Modeling and measurement of an ultrasound power delivery system for charging implantable devices using an AlN-based pMUT as receiver

Citation: Proto, A.; Rufer, L.; Basrour, S.; Penhaker, M. Modeling and Measurement of an Ultrasound Power Delivery System for Charging Implantable Devices Using an AlN-Based pMUT as Receiver. Micromachines 2022,13, 2127. https://doi.org/10.3390/ mi13122127 Academic Editors: Qifa Zhou and Chih-Chung Huang Received: 27 September 2022 Accepted: 29 November 2022 Published: 1 December 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). micromachines Article Modeling and Measurement of an Ultrasound Power Delivery System for Charging Implantable Devices Using an AlN-Based pMUT as Receiver Antonino Proto 1,2 , Libor Rufer 3, Skandar Basrour 3and Marek Penhaker 2,* 1Department of Neuroscience and Rehabilitation, University of Ferrara, Via Luigi Borsari, 46, 44121 Ferrara, Italy 2Department of Cybernetics and Biomedical Engineering, VŠB—Technical University of Ostrava, 17.listopadu 2172/15, Poruba, 708 00 Ostrava, Czech Republic 3UniversitéGrenoble Alpes, CNRS, Grenoble INP, TIMA, 38000 Grenoble, France *Correspondence: mar[email protected] Abstract: Ultrasound power delivery can be considered a convenient technique for charging implantable medical devices. In this work, an intra-body system has been modeled to characterize the phenomenon of ultrasound power transmission. The proposed system comprises a Langevin transducer as transmitter and an AlN-based square piezoelectric micro-machined ultrasonic transducer as receiver. The medium layers, in which elastic waves propagate, were made by polydimethylsiloxane to mimic human tissue and stainless steel to replace the case of the implantable device. To characterize the behavior of the transducers, measurements of impedance and phase, velocity and displacement, and acoustic pressure field were carried out in the experimental activity. Then, voltage and power output were measured to analyze the performance of the ultrasound power delivery system. For a root mean square voltage input of approximately 35 V, the power density resulted in 21.6 µ W cm −2 . Such a result corresponds to the data obtained with simulation through a one-dimensional lumped parameter transmission line model. The methodology proposed to develop the ultrasound power delivery (UPD) system, as well as the use of non-toxic materials for the fabrication of the intra-body elements, are a valid design approach to raise awareness of using wireless power transfer techniques for charging implantable devices. Keywords: ultrasound; acoustic; energy transfer; Langevin transducer; pMUT; lumped parameters model; implantable medical devices 1. Introduction In the current era of the Internet of Medical Things, wireless energy transfer can be a solution for charging low-power devices, especially where supplying energy through wires is difficult or inappropriate. This is the case with implantable medical devices (IMDs), which are placed inside the body and whose lifetime is limited by the operating time of battery [ 1 , 2 ]. IMDs, such as chronic pain neurostimulators or combinations of pacemakers and defibrillators need battery replacement every 5 to 10 years, which is costly and risky because the necessary surgery may introduce infections [ 3 , 4 ]. Moreover, with the increased use of implantable smart technologies to regulate organ functions and control prostheses, the IMDs require more and more energy to interface the peripheral and central nervous systems [5]. The IMD lifetime can be increased by harvesting the energy from biological sources, such as thermal gradients, vibration within the body, or biofuel cells. However, these energy sources do not produce enough electricity for most of IMDs, and body tolerance to undesired chemical or biological reactions remains the real challenge to address [6,7]. Micromachines 2022,13, 2127. https://doi.org/10.3390/mi13122127 https://www.mdpi.com/journal/micromachines Micromachines 2022,13, 2127 2 of 17 Nowadays, research efforts have focused on the wireless energy transfer to charge IMDs where an external link delivers energy in the form of electromagnetic radiation or acoustic waves [ 8 ]. Acoustic waves for medical applications are generally delivered at ultrasonic frequencies in the form of ultrasound. In comparison with electromagnetic radiations, ultrasound can propagate through electrically conductive materials without being affected by electromagnetic fields. Moreover, ultrasound allows a higher power intensity threshold for safe operation. For diagnostic medical imaging, the U.S. Food and Drug Administration (FDA) sets the ultrasound intensity parameter of spatial-peak temporal-average (I SPTA ) equal to 720, 430, 94, 17 mW cm −2 for peripheral vessel, cardiac, fetal, and ophthalmic applications, respectively [ 9 ]. These values are about two orders of magnitude higher than limits set by the U.S. Federal