Sensors & Actuators: A. Physical 345 (2022) 113798 Contents lists available at ScienceDirect Sensors and Actuators: A. Physical journal homepage: www.journals.elsevier.com/sensors-and-actuators-a-physical Remote dynamic actuation of an electrostatically driven microcantilever by a wireless power transfer system Raul Ruiz *, Gabriel Abadal Dept. Enginyeria Electrònica, Campus UAB, 08193 Bellaterra, Spain A R T I C L E I N F O A B S T R A C T Keywords: The design, modelling, fabrication and test of a device prototype, based on a microcantilever capacitively RF-MEMS connected to a folded-end half-wave dipole antenna, which is remotely actuated by a wireless power transfer Wireless power transfer (WPT) system are presented here. The microcantilever and the antenna, which are coupled at the antenna Electrostatic actuation feeding point, work as a new device, is able to harness the radiated energy wirelessly transferred from an emitter antenna to directly excite the mechanical vibration modes of the microcantilever. The response to an amplitude- modulated (AM) RF radiated signal excitation produced by a transmitting antenna is experimentally analysed and fit to a simple model when the distance between both antennas varies from the near field to the radiated far field regime. 1. Introduction the voltage is the base of operation of mechanical mixers. With the advance in MEMS technologies, new devices with high Q-factors made it Since Nicola Tesla’s patent, the system of transmission of electrical possible to design filters and combine both functionalities, mixing and energy [1] and the experiments of H. Yagi and S. Uda in wireless power filtering, in a single device named mixler [16]. RF demodulation has transfer WPT [2], multiple advances have been made in subsequent been also used in an homodyne receiver [17], where the electrostatic years, mainly due to progress in wireless technology and architectures. actuator is driven by a resonant circuit [18] consisting of a resistance Currently, applications on non-radiative or radiative field WPT range and an inductance that together with the capacitance of the electrostatic from medical implants [3,4], consumer electronics [5,6], wireless sensor actuator form an RLC circuit, whose resonant frequency is selected to be networks (WSN) [7], electric vehicles [8], internet of things (IoT) [9], equal to the carrier frequency of the RF signal. Complex cascade MEMS among others. These applications normally require converting the en­ architectures have been designed recently [19] to expand the power ergy previously captured before being used by means of a rectenna handling capability of direct amplitude demodulators, which is a key (rectifying antenna) [10], which in combination with a voltage doubler requirement for 5 G applications. However, all previously mentioned and a charge pump converts RF signals to direct current (DC). The ef­ RF-MEMS solutions can replace and improve the performance of only ficiency of rectenna-based WPTs depends on all the components some of the blocks of a radio receiver circuitry. Other blocks such as the involved [11]. low noise amplifier (LNA) or even the antenna are still implemented by In addition, the RF-MEMS technology has evolved, and MEMS have standard components. played an important role as passive components in RF-switches [12], A wise and disruptive proposal was made in the past [20] to inte­ where they have reached frequency ranges from DC to 120 GHz in os­ grate, in a NEMS structure - based on a single carbon nanotube -, all the cillators [13], filters [14] and the reconfiguration of antennas working components except for the speaker of a 40–400 MHz radio receiver: at frequency ranges of 12–200 GHz. MEMS with electrostatic actuation, antenna, tunable band-pass filter, amplifier, and demodulator. None­ have been particularly used as components of integrated AM-FM theless, a DC voltage source was needed to power the nanotube radio demodulation systems, replacing the conventional mixer circuit in het­ and even the antenna needed to be polarized to perform