS energy harvesting device. Based on theoretical models and experiments, we propose a general approach to choose the optimal interface circuit taking into the parasitic capacitance of the circuit, which is an imperfection that greatly affects the power performances. Based on the energy consumed by the last generation commercial leadless pacemakers, the proposed MEMS solution with optimal interface circuit experimentally showed the possibility to extend the pacemaker battery lifetime up to 44%.

***Index Terms***—Leadless pacemaker, MEMS, Biomechanical Energy Harvesting.

## I. INTRODUCTION

Leadless pacemakers (LPMs) have shown important improvements over conventional pacemakers (CPMs). LPMs eliminate the risk of lead-related complications: lead failure, lead fracture, insulation defect and pneumothorax. Risks of extraction such as a torn subclavian vein or tricuspid valve can be avoided because there is no lead to replace or extract. LPMs decrease the risk of infection since there is no pathway between the chest and the bloodstream for bacteria [1] [2] [3]. LPMs are more comfortable since patients are unable to see or feel the device on the chest wall.

The main limitation of commercial LPMs is the battery life time. Latest models of LPMs have Li-CFx batteries of 240mAh nominal capacity [4]. The depletion of these batteries varies from patient to patient in function of the needed pacing rate and needed R-wave amplitude. The projected life time of commercial pacemakers goes from 3.5 years for the worst case

where the LPMs is used in a 100% pacing rate and maximum R-wave amplitude. In the best case scenario, the lifetime can go up to 30 years when the pacing is inhibited at 0% pacing rate.

Given that battery depletion time is the main factor that limits the lifetime of both LPMs and CPMs [5], strong efforts have been done to increase the lifetime of pacemakers by harvesting the available energy in the surroundings of the implant [6] [7] [8].

Different sources of energy are available to harvest and power biomedical implants. Biochemical energy can be harvested from the electrical potential difference in the cell membrane [9] [10]. Glucose is another source of biochemical energy that can be used to power implants. In [11] an implantable glucose biofuel cell is presented. The biofuel cell was implanted in a rat, a peak power of 6.5 µW was found.

Another source of energy available in the environment is sunlight [12] [13]. In [13] a subcutaneous solar module was tested ex vivo under real sunlight under pig skin. A median output power of 4941µW/cm² was measured. In vivo pacemaker tests showed that the energy consumption of the pacemaker could be covered by the energy harvested by the solar module.

Harvesting heart mechanical energy in vivo test on rats, sheep, pig and dogs have been reported [14]–[18]. In [16] authors use a triboelectric generator aiming to supply energy to a pacemaker achieving cardiac pacing using mechanical work done by the heart. The generator achieves to generate an average energy of 0.495µJ per cardiac cycle by attaching a flexible biocompatible triboelectric generator on the side of a pig’s heart.

Authors in [15] designed an inertial triboelectric harvester to get energy from the acceleration resulting from dog walk. The device best performance was 4.9 µW/cm³ power density in a laboratory experiment exciting the device with a shaker at 3Hz.

An inertial electromagnetic harvester was reported in [18], it uses an inertial mechanism from a commercially available

The next few paragraphs should contain the authors' current affiliations, including current address and e-mail. For example, First A. Author is with the National Institute of Standards and Technology, Boulder, CO 80305 USA (e-mail: author@boulder.nist.gov).

<footnote>This paragraph of the first footnote will contain the date on which you submitted your paper for review, which is populated by IEEE. It is IEEE style to display support information, including sponsor and financial support acknowledgment, here and not in an acknowledgment section at the end of the article. For example, "This work was supported in part by the U.S. Department of Commerce under Grant 123456." The name of the corresponding author appears after the financial information, e.g. (Corresponding author: Second B. Author). Here you may also indicate if authors contributed equally or if there are co-first authors.</footnote>
wrist watch. The mechanism moves due to the heart beat of a sheep. The mobile pendulum compresses a spring until a certain threshold is reached. The spring energy is then released to drive an electromagnetic generator. In vivo test on a sheep's heart showed that the harvester generated an average power of 16.7µW.

In [15] [16] [18] suturing methods were used to implant devices, which makes the procedure invasive. A less invasive approach was proposed in [17]: a flexible biocompatible piezoelectric material was integrated into the lead of a pacemaker, using bending and twisting motions of the lead plugged in a pig's heart to generate energy.

The present work proposes a non-invasive solution to power the last generation of LPMs using inertial energy harvesting. Limited space available inside the heart cavity and arteries have imposed certain constraints for the development of LPMs. The first constraint is the implant's diameter limitation. It comes from the fact that LPMs are implanted with catheters through the arteries. The second constraint is the heart cavity size limiting the implant's length. Typically, a LPM has 5-6mm diameter and 30-50mm length.

Another factor to take into account is the energy consumption of LPMs. Due to the lower space available for batteries, LPMs energy consumption has to be much lower than CPMs.

In [4] the lifetime expectancy of a commercial LPM is reported according to projections based on battery size and modes of operation. For a LPM working at 100% pacing rate, 50bpm, pulse duration of 2.5V and a 500Ω pacing load, consumes 2.3µA of current, meaning at least 6µW of average consumption. A battery of 240mAh would be depleted after 11 years under these conditions.

We designed the MEMS device with the aim of contributing to powering a LDP under the conditions mentioned previously. The objective is to generate the largest possible part of the LPM power needs in order to significantly extend the battery lifetime.

<figure><img src="image_2.png" /><figcaption>Fig. 1. LPM implanted in the right ventricle.</figcaption></figure>

Contrary to piezoelectric material based energy harvester, whose transduction coupling is determined by the device geometry and materials used, electrostatic transducers bring the advantage of tunable transduction coupling through the interface circuit. Having this extra degree of freedom facilitates the design of high performance MEMS energy harvesters.