Communications Commission and IEEE for radio frequency (RF) exposure, which are approximately in the range 1–10 mW cm−2 [ 10 , 11 ]. A further advantage of ultrasound is less attenuation in tissues; in fact, the attenuation coefficient for 1 MHz ultrasound is 0.6 dB cm −1 , compared to 9.2 dB cm −1 for 100 MHz RF [ 8 ]. Ultrasound techniques are also widely used for domestic and industrial needs, for example, for object localization and tracking systems, cleaning solutions, air and water navigation, and in speech processing applications, among others [12–14]. Awareness in the use of ultrasound power delivery (UPD) systems for charging IMDs was achieved about 10 years ago by using centimeter-scale transducers. In 2010, Ozeri and Shmilovitz [ 15 ] proposed the most effective UPD system ever seen before. They fabricated a disc-shaped piezoelectric plate of 1.5 cm diameter and 0.3 cm thickness, operating in continuous wave mode at 673 kHz. For a given transmitter (TX) to receiver (RX) distance of 5 mm, the UPD system was able to generate a load power of 70 mW for a power transfer efficiency of 27%. However, the efficiency decreases as the TX-RX distance increases. In a study proposed by Mazzilli et al. in 2014 [ 16 ], they measured a system efficiency of 1.6% while transferring ultrasound power at 10.5 cm TX-RX distance by using an RX with cross-section area of 0.5 cm 2 . About commercialized centimeter scale device for UPD, Piezo Energy Technologies LLC company, Arizona, developed a portable system able of accomplishing it. It was the research effort of Radziemski and Makin, who together demonstrated continuous stable power transfer at a steady current of 70 mA by means of circular piezoelectric transducers of 2.5 cm diameter for both TX and RX structures [17]. Nowadays, the idea of having a UPD system, including a wearable TX that supplies energy to a network of IMDs within human tissues, is a challenge for many research groups. In this scenario, the most important technological challenge is to reduce the device size [18,19]. By reducing the piezoelectric plate dimension to the millimeter scale, the operating frequency shifts to higher values. For a piezoelectric plate working in thickness mode, the plate thickness of about 1.5 mm results in an operating frequency between 1 and 2 MHz [ 20 ]. Working at frequencies above 1 MHz leads to higher wave attenuation, which may result in heating of tissues if the exposure time is prolonged [ 21 ]. The maximum temperature increase, in situ, would not exceed 2 ◦ C. To avoid this issue, intermittent ultrasound waves can be delivered from TX to RX with a set duty cycle to control the rise of temperature in situ. Such miniaturized piezoelectric plates are widely used in implantable brain devices for wireless optogenetic stimulation [ 22 ]. Another issue of setting an operating frequency above 1 MHz regards the impedance matching problem. Usually, coupling materials and circuits for adaptive matching are used to avoid it [23]. In order to maintain reduced size for the RX while working below 1 MHz, piezoelectric diaphragm structures are an innovative solution [ 21 ]. Compared to a piezoelectric plate working in the thickness “33” mode, the piezoelectric diaphragm works in the bending “31” mode and is composed of less piezoelectric material, resulting in lower energy generation than a plate structure when excited from outside. Nonetheless, for a given geometrical dimension of the piezo material, diaphragm structures can operate at much lower frequencies than plates, so reducing the heating of tissue and having less attenuation of signal within the body [21]. Micromachines 2022,13, 2127 3 of 17 Piezoelectric micromachined ultrasonic transducers (pMUTs), developed with MEMS technology, are widely used to detect and generate ultrasound waves. Thanks to the full maturation of lithography process, pMUTs can have multiple geometries, thus adapting their operation to the needs of the application [ 24 , 25 ]. The piezoelectric diaphragm is usually deposited on silicon substrate which forms a backed air cavity. The pMUT structures can be squareor circular-shaped [ 26 , 27 ], can have one or two electrical ports [ 28 ], and they can be linked together to form an array of multiple units or concentric geometries [ 25 , 29 ]. They are implemented in haptic feedback and for gesture recognition, and they can be used as air-coupled actuators and for range finding in in-air applications [30–34]. The most promising work using a pMUT to charge an IMD was shown by Basaeri et al. in 2019 [ 35 ]. They evaluate the ratio between the thickness of the piezoelectric diaphragm to the thickness of the silicon substrate to obtain the maximum power output. For a 2 mm × 2 mm square diaphragm with a silicon substrate of 50 µ m, they found an optimum piezoelectric thickness of 20 µ m. To verify their numeric simulations, the pMUT was tested in water at 2 cm distance from the TX. For a