Piezoelectric MEMS Flexural-Plate-Wave Transducer for Alignment of Microparticles in a Drying Droplet

The possibility of obtaining aligned clusters of microparticles in a drying water droplet by employing standing flexural plate waves (FPWs) generated by a piezoelectric MEMS transducer has been explored. The MEMS device has a squared cavity etched out in a silicon (Si) substrate forming a $6\times6$ mm diaphragm composed of a stack of doped Si and aluminum nitride (AlN) layers. Metal interdigital transducers (IDTs) placed at the edges of the diaphragm allow to electrically drive the AlN layer to excite FPWs in the diaphragm at its first antisymmetric Lamb mode (A0). The working principle has been validated through finite-element analysis and experimentally verified. For experimental testing, a droplet of tap water with an approximate radius of $850 \mu \text{m}$ was placed on the diaphragm and let dry at room temperature while applying voltage excitations to two opposed IDTs. After droplet evaporation, dry clusters of microparticles, originally dispersed therein, have been successfully patterned with a regular spacing of half wavelength, as expected, and remained adhered to the diaphragm without the need for additional substances for clot creation. The innovative exploitation of a noncontact and noninvasive flow-field-based approach combined with the evaporation process in a piezoelectric MEMS transducer can enhance the assembly control of microparticles or biological cells in lab-on-chip applications.

T HE capability to control the assembly of microscale objects has long been instrumental for tailoring the mechanical, optical, and electronic properties of materials.For instance, the assembly of G-wires [1] is of interest in the biomedical field since it can lead to the synthesis of four-stranded deoxyribonucleic acid (DNA) with enhanced optical and electronic properties, superior resis-tance to enzymatic degradation as well as mechanical and thermal stability on substrates [2].The electrochemical, optical, and electromechanical properties of elongated particles such as carbon nanotubes can be enhanced by controlling the synthesis process along a preferred spatial direction [3].Oriented assembly of single-crystalline TiO 2 nanorods on a transparent conductive substrate has allowed to successfully develop dye-sensitized solar cells [4].Controlled assembly of microparticles has been effectively employed to build tailored bioactive membranes for drug delivery [5] and to develop platforms for cell analysis [6].Microassembly approaches typically mimic nature by employing rather weak and specific interaction forces, which are essential to achieve the desired structures and functionalities.However, this requires a high degree of control to direct the aggregation and alignment processes [7].Microparticle assembly can be typically achieved by relying on interparticle interactions or employing external stimuli and fields.
Chemical-based processes offer control through molecular interactions but have the drawback of being ineffective to cover large surface areas with respect to particle volume [8].Electric-based processes leverage on the possibility to polarize microparticles with electric fields exploiting their dielectric properties that are mismatched with the surrounding medium [9], while magnetic-based processes manage to align and pattern particles relying on permanent magnetic dipoles [10].
However, both approaches have the disadvantage of not being fully compliant with biological applications since they can alter cell integrity, thus irreversibly damaging the biological tissue [11].
To achieve microassembly ensuring biocompatibility, flowfield approaches exploiting macroscopic viscous flows to direct the assembly of a disordered suspension of particles into ordered structures represent a valid alternative [12], [13].Among flow-field techniques, acoustophoresis, i.e., the use of acoustic forces to act on particles and cells in microfluidic systems, has attracted interest to manipulate bioparticles due to its label-free noninvasive approach [14], [15].Specifically, microfluidic systems based on acoustic waves generated through the piezoelectric effect have been largely adopted in biological and medical fields for mixing, separating, and aligning particles or cells [16], [17], [18].Surface acoustic wave (SAW), bulk acoustic wave (BAW), and flexural plate wave (FPW) acoustic modes can be generated and detected by piezoelectric transducers [19], [20], [21], [22].Compared with SAW and BAW, FPW-based devices typically exhibit, for a given wavelength, a lower excitation frequency in the range of 5-20 MHz, which reduces the demands on the driving electronics [23].The acoustic waves are employed to interact with fluids, steer particles dispersed therein, and assemble microstructures at micrometric resolution [24].A possible limitation in some applications is that, once the flow is removed, the created assembly can possibly revert into disordered particles unless additional substances are added to create clots [13].To this purpose, an evaporation-based assembly process employing droplets deposited on surfaces can be an effective solution [25].Droplets are used as vehicles to obtain patterned deposits of microparticles, which remain adhered to the surface after liquid evaporation [26].Furthermore, the dynamics of the acousto-mechanical impedance of drying droplets in combination with the pattern left after liquid evaporation can be used as a diagnostic tool [27].The use of an evaporation-based process with ultrasonic excitation has been employed to form a circular spot of silver nanowires (AgNWs) and to radially align AgNWs on the device surface [28].Battery electrodes have been developed by exploiting a rapid evaporation of mixed solvents to enable directional ion transport via forming vertically aligned nanosheets [29].In this context, this work explores the possibility to innovatively combine a noncontact and noninvasive flow-field-based approach with the label-free evaporation process in an FPW piezoelectric MEMS transducer for the controlled alignment of dry microparticle clusters at the microscale starting from a liquid droplet with microparticles dispersed therein.This article is organized as follows: working principle (Section II), design and fabrication of the MEMS transducer (Section III), 2-D finite-element analysis (Section IV), experimental results (Section V), and conclusion (Section VI).