Crystalline silicon at room temperature doesn't deform plastically, showing no hardening effect. This property makes silicon able to deform in principle an infinite number of cycles

without aging. Whereas amorphous piezo becomes brittle due to fatigue effects and may also lose polarization with use.

Sometimes, electrostatic energy harvesters are covered with an electret layer to bias the transducer. However, the charge stability of electrets cannot be guaranteed for very long time. Therefore, no electret was added in the present application for the sake of reliability and durability.

Section II presents the MEMS structure and the fabrication process of the transducer. The energy conversion principle is then presented in Section III. Energy extraction circuits and their imperfections are analyzed in Sections IV and V. Global performance of the energy harvesting system are then studied in harmonic and heart beat excitation regimes in Section VI and VII. Finally, experimental and theoretical results are compared and discussed in Section VIII.

## II. MEMS STRUCTURE AND FABRICATION

For implantation procedure, LPM implant has to be inserted into the right ventricle through the femoral artery with a catheter. To comply with this constraint, commercial LPM capsules are cylindrical with typically 6.5mm of diameter and 40mm of length [4]. The presented MEMS device was designed to comply with available space in the capsule. The MEMS transducer takes half of the space of the implant. The rest of space is dedicated for LPM electronics and the battery as illustrated in Fig. 2.

The MEMS devices were fabricated on 4 inches Silicon on Glass (SoG) wafers, with 1mm thickness of glass and 200µm of p-doped crystalline silicon. Two MEMS devices can fit inside the implant one stick to the back of the other as depicted in Fig. 2.

A tungsten mass is added on top of the MEMS in order to bring down the frequency response of the device to match the low frequency spectrum of the heartbeat and human movement. A similar approach was presented in [19] to fabricate near-zero power accelerometers to detect human movement.

<figure><img src="image_3.png" /><figcaption>Fig. 2. LPM internal structure: MEMS energy harvester, battery and pacemaker electronics.</figcaption></figure>

### A. MEMS Structure

The device is a mechanical resonator consisting on a mobile mass coupled to a spring, the resonator oscillates under the influence of heart beat accelerations. The mobile part consists also of capacitor finger combs that engage and disengage with the oscillatory movement in the desired direction of motion as
illustrated in Fig. 3. Engaging and disengaging the combs varies the electrical capacitance between fixed and moving combs. Changes of capacitance can be exploited to convert the biomechanical work done to change the capacitance into electricity [20] [21].

Heart beat excitation frequency spectrum is composed of very low frequencies compared to the typical resonant frequencies of MEMS resonators. This led to design very specific springs geometry with outstandingly low rigidity.

The folded beam structure is widely used in MEMS devices where a linear spring is needed [22]. However, unwanted displacement of the resonator mobile part could be generated by complex multi-axis components of heart beat acceleration. This would bring the combs into contact causing a short circuit.

To tackle this problem, folded suspension beams can be used to block movement in all directions except in the desired one [23] [24]. The original solution proposed here, was to use the double-beam structure depicted in Fig. 3. It consists of a folded spring with two beams instead of one, which blocks all rotations of the moving part. The double beam structure enables also to block any in-plane movements in the perpendicular direction [25]. Therefore, all unwanted contacts and risk of short circuits are avoided. The top view of the device is illustrated in Fig. 3.

<figure><img src="image_4.png" /><figcaption>**Fig. 3.** Top view of the MEMS device. a) Mechanical Layout: moving part (blue), fixed parts (black) and double-beams (red) b) Electrical Layout: electrical potential of fixed combs (black) and electrical potential of moving combs (green).</figcaption></figure>

Stoppers were included in the design to set the maximum displacement of the mobile part. This limits the maximum stress on the deformable parts, thus avoiding the risk of breakage.

<table><caption>**TABLE I**
MEMS PARAMETERS</caption><tr><td>Silicon thickness</td><td>200 µm</td></tr><tr><td>Glass thickness</td><td>1 mm</td></tr><tr><td>Beams length</td><td>3 mm</td></tr><tr><td>Beams width</td><td>30 µm</td></tr><tr><td>Maximum displacement</td><td>±200µm</td></tr></table>

<table><tr><td>Complete travel range</td><td>400µm</td></tr><tr><td>Finger combs length</td><td>190 µm</td></tr><tr><td>Combs gap</td><td>2 µm</td></tr><tr><td>Number of comb capacitors</td><td>2412</td></tr><tr><td>Tungsten mass</td><td>750 mg</td></tr><tr><td>Tungsten mass height</td><td>1.8 mm</td></tr></table>

The MEMS combs are arranged in a symmetrical gap-overlap configuration: fingers engage and disengage as the mobile part oscillates. This design was preferred over the classical gap closing design to avoid squeeze film damping which reduces the power performances. Solutions to reduce squeeze film damping were proposed in [26] based on trapezoidal shape. Despite its effectiveness, the power density remains lower than the solution of this work. The specificity of the presented design is to provide large capacitance variation, which is a key parameter for energy harvesting. This was obtained with a very small gap between the combs and a very large displacement of the moving part.

## B. Fabrication

The MEMS device was fabricated using a silicon on glass (SOG) wafer composed of 200µm thickness silicon bonded on 1 mm glass wafer. The fabrication process is illustrated in Fig. 4. Photoresist film was spin-coated to transfer the pattern on the wafer by photolithography. The photoresist pattern was transferred into silicon by deep reactive ion etching (DRIE). Each wafer contains 36 MEMS devices. In order to separate each MEMS, a silicon carrier wafer was glued on top of the SOG before dicing the glass on the backside of the SOG. The carrier wafer protects the device and the dicing tool from breakage. After partial dicing of the glass wafer, the remaining glass was cut with a cleaving tool to get each MEMS separated. Once devices were separated, each device was immersed in hydrofluoric acid (HF) to etch the glass underneath the MEMS mobile part.