given power intensity input of 322 mW cm −2 , the pMUT delivered an average power, to a pure resistive load of 4.3 k Ω , of about 0.7 mW at an operating frequency of 88 kHz, which is a value much lower than the operating frequency for a piezoelectric plate. The advantage of working at lower operating frequencies is an improvement related to the impedance matching between the piezoelectric transducers and the human body tissue. If the operating frequency is less than approximately 70 kHz, no coupling material is needed to match the impedances [ 21 ]. In the work of Basaeri et al. [ 35 ], the piezoelectric material used as the active element for developing the pMUT is lead zirconate titanate (PZT). The PZT material is toxic and can lead to the body’s immune rejection, thus becoming an obstacle to the widespread clinical application of IMD for personalized medicine [36]. In this work, aluminum nitride (AlN) material was used to develop a pMUT for testing in a UPD system. The non-toxicity of the AlN increases the sensor biocompatibility and reduces the tissue mismatching for a longer functionality. The proposed AlN-based pMUT is tested in this work to add valuable information on the research topic of wireless energy transfer for charging IMD without having surgery. The modeling of the entire UPD system is therefore given to optimize the amount of power on the RX side. 2. Materials and Methods 2.1. The UPD System Model Figure 1shows the six blocks representing the UPD system. Block (1) is the piezoelectric plate transmitting the ultrasound. Block (2) represents the tissue layers in between the TX and RX structures. The tissue layer can be represented by solely the skin, but also with a combination of skin, muscles, and body fat. Block (3) is a thin layer of metal that depicts the IMD housing. Common materials for hermetically sealing implants are titanium or stainless steel (SST). Block (4) is an air cavity. Into the air cavity the RX is placed, and it resonates based on the resulting acoustic pressure within the coupling cavity. Block (5) is the piezoelectric diaphragm structure in the form of pMUT, and block (6) represents schematically the RX electrical load. In terms of the energy transfer, the load is a pure resistive component representing the input impedance of the power management circuitry of the IMD. Some geometric relations have been taken into consideration to optimize the performance of the UPD system. Firstly, the piezoelectric RX should be placed at a distance equal or greater than the Rayleigh distance (RD) in order to avoid the near-field region. It is known from acoustics theory that a mechanical wave generated by a source converges to a natural focus at the transition between nearand far-field regions, where it assumes a stable value. In the near field, the amplitude of the generated ultrasound wave at a given point is difficult to predict as it oscillates between two extremes and can vary with small changes in location. Calculation of the RD distance is given by: Micromachines 2022,13, 2127 4 of 17 RD =r2 TX cmedium ·fexc (1) where rTX is the TX radius, cmedium is the value of sound speed into the propagating medium, and fexc is the excitation frequency given by an external electrical generator. A further geometrical consideration for the design of the UPD system relates to the value of the air cavity thickness, tcav , which should be less than a quarter of wavelength in order to avoid the generation of standing waves within the coupling cavity. Thus, to calculate the maximum value of tcav , to comply the above-mentioned geometrical consideration, the following equation is computed: tcav =1 4·λcav =1 4·cair fexc (2) Regarding the IMD housing, its thickness usually varies between 100 and 400 µ m. To conclude, in order to obtain the maximum amount of power transfer in the UPD system, the value of the resonant frequency of the RX should correspond to the value of the resonant frequency of the TX. Micromachines 2022, 13, x FOR PEER REVIEW 4 of 19 Figure 1. The six blocks representing the UPD system. Some geometric relations have been taken into consideration to optimize the performance of the UPD system. Firstly, the piezoelectric RX should be placed at a distance equal or greater than the Rayleigh distance (RD) in order to avoid the near-field region. It is known from acoustics theory that a mechanical wave generated by a source converges to a natural focus at the transition between nearand far-field regions, where it assumes a stable value. In the near field, the amplitude of the generated ultrasound wave at a given point is difficult to predict as it oscillates between two extremes and can vary with small changes in location. Calculation of the RD distance is given by: RD= 𝑟  𝑐 · 𝑓  (1) where 𝑟 is the TX radius, 𝑐 is the value of sound speed into the propagating medium, and 𝑓 is the excitation frequency given by an external electrical generator. A further geometrical