its functionality. erodyne communication receivers by a mechanical mixer [15], reducing In a previous work, we demonstrated the operation in reception of a size, cost and power consumption of the traditional mixer blocks. The fully passive mechanical antenna based on a microcantilever with a second order nonlinear relationship between the electrostatic force and permanent charge implanted, which directly interacted with the electric * Corresponding author. E-mail address: raul.ruizl@autonoma.cat (R. Ruiz). https://doi.org/10.1016/j.sna.2022.113798 Received 25 April 2022; Received in revised form 21 July 2022; Accepted 30 July 2022 Available online 2 August 2022 0924-4247/© 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by- nc-nd/4.0/). R. Ruiz and G. Abadal Sensors and Actuators: A. Physical 345 (2022) 113798 Fig. 2. Thévenin equivalent circuit of the MEMSTENNA as a dipole antenna (left side) loaded by the capacitance Cm of the MEMS capacitive actuator (right side), represented by its spring (k) mass (m) damper (b) model and a parasitic capacitance Cp. Table 1 Datasheet of the MEMSTENNA prototype. Parameter Value Units Dipole arm length (ld1/ld2) 35/30 mm Dipole width (wd) 2 mm Dipole thickness (td) 35 μm Cantilever length (lc) 200 μm Cantilever width (wc) 28 μm Cantilever base with (wb) 184 μm Cantilever spring constant (kc) 0.08 N/m Cantilever thickness, Si3N4 (tc) 0.6 μm Capacitive gap (go) 34 μm Overlapping Area (A) 162 μm2 Dipole resonant frequency (fd): measured/simulated 0.88/0.82 GHz Cantilever resonant frequency (fc) 17 kHz resonance frequency at 17 kHz, as it can be observed in Fig. 1b and c. The folded-end dipole antenna consists of two arms (arm1 and arm2) of Fig. 1. Layout of the MEMSTENNA. Top view of the dipole antenna with the length λ/4 each separated by a gap which corresponds to the feeding cantilever coupled into its feeding point (a). Detail of the top V-shaped point of the antenna. The triangular microcantilever, composed of two microcantilever (b) and lateral cross section with a local thickness reduction on clamped-free microbeams parallelly connected in a V-shaped configu­ arm2 allowing to define a vertical capacitive gap, go, for the electrostatic excitation of the cantilever (c). Top view photograph of the MEMSTENNA ration, is placed at the feeding point of the dipole as it is sketched in prototype with a detail of the microcantilever in the feeding point region (d). Fig. 1: the microcantilever is turned upside down so that its clamping support is electrically contacted to arm1 through its conductive surface. Its free end stays parallelly placed on top of arm2 along an overlap area, field of a RF radiation [21]. Although such MEMS antenna entailed a A= 162 µm2 and separated by a gap, go= 34 µm. The gap is defined by huge miniaturization, it operated at 11 kHz, which is a frequency far the local Cu thickness reduction of arm2 (Fig. 2c). The dimensions of the from the GHz bands of the modern application trends. Recently, we antenna and the microcantilever are reported in Table 1. proposed a new device called MEMSTENNA [22], which combines the It can be noticed that from an electrical point of view, the micro­ radiation absorption functionality of the antenna with the AM demod­ cantilever placed as described above implies a capacitive load for the ulation, filtering and mechanical actuation capabilities of a capacitive antenna with a capacitance described by Eq. (1): MEMS. Such a MEMSTENNA transduces the electromagnetic power radiated by a transmitter antenna directly to a static or dynamic me­ ϵ0 ⋅A Cm = (1) chanical actuation of the microcantilever. The same transduction 2⋅ go mechanism has been described previously in an optomechanical THz detector [23]. The working principle, DC operation and preliminary When the dipole antenna is excited by the electric field, Einc z of a results of AC operation in the near field regime have been recently re­ radiated electromagnetic plane wave (see Fig. 1.c), a voltage is gener­ ported [24]. A MEMSTENNA functioning as a wireless switch has a field