<figure><img src="image_5.png" /><figcaption>**Fig. 4.** MEMS device fabrication process.</figcaption></figure>

A tungsten mass was glued on top of the MEMS mobile part with an epoxy resin and positioned with a pick-and-place robot. A printed circuit board (PCB) was used to connect the MEMS with energy extraction interface circuits.

A picture of the tested device is shown in Fig. 5a. The device
has 22mm of length, 5.6mm of width and 3mm high including the tungsten mass. Note that the device dimensions can easily be reduced by reducing the size of the connections and the frame, as it will be done in industrial scale. This way, the dimensions would be 19mm x 4.3mm without altering the MEMS performances.

Although the MEMS device dimensions can be further reduced, it is small enough to place two units inside the capsule of the latest models of LPMs [4] while occupying only half of the volume of the capsule.

<figure><img src="image_6.png" /><figcaption>Fig. 5. Images of the fabricated MEMS device. a) Photo of the device fully assembled, b) SEM picture of the finger combs, c) Optical microscopy of a double-beam spring with stopper.</figcaption></figure>

### III. ELECTROSTATIC ENERGY CONVERSION

Mechanically actuated variable capacitor can generate electrical energy with appropriate electrical conditions [27] [28]. The amount of energy that the transducer converts strongly depends on the interface circuit that drives the energy extraction [29].

The charge-voltage diagram (QV diagram), is often used to picture the path that a transducer follows in the electrical domain. Electrostatic energy harvesters work in cycles. These cyclic process yield QV diagrams in the form of closed curves. The energy harvested per cycle is the surface enclosed inside the closed curve QV trajectory. The bigger the enclosed surface, the bigger the energy the transducer harvests on each cycle.

Different kind of energy extraction interface circuits can be considered, corresponding to different QV cycle shapes. Triangular QV cycles can be constrained in voltage or constrained in charge [30] [31]. Elliptical QV cycles can be obtained with diode rectifier and resistive load [32]. Finally, a large variety of interface circuits perform rectangular QV cycles [28] [29] [33].

All electrostatic energy harvesting devices need a bias voltage to work. This bias voltage may come from a voltage source or an electret, the latter being excluded because the long term charge stability problem. The bias voltage influences the size of the QV cycle, hence also the harvested energy and electro-mechanical coupling.

It is well known that among all possible solutions, interface circuits that perform triangular voltage constrained QV cycles are the circuits that extract most of energy for a given maximum

voltage.

Triangular voltage constrained interface circuits and triangular charge constrained interface circuits need active synchronized switches with dedicated control electronics, which makes them difficult to use in practice due to their intrinsic power consumption.

Despite interface circuits that perform rectangular QV cycles are less performant in terms of extracted energy, they are best suited for ultra-low power applications such the pacemaker application. Indeed, contrary to the previous interfaces, they do not require active switches and control. They only use passive components (diodes, capacitors) and they are self-synchronized, which allows the transducer to convert energy from stochastic non-periodic accelerations like the heart-beat with minimum intrinsic energy consumption.

All interface circuits that perform rectangular QV cycles can be modeled by the circuit depicted in Fig. 6 [29]. This simplified interface circuit has no resistance, no parasitic capacitances connected in parallel with the transducer.

<figure><img src="image_7.png" /><figcaption>Fig. 6. Conceptual circuit performing rectangular QV cycles bounded between $V_{min}$ and $V_{max}$.</figcaption></figure>

Electrostatic transducers change capacitance between a minimal and maximal capacitance $C_{min} \le C(t) \le C_{max}$. For instance, the capacitance of the transducer presented in Section II takes the value of $C_{max}$ when the combs are engaged and $C_{min}$ when they are disengaged. Let $\eta$ be the ratio between maximal and minimal capacitances.

$$ \eta = C_{max}/C_{min} \qquad (1) $$

The amount of energy harvested per cycle strongly depends on $\eta$. The bigger $\eta$, the bigger the converted energy. Another useful dimensionless parameter is the ratio $\gamma$:

$$ \gamma = V_{max}/V_{min} \qquad (2) $$

Defining these two dimensionless parameters $\eta$ and $\gamma$ allows to simplify the following study of rectangular QV cycles.

### IV. RECTANGULAR QV CYCLES

The working principles of the circuit depicted in Fig. 6 are studied in depth in [34]. In the present article, basic principles are presented to tackle the question of which QV rectangular interface circuit is the best suited for the presented MEMS.

For QV rectangular cycles, all energy exchanges with the circuit interface are done at constant voltage. The electrical
energy transferred in the process is:

$$ \Delta W_E = V(Q_f - Q_0) \quad (3) $$

Where $\Delta W_E$ is the electrical energy exchanged in the process, $V$ is the voltage at which the process takes place, $Q_0$ is the charge at the beginning of the transfer and $Q_f$ is the charge at the end of the transfer.

<table><caption>TABLE II
CAPACITANCE VALUES AT EACH STAGE</caption><tr><td>C(①)</td><td>C<sub>min</sub></td></tr><tr><td>C(②)</td><td>γC<sub>min</sub></td></tr><tr><td>C(③)</td><td>ηC<sub>min</sub></td></tr><tr><td>C(④)</td><td>ηC<sub>min</sub>/γ</td></tr></table>

The capacitance at each stage are listed in Table II. The sub index of capacitance corresponds to the number of stage in Fig. 7.

Rectangular cycles are composed of four processes as depicted in Fig. 7. Process ② → ③ happens at constant voltage in which the transducer extracts charge from the voltage source $V_{min}$. The diode $D_1$ is ON and $D_2$ is OFF. The transducer receives an amount of electrical energy $\Delta W_{E23} = (\eta - \gamma)C_{min}V_{min}^2$.