consideration for the design of the UPD system relates to the value of the air cavity thickness, 𝑡, which should be less than a quarter of wavelength in order to avoid the generation of standing waves within the coupling cavity. Thus, to calculate the maximum value of 𝑡, to comply the above-mentioned geometrical consideration, the following equation is computed: 𝑡 =1 4 · 𝜆 =1 4 · 𝑐 𝑓  (2) Regarding the IMD housing, its thickness usually varies between 100 and 400 µm. To conclude, in order to obtain the maximum amount of power transfer in the UPD system, the value of the resonant frequency of the RX should correspond to the value of the resonant frequency of the TX. 2.2. Elements Constituting the UPD System The following, Figure 2, shows the elements constituting the UPD system in the proposed study. Figure 1. The six blocks representing the UPD system. 2.2. Elements Constituting the UPD System The following, Figure 2, shows the elements constituting the UPD system in the proposed study. The TX is a Langevin transducer made by a stack of piezoelectric plates comprised of a solid waveguide on the front side and the backing on the other side. In this case, two outward oriented plates of SM118 piezoceramic material are linked together with a steel screw bolt, which ensures the mechanical pre-stress and the electrical parallel connection of the plate electrodes. The backing side is made of steel and the front waveguide is made of aluminum. The RX is a uniform square pMUT with lateral side of 1.5 mm. It is a laminate structure formed on a silicon (Si) substrate by a silicon oxide (SiO 2 ) thin layer, a nontoxic AlN piezoelectric diaphragm covered by Al/Cr metal pads and backed by an air cavity of cross-section area, Am , which can be approximated to a third of the AlN diaphragm cross-section area, S [ 37 ]. Electrodes of the pMUT are placed at the edges of the diaphragm above the AlN film. The top electrode is an Al/Cr metal pad, while the bottom is formed Micromachines 2022,13, 2127 5 of 17 by a doped silicon layer. The square pMUT (RX) is fabricated using the PiezoMUMPs TM process flow [38]. Micromachines 2022, 13, x FOR PEER REVIEW 5 of 19 Figure 2. Elements constituting the UPD system. Langevin transducer (A); square pMUT (B); Langevin transducer geometrical dimensions (C); square pMUT structure (D); medium layers and air cavity structure for the pMUT placement (E). The TX is a Langevin transducer made by a stack of piezoelectric plates comprised of a solid waveguide on the front side and the backing on the other side. In this case, two outward oriented plates of SM118 piezoceramic material are linked together with a steel screw bolt, which ensures the mechanical pre-stress and the electrical parallel connection of the plate electrodes. The backing side is made of steel and the front waveguide is made of aluminum. The RX is a uniform square pMUT with lateral side of 1.5 mm. It is a laminate structure formed on a silicon (Si) substrate by a silicon oxide (SiO2) thin layer, a nontoxic AlN piezoelectric diaphragm covered by Al/Cr metal pads and backed by an air cavity of crosssection area, 𝐴, which can be approximated to a third of the AlN diaphragm cross-section area, S [37]. Electrodes of the pMUT are placed at the edges of the diaphragm above the AlN film. The top electrode is an Al/Cr metal pad, while the bottom is formed by a doped silicon layer. The square pMUT (RX) is fabricated using the PiezoMUMPsTM process flow [38]. Table 1 shows the values of parameters characterizing the piezoelectric material in both TX and RX. Table 1. Values of parameters characterizing the piezoelectric material in both TX and RX. Parameter PZT-8 (TX) AlN (RX) Cross-section Area (S) [m2] 9.1185·10–4 2.25·10–6 Thickness (t) [m] 5.75·10–3 5·10–7 Length (l) [m] - 1.5·10–3 Density (ρ) [kg m–3] 7600 3260 Young’s Modulus (E) [Pa] 7.4·1010 3.45·1011 Poisson’s Ratio (υ) - 0.32 Plate Modulus ( Y ) [Pa] - 3.8436·1011 Dielectric Constant (ε) 1200 7.9059 Figure 2. Elements constituting the UPD system. Langevin transducer ( A ); square pMUT ( B ); Langevin transducer geometrical dimensions ( C ); square pMUT structure ( D ); medium layers and air cavity structure for the pMUT placement (E). Table 1shows the values of parameters characterizing the piezoelectric material in both TX and RX. Table 1. Values of parameters characterizing the piezoelectric material in both TX and RX. Parameter PZT-8 (TX) AlN (RX) Cross-section Area (S) [m2] 9.1185·10−42.25·10−6 Thickness (t) [m] 5.75·10−35·10−7 Length (l) [m] - 1.5·10−3 Density (ρ) [kg m−3]7600 3260 Young’s Modulus (E) [Pa] 7.4·1010 3.45·1011 Poisson’s Ratio (υ) - 0.32 Plate Modulus (Y) [Pa] - 3.8436·1011 Dielectric Constant (ε) 1200 7.9059 Piezo Charge Coeff. (d31, d33) [pC N−1]-, 240 −2.3259, - Piezo Constant (e31, e33) [C m−2]-, 14.6385 −0.8024, - Coupling Factor (k) 0.48 0.17 Quality Factor (Q) 1000 231 1 Dielectric Loss (tan δ0) 0.004 0.001 1Experimentally calculated with