ated at the feeding point of the antenna. In open circuit conditions it is of application in wake-up radio receiver architectures [25–27] where denoted by Voc and called open circuit voltage. The relationship between one of the objectives is to minimize power consumption. the electric field and the induced voltage in the antenna is a parameter of In this paper, we present an equivalent circuit model of the MEM­ the antenna called antenna factor AF [29]: STENNA that describes the electromechanical dynamics of the device Einc and predicts its response to an AM-modulated signal excitation. Exper­ Voc = z (2) AF imental results of this response in the far-field regime obtained from the characterization of a test prototype and fit to the model predictions are The antenna factor is defined in Eq. (3) as: also presented. √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ 4⋅π⋅η⋅f 2 AF = (3) 2. MEMSTENNA prototype and equivalent circuit model c2 ⋅G⋅Zload Where η is the intrinsic impedance of the free space, approximately Our MEMSTENNA test prototype is based on a folded-end half-wave 377 Ω, c is the speed of light, f is the frequency of the plane wave, Zload is dipole antenna designed from a resonance frequency specification at 0.8 the impedance of the antenna load and G is the gain of the antenna. As GHz on a Cu-FR4 substrate (Fig. 1a) and a commercial silicon nitride indicated in the equivalent circuit of Fig. 2, Voc, generated by the inci­ microcantilever [28] with Au coating (70 nm top / 35 nm bottom) and a dence of the electric field in the dipole, is distributed between the thickness of tc= 600 nm with a spring constant of 0.08 N/m and 2 R. Ruiz and G. Abadal Sensors and Actuators: A. Physical 345 (2022) 113798 Moreover, the electromechanical model of the microcantilever capacitive actuator is based on a spring-mass-damper system. The movement Eq. (5) describes the dynamic behaviour of the microcantilever: d2 z(t) dz(t) m⋅ + b⋅ + k⋅z(t) = Fee (t) (5) dt2 dt where m is the effective mass, k is the spring constant and b is the damping factor. The deflection of the beam, in terms of the displacement of the cantilever free end, is represented by z(t). Fee represents the electrostatic force as defined in Eq. (4). Eq. (5) can be rewritten as Eq. (6) by replacing Fee by its explicit form (4): d2 z(t) dz(t) ϵ0 ⋅A⋅V2m (t) m⋅ + b⋅ + k⋅z(t) = (6) dt2 dt 2⋅(g0 − z(t))2 Fig. 3. Frequency response of the MEMSTENNA dipole impedance components obtained with the method of moments (MoM). When the dipole is excited by a carrier signal of frequency fc= 531–571 MHz, the impedance of the antenna is capacitive as Fig. 3 shows, then the dynamic behaviour of the dipole circuit is described by impedance of the antenna Za=Ra+jZa and the impedance of the capac­ Eq. (7): itive load produced by the microcantilever Zload = − j/wCm , as described in Eq. (1). The voltage drop in the cantilever, Vm, induces an dq(t) q(t) Ra ⋅ + = Voc (t) (7) electrostatic force: dt Ctt ϵ0 ⋅A⋅V2m Here, q is the electric charge and Ctt is the total equivalent capacitance of Fee = (4) 2⋅(g0 − z(t))2 the MEMSTENNA, obtained by connecting the antenna capacitance, Ca, in series with the total microcantilever load capacitance, Cmt, as defined which, as depicted in Fig. 1.c, acts on the microcantilever and produces by: its vertical displacement z(t), as represented in Fig. 2. The nonlineratity of the electrostatic force [30], due to its inversely squared dependence Cmt = Cm (g(t)) + Cp (8) on the displacement, z, but especially because of its quadratic depen­ dence on the voltage Vm, will play a crucial role on the transducing Ctt = (Cmt • Ca ) /(Cmt + Ca ) (9) mechanism of the MEMSTENNA in the dynamical regime as will be where Cmt includes a parallel parasitic capacitance, Cp, which describes described below. The complex dynamics involved by the non-linear the static capacitive coupling between the two arms of the dipole and the dependence of the excitation force on the free-end cantilever position clamping support of the microcantilever. over time, z(t), is described by the