Process ③ → ④ is adiabatic, both diodes are OFF and no energy is exchanged between the transducer and the voltage sources $\Delta W_{E34} = 0$. Voltage rises as capacitance decreases; the inertial mass does work to decrease the capacitance.

Process ④ → ① is another energy transfer at constant voltage. The diode $D_2$ is ON and $D_1$ is OFF. The transducer gives energy $\Delta W_{E41} = -\gamma(\eta - \gamma)C_{min}V_{min}^2$ to the voltage source $V_{max}$.

<figure><img src="image_8.png" /><figcaption>Fig. 7. Rectangular QV cycle performed by an ideal circuit.</figcaption></figure>

Finally, to complete the cycle and close the curve, process ① → ② is adiabatic, both diodes are OFF. No energy exchange takes place with the voltage sources $\Delta W_{E12} = 0$.

The total amount of electrical energy generated is the sum of all electrical energy exchanges $\Delta W_{ET} = \Delta W_{E23} + \Delta W_{E41}$. The total electric energy exchanges read as:

$$ \Delta W_E = -(\eta - \gamma)(\gamma - 1)C_{min}V_{min}^2 \quad (4) $$

The total electrical energy is negative because it is calculated from the transducer point of view. The transducer is giving more electrical energy that what it is receiving. This supplementary amount of energy that the transducer is giving comes from the work done by the mobile mass.

### A. Practical realizations of rectangular QV cycles

There are several kinds of interface circuits that perform rectangular QV cycles [33] [27] [35]. The main difference between these interface circuits is the relation between maximum and minimal voltages $\gamma$.

The Bennet's doubler was the first circuit that performed rectangular QV cycles. Its first implementation in electrostatic energy harvesting was reported in [27]. This interface circuit does QV cycles of $\gamma = 2$. This circuit served as a reference for circuits with different values of $\gamma$ [33] [35].

A self-synchronized, self-biased interface circuit was proposed in [33]. The circuit performs rectangular QV cycles with $\gamma = (n + 1)/n$ for $n \ge 1$ where $n$ is the number of so-called multiplying cells. The working voltages are set by the voltage in the $C_{store}$ capacitor $V_{store}$ as depicted in Fig. 8. The working voltages are $V_{min} = nV_{store}$ and $V_{max} = (n + 1)V_{store}$.

<figure><img src="image_9.png" /><figcaption>Fig. 8. a) QV cycles performed by the circuit in [33]. b) Interface circuit performing the QV cycles depicted in Fig. 8a.</figcaption></figure>

Another self-synchronized, self-biased modification of Bennet's doubler was proposed in [35]. The voltage relation for this circuit is $\gamma = N$ where $N$ is the number of capacitors in the circuit. The circuit achieves multiplying by $N$ the minimal voltage $V_{min}$ by alternating connecting all capacitors in series and connecting all capacitors in parallel.

<figure><img src="image_10.png" /><figcaption>Fig. 9. a) QV cycles performed by the series-parallel circuit b) Series-Parallel circuit performing the QV cycles depicted in Fig. 9a.</figcaption></figure>

## V. OPTIMAL INTERFACE CIRCUIT

The best suited interface circuit is the one that maximizes the extracted energy for a given transducer and a given mechanical
excitation. For a given capacitance variation, there is an optimal voltage ratio in a rectangular QV cycle [34].

The optimal voltage ratio $\gamma_{opt}$ is the one that maximizes the converted energy $-\Delta W_E$ (Eq. 4) for a given capacitance variation $\eta$.

In [34], it was found an optimal voltage relation $\gamma_{opt}$ for a given capacitance ratio $\eta$ and fixing $V_{max}$, as expressed in Eq. 5. In the present work, all circuit comparisons are also done by fixing $V_{max}$.

From a circuit design point of view, having an expression for a fixed $V_{max}$ is more relevant than fixing $V_{min}$. $V_{max}$ is indeed an important design parameter that serves as an upper-boundary for the system's working voltage. It can be set by the rating voltage of the electronic components in the interface circuits. It can also be set by the maximum voltage of the MEMS, related to the pull-in voltage or the breakdown voltage.

For a fixed $V_{max}$, the optimal voltage ratio $\gamma_{opt}$ reads as [34]:

$$ \gamma_{opt} = \frac{2\eta}{\eta+1} \qquad (5) $$

<table><caption>TABLE III
OPTIMAL CIRCUITS FOR DIFFERENT CAPACITANCE VARIATIONS</caption><thead><tr><th>η</th><th>γ<sub>opt</sub></th><th>Optimal Circuit</th></tr></thead><tbody><tr><td>1.67</td><td>1.25</td><td>4 cell circuit from [33]</td></tr><tr><td>2</td><td>1.33</td><td>3 cell circuit from [33]</td></tr><tr><td>3</td><td>1.5</td><td>2 cell circuit from [33]</td></tr><tr><td>∞</td><td>2.0</td><td>Bennet Doubler [27]</td></tr></tbody></table>

### A. Effect of parasitic capacitances

The choice of interface circuit based on Eq. 5 is valid under two conditions: The capacitors in the interface circuit have to be much bigger than the transducer capacitance: $C_1, C_2 \gg C_{max}$, see Fig. 7. This way, the capacitor voltages can be considered as almost constant during charge exchanges.

The second condition is that the parallel parasitic capacitance $C_{para}$ in the interface circuit must be much lower than the minimal capacitance of the transducer: $C_{para} \ll C_{min}$.

<figure><img src="image_11.png" /><figcaption>Fig. 10. Example of a Bennet doubler with a parasitic capacitance.</figcaption></figure>

The first condition can be met by choosing fixed capacitors of two or three orders of magnitude bigger than the transducer's

maximal capacitance.