the pMUT in transmitter mode (see Supplementary Materials). Micromachines 2022,13, 2127 6 of 17 Table 2shows the values of parameters of all layers constituting the pMUT. Table 2. Parameter values of all layers constituting the pMUT (RX). Parameter Si Layer Dioxide (SiO2) AlN Diaphragm Al Pad Cr Pad Cross-section Area (S) [m2] 2.25·10−62.25·10−62.25·10−62.25·10−62.25·10−6 Thickness (t) [m] 10·10−62·10−75·10−71·10−620·10−9 Length (l) [m] 1.5·10−31.5·10−31.5·10−31.5·10−31.5·10−3 Volume (V) [m3] 2.25·10−11 4.5·10−13 1.125·10−12 2.25·10−12 4.5·10−14 Density (ρ) [kg m−3]2330 2200 3260 2680 7140 Mass (M) [kg] 5.243·10−89.9·10−10 3.668·10−96.03·10−93.213·10−10 Young’s Modulus (E) [Pa] 1.65·1011 0.73·1011 3.45·1011 0.71·1011 2.45·1011 Poisson’s Ratio (υ) 0.22 0.17 0.32 0.33 0.2 Plate Modulus (Y) [Pa] 1.734·1011 0.752·1011 3.844·1011 0.797·1011 2.552·1011 Mid-plane Location (z) [m] 5·10−61.01·10−51.045·10−51.12·10−51.171·10−5 Top-plane Location (h) [m] 1·10−51.02·10−51.07·10−51.17·10−51.172·10−5 Regarding the medium layers, polydimethylsiloxane (PDMS) material—Sylgard ® 184—was chosen to mimic the human skin because of its density and speed of sound values, which are like those of the body. The PDMS is formed by a base part and a curing agent, which were mixed at a ratio of 10:1. Then, the resulting compound was poured into a mold and later placed into a furnace at 70 ◦ C for 2 h. The housing of the IMD is a thin layer of Type 316L SST. It is a bio-compatible material used for designing implants. 2.3. Measurement Setup For the characterization of the TX and RX, measurement of their impedance and phase values were carried out by means of the impedance analyzer IM3570—HIOKI, Hioki Europe Gmbh, Eschborn, Germany. Moreover, for the TX, velocity and displacement values were obtained using together a Polytec OFV-502 Fiber Optic Interferometer and a Polytec OFV-3001 Vibrometer Controller, Polytec, Baden-Württemberg, Germany. A LabView 2019 software (SW) application, National Instruments, Austin, Texas, United States, to sweep the excitation frequency in a defined value range, was used to control the amplitude of the input signal generated by an Agilent 33500B waveform generator, Keysight Technologies, Santa Rosa, California, USA. The signal generated by the waveform generator goes through a high voltage amplifier, WMA-300 Falco System, Falco Systems, Amsterdam, Netherlands, which is used to amplify the input signal and to adapt, as much as possible, the capacitive behavior of the TX. Then, the output signal of the Falco System is the electrical input signal of the TX. Acoustic pressure measurements were carried out through a calibrated 1/8-inch pressure-field microphone, Brüel & Kjær Type 4138, connected to a conditioning amplifier, Brüel & Kjær Type WH-3219, Brüel & Kjær, Nærum, Denmark. The microphone was placed perpendicular to the TX surface at the center point of the radiating area. All the measurements carried out in this study were displayed on an Agilent DSO-X 2002A digital oscilloscope, Keysight Technologies, Santa Rosa, California, USA, and in the LabView 2019 SW application, National Instruments, Austin, Texas, USA. The results were stored as .csv file for post-processing in MATLAB®SW environment. Figure 3shows the experimental bench including all the instrumentation used to carry out the characterization of the TX and RX as well as the measurements of acoustic pressure field and the values of voltage and power output. Micromachines 2022,13, 2127 7 of 17 Micromachines 2022, 13, x FOR PEER REVIEW 7 of 19 LabView 2019 SW application, National Instruments, Austin, Texas, USA. The results were stored as .csv file for post-processing in MATLAB® SW environment. Figure 3 shows the experimental bench including all the instrumentation used to carry out the characterization of the TX and RX as well as the measurements of acoustic pressure field and the values of voltage and power output. Figure 3. Experimental bench. Waveform generator, high voltage amplifier, conditioning amplifier for pressure-field microphone output, oscilloscope, and National Instrument DAQ and LabVIEW (A). Impedance analyzer and Polytec Vibrometer controller for dual point interferometer (B). Schematic block diagram of the circuit used for measuring the electrical power output on the load, the acoustic pressure field, and velocity and displacement values for the TX (C). Schematic block diagram to measure impedance and phase values of TX and RX (D). Figure 3. Experimental bench. Waveform generator, high voltage amplifier, conditioning amplifier for pressure-field microphone output, oscilloscope, and National Instrument DAQ and LabVIEW ( A ). Impedance analyzer and Polytec Vibrometer controller for dual point interferometer ( B ). Schematic block diagram of the circuit used for measuring the electrical power output on the load, the acoustic pressure field, and velocity and displacement values for the TX ( C ). Schematic block diagram to measure impedance and phase values of TX and RX (D). 