MEMSTENNA model represented in When the MEMSTENNA is excited by an amplitude-modulated radio Fig. 2. frequency signal (AM), the voltage at the terminals of the microcanti­ The MEMSTENNA dipole antenna part, which is a receiving antenna, lever is defined as (10): is electrically modelled by its Thévenin equivalent circuit, as shown in Fig. 2. Vm (t) = |Vm |⋅[1 + m⋅Am ⋅sin(ωm ⋅t)]⋅sin(ωc ⋅t) (10) The values of the components of the antenna dipole impedance, resistance Ra and reactance Xa, in the frequency interval between where m is the modulation index (m≤1), Am is the modulating ampli­ 400 MHz and 2.5 GHz are calculated by the method of moments (MoM) tude, ωc is the carrier frequency and ωm is the modulating frequency. If and represented in Fig. 3. the voltage expression of Eq. (10) is introduced in the force Eq. (4) and if Fig. 4. Calculated cantilever free-end displacement corresponding to the demodulated signal at frequency fm= 17 kHz and fm= 34 kHz with modulation index= 0.8. 3 R. Ruiz and G. Abadal Sensors and Actuators: A. Physical 345 (2022) 113798 Fig. 5. Diagram (a) and general view photograph of the test setup (b). Used components: CCD: Digital camera, BS: Beam Splitter, WLS: White Light Source, 4QPD: 4- Quadrants Photodetector, MO: Microscope Objective (50X), OW1: Optical Window, OW2: Optical Window, RFPA: RF Power Amplifier (2 W), ED: Emitter Dipole, RL: Red Laser (λ = 673.8 nm), VC: Vacuum Chamber. 3. Measurement setup The experimental measurements were performed using the setup shown in Fig. 5. The dipole antenna of the MEMSTENNA prototype and the emitter dipole antenna (ED) are placed in parallel at a distance, d. Both antennas have the same physical characteristics, resonance fre­ quency, dimensions and S11 response as shown in Fig. 6. The MEM­ STENNA is placed inside the vacuum chamber and the ED outside of it. Although the response of the antenna (Fig. 6) shows a maximum absorbed power peak at 0.8 GHz, the maximum coupling between an­ tennas is achieved at fc= 557 MHz. This is because the two antennas are not perfectly identical and the MEMSTENNA cantilever loading will shift its resonance frequency. In addition, reflections on the vacuum chamber metal walls will modify the MEMSTENNA frequency response too. The emitter dipole ED is driven by an AM-modulated signal whose carrier is generated by a HP8647A signal generator and whose modulating signal is generated by the output of an Agilent 5061B Network Analyser. The modulated signal is amplified by a 2 W RF amplifier. The mechanical Fig. 6. Measured and MATLAB simulated S11 parameter of the MEMSTENNA vibrations of the MEMSTENNA’s microcantilever are detected by a and emitter dipole. conventional AFM-like optical readout system based on a red diode laser (RL) coupled to a 4- quadrant photodetector (4QPD). The readout signal we neglect high frequency components ω > > ωm that are filtered by obtained from the output of the photodetector is analysed in frequency microcantilever, since they do not produce any mechanical response on through the Agilent 5061B Network Analyzer. A standard optical mi­ it, it is derived that the electrostatic force has, in this case, frequency croscope configuration consisting of a 50X long working distance mi­ components at ω = 0 (DC), ω = ωm and ω = 2⋅ωm, yielding Eq. (11): croscope objective (MO: Mitutoyo M Plan APO SL50X NA=0.42) and a [ ] CCD camera with paraxial illumination through a white light source Fee,DC+AC = ϵ0 ⋅A |Vm |2 + 1 m2 + msin(ωm ⋅t) + m2 cos(2ωm ⋅t) (11) (WLS) and a beam splitter (BS) is used to focus the red laser at the tip of the microcantilever. 