The second condition is that the parallel parasitic capacitance of the interface circuit needs to be much smaller than the transducers $C_{min}$. As the parasitic elements cannot be easily controlled, meeting the second condition is not as straightforward as the first. All circuit connections bring their intrinsic parasitic capacitance that depends on shape, materials and dimensions.

For MEMS devices, the parasitic capacitance in the circuit may be in the same order of magnitude as the minimal capacitance of the transducer. Having a parasitic capacitance in the same of magnitude as $C_{min}$ makes the harvested energy per cycle drop drastically [23].

As mentioned before, expression in Eq. 5 was obtained under the assumption of no parasitic capacitance in the interface circuit.

To take into account the effect of the circuit's parasitic capacitance, we introduce $\beta = C_{para}/C_{min}$ where $C_{para}$ is the parasitic capacitance of the interface circuit.

<figure><img src="image_12.png" /><figcaption>Fig. 11. QV diagram taking into account the influence of the parasitic capacitance in the interface circuit.</figcaption></figure>

Instead of constant charge Processes ① → ② and ③ → ④, the parasitic capacitance induces a negative slope on the QV cycle (Fig 11), corresponding to the discharge and the charge of $C_{para}$ respectively. This effect reduces the harvested energy per cycle represented in red in Fig 11.

Taking into account the effect of the parasitic capacitance, the harvested energy per cycle is:

$$ E_h = \frac{(\gamma-1)(\eta-\gamma(\beta+1)+\beta)}{\gamma^2} C_{min} V_{max}^2 \qquad (6) $$

Parameter $\eta$ depends on the MEMS capacitor comb design and travel range, $\beta$ is an intrinsic parameter of the interface circuit. Given these two parameters, one can find the optimal voltage ratio $\gamma_{opt}$:

$$ \gamma_{opt} = \frac{2(\eta+\beta)}{\eta+2\beta+1} \qquad (7) $$

The best suited interface circuit changes in function of the parasitic capacitance in the interface circuit. In Table IV are shown the optimal interface circuits for a given combination of capacitance change $\eta$ and parasitic capacitance $\beta$.

Comparing Table III and Table IV shows that the parasitic capacitance changes drastically the optimal circuit.
<table><caption>TABLE IV
OPTIMAL CIRCUITS FOR DIFFERENT CAPACITANCE
VARIATIONS TAKING INTO ACCOUNT CIRCUIT'S PARASITIC
CAPACITANCE</caption><thead><tr><th>η</th><th>β</th><th>γ<sub>opt</sub></th><th>Optimal Circuit</th></tr></thead><tbody><tr><td>2.33</td><td>1</td><td>1.25</td><td>4 cell circuit from [33]</td></tr><tr><td>3</td><td>1</td><td>1.33</td><td>3 cell circuit from [33]</td></tr><tr><td>5</td><td>1</td><td>1.5</td><td>2 cell circuit from [33]</td></tr><tr><td>3</td><td>2</td><td>1.25</td><td>4 cell circuit from [33]</td></tr><tr><td>4</td><td>2</td><td>1.33</td><td>3 cell circuit from [33]</td></tr><tr><td>7</td><td>2</td><td>1.5</td><td>2 cell circuit from [33]</td></tr><tr><td>3.67</td><td>3</td><td>1.25</td><td>4 cell circuit from [33]</td></tr><tr><td>5</td><td>3</td><td>1.33</td><td>3 cell circuit from [33]</td></tr><tr><td>9</td><td>3</td><td>1.5</td><td>2 cell circuit from [33]</td></tr></tbody></table>

VI. HARVESTED ENERGY ON HARMONIC EXCITATION

A. Characterization of the MEMS capacitance

As described in Eq. 4, harvested energy is proportional to the capacitance variation $η$. To characterize the transducer's capacitance variation, a RC high pass first order filter was implanted. A resistance was connected in series between the capacitor and ground.

<figure><img src="image_13.png" /><figcaption>Fig. 12. Circuit to determine the capacitance as function of position.</figcaption></figure>

The amplitude of the voltage across the resistor $V_R$ depends on the transducer's capacitance. The voltage $V_R$ is modulated by the capacitance value of the transducer, which varies with the mechanical excitation.

The transducer was excited with a shaker at its mechanical resonant frequency $f_0 = 40.8$ Hz. The acceleration induced by the shaker was chosen so that the mass did the complete travel range from $-x_{max}$ to $x_{max}$.

<figure><img src="image_14.png" /><figcaption>Fig. 13. a) Displacement of the MEMS moving part. b) Voltage measured across the resistance $V_R$.</figcaption></figure>

The capacitance variation modulates the voltage across the capacitor, the envelope $V_E$ of the signal $V_R$ is used to calculate the capacitance.

The electrical input signal was a sinusoidal at $f_{in} = 10kHz$ and $V_{in} = 5V$ of amplitude, a series resistance of $R = 100kΩ$ was used to make the RC filter with the transducer.

Transducer's capacitance is calculated with the envelope signal $V_E$, series resistance and input signal:

$$C(t) = \frac{V_E(t)}{2\pi f_{in}R \sqrt{V_{in}^2 - V_E^2(t)}} \quad (8)$$

By correlating the capacitance and the displacement measurements, we obtain the capacitance as a function of the position of the moving part $C(x)$ as depicted in Fig. 14.

<figure><img src="image_15.png" /><figcaption>Fig. 14. Capacitance variation as a function of displacement.</figcaption></figure>

The above measurements determined the experimental values of $C_{min} = 8pF$, $C_{max} = ηC_{min} = 67.5pF$ and $η = 8.4$. Note the $η = 8.4$ corresponds to the maximal travel range going from $-x_{max}$ to $x_{max}$. $η$ varies linearly with the amplitude of displacement, meaning that the value of $η$ increases with the mechanical excitation level to finally saturate at $η = 8.4$ for the maximum displacement.