3. Results The results section provides data about the characterization of the TX and RX as well as the results of the measurements for testing the proposed UPD system. The characterization of the TX and RX regards measurements of the values of impedance, phase, velocity, and displacement for the TX and measurements of the values of impedance and phase for the RX. Moreover, measurements to show the acoustic pressure field in air Micromachines 2022,13, 2127 8 of 17 of both the TX and RX were carried out before to test the performance of the proposed UPD system. While testing the UPD system, the results are given in terms of root mean square (RMS) values of voltage and power output over a resistive load. 3.1. Measurements for the TX and RX Characterization The results of the experimental activity for the characterization of the TX and the RX are shown in Figure 4. Micromachines 2022, 13, x FOR PEER REVIEW 8 of 19 3. Results The results section provides data about the characterization of the TX and RX as well as the results of the measurements for testing the proposed UPD system. The characterization of the TX and RX regards measurements of the values of impedance, phase, velocity, and displacement for the TX and measurements of the values of impedance and phase for the RX. Moreover, measurements to show the acoustic pressure field in air of both the TX and RX were carried out before to test the performance of the proposed UPD system. While testing the UPD system, the results are given in terms of root mean square (RMS) values of voltage and power output over a resistive load. 3.1. Measurements for the TX and RX Characterization The results of the experimental activity for the characterization of the TX and the RX are shown in Figure 4. Figure 4. Characterization of the TX and the RX. Impedance and phase of TX (A); velocity and displacement of TX (B); TX acoustic pressure in air (C); impedance and phase of RX (D); RX acoustic pressure in air (E). Figure 4. Characterization of the TX and the RX. Impedance and phase of TX ( A ); velocity and displacement of TX ( B ); TX acoustic pressure in air ( C ); impedance and phase of RX ( D ); RX acoustic pressure in air (E). In Figure 4A,B, the values of impedance, phase, velocity, and displacement of the TX are displayed on the frequency range between 20 and 140 kHz. Although the TX is designed to operate at 40 kHz [ 39 ], it exhibits also higher mode resonances, which are Micromachines 2022,13, 2127 9 of 17 clearly visible in Figure 4A. This behavior of the TX is due to the complex system composed by the piezo stack and the loads on the back and front sides. Regarding the operating frequency of interest for the proposed experiment, fexc , which corresponds to a resonant frequency of the TX, fTX r , it must be as closely as possible to the value of the resonant frequency of the receiver, fRX r , in order to optimize the amount of power transfer for the UPD system [ 21 ]. Based on this, the selected operating frequency value, fTX r = fexc , is 67.34 kHz. Indeed, this value is comparable to the value of fRX r shown in Figure 4D, which was measured with the impedance analyzer and found to be 66.92 kHz. Regarding the impedance value of TX, ZTX , measured to fTX r , is approximately 50 Ω , the velocity, vTX , is 0.016 m s −1 , and the displacement, xTX , is 38 nm. Regarding the RX, the impedance value, ZRX, measured to fRX r, is approximately 9.04 kΩ. In Figure 4C we measured the acoustic pressure field in air for the TX on the frequency range in the surrounding of fTX r , from 66.7 to 67.7 kHz. The peak-to-peak amplitude of the input voltage signal was set to 2.5 V, and the maximum root mean square (RMS) value of the acoustic pressure field to the fTX r , pTX rms , was approximately 6 Pa in the near field close to the TX emitting surface, and 5 Pa at the Rayleigh distance. Regarding the acoustic pressure field generated in air by the pMUT, Figure 4E, the maximum obtained pRX rms value is approximately 3 Pa when the distance between the microphone and the pMUT is 2 mm, and the pRX rms value is around 1 Pa at a distance of 14 mm. 3.2. UPD System Measurements Figure 5shows the results of measurements carried out for testing the UPD system. Micromachines 2022, 13, x FOR PEER REVIEW 9 of 19 In Figures 4A,B, the values of impedance, phase, velocity, and displacement of the TX are displayed on the frequency range between 20 and 140 kHz. Although the TX is designed to operate at 40 kHz [39], it exhibits also higher mode resonances, which are clearly visible in Figure 4A. This behavior of the TX is due to the complex system composed by the piezo stack and the loads on the back and front sides. Regarding the operating frequency of interest for the proposed experiment, 𝑓, which corresponds to a resonant frequency of the TX, 𝑓, it must be as closely as possible to the value of the resonant frequency