II. WORKING PRINCIPLE
The possibility of achieving aligned clusters of microparticles after complete evaporation of a liquid droplet into which they are initially dispersed has been explored by designing a dedicated piezoelectric MEMS transducer.Water has been used as the liquid in this study.The schematic top and  A squared cavity etched out in a silicon (Si) substrate is bounded by a composite diaphragm made of a stack of Si and piezoelectric layers.The composite diaphragm can be electrically actuated by means of metal interdigital transducers (IDTs) composed of interleaved comb-shaped electrodes with equally spaced fingers with pitch p.The liquid droplet is deposited on the substrate face of the diaphragm and used as a vehicle containing dispersed microparticles, as illustrated in Fig. 2(a).By applying sinusoidal excitation voltages between the fingers of the IDTs, a deformation of the piezoelectric layer is induced, which produces mechanical vibrations in the diaphragm in the form of Lamb plate waves.Specifically, by properly driving two opposed IDTs disposed symmetrically with respect to the device center, the first antisymmetric vibration mode (A 0 ) has been excited to generate standing FPWs in the diaphragm.The acoustic waves interact with the droplet transferring energy into the liquid in the form of compressional acoustic waves, as schematically shown in Fig. 2(b).The waves are attenuated in the liquid, thus forming a pressure gradient that initiates a flow inside the droplet, i.e., the acoustic stream flow (ASF) [30].Due to evaporation, the contact angle θ c between the diaphragm and the line tangent to the edge of the water droplet is progressively reduced [31] to θ ′ c , as shown in Fig. 2(c).With reducing θ c , the pressure gradient lowers and the velocity and intensity of the ASF decrease in turn [32].After complete evaporation, the electrical excitation is turned off and clusters of microparticles are expected to remain adhered to the diaphragm surface following a regular pattern with gap set by the acoustic wavelength [33], as shown in Fig. 2(d).