The transducer was then tested with five interface circuits providing different voltage ratios $γ$. The chosen circuits are listed in Table V. Capacitors of $10nF$ in the interface circuits were
chosen to be much bigger than the transducer's maximal capacitance $\eta C_{min} = 67.5pF$.

<table><caption>TABLE V
INTERFACE CIRCUITS USED FOR CHARACTERIZING THE MEMS ENERGY HARVESTER</caption><thead><tr><th>γ</th><th>Circuit</th><th>Acceleration [g]</th><th>Frequency [Hz]</th></tr></thead><tbody><tr><td>1.25</td><td>4 cell circuit from [33]</td><td>0.190</td><td>36.5</td></tr><tr><td>1.33</td><td>3 cell circuit from [33]</td><td>0.148</td><td>37.7</td></tr><tr><td>1.5</td><td>2 cell circuit from [33]</td><td>0.148</td><td>37.7</td></tr><tr><td>2</td><td>Bennet Doubler [27]</td><td>0.148</td><td>38.1</td></tr><tr><td>3</td><td>3 capacitor circuit from [35]</td><td>0.148</td><td>38.3</td></tr></tbody></table>

## B. Measurement of converted energy

The transducer was tested with the interface circuits listed in Table V. Each circuit has a different dynamic effect on the transducer due to the electrostatic softening effect [36]. The excitation acceleration amplitudes and frequencies were chosen so that the mobile mass did the complete travel range, having the maximum capacitance change of $\eta = 8.4$. In Table V are listed the frequencies and the amplitudes of acceleration that made the mobile mass do the complete travel range when the transducer was connected to the corresponding interface circuit.

The energy extracted from the transducer was determined from current and voltage measurements in the transducer, as illustrated in Fig 15. The voltage across the transducer $V_c$ was measured using a high impedance probe to avoid discharging the transducer. The current was measured by connecting an oscilloscope probe in series with the transducer. The internal resistance of the probe is $R_{senseIn} = 10M\Omega$.

<figure><img src="image_16.png" /><figcaption>Fig. 15. Circuit setup used to measure the output energy of the transducer and the output energy of the interface.</figcaption></figure>

Fig. 16 shows the waveforms of the input current $I_{Rin} = V_{Rin}/R_{senseIn}$, input voltage $V_c$ and output current $I_{Rout}/R_{senseOut}$ as a function of time for the circuit $\gamma = 1.5$. Similar waveforms were obtained for the other four circuits. For all measurements, the maximum voltage was fixed to $V_{max} = 50V$.

<figure><img src="image_17.png" /><figcaption>Fig. 16. Voltage and current experimental waveforms of the interface circuit with $\gamma = 1.5$.</figcaption></figure>

By integrating with respect to time the input current $V_{Rin}/R_{in}$, the instantaneous charge in the transducer $Q(t)$ can be calculated. Plotting $Q(t)$ versus $V_c(t)$ yields the QV cycles described in section 5A. Fig. 17 shows the QV cycles of the transducer connected to the considered interface circuits under the conditions described in Table V. The two dotted lines represent the charge-voltage relation for maximal and minimal capacitance. The slope of these dotted lines corresponds to $C_{min} = 8pF$ (bottom) and $C_{max} = \eta C_{min} = 67.5pF$ (top) respectively.

Green's theorem was used to calculate the energy per cycle of the different QV cycles. The energy harvested per cycle in each case is shown in Table VI.

<figure><img src="image_18.png" /><figcaption>Fig. 17. Charge-Voltage diagrams of the MEMS transducer connected to the considered interface circuits.</figcaption></figure>

The circuit's parasitic capacitance $C_{para}$ can be estimated from the QV cycle. The slope of the quasi-adiabatic process is the parasitic capacitance that we express as $C_{para} = \beta C_{min}$. In Table VI are listed the values of $C_{para}$ and $\beta$ for each circuit.

<table><caption>TABLE VI
CIRCUIT MEASUREMENTS</caption><thead><tr><th>γ</th><th>Energy per cycle [nJ]</th><th>Parasitic Capacitance [pF]</th><th>β</th></tr></thead><tbody><tr><td>1.25</td><td>21.7890</td><td>24.0838</td><td>3.0105</td></tr><tr><td>1.33</td><td>23.6558</td><td>20.8098</td><td>2.6012</td></tr><tr><td>1.5</td><td>26.3687</td><td>18.2307</td><td>2.2788</td></tr></tbody></table>
<table><tr><td>2</td><td>25.2953</td><td>15.1975</td><td>1.8997</td></tr><tr><td>3</td><td>3.5112</td><td>17.1447</td><td>2.1431</td></tr></table>

The value of the parasitic capacitance varies from circuit to circuit. Although we do not know the exact origin of the parasitic capacitance, it was found that the parasitic capacitance increases with the number of diodes soldered on the PCB board as depicted in Fig 18.

<figure><img src="image_19.png" /><figcaption>**Fig. 18.** Parasitic Capacitance as a function of total number of diodes soldered on the PCB.</figcaption></figure>

To compare the five circuits and validate Eq. 6 with the experimental data, we assume the parasitic capacitance of the five circuits is the average of all of them. The average parasitic capacitance of all circuits is $\langle C_{para} \rangle = 19.09 \text{ pF}$ translating to a normalized value of $\beta = 2.39$.

The solid black line in Fig. 19 is the result of plugging into Eq. 6 the values of $\beta = 2.39$, $\eta = 8.4$, $C_{min} = 8 \text{ pF}$ and $V_{max} = 50 \text{V}$. In the same figure, the dotted line represents the energy per cycle supposing the effect of parasitic capacitance was negligible. The red dots represent the measured value of energy per cycle in Table VI. The experimental data point for $\gamma = 2$ is over the theoretical line because this is the circuit with the lowest parasitic capacitance, as reported in Table VI.