of the receiver, 𝑓, in order to optimize the amount of power transfer for the UPD system [21]. Based on this, the selected operating frequency value, 𝑓 = 𝑓, is 67.34 kHz. Indeed, this value is comparable to the value of 𝑓 shown in Figure 4D, which was measured with the impedance analyzer and found to be 66.92 kHz. Regarding the impedance value of TX, 𝑍, measured to 𝑓, is approximately 50 Ω, the velocity, 𝑣, is 0.016 m s–1, and the displacement, 𝑥, is 38 nm. Regarding the RX, the impedance value, 𝑍, measured to 𝑓, is approximately 9.04 kΩ. In Figure 4C we measured the acoustic pressure field in air for the TX on the frequency range in the surrounding of 𝑓, from 66.7 to 67.7 kHz. The peak-to-peak amplitude of the input voltage signal was set to 2.5 V, and the maximum root mean square (RMS) value of the acoustic pressure field to the 𝑓, p  , was approximately 6 Pa in the near field close to the TX emitting surface, and 5 Pa at the Rayleigh distance. Regarding the acoustic pressure field generated in air by the pMUT, Figure 4E, the maximum obtained p  value is approximately 3 Pa when the distance between the microphone and the pMUT is 2 mm, and the p  value is around 1 Pa at a distance of 14 mm. 3.2. UPD System Measurements Figure 5 shows the results of measurements carried out for testing the UPD system. Figure 5. UPD system measurements. Comparison between the impedance value for the free TX and for the TX covered by the PDMS and the SST layer (A); acoustic pressure field (B); RX voltage output (C); RX power output (D). Figure 5. UPD system measurements. Comparison between the impedance value for the free TX and for the TX covered by the PDMS and the SST layer ( A ); acoustic pressure field ( B ); RX voltage output (C); RX power output (D). Micromachines 2022,13, 2127 16 of 17 37. Horsley, D.A.; Rozen, O.; Lu, Y.; Shelton, S.; Guedes, A.; Przybyla, R.; Tang, H.-Y.; Boser, B.E. Piezoelectric Micromachined Ultrasonic Transducers for Human-Machine Interfaces and Biometric Sensing. In Proceedings of the IEEE Sensors Conference, Busan, Republic of Korea, 1–4 November 2015. [CrossRef] 38. Cowen, A.; Hames, G.; Glukh, K.; Hardy, B. PiezoMUMPs Design Handbook; MEMSCAP Inc.: Windsor, ON, Canada, 2013. 39. Bolt Clamped Langevin Transducer 40 KHz. Available online: https://www.steminc.com/PZT/en/bolt-clamped-langevintranducer-40-khz (accessed on 27 September 2022). 40. Yoo, S.; Lee, J.; Joo, H.; Sunwoo, S.-H.; Kim, S.; Kim, D.-H. Wireless Power Transfer and Telemetry for Implantable Bioelectronics. Adv. Healthc. Mater. 2021,10, 2100614. [CrossRef] 41. Khan, S.R.; Pavuluri, S.K.; Cummins, G.; Desmulliez, M.P.Y. Wireless power transfer techniques for implantable medical devices: A review. Sensors 2020,20, 3487. [CrossRef] 42. Todar, M.T.; Guido, F.; Algieri, L.; Mastronardi, V.M.; Desmaele, D.; Epifani, G.; De Vittorio, M. Biocompatible, flexible, and compliant energy harvesters based on piezoelectric thin films. IEEE Trans. Nanotechnol. 2018,17, 220–230. [CrossRef] 43. Fei, C.; Liu, X.; Zhu, B.; Li, D.; Yang, X.; Yang, Y.; Zhou, Q. AlN piezoelectric thin films for energy harvesting and acoustic devices. Nano Energy 2018,51, 146–161. [CrossRef] 44. Peres, P.L.D.; de Souza, C.R.; Bonatti, I.S. ABCD matrix: A unique tool for linear two-wire transmission line modelling. Int. J. Electr. Eng. Educ. 2003,40, 220–229. [CrossRef] 45. Frickey, D.A. Conversions between S, Z, Y, H, ABCD, and T parameters which are valid for complex source and load impedances. IEEE Trans. Microw. Theory Tech. 1994,42, 205–211. [CrossRef] 46. Turner, B.L.; Senevirathne, S.; Kilgour, K.; McArt, D.; Biggs, M.; Menegatti, S.; Daniele, M.A. Ultrasound-Powered Implants: A Critical Review of Piezoelectric Material Selection and Applications. Adv. Healthc. Mater. 2021 ,10, 2100986. [CrossRef] [PubMed] 47. Sun, Y.; Gao, X.; Wang, H.; Chen, Z.; Yang, Z. A wideband ultrasonic energy harvester using 1-3 piezoelectric composites with non-uniform thickness. Appl. Phys. Lett. 2018,112, 043903. [CrossRef] 48. He, Q.; Liu, J.; Yang, B.; Wang, X.; Chen, X.; Yang, C. MEMS-based ultrasonic transducer as the receiver for wireless power supply of the implantable microdevices. Sens. Actuator A Phys. 2014,219, 65–72. [CrossRef] 49. Joseph, J.; Singh, S.G.; Vanjari, S.R.K. Piezoelectric Micromachined Ultrasonic Transducer Using Silk Piezoelectric Thin Film. IEEE Electron. Device Lett. 2018,39, 749–752. [CrossRef] 50. Jiang, L.; Yang, Y.; Chen, R.; Lu, G.; Li, R.; Xing, J.; Shung, K.K.; Humayun, M.S.; Zhu, J.; Chen, Y.; et al. Ultrasound-induced wireless energy harvesting for potential retinal electrical stimulation application. Adv. Funct. Mater. 2019 ,29, 1902522. [CrossRef] 51. Al-Shidaifat, A.; Kumar, S.; Chakrabartty, S.; Song, H.J. A Conceptual Investigation at the Interface between Wireless Power Devices and CMOS Neuron IC for Retinal Image Acquisition. Appl. Sci. 2020,10, 6154. [CrossRef] 52. Liu, X.; Chen, D.; Yang, D.; Chen, X.; Le, X.; Xie, J. A Computational Piezoelectric Micro-Machined Ultrasonic Transducer Toward Acoustic Communication. IEEE Electron. Device Lett. 2019,40, 965–968. [CrossRef] 53. Defoort, M.; Rufer, L.; Fesquet, L.; Basrour, S. A dynamical approach to generate chaos in a micromechanical resonator. Microsyst. Nanoeng. 