III. DESIGN AND FABRICATION OF THE MEMS TRANSDUCER
The transducer has been designed and fabricated by using the piezoelectric multiuser MEMS process (PiezoMUMPs) made available by MEMSCAP, Crolles Cedex, France [34].Material properties of the doped Si and aluminum nitride (AlN) piezoelectric layers that compose the diaphragm are shown in Table I.The design has been carried out considering the acoustic-fluidic coupling between the composite diaphragm and water by analyzing the symmetric (Sn) and antisymmetric (An) modes of plate waves [23].The Young's modulus E, Poisson's ratio η, and mass density ρ of the Si/AlN composite diaphragm can be estimated as [35] and where t = t Si + t AlN is the overall diaphragm thickness, as shown in Fig. 3, and subscripts Si and AlN refer to Si and piezoelectric layers, respectively.With the parameter values of Table I, it results E = 167 GPa, η = 0.268, and ρ = 2373 kg/m 3 .Fig. 4 shows the computed dispersion curves of the Lamb waves for the composite unbounded Si/AlN twolayer diaphragm.Specifically, the phase velocity v is plotted as a function of the product of angular frequency ω and thickness t.Both quantities are normalized to the phase velocity v s of shear Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.waves in the Si/AlN bulk material of the diaphragm given by [36] which results equal to 5267 m/s.For the device under consideration, the symmetric S 0 and antisymmetric A 0 modes, related, respectively, to extensional and flexural waves [37], are the only two modes allowed for excitation frequencies lower than about 300 MHz.As the frequency increases, higher order plate modes arise while the phase velocities of S 0 and A 0 modes asymptotically converge to the velocity of the Rayleigh wave that is about 0.92v s [38].The frequencies f A0 and f S0 for the A 0 antisymmetric and S 0 symmetric modes can be expressed as [35], [39] and By employing (1)-( 3), ( 5), (6), and the material parameters of Table I, a numerical analysis of the frequency-to-wavelength relationship of S 0 and A 0 modes has been carried out.The results are shown in Fig. 5, which also includes the frequencyto-wavelength relationship of acoustic waves in water given by where c w is the sound speed in water of about 1460 m/s [40].
It can be observed that the A 0 mode intersects (7) at the frequency of 13 MHz where the wavelengths of the A 0 mode in the diaphragm and the longitudinal wave in water are equal.Blue dashed curves detail the f -λ relationship of the A 0 mode considering the manufacturing tolerances in the Si layer thickness.Specifically, given the Si thickness t Si = 10 ± 1 µm, the intersection can be expected in the range λ ≈ 112 ± 11 µm and f ≈ 13 ± 1.4 MHz, as illustrated in the inset of Fig. 5. Therefore, the pitch p of the IDTs has been dimensioned to equal the nominal λ = 112 µm.More generally than the scope of this work, the device has been designed as a multipurpose piezoelectric MEMS platform that can be exploited to explore different applications [41], [42], [43].
The graphic design system (GDS) file displayed in Fig. 6(a) shows the bottom view of the device that includes eight IDTs placed at the inner and outer edges of the diaphragm symmetrically with respect to its center.Each IDT is composed of two interleaved comb-shaped arrays of 20 equally spaced fingers with an aperture of 3.5 mm to adequately couple the droplet with the generated 1-D acoustic field pattern and a width w of 28 µm, as visible in Fig. 6(b) and (c), respectively.
The silicon dioxide (SiO 2 ) and Si substrate layers have a thickness of 1 ± 0.05 and 400 ± 5 µm, respectively.The IDTs are made by a metal stack of 20 nm of chrome (Cr) and 1 µm of aluminum (Al).These values are defined by the fabrication process steps [34].The top and bottom views of the fabricated piezoelectric MEMS transducer are shown in Fig. 7(a) and (b), respectively.Electrical terminal pads are provided for each IDT, as shown in Fig. 7(c).To induce standing FPWs in the diaphragm generating 1-D acoustic field pattern, the configuration of Fig. 8 has been adopted where only IDT1 and IDT3 are used, while the remaining IDTs included in the transducer are irrelevant for the present scope.A sinusoidal excitation voltage v exc (t) with peak amplitude A exc and tunable frequency f exc has been applied between the fingers of both IDT1 and IDT3, which are located symmetrically with respect to the diaphragm center [44].