<figure><img src="image_20.png" /><figcaption>**Fig. 19.** Theoretical energy converted per cycle without parasitic capacitance (dotted line), considering the average parasitic capacitance (solid line), and experimental results (diamond dots).</figcaption></figure>

Fig. 19 shows a comparison of theoretical energy converter energy per cycle for the case when parasitic capacitance ratio

$\beta = 2.38$ and for the case where $\beta = 0$, and experimental values. The theoretical model taking into account the average parasitic capacitance exhibits clearly a better agreement with experimental results. This analysis shows the importance of taking into account the effects of the parasitic capacitance on circuit design. Not taking into consideration this effect will lead to an overestimation of converted energy.

<figure><img src="image_21.png" /><figcaption>**Fig. 20.** Average converted power at the input and output of the interface circuits.</figcaption></figure>

### C. Power consumption of the interface circuits

Due to the symmetrical structure of the combs, one mechanical vibration cycle induces two QV electrical cycles. This doubling frequency effect is reflected in the expression used to compute the average electrical input power $P_{in}$ of the interface circuit: $P_{in} = 2f_{mecha}E_h$, where $f_{mecha}$ is the mechanical excitation frequency. The interface circuit output power $P_{out}$ was computed from measurements of the voltage across the resistance $R_{senseOut}$ to calculate the current injected into the energy storage component $V_{bias}$ (Fig. 15) using Eq. 9:

$$P_{out} = \left\langle \frac{1}{R_{senseOut}} \left[ V_{Rout}(t)(V_{bias} + V_{Rout}(t)) \right] \right\rangle_t \quad (9)$$

Fig. 20 shows the experimental input and output power of the considered interface circuits.

The difference between $P_{in}$ and $P_{out}$ is the power consumed by the circuits. One can notice that the difference is almost the same for all interface circuits. In average, the power consumption of the interface circuits operating at the maximum voltage of 50V and maximum capacitance variation of the MEMS is nearly 250nW.

Given the results in Fig 19 and Fig 20, the circuit that performs the best is the one of two cells from [33], which voltage ratio is $\gamma = 1.5$. This is well predicted by Eq. 7: plugging the values of $\eta = 8.4$, $\beta = 2.3867$ into this equation yields a theoretical optimal voltage ratio of $\gamma_{opt} = 1.52$.

## VII. HARVESTED ENERGY ON HEART BEAT EXCITATION

In the sinusoidal case studied in the previous section, the change of the MEMS capacitance $\eta$ remains constant though time, which corresponds mechanically to displacement oscillations with constant amplitude.

In the case of heart beat excitation, the amplitude of
displacement changes due the pulse-like shape of heart beat accelerations as depicted in Fig. 21.

<figure><img src="image_22.png" /><figcaption>Fig. 21. Typical heart wall acceleration and experimental MEMS mobile mass displacement at 130bpm, $\gamma = 1.5$ interface circuit and $V_{max} = 60V$.</figcaption></figure>

The acceleration signal was obtained by recording the heart wall acceleration of a pig's heart in the right atrium. The acceleration signal was then reproduced using an electromagnetic shaker to emulate the heart environment to excite the MEMS.

Power extracted from the transducer by the interface circuit was measured by averaging the product of the voltage $V_C$ with the current $I_{Rin}$ in the transducer.

The transducer was tested under four different heart-beat rates: 130bpm, 110bpm, 85bpm and 65bpm. The amplitude of these signals was 10 $m/s^2$ peak to peak. All the combinations of interface circuits and heart-beat rates were tested by fixing $V_{max} = 60V$ for all the cases. The experimental measures of power are depicted in Fig. 22.

<figure><img src="image_23.png" /><figcaption>Fig. 22. Powers extracted from the MEMS transducer as a function of the heartbeat rate, using the considered interface circuits.</figcaption></figure>

In order to better understand the system behavior, another set of experiments was done to explore the dependence of the harvested power in the amplitude of the heartbeat acceleration signal. The best performing circuit $\gamma = 1.5$ was taken for this study.

In Fig. 23, the harvested power was plotted for different amplitudes of heartbeat acceleration. Below $2m/s^2$ acceleration, the mobile mass motion remains negligible and no power can be extracted. Then, one can observe quasi-linear increase of the power versus acceleration until a saturation occurs,

corresponding to the maximum displacement of the MEMS mobile part.

<figure><img src="image_24.png" /><figcaption>Fig. 23. Converted power as function of heartbeat acceleration at 130bpm with interface circuit $\gamma = 1.5$ and $V_{max} = 60V$.</figcaption></figure>

Fig. 24 shows the complex QV cycles recorded over a heartbeat period. This spiral-like trajectory comes from the modulated oscillation amplitude of the MEMS mobile part. This makes that the capacitance changes are changing through time, with different local $C_{max}$ values.

<figure><img src="image_25.png" /><figcaption>Fig. 24. QV cycle for a heartbeat excitation 110bpm for a transducer connected to an interface circuit with $\gamma = 1.5$ and $V_{max} = 60V$.</figcaption></figure>

In order to translate this phenomenon to the simple model previously used for predicting the energy converted per cycle in the case of a constant displacement amplitude, we define $\eta_{eff}$ which is the effective change of capacitance for a given acceleration signal and a given interface circuit over several heartbeats time.

Eq. 10 describes a very coarse-grained approximation we define to roughly describe the change of capacitance.

$$ \eta_{eff} = \sqrt{2\eta_{max}} \frac{x_{RMS}}{x_{max}} \quad (10) $$

The idea behind this approximation comes from the fact that the capacitance varies proportionally to displacement. Then, one can suppose $\eta_{eff}/x_{eff} = \eta_{max}/x_{max}$, where $x_{eff} = \sqrt{2x_{RMS}}$ and $\eta_{max} = 8.4$ is the MEMS maximum capacitance variation.