2021,7, 17. [CrossRef] 54. Ahmadi, F.; McLoughlin, I.V.; Chauhan, S.; ter-Haar, G. Bio-effects and safety of low-intensity, low-frequency ultrasonic exposure. Prog. Biophys. Mol. Biol. 2012,108, 119–138. [CrossRef] 55. Boucaud, A.; Montharu, J.; Machet, L.; Arbeille, B.; Machet, M.C.; Patat, F.; Vaillant, L. Clinical, histologic, and electron microscopy study of skin exposed to low-frequency ultrasound. Anat. Rec. 2001,264, 114–119. [CrossRef] [PubMed] 56. Kim, S.; Ho, J.S.; Chen, L.Y.; Poon, A.S.Y. Wireless power transfer to a cardiac implant. Appl. Phys. Lett. 2012 ,101, 073701. [CrossRef] 57. Kazanc, O.; Maloberti, F.; Dehollain, C. Simulation oriented rectenna design methodology for remote powering of wireless sensor systems. In Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS), Seoul, Republic of Korea, 20–23 May 2012; pp. 2877–2880. [CrossRef] 58. Ko, Y.Y.; Ho, S.L.; Fu, W.N.; Zhang, X. A novel hybrid resonator for wireless power delivery in bio-implantable devices. IEEE Trans. Magn. 2012,48, 4518–4521. [CrossRef] 59. Cong, P.; Suster, M.A.; Chaimanonart, N.; Young, D.J. Wireless power recharging for implantable bladder pressure sensor. In Proceedings of the IEEE Sensors Conference (SENSORS), Christchurch, New Zealand, 25–28 October 2009; pp. 1670–1673. [CrossRef] 60. Sanni, A.; Vilches, A.; Toumazou, C. Inductive and ultrasonic multi-tier interface for low-power, deeply implantable medical devices. IEEE Trans. Biomed. Circuits Syst. 2012,6, 297–308. [CrossRef] [PubMed] 61. Mazzilli, F.; Thoppay, P.E.; Praplan, V.; Dehollaini, C. Ultrasound energy harvesting system for deep implanted-medical-devices (IMDs). In Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS), Seoul, Republic of Korea, 20–23 May 2012; pp. 2865–2868. [CrossRef] 62. Jiang, L.; Yang, Y.; Chen, R.; Lu, G.; Li, R.; Li, D.; Humayun, M.S.; Shung, K.K.; Zhu, J.; Chen, Y. Flexible piezoelectric ultrasonic energy harvester array for bio-implantable wireless generator. Nano Energy 2019,56, 216–224. [CrossRef] 63. Herrera, B.; Pop, F.; Cassella, C.; Rinaldi, M. AlN PMUT-based Ultrasonic Power Transfer Links for Implantable Electronics. In Proceedings of the 20th International Conference on Solid-State Sensors, Actuators and Microsystems and Eurosensors XXXIII, TRANSDUCERS 2019 and EUROSENSORS XXXIII, Berlin, Germany, 23–27 June 2019; pp. 861–864. [CrossRef] Micromachines 2022,13, 2127 17 of 17 64. Gong, D.; Ma, S.; Chiu, Y.; Lee, H.; Jin, Y. Study of the properties of AlN PMUT used as a wireless power receiver. In Proceedings of the IEEE 69th Electronic Components and Technology Conference (ECTC), Las Vegas, NV, USA, 28–31 May 2019; pp. 1503–1508. [CrossRef] 65. Rong, Z.; Zhang, M.; Ning, Y.; Pang, W. An ultrasound-induced wireless power supply based on AlN piezoelectric micromachined ultrasonic transducers. Sci. Rep. 2022,12, 16174. [CrossRef] 66. Moerke, C.; Wolff, A.; Ince, H.; Ortak, J.; Oner, A. New strategies for energy supply of cardiac implantable devices. Herzschr. Elektrophys. 2022,33, 224–231. [CrossRef] 67. Zhang, J.-G.; Long, Z.-L.; Ma, W.-J.; Hu, G.-H.; Li, Y.-M. Electromechanical dynamics model of ultrasonic transducer in ultrasonic machining based on equivalent circuit approach. Sensors 2019,19, 1405. [CrossRef] 68. Sherrit, S.; Leary, S.P.; Dolgin, B.P.; Bar-Cohen, Y. Comparison of the Mason and KLM equivalent circuits for piezoelectric resonators in the thickness mode. In Proceedings of the IEEE Ultrasonics Symposium, Tahoe, NV, USA, 17–20 October 1999; Volume 2, pp. 921–926. [CrossRef] 69. Kim, J.; Lee, J. Theoretical Resonance Analysis of Langevin Transducers with Equivalent Circuit Models for Therapeutic Ultrasound. J. Electr. Eng. Technol. 2019,14, 2437–2445. [CrossRef] 70. Meeker, T.R. Publication and proposed revision of ANSI/IEEE standard 176-1987 “ANSI/IEEE standard on piezoelectricity”. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 1996,43, 717–771. [CrossRef] 71. Uchino, K. High-Power Piezoelectrics and Loss Mechanisms. In Advanced Piezoelectric Materials: Science and Technology, 2nd ed.; Woodhead Publishing: Sawston, UK, 2017; pp. 647–754. 72. Ashby, M.F. Material Property Charts. In Materials Selection in Mechanical Design, 4th ed.; Elsevier Ltd.: London, UK, 2011; pp. 57–96. 73. Horsley, D.; Lu, Y.; Rozen, O. Flexural Piezoelectric Resonators. In Piezoelectric MEMS Resonators; Bhurgra, H., Piazza, G., Eds.; Springer: Cham, Switzerland, 2017; pp. 153–173. 74. Marzencki, M.; Basrour, S. Modeling of Piezoelectric MEMS Vibration Energy Harvesters. In MEMS: Fundamental Technology and Applications; Choudhary, V., Iniewski, K., Eds.; CRC Press: Boca Raton, FL, USA, 2013; pp. 131–160.