IV. 2-D FINITE-ELEMENT ANALYSIS
The electromechanical behavior of the piezoelectric MEMS transducer, described in Section II, has been investigated by means of 2-D finite-element modeling in COMSOL Multiphysics. 1  The developed 2-D geometry is illustrated in Fig. 9(a) while Fig. 9(b) shows an enlarged view of the structural layers that have been considered in the model.
The nominal dimensions have been used, neglecting tolerances.Since the Al thickness is 50 times higher than the Cr thickness, only Al has been included in the model as the metal layer.SiO 2 and ⟨100⟩ Si have been used as the oxide layer and the substrate and Si layer materials, respectively.For the AlN layer, the piezoelectric coefficients d 31 = −2.78pC/N and d 33 = 6.5 pC/N have been specified [45].A generalized plane strain approximation has been assumed for the 2-D analysis. 1Registered trademark.The piezoelectric effect has been simulated by including the piezoelectric multiphysics combining the solid mechanics with the electrostatics physics.Regarding the solid mechanics physics, a fixed constraint has been imposed to the top surface of the substrate while gravity constraint has been considered for the whole volume.To investigate the feasibility to induce standing waves in the composite diaphragm, an isotropic damping with a loss factor of 0.004 has also been considered and applied to the whole structure [46].
Dielectric losses and strain-charge constitutive relations have been specified for the piezoelectric layer including the AlN material properties, and a charge conservation boundary condition has been applied to the AlN layer in the electrostatics physics.Electrical domain constraints have been specified to the IDT fingers by alternating voltage and ground terminals.A floating potential group has been applied to the Si surface in contact with the AlN layer to take into account the high doping concentration and model a conductive electrode.
To identify the presence of standing FPWs and the position of pressure nodes, a time-domain simulation analysis has been performed by setting for the voltage of the IDTs a sinusoidal excitation v exc (t) with peak amplitude A exc of 10 V and nominal frequency f exc of 13 MHz as estimated in Section II.The obtained simulation results for the y-axis displacement are shown, not to scale, for the left and right sides of the diaphragm in Fig. 10(a) and (b), respectively.A standing flexural wave is induced with a maximum y-axis displacement of 0.45 nm and with pressure nodes evenly spaced by 56 µm, i.e., half the wavelength, in good agreement with the theoretical predictions of Section II.

V. EXPERIMENTAL RESULTS
The electronic driving configuration adopted for experimental tests is shown in Fig. 11.By means of a two-channel waveform generator (Keysight 33522A), two sinusoidal signals v s0 (t) and v s1 (t) with the same peak-to-peak amplitude of 10 V Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Electrical configuration employed to generate deposits of aligned microparticles after evaporation of a water droplet.and zero relative phase shift have been fed to IDT1 and IDT3 to drive the piezoelectric MEMS diaphragm at up to 15 MHz.The adopted experimental setup is shown in Fig. 12(a).A dedicated printed circuit board (PCB) hosts the MEMS transducer as visible in Fig. 12(b) and (c).A droplet of tap water with an approximate radius of 850 µm has been placed on the substrate face of the diaphragm as shown in the microscope (Motic PSM-1000) image of Fig. 13(a).As described in Section II, the droplet has been used as a vehicle to align microparticles, which are dissolved therein by exploiting evaporation at room temperature.Sinusoidal excitation voltages have been applied between the fingers of the IDTs located symmetrically with respect to the diaphragm center.This induces a deformation of the piezoelectric layer, which produces mechanical vibrations in the diaphragm in the form of Lamb plate waves, thus generating 1-D acoustic field pattern.The frequency of both the excitation signals v s0 (t) and v s1 (t) has been finely tuned until ripples into the water droplet were clearly visible from light reflections.This experimental approach allows to accurately adjust to the target condition.Such condition has been reached at the excitation frequency f exc = 12.5 MHz, which lays in the 13 ± 1.4 MHz range theoretically predicted in Section II, corresponding to the situation where the wavelengths of the A 0 mode in the composite diaphragm and the longitudinal wave in water are equal.The driving sinusoidal signals v s0 (t) and v s1 (t) have then been maintained at such excitation frequency for the entire evaporation process, which took approximately 4 min.
An intermediate evaporation step showing the progressive reduction of the droplet volume is captured in Fig. 13(b).In Fig. 13(c), showing a subsequent image taken before the complete evaporation of the droplet, the 1-D acoustic field pattern can be clearly seen in the form of aligned ripples.This captured frame shows that by reducing the droplet volume and thus the contact angle, the pressure gradient induced by acoustic actuation lowers and the velocity and intensity of the ASF decrease in turn.This makes the acoustic radiation force generated by the 1-D acoustic field prevailing over the ASF, thus steering, agglomerating, and trapping microparticles and minerals dissolved in the tap water droplet at the nearest standing-wave node.After complete evaporation has occurred, clusters remain deposited on the diaphragm along a regular pattern with a gap of 56 µm, as shown in Fig. 13(d).The achieved gap is in accordance with theoretical predictions and finite element method (FEM) simulations since it corresponds to half the acoustic wavelength, i.e., where the standing-wave nodes are located [47].The obtained experimental results confirm the feasibility to align clusters of microparticles in a drying water droplet by employing standing FPWs generated by a piezoelectric MEMS transducer.