TABLE VII

$\eta_{eff}$ FOR EACH INTERFACE CIRCUIT AND DIFFERENT HEART BEAT RATE
<table><thead><tr><th>Rate [bpm]</th><th>γ = 1.25</th><th>γ = 1.33</th><th>γ = 1.5</th><th>γ = 2.0</th><th>γ = 3.0</th></tr></thead><tbody><tr><td>130</td><td>3.3585</td><td>3.4021</td><td>5.1843</td><td>5.5938</td><td>7.1156</td></tr><tr><td>110</td><td>4.1302</td><td>4.0544</td><td>4.5451</td><td>5.5981</td><td>6.1557</td></tr><tr><td>85</td><td>3.8132</td><td>3.8271</td><td>3.9057</td><td>4.8512</td><td>6.5344</td></tr><tr><td>65</td><td>3.9377</td><td>3.1936</td><td>3.4687</td><td>4.1075</td><td>4.0590</td></tr></tbody></table>

Based on the values of $\eta_{eff}$ listed in Table VII, extracted energy values were computed using Eq. 11 (adapted from Eq. 6), enabling to determine the circuit $\gamma_{opt}^{th}$ which extracts the maximum of energy for a given heartbeat rate.

$$E_h = \frac{(\gamma-1)(\eta_{eff} - \gamma(\beta+1)+\beta)}{\gamma^2} C_{min}V_{max}^2 \quad (11)$$

Similarly, the best circuit from experiments is represented by $\gamma_{opt}^{exp}$. In Table VIII are listed the best performing circuits predicted by Eq. 11 $\gamma_{opt}^{th}$ and the circuits best ones experimentally $\gamma_{opt}^{exp}$.

<table><caption>TABLE VIII
COMPARISON OF THEORETICAL AND EXPERIMENTAL BEST PERFORMING CIRCUITS</caption><thead><tr><th>Rate [bpm]</th><th>γ<sup>th</sup><sub>opt</sub></th><th>γ<sup>exp</sup><sub>opt</sub></th></tr></thead><tbody><tr><td>130</td><td>1.5</td><td>1.5</td></tr><tr><td>110</td><td>2.0</td><td>2.0</td></tr><tr><td>85</td><td>1.33</td><td>1.33</td></tr><tr><td>65</td><td>1.25</td><td>1.33</td></tr></tbody></table>

The obtained values for $\gamma_{opt}^{exp}$ and $\gamma_{opt}^{th}$ show a good accordance, the best performing circuits being the same in both cases exempting the case of a heart rate of 65 bpm.

Overall, the best performing circuit is the 2-cell circuit from [33] again. The converted power per MEMS device goes from 0.4 to 1.1 µW depending on the heart-beat rate. With two MEMS devices inside a leadless pacemaker, the converted power would go from 0.8 to 2.2 µW.

## VIII. DISCUSSION

The average power consumption of a commercial leadless pacemaker goes from 2.4 µW for 0% pacing rate to 7.5 µW for 100% pacing rate [4]. A battery of 234mAh capacity allows a battery projected lifetime of 29.7 years for 0% pacing rate and 10.8 years for 100% pacing rate.

The working voltage of battery is 3V. It provides 0.8 µA of current for the case of 0% pacing (self-discharge) and 2.5 µA for 100% pacing. Considering lossless DC-DC power transfer to the 3V battery, the presented energy harvester would cover a part of the pacemaker current consumption, going from 0.26 µA to 0.73 µA depending on the heartbeat rate.

Therefore, if the proposed energy harvester was integrated in the leadless pacemaker described above, the current provided by the battery would drop from 2.5µA to the range of [2.24-1.77µA]. The current supplied by the energy harvester would extend the battery's lifetime from 10.8 years to [12.4-15.6

years], resulting to an increase of the battery lifetime up to 44% thanks to the additional energy provided by the two MEMS energy harvesters.

## IX. CONCLUSIONS

A MEMS electrostatic energy harvester with dimensions compliant with leadless pacemaker catheter implantation requirements was presented, along with simple and efficient interface circuit performing rectangular QV cycles.

The studied effect of the parasitic capacitance of the interface circuits on the energy conversion cycle showed that this parameter may significantly modify the shape of the QV cycles, and therefore the amount of converted energy.

We proposed an approach enabling to determine the optimal interface circuit based on the MEMS device and the interface circuit actual properties. For this purpose, a simple analytical model was developed to predict the converted energy per cycle in the case of a harmonic mechanical excitation.

In the case of heartbeat mechanical excitation, the system behavior is much more complex and exact analytical modelling could not be developed. To overcome this limitation, a coarse-grained approximation was proposed, enabling to transpose the model for the harmonic excitation to heartbeat excitation.

For both harmonic and heartbeat mechanical excitation, a good agreement was found between theory and experimental data.

Ex-vivo experimental results showed that the proposed solution including two MEMS energy harvesting devices with optimal interface circuits could increase the battery lifetime of commercial leadless pacemakers up to 44%.

Ongoing works aim at optimizing the MEMS design and fabrication, with the objective of increasing the performances so that the energy harvesting device can cover the whole power consumption of the pacemaker.

## ACKNOWLEDGMENT

This work was done within the C2N micro nanotechnologies platforms and partly supported by the RENATECH network and the General Council of Essonne.

The authors acknowledge the support of the French Agence Nationale de la Recherche (ANR), under grant ANR-22-CE05-0014-02 (project Near-Limits).

The authors would like to acknowledge the precious help of Xavier Leroux during the design and fabrication of the MEMS device.

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