2⋅g0 2 2 4 4 Consequently, when the frequency of the modulating signal ωm or twice this frequency, 2⋅ωm is tunned at the frequency of one of the vi­ 4. Test results bration modes of the microcantilever, it is excited to resonate at one of these modes. The effect of these AC forces on the microcantilever pre­ Once the coupling between the emitter dipole and the MEMSTENNA dicted by the model are presented in Fig. 4, which shows the deflection has been maximized, the frequency response of the MEMSTENNA vi­ of the MEMSTENNA, z(t), when the emitter dipole has been excited by a bration amplitude of the first mechanical mode at different inter- carrier signal of frequency fc= 531 MHz, AM-modulated by a modula­ antenna distances, d, is obtained by exciting with an amplitude modu­ tion signal of frequency fm= 17 kHz and fm= 34 kHz. lated signal whose carrier frequency is fc= 557 MHz and sweeping the modulating frequency, fm, around the first resonance mode, under 4 R. Ruiz and G. Abadal Sensors and Actuators: A. Physical 345 (2022) 113798 Fig. 7. Experimental frequency response of the MEMSTENNA’s microcantilever vibration amplitude excited by an AM-modulated signal in air (a) and vacuum (b) (solid curves) together with the corresponding calculated predicted response (dash curves). In the insets, the peak amplitude values as a function of the inter-antenna distance, d, are represented along with their corresponding 1/d2 fit curves. vacuum and atmospheric pressure conditions, as shown in Fig. 7a and b, 5. Conclusions respectively. As shown in Fig. 7, the experimental resonant frequency measured value in air conditions was found to be 19.85 kHz. At this In summary, an electromechanical model of a MEMSTENNA device frequency the vibration peak amplitude detected by the photodetector based on a folded-end dipole antenna and a commercial microcantilever was measured to be 30 nm. In vacuum conditions the experimental has been presented. A test prototype has been built in order to charac­ resonant frequency measured value was 14.405 kHz and the corre­ terize the mechanical dynamic response of the microcantilever to a sponding detected vibration peak amplitude was 68 nm. The measure­ remote excitation of the MEMSTENNA using an AM-modulated RF ments at atmospheric pressure are performed within the range of radiated signal, for different distances between the transmitting and 9–19 cm, which corresponds to the radiating near field zone as defined receiving antennas, which cover from the near field to the transition in [32]. For f = 557 MHz, the boundary between Reactive near fields zone between near and far field. Measurements performed with the and Radiating near-fields is, for a short dipole, λ/2π = 0.0857 m. From MEMSTENNA into a vacuum chamber show that the increase of its Q- the d= 9 cm curve, the obtained values of the maximum vibration factor to 960 allows to extend the distances between antennas up to amplitude and quality factor are 32 nm and 20 respectively in air d≈ λ = 0.5 m, and at the same time, it also allows for an increase in the conditions. amplitude of oscillation up to 70 nm. The electromechanical model has When increasing the distance between antennas, d, the received been validated with the experimental data obtained from test mea­ power decreases by a factor of 1/d2. To analyse the response of the surements using a RF-AM signal with a 557 MHz carrier frequency and a microcantilever at distances close to the far field regime, where for very modulator frequency in the range of the mechanical frequency of the small antennas the far field or Fraunhofer region is defined for a distance cantilever. d1 ≈ 2λ [32], the pressure of the vacuum chamber enclosing the MEMSTENNA is pumped down, increasing the quality factor of the Declaration of Competing Interest microcantilever to Q = 960. The maximum vibration amplitude of the microcantilever is also increased to 70 nm despite the fact that the The authors declare that they have no known competing financial inter-antenna distance is also increased up to 50 cm, which corresponds interests or personal relationships that could have appeared to influence to d≈ λ, meaning that the system is in a transition zone between near the work reported in this paper. and far field. Inset of Fig. 7a and b show that the vibration amplitude of the Data Availability microcantilever of the MEMSTENNA decays by a factor of 1/d2 as ex­ pected, considering that the exciting electric field will decay according Data will be made available on request. to the same trend as