VI. CONCLUSION
This work has presented a piezoelectric MEMS transducer able to achieve patterned clusters of microparticles after complete evaporation of a tap water droplet by employing standing FPWs.The acousto-fluidic coupling between the MEMS diaphragm and the liquid has been taken into account in the design of the device.The pitch of the IDTs has been set equal to the acoustic wavelength to generate at the same excitation frequency the A 0 flexural mode in the diaphragm and the longitudinal wave in the water droplet.The possibility to induce standing FPWs in the diaphragm has been investigated through a time-domain FEM analysis in COMSOL Multiphysics.A droplet with a radius of 850 µm of tap water has been deposited on the diaphragm and let dry at room temperature while tuning the frequency of the excitation sinusoidal signals applied to two opposed IDTs, until ripples were clearly visible from light reflections.This condition has been reached at the excitation frequency of 12.5 MHz, in good agreement with theoretical expectations and simulations.After complete water evaporation, the microparticles initially dispersed in the droplet have been arranged in dry clusters regularly spaced on the diaphragm with a pitch of half the acoustic wavelength, demonstrating that the proposed MEMS device is suitable for microassembly processes.The achieved results validate the possibility of innovatively combine the noncontact and noninvasive attributes of a flow-field-based approach with the label-free property of the evaporation process in a piezoelectric MEMS transducer.This can pave the way to the enhancement of assembly control of microparticles or biological cells in lab-on-chip applications and the development of novel diagnostic microtools for biomedical applications.

Fig. 1 .
Fig. 1.(a) Top and (b) bottom schematic views of the proposed piezoelectric MEMS transducer.

Fig. 5 .
Fig. 5. Numerical analysis of frequency-to-wavelength relationships for the A 0 (blue curve) and S 0 (red curve) modes in the composite diaphragm and for the acoustic wave in water (green curve).Variations from the nominal curve, due to the fabrication tolerances, are shown in the inset (dashed curves).

Fig. 6 .
Fig. 6.(a) Bottom-view image of the proposed piezoelectric MEMS and (b) and (c) enlarged views of the IDTs taken from the GDS file.

Fig. 7 .
Fig. 7. (a) Top and (b) bottom views of the fabricated piezoelectric MEMS transducer.(c) Enlarged view of the terminal pads of the combshaped IDTs.

Fig. 8 .
Fig. 8. Simplified schematic view of the piezoelectric MEMS transducer configured to achieve 1-D acoustic field pattern.

Fig. 9 .
Fig. 9. (a) View of the 2-D model adopted for the proposed piezoelectric MEMS.(b) Enlarged view of the layers included in the simulation.

Fig. 10 .
Fig. 10.Simulated y -axis displacement (not to scale) of the: (a) left and (b) right sides of the MEMS diaphragm under sinusoidal voltage excitation at a frequency of 13 MHz.

Fig. 11 .
Fig. 11.Electrical configuration employed to generate deposits of aligned microparticles after evaporation of a water droplet.

Fig. 12 .
Fig. 12.(a) Experimental setup.(b) Top and (c) bottom views of the dedicated PCB hosting the piezoelectric MEMS device.

Fig. 13 .
Fig. 13.Evaporation process steps of a tap water droplet deposited on the membrane of the piezoelectric MEMS device: (a) water droplet deposition; (b) intermediate evaporation step; (c) 1-D acoustic field pattern formation; and (d) particle alignment after complete evaporation.

TABLE I GEOMETRICAL
AND MATERIAL PROPERTIES OF THE SI AND ALN LAYERS