well. Interestingly, we have found that the resonance frequency shifts Acknowledgements down when pressure is decreased from air conditions (fres=19.9 kHz) to vacuum (fres=14.405 kHz). Such effect, which cannot be explained by We would like to acknowledge Prof. Jordi Bonache and Dr. Ferran the direct dependence of resonance frequency on the quality factor, Paredes for their unvaluable scientific support and guidance through the fres=f0⋅(1–1/2⋅Q2)1/2, being f0 the undamped resonance frequency, is microwave and antenna technologies. We would also like to acknowl­ probably due to the temperature dependence of the resonance frequency edge the financial support by Spain’s Ministerio de Ciencia, Innovación [31]. Effectively, as reported previously [24], the MEMSTENNA tem­ y Universidades under Grant No. RTI2018-097876-B-C21 (MCIU/AEI/ perature in vacuum is higher than in air, since heat induced in the an­ FEDER, UE). tenna by the joule effect produced when excited by the RF signal is evacuated much less efficiently in vacuum than in air conditions. References [1] N. Tesla, ¨Electrical Transmission of Power¨, U.S. patent 511,915 Jan. 10, 1894. 5 R. Ruiz and G. Abadal Sensors and Actuators: A. Physical 345 (2022) 113798 [2] H. Yagi, S. Uda, ‘On the feasibility of power transmission by electric waves’, Proc. [20] K. Jensen, J. Weldon, H. Garcia, A. Zettl, Nanotube radio, Nano Lett. 7 (11) (2007) 3rd Pan-Pac. Sci. Congr. Vol. 2 (1926) 1307–1313. 3508–3511. Nov 14. [3] J. Kim, H. Kim, D. Kim, D. Jeong, S. Ahn, "Analysis of Efficiency According to the [21] G. Abadal, P. Bramon, M. López-Suárez, J. Agustí, F. 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He has more than 18 years of experience in tasks of design and doi: 10.1109/MEMS.2004.1290667. verification of ASIC. At present he works at EKRAN SYSTEMS as ASIC/SoC consulting [14] I.C. Reines, et al., A low loss RF MEMS Ku-band integrated switched filter bank, engineer. His research interests include design, characterization and integration of micro IEEE Microw. Wirel. Compon. Lett. vol. 15 (2) (2005) 74–76, https://doi.org/ and nanoelectromechanical systems (MEMS and NEMS). He is currently developing his 10.1109/LMWC.2004.842823. PhD in MEMS direct transduction from electromagnetic to mechanical domain [15] A.T. Alastalo, M. Koskenvuori, H. Seppa, J. Dekker, "A micro mechanicaI resonating RF mixer", 34th European Microwave Conference, Amsterdam, Netherlands, Vol. 3, pp. 1297–1300, 2004. Dr. Gabriel Abadal received his degree in physics in 1991 and his PhD in electrical en­ [16] Ark-Chew Wong, C.T.-C. Nguyen, Micromechanical mixer-filters (“mixlers”), gineering in 1997 from the UAB. Since 2002 he is an Associate Professor in the Electronics J. Micro Syst. vol. 13 (1) (2004) 100–112, https://doi.org/10.1109/ Engineering Department of the UAB, where he currently leads the NANERG LAB group JMEMS.2003.823218. (http://grupsderecerca.uab.cat/nanerglab/). During the last 28 years he has participated [17] S. Chung, E.M. Abdel-Rahman, J. Yeow, "A MEMS Analog demodulator," IECON in more than 30 national and European research projects, he has contributed to more than 2012 - 38th Annual Conference on IEEE Industrial Electronics Society, 2012, pp. 160 conferences and he has published more than 80 papers in journals (H-index: 21). Since 3946–3951, doi: 10.1109/IECON.2012.6389261. 2006, he focused his activity in the application of MOEMS and NOEMS to harvest energy [18] S. Park, E.M. Abdel-Rahman, "Low Voltage Electrostatic Actuation and from ambient vibrations and electromagnetic radiation sources at the nanoscale. His actual Displacement Measurement through a Resonant Drive Circuit, ASME IDETC/CIE, interest is oriented towards the study of graphene and other 2D materials as basic com­ August 2012, Chicago, IL, DETC2012–71268. ponents of the future nanoenergy harvesting strategies. [19] Hao Yan, Xiaoping Liao, Chenglin Li, Chen Chen, A Cascaded MEMS amplitude demodulator for large dynamic range application in RF receiver, Micromachines 12 (2021) 1515, https://doi.org/10.3390/mi12121515. 6